Octave 3.8, jcobi/4
Time bar (total: 14.4s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 14% | 86% | 0% | 0% | 0% | 0 |
| 0% | 0% | 14% | 86% | 0% | 0% | 0% | 1 |
| 0% | 0% | 14% | 86% | 0% | 0% | 0% | 2 |
| 25% | 3.5% | 10.5% | 86% | 0% | 0% | 0% | 3 |
| 62.5% | 8.8% | 5.3% | 86% | 0% | 0% | 0% | 4 |
| 75% | 10.5% | 3.5% | 86% | 0% | 0% | 0% | 5 |
| 84.4% | 11.8% | 2.2% | 86% | 0% | 0% | 0% | 6 |
| 92.2% | 12.9% | 1.1% | 86% | 0% | 0% | 0% | 7 |
| 93.8% | 13.2% | 0.9% | 86% | 0% | 0% | 0% | 8 |
| 95.7% | 13.4% | 0.6% | 86% | 0% | 0% | 0% | 9 |
| 97.9% | 13.7% | 0.3% | 86% | 0% | 0% | 0% | 10 |
| 98.4% | 13.8% | 0.2% | 86% | 0% | 0% | 0% | 11 |
| 99% | 13.9% | 0.1% | 86% | 0% | 0% | 0% | 12 |
Compiled 65 to 24 computations (63.1% saved)
| 1.2s | 8 256× | 0 | valid |
ival-mult: 376.0ms (42.3% of total)ival-add: 202.0ms (22.7% of total)ival->: 126.0ms (14.2% of total)ival-div: 91.0ms (10.2% of total)ival-sub: 62.0ms (7% of total)ival-and: 16.0ms (1.8% of total)exact: 13.0ms (1.5% of total)ival-assert: 3.0ms (0.3% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 215 | 0 | - | 0 | - | (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) |
| 138 | 1 | (5.292187200788989e+280 3.454472654718856e+51 2.7992366970968838e+119) | 0 | - | (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | i |
| 0 | 0 | - | 0 | - | (*.f64 i (+.f64 (+.f64 alpha beta) i)) |
| 0 | 0 | - | 0 | - | (*.f64 #s(literal 2 binary64) i) |
| 0 | 0 | - | 0 | - | (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) |
| 0 | 0 | - | 0 | - | beta |
| 0 | 0 | - | 0 | - | (+.f64 alpha beta) |
| 0 | 0 | - | 0 | - | (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) |
| 0 | 0 | - | 0 | - | (+.f64 (+.f64 alpha beta) i) |
| 0 | 0 | - | 0 | - | alpha |
| 0 | 0 | - | 0 | - | (*.f64 beta alpha) |
| 0 | 0 | - | 0 | - | (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) |
| 0 | 0 | - | 0 | - | (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))) |
| 0 | 0 | - | 0 | - | (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
/.f64 | (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) | o/o | 156 | 0 |
| ↳ | (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))) | overflow | 135 | |
| ↳ | (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) | overflow | 215 | |
| ↳ | (*.f64 beta alpha) | overflow | 10 | |
| ↳ | (*.f64 i (+.f64 (+.f64 alpha beta) i)) | overflow | 268 | |
| ↳ | (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) | overflow | 156 | |
/.f64 | (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | o/o | 117 | 0 |
| ↳ | (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))) | overflow | 135 | |
| ↳ | (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) | overflow | 215 | |
| ↳ | (*.f64 beta alpha) | overflow | 10 | |
| ↳ | (*.f64 i (+.f64 (+.f64 alpha beta) i)) | overflow | 268 | |
| ↳ | (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) | overflow | 156 | |
| ↳ | (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) | overflow | 117 | |
| ↳ | (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) | overflow | 156 | |
| ↳ | (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) | overflow | 156 | |
/.f64 | (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) | o/n | 59 | 0 |
| ↳ | (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))) | overflow | 135 | |
| ↳ | (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) | overflow | 215 | |
| ↳ | (*.f64 beta alpha) | overflow | 10 | |
| ↳ | (*.f64 i (+.f64 (+.f64 alpha beta) i)) | overflow | 268 | |
/.f64 | (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | n/o | 22 | 0 |
| ↳ | (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) | overflow | 156 | |
| ↳ | (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) | overflow | 156 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 215 | 0 |
| - | 0 | 41 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 215 | 0 | 0 |
| - | 0 | 0 | 41 |
| number | freq |
|---|---|
| 0 | 41 |
| 1 | 76 |
| 2 | 139 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 72.0ms | 512× | 0 | valid |
Compiled 426 to 55 computations (87.1% saved)
ival-mult: 35.0ms (67.1% of total)ival-add: 8.0ms (15.3% of total)ival-div: 5.0ms (9.6% of total)ival-sub: 2.0ms (3.8% of total)exact: 1.0ms (1.9% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 12 580× | lower-fma.f64 |
| 12 580× | lower-fma.f32 |
| 4 108× | lower-*.f32 |
| 4 098× | lower-*.f64 |
| 3 894× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 81 | 508 |
| 1 | 377 | 482 |
| 2 | 2068 | 478 |
| 0 | 17 | 53 |
| 0 | 29 | 53 |
| 1 | 76 | 53 |
| 2 | 324 | 53 |
| 3 | 2002 | 53 |
| 4 | 6883 | 53 |
| 0 | 8193 | 47 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
| Outputs |
|---|
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(/.f64 (*.f64 i (*.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))) |
(sort alpha beta)
Compiled 56 to 17 computations (69.6% saved)
Compiled 3 to 3 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 16.7% | (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
Compiled 56 to 17 computations (69.6% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 128 | (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) | |
| cost-diff | 128 | (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) | |
| cost-diff | 128 | (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))) | |
| cost-diff | 384 | (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
| 12 580× | lower-fma.f64 |
| 12 580× | lower-fma.f32 |
| 4 108× | lower-*.f32 |
| 4 098× | lower-*.f64 |
| 3 894× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 183 |
| 0 | 29 | 183 |
| 1 | 76 | 183 |
| 2 | 324 | 183 |
| 3 | 2002 | 183 |
| 4 | 6883 | 183 |
| 0 | 8193 | 166 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) |
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) |
(*.f64 i (+.f64 (+.f64 alpha beta) i)) |
i |
(+.f64 (+.f64 alpha beta) i) |
(+.f64 alpha beta) |
alpha |
beta |
(+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))) |
(*.f64 beta alpha) |
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) |
(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) |
(*.f64 #s(literal 2 binary64) i) |
#s(literal 2 binary64) |
(-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
| Outputs |
|---|
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(/.f64 (*.f64 i (*.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))) |
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) |
(/.f64 (*.f64 i (*.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) |
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) |
(*.f64 i (*.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) |
(*.f64 i (+.f64 (+.f64 alpha beta) i)) |
(*.f64 i (+.f64 i (+.f64 alpha beta))) |
i |
(+.f64 (+.f64 alpha beta) i) |
(+.f64 i (+.f64 alpha beta)) |
(+.f64 alpha beta) |
alpha |
beta |
(+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))) |
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) |
(*.f64 beta alpha) |
(*.f64 alpha beta) |
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) |
(*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) |
(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(*.f64 #s(literal 2 binary64) i) |
(*.f64 i #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) |
(fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) |
#s(literal 1 binary64) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.01953125 | (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) | |
| accuracy | 0.0703125 | (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) | |
| accuracy | 33.079017936929866 | (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | |
| accuracy | 46.36529632003697 | (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) |
| 31.0ms | 256× | 0 | valid |
Compiled 185 to 19 computations (89.7% saved)
ival-mult: 10.0ms (53.3% of total)ival-add: 4.0ms (21.3% of total)ival-div: 3.0ms (16% of total)ival-sub: 1.0ms (5.3% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) (patch (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))) (patch (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))) #<representation binary64>) () ()) |
#s(alt (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (patch (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #<representation binary64>) () ()) |
#s(alt (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) (patch (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (patch (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) #<representation binary64>) () ()) |
#s(alt (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (patch (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) #<representation binary64>) () ()) |
#s(alt (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) (patch (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #<representation binary64>) () ()) |
| Outputs |
|---|
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#s(alt (* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) (taylor 0 i) (#s(alt (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) (patch (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1/16 (taylor inf i) (#s(alt (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) (patch (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) (taylor inf i) (#s(alt (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) (patch (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) (taylor inf i) (#s(alt (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) (patch (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) (taylor inf i) (#s(alt (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) (patch (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
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63 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 5.0ms | i | @ | 0 | (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) |
| 4.0ms | beta | @ | -inf | (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) |
| 4.0ms | beta | @ | 0 | (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) |
| 4.0ms | i | @ | inf | (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) |
| 2.0ms | alpha | @ | 0 | (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) |
| 1× | egg-herbie |
| 9 164× | lower-fma.f64 |
| 9 164× | lower-fma.f32 |
| 5 962× | lower-+.f64 |
| 5 962× | lower-+.f32 |
| 4 964× | lower-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1089 | 12630 |
| 1 | 3841 | 11840 |
| 0 | 8260 | 10972 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
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1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(/ (* i (+ beta i)) (pow alpha 2)) |
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2)) |
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
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(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1))))))) alpha)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
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(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2)) |
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(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(* i (+ alpha i)) |
(+ (* beta (+ alpha i)) (* i (+ alpha i))) |
(+ (* beta (+ alpha i)) (* i (+ alpha i))) |
(+ (* beta (+ alpha i)) (* i (+ alpha i))) |
(* beta (+ alpha i)) |
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta)))) |
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta)))) |
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta)))) |
(* -1 (* beta (+ (* -1 alpha) (* -1 i)))) |
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta)))))) |
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta)))))) |
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta)))))) |
(* i (+ beta i)) |
(+ (* alpha (+ beta i)) (* i (+ beta i))) |
(+ (* alpha (+ beta i)) (* i (+ beta i))) |
(+ (* alpha (+ beta i)) (* i (+ beta i))) |
(* alpha (+ beta i)) |
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha)))) |
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha)))) |
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha)))) |
(* -1 (* alpha (+ (* -1 beta) (* -1 i)))) |
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))) |
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))) |
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))) |
(* alpha beta) |
(+ (* alpha beta) (* i (+ alpha beta))) |
(+ (* alpha beta) (* i (+ alpha (+ beta i)))) |
(+ (* alpha beta) (* i (+ alpha (+ beta i)))) |
(pow i 2) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i)))) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2)))))) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2)))))) |
(pow i 2) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i)))) |
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i)))) |
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i)))) |
(+ beta (* 2 i)) |
(+ alpha (+ beta (* 2 i))) |
(+ alpha (+ beta (* 2 i))) |
(+ alpha (+ beta (* 2 i))) |
alpha |
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha)))) |
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha)))) |
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha)))) |
alpha |
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1))) |
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1))) |
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1))) |
(+ alpha (* 2 i)) |
(+ alpha (+ beta (* 2 i))) |
(+ alpha (+ beta (* 2 i))) |
(+ alpha (+ beta (* 2 i))) |
beta |
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta)))) |
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta)))) |
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta)))) |
beta |
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1))) |
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1))) |
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1))) |
(+ alpha beta) |
(+ alpha (+ beta (* 2 i))) |
(+ alpha (+ beta (* 2 i))) |
(+ alpha (+ beta (* 2 i))) |
(* 2 i) |
(* i (+ 2 (+ (/ alpha i) (/ beta i)))) |
(* i (+ 2 (+ (/ alpha i) (/ beta i)))) |
(* i (+ 2 (+ (/ alpha i) (/ beta i)))) |
(* 2 i) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2))) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2))) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2))) |
(- (pow (+ beta (* 2 i)) 2) 1) |
(- (+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1) |
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1) |
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha))))) |
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2)))) |
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2)))) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha)))) |
(- (pow (+ alpha (* 2 i)) 2) 1) |
(- (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) |
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1) |
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta))))) |
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2)))) |
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2)))) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta)))) |
(- (pow (+ alpha beta) 2) 1) |
(- (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) 1) |
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1) |
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2)))) |
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2)))) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i)))) |
(/ (* alpha (* beta i)) (+ alpha beta)) |
(* i (+ (* i (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (+ (* 2 (/ beta (pow (+ alpha beta) 2))) (* i (- (/ 1 (pow (+ alpha beta) 2)) (+ (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (pow (+ alpha beta) 2))) (* 4 (/ (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta))))) (+ alpha beta)))))))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(* 1/4 (pow i 2)) |
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (+ alpha beta) i)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)))))) |
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 3))) (+ (* 1/4 (/ (+ alpha beta) i)) (+ (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/16 (pow (+ alpha beta) 2)) (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))))) (pow i 3)))))))) |
(* 1/4 (pow i 2)) |
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* 1/4 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)) (* -1/16 (/ (pow (+ alpha beta) 2) i)))) i)))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) (* 1/4 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) i)) (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)))) i))) i)))) |
(/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2)) |
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
(+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
(+ (* alpha (- (+ (* alpha (- (+ (* alpha (- (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 6)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (pow (+ beta (* 2 i)) 2))))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
(* i (+ beta i)) |
(- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha)) |
(- (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))))) |
(- (+ (* -1 (/ (+ (* (+ (* 2 beta) (* 4 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))))) |
(* -1 (* i (+ (* -1 beta) (* -1 i)))) |
(+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) |
(+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) |
(+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i)))))))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) alpha))) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2)) |
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))) |
(+ (* beta (- (+ (* beta (- (+ (* beta (- (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 6)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (pow (+ alpha (* 2 i)) 2))))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))) |
(* i (+ alpha i)) |
(- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta)) |
(- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))))) |
(- (+ (* -1 (/ (+ (* (+ (* 2 alpha) (* 4 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))))) |
(* -1 (* i (+ (* -1 alpha) (* -1 i)))) |
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) |
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) |
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i)))))))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) beta))) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) |
(* alpha (* beta (* i (+ alpha beta)))) |
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (pow (+ alpha beta) 2))))) |
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (+ (* i (+ (* 2 alpha) (* 2 beta))) (pow (+ alpha beta) 2)))))) |
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (+ (* i (+ i (+ (* 2 alpha) (* 2 beta)))) (pow (+ alpha beta) 2)))))) |
(pow i 4) |
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (* 2 (/ beta i))))) |
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (+ (* 2 (/ beta i)) (+ (/ (* alpha beta) (pow i 2)) (/ (pow (+ alpha beta) 2) (pow i 2))))))) |
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (+ (* 2 (/ beta i)) (+ (/ (* alpha beta) (pow i 2)) (+ (/ (* alpha (* beta (+ alpha beta))) (pow i 3)) (/ (pow (+ alpha beta) 2) (pow i 2)))))))) |
(pow i 4) |
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (* 2 (/ beta i))))) |
(* (pow i 4) (+ 1 (* -1 (/ (+ (* -1 (+ (* 2 alpha) (* 2 beta))) (+ (* -1 (/ (* alpha beta) i)) (* -1 (/ (pow (+ alpha beta) 2) i)))) i)))) |
(* (pow i 4) (+ 1 (* -1 (/ (+ (* -1 (+ (* 2 alpha) (* 2 beta))) (* -1 (/ (+ (* -1 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (/ (* alpha (* beta (+ alpha beta))) i)) i))) i)))) |
(* (pow i 2) (pow (+ beta i) 2)) |
(+ (* alpha (* i (+ (* i (+ beta i)) (pow (+ beta i) 2)))) (* (pow i 2) (pow (+ beta i) 2))) |
(+ (* alpha (+ (* alpha (* i (+ beta i))) (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))))) (* (pow i 2) (pow (+ beta i) 2))) |
(+ (* alpha (+ (* alpha (* i (+ beta i))) (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))))) (* (pow i 2) (pow (+ beta i) 2))) |
(* (pow alpha 2) (* i (+ beta i))) |
(* (pow alpha 2) (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha))) |
(* (pow alpha 2) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) |
(* (pow alpha 2) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) |
(* -1 (* (pow alpha 2) (* i (+ (* -1 beta) (* -1 i))))) |
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) alpha)))) |
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) alpha)))) |
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) alpha)))) |
(* (pow i 2) (pow (+ alpha i) 2)) |
(+ (* beta (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2)))) (* (pow i 2) (pow (+ alpha i) 2))) |
(+ (* beta (+ (* beta (* i (+ alpha i))) (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))))) (* (pow i 2) (pow (+ alpha i) 2))) |
(+ (* beta (+ (* beta (* i (+ alpha i))) (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))))) (* (pow i 2) (pow (+ alpha i) 2))) |
(* (pow beta 2) (* i (+ alpha i))) |
(* (pow beta 2) (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta))) |
(* (pow beta 2) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) |
(* (pow beta 2) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) |
(* -1 (* (pow beta 2) (* i (+ (* -1 alpha) (* -1 i))))) |
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) beta)))) |
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ alpha i) 2)) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) beta)))) |
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ alpha i) 2)) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) beta)))) |
(pow (+ beta (* 2 i)) 2) |
(+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) |
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha))))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(pow (+ alpha (* 2 i)) 2) |
(+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta))))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(pow (+ alpha beta) 2) |
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
| Outputs |
|---|
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(/.f64 (*.f64 alpha (*.f64 beta i)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) |
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(*.f64 i (fma.f64 alpha (/.f64 beta (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (*.f64 i (+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (*.f64 alpha (-.f64 (/.f64 beta (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (*.f64 beta (*.f64 #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(*.f64 i (fma.f64 i (fma.f64 i (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 beta (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (*.f64 alpha (-.f64 (/.f64 beta (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (*.f64 beta (*.f64 #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))))) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 alpha beta) (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64)))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))) (+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (*.f64 alpha (-.f64 (/.f64 beta (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (*.f64 beta (*.f64 #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))))) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(*.f64 i (fma.f64 i (+.f64 (fma.f64 i (-.f64 (fma.f64 i (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 beta (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (*.f64 alpha (-.f64 (/.f64 beta (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (*.f64 beta (*.f64 #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))))) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 alpha beta) (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64)))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (fma.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (*.f64 alpha (-.f64 (/.f64 beta (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (*.f64 beta (*.f64 #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))))) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (*.f64 #s(literal 32 binary64) (*.f64 alpha beta)) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))))) (*.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 beta (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))) (fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (*.f64 alpha (-.f64 (/.f64 beta (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (*.f64 beta (*.f64 #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))))) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 alpha beta) (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64)))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (*.f64 alpha (-.f64 (/.f64 beta (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (*.f64 beta (*.f64 #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))))) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) |
1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64))) i)) |
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta)))))) |
(*.f64 (neg.f64 beta) (-.f64 (neg.f64 (fma.f64 i (/.f64 (+.f64 alpha i) beta) i)) alpha)) |
(* i (+ beta i)) |
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(+ (* alpha (+ beta i)) (* i (+ beta i))) |
(*.f64 (+.f64 beta i) (+.f64 alpha i)) |
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(*.f64 (+.f64 beta i) (+.f64 alpha i)) |
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(*.f64 (+.f64 beta i) (+.f64 alpha i)) |
(* alpha (+ beta i)) |
(*.f64 alpha (+.f64 beta i)) |
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha)))) |
(*.f64 alpha (+.f64 beta (fma.f64 i (/.f64 (+.f64 beta i) alpha) i))) |
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha)))) |
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(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha)))) |
(*.f64 alpha (+.f64 beta (fma.f64 i (/.f64 (+.f64 beta i) alpha) i))) |
(* -1 (* alpha (+ (* -1 beta) (* -1 i)))) |
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(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))) |
(neg.f64 (*.f64 alpha (-.f64 (neg.f64 (fma.f64 i (/.f64 (+.f64 beta i) alpha) i)) beta))) |
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))) |
(neg.f64 (*.f64 alpha (-.f64 (neg.f64 (fma.f64 i (/.f64 (+.f64 beta i) alpha) i)) beta))) |
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))) |
(neg.f64 (*.f64 alpha (-.f64 (neg.f64 (fma.f64 i (/.f64 (+.f64 beta i) alpha) i)) beta))) |
(* alpha beta) |
(*.f64 alpha beta) |
(+ (* alpha beta) (* i (+ alpha beta))) |
(fma.f64 alpha beta (*.f64 i (+.f64 alpha beta))) |
(+ (* alpha beta) (* i (+ alpha (+ beta i)))) |
(*.f64 (+.f64 beta i) (+.f64 alpha i)) |
(+ (* alpha beta) (* i (+ alpha (+ beta i)))) |
(*.f64 (+.f64 beta i) (+.f64 alpha i)) |
(pow i 2) |
(*.f64 i i) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i)))) |
(*.f64 (*.f64 i i) (+.f64 (/.f64 alpha i) (+.f64 (/.f64 beta i) #s(literal 1 binary64)))) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2)))))) |
(*.f64 (*.f64 i i) (+.f64 (/.f64 alpha i) (+.f64 (fma.f64 alpha (/.f64 beta (*.f64 i i)) (/.f64 beta i)) #s(literal 1 binary64)))) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2)))))) |
(*.f64 (*.f64 i i) (+.f64 (/.f64 alpha i) (+.f64 (fma.f64 alpha (/.f64 beta (*.f64 i i)) (/.f64 beta i)) #s(literal 1 binary64)))) |
(pow i 2) |
(*.f64 i i) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i)))) |
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(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i)))) |
(*.f64 (*.f64 i i) (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (fma.f64 alpha (/.f64 beta i) (+.f64 alpha beta))) i))) |
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i)))) |
(*.f64 (*.f64 i i) (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (fma.f64 alpha (/.f64 beta i) (+.f64 alpha beta))) i))) |
(+ beta (* 2 i)) |
(fma.f64 i #s(literal 2 binary64) beta) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
alpha |
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha)))) |
(+.f64 alpha (*.f64 alpha (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (/.f64 beta alpha)))) |
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha)))) |
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(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha)))) |
(+.f64 alpha (*.f64 alpha (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (/.f64 beta alpha)))) |
alpha |
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha)) #s(literal -1 binary64))) |
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha)) #s(literal -1 binary64))) |
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha)) #s(literal -1 binary64))) |
(+ alpha (* 2 i)) |
(fma.f64 i #s(literal 2 binary64) alpha) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
beta |
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta)))) |
(+.f64 beta (*.f64 beta (fma.f64 #s(literal 2 binary64) (/.f64 i beta) (/.f64 alpha beta)))) |
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta)))) |
(+.f64 beta (*.f64 beta (fma.f64 #s(literal 2 binary64) (/.f64 i beta) (/.f64 alpha beta)))) |
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta)))) |
(+.f64 beta (*.f64 beta (fma.f64 #s(literal 2 binary64) (/.f64 i beta) (/.f64 alpha beta)))) |
beta |
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1))) |
(*.f64 (neg.f64 beta) (+.f64 (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) (neg.f64 beta)) #s(literal -1 binary64))) |
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1))) |
(*.f64 (neg.f64 beta) (+.f64 (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) (neg.f64 beta)) #s(literal -1 binary64))) |
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1))) |
(*.f64 (neg.f64 beta) (+.f64 (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) (neg.f64 beta)) #s(literal -1 binary64))) |
(+ alpha beta) |
(+.f64 alpha beta) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(* 2 i) |
(*.f64 i #s(literal 2 binary64)) |
(* i (+ 2 (+ (/ alpha i) (/ beta i)))) |
(*.f64 i (+.f64 (/.f64 alpha i) (+.f64 (/.f64 beta i) #s(literal 2 binary64)))) |
(* i (+ 2 (+ (/ alpha i) (/ beta i)))) |
(*.f64 i (+.f64 (/.f64 alpha i) (+.f64 (/.f64 beta i) #s(literal 2 binary64)))) |
(* i (+ 2 (+ (/ alpha i) (/ beta i)))) |
(*.f64 i (+.f64 (/.f64 alpha i) (+.f64 (/.f64 beta i) #s(literal 2 binary64)))) |
(* 2 i) |
(*.f64 i #s(literal 2 binary64)) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2))) |
(*.f64 (neg.f64 i) (+.f64 (/.f64 (-.f64 (neg.f64 alpha) beta) i) #s(literal -2 binary64))) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2))) |
(*.f64 (neg.f64 i) (+.f64 (/.f64 (-.f64 (neg.f64 alpha) beta) i) #s(literal -2 binary64))) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2))) |
(*.f64 (neg.f64 i) (+.f64 (/.f64 (-.f64 (neg.f64 alpha) beta) i) #s(literal -2 binary64))) |
(- (pow (+ beta (* 2 i)) 2) 1) |
(fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) |
(- (+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1) |
(fma.f64 alpha (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) |
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1) |
(fma.f64 alpha (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) alpha)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) |
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1) |
(fma.f64 alpha (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) alpha)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) |
(pow alpha 2) |
(*.f64 alpha alpha) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha))))) |
(*.f64 (*.f64 alpha alpha) (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64)))) |
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2)))) |
(*.f64 (*.f64 alpha alpha) (+.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64))) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 alpha alpha))) (/.f64 #s(literal -1 binary64) (*.f64 alpha alpha)))) |
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2)))) |
(*.f64 (*.f64 alpha alpha) (+.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64))) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 alpha alpha))) (/.f64 #s(literal -1 binary64) (*.f64 alpha alpha)))) |
(pow alpha 2) |
(*.f64 alpha alpha) |
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha)))) |
(*.f64 (*.f64 alpha alpha) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha) #s(literal 1 binary64))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha)))) |
(*.f64 (*.f64 alpha alpha) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta)) (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) alpha)) alpha))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha)))) |
(*.f64 (*.f64 alpha alpha) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta)) (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) alpha)) alpha))) |
(- (pow (+ alpha (* 2 i)) 2) 1) |
(fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)) |
(- (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) |
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(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1) |
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(pow beta 2) |
(*.f64 beta beta) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta))))) |
(*.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64)))) |
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2)))) |
(*.f64 (*.f64 beta beta) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 beta beta)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 beta beta))))) |
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2)))) |
(*.f64 (*.f64 beta beta) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 beta beta)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 beta beta))))) |
(pow beta 2) |
(*.f64 beta beta) |
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta)))) |
(*.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta) #s(literal 1 binary64))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta)))) |
(*.f64 (*.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha)) (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)) beta)) beta))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta)))) |
(*.f64 (*.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha)) (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)) beta)) beta))) |
(- (pow (+ alpha beta) 2) 1) |
(fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) |
(- (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) 1) |
(fma.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) |
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1) |
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(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1) |
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 alpha (+.f64 beta i))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) |
(* 4 (pow i 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 i i)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64))) |
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2)))) |
(*.f64 (*.f64 i i) (+.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)) (+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i)) (/.f64 #s(literal -1 binary64) (*.f64 i i))))) |
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2)))) |
(*.f64 (*.f64 i i) (+.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)) (+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i)) (/.f64 #s(literal -1 binary64) (*.f64 i i))))) |
(* 4 (pow i 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 i i)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i)))) |
(*.f64 (*.f64 i i) (-.f64 #s(literal 4 binary64) (/.f64 (-.f64 (*.f64 (+.f64 alpha beta) #s(literal -4 binary64)) (/.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) i)) i))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i)))) |
(*.f64 (*.f64 i i) (-.f64 #s(literal 4 binary64) (/.f64 (-.f64 (*.f64 (+.f64 alpha beta) #s(literal -4 binary64)) (/.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) i)) i))) |
(/ (* alpha (* beta i)) (+ alpha beta)) |
(/.f64 (*.f64 alpha (*.f64 beta i)) (+.f64 alpha beta)) |
(* i (+ (* i (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(*.f64 i (fma.f64 i (+.f64 (fma.f64 alpha (/.f64 beta (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64)) (*.f64 #s(literal -4 binary64) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (*.f64 alpha beta) (+.f64 alpha beta)))) |
(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(*.f64 i (fma.f64 alpha (/.f64 beta (+.f64 alpha beta)) (*.f64 i (+.f64 (fma.f64 i (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 beta (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (*.f64 #s(literal -4 binary64) (fma.f64 alpha (/.f64 beta (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (+.f64 (fma.f64 alpha (/.f64 beta (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64)) (*.f64 #s(literal -4 binary64) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (+.f64 alpha beta))))) (fma.f64 alpha (/.f64 beta (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64))) (*.f64 #s(literal -4 binary64) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))))) |
(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (+ (* 2 (/ beta (pow (+ alpha beta) 2))) (* i (- (/ 1 (pow (+ alpha beta) 2)) (+ (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (pow (+ alpha beta) 2))) (* 4 (/ (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta))))) (+ alpha beta)))))))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(*.f64 i (fma.f64 i (+.f64 (fma.f64 i (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 beta (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (fma.f64 i (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 #s(literal -4 binary64) (+.f64 (/.f64 (+.f64 (fma.f64 alpha (/.f64 beta (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64)) (*.f64 #s(literal -4 binary64) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 beta (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (*.f64 #s(literal -4 binary64) (fma.f64 alpha (/.f64 beta (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (+.f64 (fma.f64 alpha (/.f64 beta (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64)) (*.f64 #s(literal -4 binary64) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (+.f64 alpha beta))))) (+.f64 alpha beta))))) (*.f64 #s(literal -4 binary64) (fma.f64 alpha (/.f64 beta (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (+.f64 (fma.f64 alpha (/.f64 beta (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64)) (*.f64 #s(literal -4 binary64) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (+.f64 alpha beta)))))) (fma.f64 alpha (/.f64 beta (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64))) (*.f64 #s(literal -4 binary64) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (*.f64 alpha beta) (+.f64 alpha beta)))) |
(* 1/4 (pow i 2)) |
(*.f64 (*.f64 i i) #s(literal 1/4 binary64)) |
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) |
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (+ alpha beta) i)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)))))) |
(*.f64 (*.f64 i i) (-.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) i) (/.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta)) (*.f64 i i))) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i)) (fma.f64 (+.f64 alpha beta) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (*.f64 i i)) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/4 binary64)) i))))) |
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 3))) (+ (* 1/4 (/ (+ alpha beta) i)) (+ (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/16 (pow (+ alpha beta) 2)) (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))))) (pow i 3)))))))) |
(*.f64 (*.f64 i i) (-.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 alpha (/.f64 (*.f64 beta (+.f64 alpha beta)) (*.f64 i (*.f64 i i))) (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) i) (/.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta)) (*.f64 i i)))) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (*.f64 i (*.f64 i i))) (/.f64 (+.f64 alpha beta) i)) (fma.f64 (+.f64 alpha beta) (+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (*.f64 i i)) (/.f64 (+.f64 (fma.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta)) #s(literal 1/4 binary64) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal -1/16 binary64))) (*.f64 (+.f64 alpha beta) (*.f64 #s(literal -1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))))) (*.f64 i (*.f64 i i)))) (*.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i))))))) |
(* 1/4 (pow i 2)) |
(*.f64 (*.f64 i i) #s(literal 1/4 binary64)) |
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* 1/4 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)) (* -1/16 (/ (pow (+ alpha beta) 2) i)))) i)))) |
(*.f64 (*.f64 i i) (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (fma.f64 (/.f64 (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta))) i) #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i) (/.f64 (*.f64 (+.f64 alpha beta) (*.f64 #s(literal -1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))) i))) i))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) (* 1/4 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) i)) (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)))) i))) i)))) |
(*.f64 (*.f64 i i) (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (/.f64 (-.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 alpha (*.f64 beta (+.f64 alpha beta)))) i) (+.f64 (fma.f64 (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta))) #s(literal 1/4 binary64) (*.f64 (+.f64 alpha beta) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))))) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 1/16 binary64)))) (fma.f64 (-.f64 (neg.f64 alpha) beta) (/.f64 (+.f64 (fma.f64 (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta))) #s(literal 1/4 binary64) (*.f64 (+.f64 alpha beta) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))))) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 1/16 binary64))) i) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))) i)))) i)) i))) |
(/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2)) |
(/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) |
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
(fma.f64 alpha (fma.f64 i (/.f64 (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (*.f64 (*.f64 i (neg.f64 i)) (/.f64 (*.f64 (*.f64 (+.f64 beta i) (+.f64 beta i)) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64))))) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))) |
(+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
(fma.f64 alpha (fma.f64 alpha (-.f64 (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))) (/.f64 (fma.f64 i (/.f64 (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (*.f64 (*.f64 i (neg.f64 i)) (/.f64 (*.f64 (*.f64 (+.f64 beta i) (+.f64 beta i)) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64))))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64))))) (fma.f64 i (/.f64 (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (*.f64 (*.f64 i (neg.f64 i)) (/.f64 (*.f64 (*.f64 (+.f64 beta i) (+.f64 beta i)) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64)))))) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))) |
(+ (* alpha (- (+ (* alpha (- (+ (* alpha (- (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 6)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (pow (+ beta (* 2 i)) 2))))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
(fma.f64 alpha (fma.f64 alpha (fma.f64 alpha (-.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 (*.f64 (+.f64 beta i) (+.f64 beta i)) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 6 binary64))) (fma.f64 (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))) (/.f64 (-.f64 (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))) (/.f64 (fma.f64 i (/.f64 (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (*.f64 (*.f64 i (neg.f64 i)) (/.f64 (*.f64 (*.f64 (+.f64 beta i) (+.f64 beta i)) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64))))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64))))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (*.f64 i (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64))))) (-.f64 (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))) (/.f64 (fma.f64 i (/.f64 (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (*.f64 (*.f64 i (neg.f64 i)) (/.f64 (*.f64 (*.f64 (+.f64 beta i) (+.f64 beta i)) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64))))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64)))))) (fma.f64 i (/.f64 (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (*.f64 (*.f64 i (neg.f64 i)) (/.f64 (*.f64 (*.f64 (+.f64 beta i) (+.f64 beta i)) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64)))))) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))) |
(* i (+ beta i)) |
(*.f64 i (+.f64 beta i)) |
(- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha)) |
(fma.f64 i (+.f64 beta i) (*.f64 i (-.f64 (/.f64 (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) alpha) (/.f64 (*.f64 (+.f64 beta i) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) alpha)))) |
(- (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))))) |
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(- (+ (* -1 (/ (+ (* (+ (* 2 beta) (* 4 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))))) |
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(* i (+ alpha i)) |
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(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) |
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(* alpha (* beta (* i (+ alpha beta)))) |
(*.f64 (*.f64 alpha beta) (*.f64 i (+.f64 alpha beta))) |
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (pow (+ alpha beta) 2))))) |
(*.f64 i (fma.f64 i (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta)) (*.f64 alpha (*.f64 beta (+.f64 alpha beta))))) |
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (+ (* i (+ (* 2 alpha) (* 2 beta))) (pow (+ alpha beta) 2)))))) |
(*.f64 i (fma.f64 i (fma.f64 i (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta))) (*.f64 alpha (*.f64 beta (+.f64 alpha beta))))) |
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (+ (* i (+ i (+ (* 2 alpha) (* 2 beta)))) (pow (+ alpha beta) 2)))))) |
(*.f64 i (fma.f64 i (fma.f64 i (fma.f64 #s(literal 2 binary64) (+.f64 alpha beta) i) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta))) (*.f64 alpha (*.f64 beta (+.f64 alpha beta))))) |
(pow i 4) |
(pow.f64 i #s(literal 4 binary64)) |
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (* 2 (/ beta i))))) |
(*.f64 (pow.f64 i #s(literal 4 binary64)) (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha i) (/.f64 beta i)) #s(literal 1 binary64))) |
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (+ (* 2 (/ beta i)) (+ (/ (* alpha beta) (pow i 2)) (/ (pow (+ alpha beta) 2) (pow i 2))))))) |
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(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (+ (* 2 (/ beta i)) (+ (/ (* alpha beta) (pow i 2)) (+ (/ (* alpha (* beta (+ alpha beta))) (pow i 3)) (/ (pow (+ alpha beta) 2) (pow i 2)))))))) |
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(pow i 4) |
(pow.f64 i #s(literal 4 binary64)) |
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (* 2 (/ beta i))))) |
(*.f64 (pow.f64 i #s(literal 4 binary64)) (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha i) (/.f64 beta i)) #s(literal 1 binary64))) |
(* (pow i 4) (+ 1 (* -1 (/ (+ (* -1 (+ (* 2 alpha) (* 2 beta))) (+ (* -1 (/ (* alpha beta) i)) (* -1 (/ (pow (+ alpha beta) 2) i)))) i)))) |
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(* (pow i 4) (+ 1 (* -1 (/ (+ (* -1 (+ (* 2 alpha) (* 2 beta))) (* -1 (/ (+ (* -1 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (/ (* alpha (* beta (+ alpha beta))) i)) i))) i)))) |
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(* (pow i 2) (pow (+ beta i) 2)) |
(*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) |
(+ (* alpha (* i (+ (* i (+ beta i)) (pow (+ beta i) 2)))) (* (pow i 2) (pow (+ beta i) 2))) |
(fma.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i)) (*.f64 alpha (*.f64 i (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i))))) |
(+ (* alpha (+ (* alpha (* i (+ beta i))) (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))))) (* (pow i 2) (pow (+ beta i) 2))) |
(fma.f64 alpha (fma.f64 alpha (*.f64 i (+.f64 beta i)) (*.f64 i (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)))) (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i)))) |
(+ (* alpha (+ (* alpha (* i (+ beta i))) (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))))) (* (pow i 2) (pow (+ beta i) 2))) |
(fma.f64 alpha (fma.f64 alpha (*.f64 i (+.f64 beta i)) (*.f64 i (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)))) (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i)))) |
(* (pow alpha 2) (* i (+ beta i))) |
(*.f64 (*.f64 i (+.f64 beta i)) (*.f64 alpha alpha)) |
(* (pow alpha 2) (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha))) |
(*.f64 (*.f64 alpha alpha) (*.f64 i (+.f64 (+.f64 beta i) (/.f64 (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) alpha)))) |
(* (pow alpha 2) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) |
(*.f64 (*.f64 alpha alpha) (fma.f64 i (+.f64 (+.f64 beta i) (/.f64 (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) alpha)) (*.f64 (*.f64 i i) (/.f64 (*.f64 (+.f64 beta i) (+.f64 beta i)) (*.f64 alpha alpha))))) |
(* (pow alpha 2) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) |
(*.f64 (*.f64 alpha alpha) (fma.f64 i (+.f64 (+.f64 beta i) (/.f64 (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) alpha)) (*.f64 (*.f64 i i) (/.f64 (*.f64 (+.f64 beta i) (+.f64 beta i)) (*.f64 alpha alpha))))) |
(* -1 (* (pow alpha 2) (* i (+ (* -1 beta) (* -1 i))))) |
(*.f64 (*.f64 alpha alpha) (*.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta))) |
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) alpha)))) |
(*.f64 (*.f64 alpha alpha) (neg.f64 (*.f64 i (+.f64 (-.f64 (neg.f64 i) beta) (/.f64 (*.f64 (+.f64 beta i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta))) alpha))))) |
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) alpha)))) |
(*.f64 (*.f64 alpha alpha) (neg.f64 (fma.f64 i (-.f64 (neg.f64 i) beta) (/.f64 (fma.f64 i (*.f64 (+.f64 beta i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta))) (*.f64 (*.f64 i (neg.f64 i)) (/.f64 (*.f64 (+.f64 beta i) (+.f64 beta i)) alpha))) alpha)))) |
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) alpha)))) |
(*.f64 (*.f64 alpha alpha) (neg.f64 (fma.f64 i (-.f64 (neg.f64 i) beta) (/.f64 (fma.f64 i (*.f64 (+.f64 beta i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta))) (*.f64 (*.f64 i (neg.f64 i)) (/.f64 (*.f64 (+.f64 beta i) (+.f64 beta i)) alpha))) alpha)))) |
(* (pow i 2) (pow (+ alpha i) 2)) |
(*.f64 (*.f64 i i) (*.f64 (+.f64 alpha i) (+.f64 alpha i))) |
(+ (* beta (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2)))) (* (pow i 2) (pow (+ alpha i) 2))) |
(fma.f64 (*.f64 beta i) (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (*.f64 (*.f64 i i) (*.f64 (+.f64 alpha i) (+.f64 alpha i)))) |
(+ (* beta (+ (* beta (* i (+ alpha i))) (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))))) (* (pow i 2) (pow (+ alpha i) 2))) |
(fma.f64 beta (fma.f64 i (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (*.f64 beta (*.f64 i (+.f64 alpha i)))) (*.f64 (*.f64 i i) (*.f64 (+.f64 alpha i) (+.f64 alpha i)))) |
(+ (* beta (+ (* beta (* i (+ alpha i))) (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))))) (* (pow i 2) (pow (+ alpha i) 2))) |
(fma.f64 beta (fma.f64 i (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (*.f64 beta (*.f64 i (+.f64 alpha i)))) (*.f64 (*.f64 i i) (*.f64 (+.f64 alpha i) (+.f64 alpha i)))) |
(* (pow beta 2) (* i (+ alpha i))) |
(*.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta)) |
(* (pow beta 2) (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta))) |
(*.f64 (*.f64 beta beta) (*.f64 i (+.f64 (+.f64 alpha i) (/.f64 (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)))) |
(* (pow beta 2) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) |
(*.f64 (*.f64 beta beta) (fma.f64 i (+.f64 (+.f64 alpha i) (/.f64 (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 alpha i) (+.f64 alpha i))) (*.f64 beta beta)))) |
(* (pow beta 2) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) |
(*.f64 (*.f64 beta beta) (fma.f64 i (+.f64 (+.f64 alpha i) (/.f64 (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 alpha i) (+.f64 alpha i))) (*.f64 beta beta)))) |
(* -1 (* (pow beta 2) (* i (+ (* -1 alpha) (* -1 i))))) |
(*.f64 (*.f64 beta beta) (neg.f64 (*.f64 i (-.f64 (neg.f64 i) alpha)))) |
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) beta)))) |
(*.f64 (*.f64 beta beta) (neg.f64 (*.f64 i (+.f64 (-.f64 (neg.f64 i) alpha) (/.f64 (*.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) beta))))) |
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ alpha i) 2)) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) beta)))) |
(*.f64 (*.f64 beta beta) (neg.f64 (fma.f64 i (-.f64 (neg.f64 i) alpha) (/.f64 (fma.f64 i (*.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 alpha i) (+.f64 alpha i))) (neg.f64 beta))) beta)))) |
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ alpha i) 2)) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) beta)))) |
(*.f64 (*.f64 beta beta) (neg.f64 (fma.f64 i (-.f64 (neg.f64 i) alpha) (/.f64 (fma.f64 i (*.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 alpha i) (+.f64 alpha i))) (neg.f64 beta))) beta)))) |
(pow (+ beta (* 2 i)) 2) |
(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) |
(+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) |
(fma.f64 alpha (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) |
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
(fma.f64 alpha (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) alpha)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) |
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
(fma.f64 alpha (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) alpha)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) |
(pow alpha 2) |
(*.f64 alpha alpha) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha))))) |
(*.f64 (*.f64 alpha alpha) (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64)))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(*.f64 (*.f64 alpha alpha) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64))) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 alpha alpha)))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(*.f64 (*.f64 alpha alpha) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64))) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 alpha alpha)))) |
(pow alpha 2) |
(*.f64 alpha alpha) |
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha)))) |
(*.f64 (*.f64 alpha alpha) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha) #s(literal 1 binary64))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(*.f64 (*.f64 alpha alpha) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta)) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) alpha)) alpha))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(*.f64 (*.f64 alpha alpha) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta)) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) alpha)) alpha))) |
(pow (+ alpha (* 2 i)) 2) |
(*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) |
(+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) |
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))) (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) beta)) (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) beta)) (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))) |
(pow beta 2) |
(*.f64 beta beta) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta))))) |
(*.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64)))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(*.f64 (*.f64 beta beta) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64))) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 beta beta)))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(*.f64 (*.f64 beta beta) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64))) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 beta beta)))) |
(pow beta 2) |
(*.f64 beta beta) |
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta)))) |
(*.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta) #s(literal 1 binary64))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(*.f64 (*.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (neg.f64 beta))) beta))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(*.f64 (*.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (neg.f64 beta))) beta))) |
(pow (+ alpha beta) 2) |
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) |
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) |
(*.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta))) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 alpha (+.f64 beta i))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 alpha (+.f64 beta i))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) |
(* 4 (pow i 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 i i)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(*.f64 (*.f64 i i) (+.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i)))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(*.f64 (*.f64 i i) (+.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i)))) |
(* 4 (pow i 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 i i)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(*.f64 (*.f64 i i) (-.f64 #s(literal 4 binary64) (/.f64 (-.f64 (*.f64 (+.f64 alpha beta) #s(literal -4 binary64)) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i)) i))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(*.f64 (*.f64 i i) (-.f64 #s(literal 4 binary64) (/.f64 (-.f64 (*.f64 (+.f64 alpha beta) #s(literal -4 binary64)) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i)) i))) |
| 5 174× | lower-fma.f64 |
| 5 174× | lower-fma.f32 |
| 4 888× | lower-/.f32 |
| 4 884× | lower-/.f64 |
| 4 186× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 157 |
| 0 | 29 | 127 |
| 1 | 146 | 127 |
| 2 | 1503 | 127 |
| 0 | 8201 | 117 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i))) |
(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) |
(-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) |
(/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) |
(*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) |
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))))) #s(literal -1 binary64))) |
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (neg.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) #s(literal 1 binary64))) (/.f64 (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (neg.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) #s(literal 1 binary64)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))))) (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (neg.f64 (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (neg.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))) (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (*.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (neg.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))))) |
(neg.f64 (/.f64 (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (neg.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) #s(literal 1 binary64)))) |
(/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) |
(/.f64 (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) |
(/.f64 (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (neg.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (neg.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (neg.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) (neg.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (*.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (*.f64 (neg.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (*.f64 (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (*.f64 (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (/.f64 (neg.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (/.f64 (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (/.f64 (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))))) |
(/.f64 (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (neg.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (neg.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) #s(literal 1 binary64))) |
(/.f64 (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (neg.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) (neg.f64 (neg.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (neg.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (neg.f64 (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (*.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (neg.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))))) |
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(/.f64 (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (*.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) |
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(*.f64 (*.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i i) #s(literal 4 binary64))) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 8 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64)))) (fma.f64 (*.f64 i #s(literal 2 binary64)) (-.f64 (*.f64 i #s(literal 2 binary64)) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) |
(*.f64 (*.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i i) #s(literal 4 binary64))) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i i) #s(literal 4 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64))))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i i) #s(literal 4 binary64))) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i i) #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64)))) (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64))))))) |
(*.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (*.f64 (*.f64 (*.f64 i (*.f64 i i)) #s(literal 8 binary64)) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (-.f64 (*.f64 (*.f64 i (*.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (*.f64 i (*.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) (*.f64 (*.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (*.f64 i (*.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))))))) |
(*.f64 (-.f64 (*.f64 (*.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (*.f64 (*.f64 i (*.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (*.f64 i (*.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (*.f64 i (*.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))))) |
(*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 8 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 i #s(literal 2 binary64)) (-.f64 (*.f64 i #s(literal 2 binary64)) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) |
(*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i i) #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64)))))) |
(*.f64 (*.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 8 binary64))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 i #s(literal 2 binary64)) (-.f64 (*.f64 i #s(literal 2 binary64)) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) |
(*.f64 (*.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i i) #s(literal 4 binary64))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 #s(literal 1 binary64) (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64)))))) |
(*.f64 (exp.f64 (log.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (exp.f64 (log.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) |
Compiled 120 180 to 4 604 computations (96.2% saved)
19 alts after pruning (19 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 377 | 19 | 1 396 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 1 378 | 19 | 1 397 |
| Status | Accuracy | Program |
|---|---|---|
| 14.4% | (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (/.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i i) #s(literal 4 binary64))) (+.f64 alpha beta)) (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64)))) (*.f64 (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64)))) (*.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i i) #s(literal 4 binary64))) (*.f64 i #s(literal 2 binary64))))) (*.f64 (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64)))) (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64))))))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | |
| 42.5% | (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | |
| 23.8% | (/.f64 (*.f64 (/.f64 i (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | |
| ▶ | 37.5% | (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
| 41.9% | (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) #s(literal 1/4 binary64))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | |
| 18.0% | (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | |
| 42.3% | (*.f64 (pow.f64 (/.f64 (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64)) (*.f64 i (+.f64 i (+.f64 alpha beta)))) #s(literal -1 binary64)) (pow.f64 (*.f64 (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) #s(literal -1 binary64))) | |
| 48.3% | (*.f64 (pow.f64 (*.f64 (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64)) (/.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 i (+.f64 i (+.f64 alpha beta))))) #s(literal -1 binary64)) (pow.f64 (*.f64 (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (/.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) #s(literal -1 binary64))) | |
| ▶ | 42.5% | (*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) |
| ▶ | 48.5% | (*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) |
| 42.3% | (*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) | |
| 41.7% | (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) | |
| 14.7% | (*.f64 i (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))))) | |
| 12.4% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (fma.f64 i (+.f64 alpha i) (*.f64 i (-.f64 (/.f64 (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (*.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))) | |
| 14.5% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) | |
| ▶ | 14.6% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta))) |
| 67.7% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (-.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta))) i) (neg.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64))))) (fma.f64 #s(literal -1/256 binary64) (/.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64))) i) (/.f64 (*.f64 (*.f64 #s(literal -2 binary64) (+.f64 alpha beta)) (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64)))) i))) i))) | |
| 64.0% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (-.f64 #s(literal 1/16 binary64) (/.f64 (neg.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) #s(literal -1/8 binary64) (/.f64 (-.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 alpha (*.f64 beta (+.f64 alpha beta)))) i) (+.f64 (fma.f64 #s(literal 1/16 binary64) (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta))) (*.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64))))) (*.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/256 binary64)))) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 #s(literal 1/16 binary64) (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta))) (*.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64))))) (*.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/256 binary64)))) i) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64)))) i) (/.f64 (*.f64 #s(literal -1/256 binary64) (*.f64 #s(literal -4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) i)))) i)))) i))) | |
| ▶ | 74.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
Compiled 2 120 to 734 computations (65.4% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 384 | (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) | |
| cost-diff | 384 | (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) | |
| cost-diff | 384 | (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) | |
| cost-diff | 704 | (*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) | |
| cost-diff | 0 | (+.f64 i (+.f64 alpha beta)) | |
| cost-diff | 0 | (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) | |
| cost-diff | 384 | (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) | |
| cost-diff | 384 | (*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) | |
| cost-diff | 128 | (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) | |
| cost-diff | 128 | (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)) | |
| cost-diff | 704 | (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)) | |
| cost-diff | 704 | (*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) | |
| cost-diff | 0 | (+.f64 alpha i) | |
| cost-diff | 0 | (*.f64 i (+.f64 alpha i)) | |
| cost-diff | 0 | (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta)) | |
| cost-diff | 0 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta))) | |
| cost-diff | 0 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
| 7 306× | lower-fma.f32 |
| 7 300× | lower-fma.f64 |
| 4 218× | lower-*.f32 |
| 4 194× | lower-*.f64 |
| 3 544× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 57 | 741 |
| 0 | 93 | 729 |
| 1 | 253 | 729 |
| 2 | 795 | 689 |
| 3 | 4200 | 669 |
| 4 | 6175 | 630 |
| 0 | 8063 | 626 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(literal 1/16 binary64) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta))) |
(/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta)) |
(*.f64 i (+.f64 alpha i)) |
i |
(+.f64 alpha i) |
alpha |
(*.f64 beta beta) |
beta |
(/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
#s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) |
(*.f64 i i) |
i |
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)) |
#s(literal 1/4 binary64) |
(/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i) |
(*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) |
(-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)) |
(*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) |
#s(literal 2 binary64) |
(+.f64 alpha beta) |
alpha |
beta |
(-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) |
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) |
(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) |
(*.f64 #s(literal 2 binary64) i) |
#s(literal 1 binary64) |
(*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) |
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) |
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) |
i |
(+.f64 i (+.f64 alpha beta)) |
(+.f64 alpha beta) |
alpha |
beta |
(*.f64 alpha beta) |
(fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) |
(fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) |
#s(literal 2 binary64) |
#s(literal -1 binary64) |
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) |
(*.f64 i (+.f64 i (+.f64 alpha beta))) |
(*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) |
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) |
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) |
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) |
(*.f64 i (+.f64 i (+.f64 alpha beta))) |
i |
(+.f64 i (+.f64 alpha beta)) |
(+.f64 alpha beta) |
alpha |
beta |
(fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) |
#s(literal 2 binary64) |
(+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) |
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) |
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) |
(*.f64 alpha beta) |
(+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
| Outputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(literal 1/16 binary64) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 i alpha)) (*.f64 beta beta))) |
(/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta)) |
(/.f64 (*.f64 i (+.f64 i alpha)) (*.f64 beta beta)) |
(*.f64 i (+.f64 alpha i)) |
(*.f64 i (+.f64 i alpha)) |
i |
(+.f64 alpha i) |
(+.f64 i alpha) |
alpha |
(*.f64 beta beta) |
beta |
(/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (fma.f64 i #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 alpha beta))))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) |
#s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)))) |
#s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (fma.f64 i #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 alpha beta))))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) |
(*.f64 i (fma.f64 i #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 alpha beta)))) |
(*.f64 i i) |
i |
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)) |
(fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/4 binary64)) |
#s(literal 1/4 binary64) |
(/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i) |
(/.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 alpha beta)) i) |
(*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) |
(*.f64 #s(literal 1/4 binary64) (+.f64 alpha beta)) |
(-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)) |
(+.f64 alpha beta) |
(*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) |
#s(literal 2 binary64) |
(+.f64 alpha beta) |
alpha |
beta |
(-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) |
(fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) |
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) |
(*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) |
(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) |
(fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) |
(*.f64 #s(literal 2 binary64) i) |
(*.f64 i #s(literal 2 binary64)) |
#s(literal 1 binary64) |
(*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) |
(/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 i alpha) (+.f64 i beta))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) |
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) |
(/.f64 (*.f64 (+.f64 i alpha) (+.f64 i beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) |
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) |
(*.f64 (+.f64 i alpha) (+.f64 i beta)) |
i |
(+.f64 i (+.f64 alpha beta)) |
(+.f64 alpha beta) |
alpha |
beta |
(*.f64 alpha beta) |
(fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) |
(fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) |
#s(literal 2 binary64) |
#s(literal -1 binary64) |
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) |
(*.f64 i (+.f64 i (+.f64 alpha beta))) |
(*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) |
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) |
(/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 i alpha) (+.f64 i beta))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) |
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) |
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 #s(literal 1 binary64) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) |
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) |
(*.f64 i (+.f64 i (+.f64 alpha beta))) |
i |
(+.f64 i (+.f64 alpha beta)) |
(+.f64 alpha beta) |
alpha |
beta |
(fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) |
#s(literal 2 binary64) |
(+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) |
#s(literal 1 binary64) |
(/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) |
(/.f64 (*.f64 (+.f64 i alpha) (+.f64 i beta)) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) |
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) |
(/.f64 (*.f64 (+.f64 i alpha) (+.f64 i beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) |
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) |
(*.f64 (+.f64 i alpha) (+.f64 i beta)) |
(*.f64 alpha beta) |
(+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.01171875 | (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) | |
| accuracy | 0.09375 | (*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) | |
| accuracy | 31.404814363782457 | (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) | |
| accuracy | 31.635144686680317 | (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) | |
| accuracy | 0.01953125 | (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) | |
| accuracy | 0.08984375 | (*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) | |
| accuracy | 37.7579555123497 | (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) | |
| accuracy | 37.75844198077979 | (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) | |
| accuracy | 0.01953125 | (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) | |
| accuracy | 0.05078125 | (*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) | |
| accuracy | 12.463010696627125 | #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)))) | |
| accuracy | 33.079017936929866 | (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | |
| accuracy | 0 | (*.f64 beta beta) | |
| accuracy | 0.00390625 | (*.f64 i (+.f64 alpha i)) | |
| accuracy | 15.734599367425485 | (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta)) | |
| accuracy | 46.552331073904746 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta))) | |
| accuracy | 16.497107014582685 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
| 83.0ms | 256× | 0 | valid |
Compiled 727 to 51 computations (93% saved)
ival-mult: 27.0ms (44.6% of total)ival-add: 18.0ms (29.8% of total)ival-div: 13.0ms (21.5% of total)ival-sub: 2.0ms (3.3% of total)exact: 1.0ms (1.7% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) (patch #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #<representation binary64>) () ()) |
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#s(alt (+.f64 i (+.f64 alpha beta)) (patch (+.f64 i (+.f64 alpha beta)) #<representation binary64>) () ()) |
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#s(alt (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (patch (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) #<representation binary64>) () ()) |
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#s(alt (*.f64 beta beta) (patch (*.f64 beta beta) #<representation binary64>) () ()) |
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| Outputs |
|---|
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#s(alt 1/16 (taylor inf i) (#s(alt #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) (patch #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) (taylor inf i) (#s(alt #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) (patch #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) (taylor inf i) (#s(alt #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) (patch #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) (taylor inf i) (#s(alt #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) (patch #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1/16 (taylor -inf i) (#s(alt #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) (patch #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #<representation binary64>) () ())) ()) |
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201 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 16.0ms | i | @ | 0 | (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) -1)) |
| 8.0ms | beta | @ | 0 | (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1)) |
| 6.0ms | beta | @ | inf | (* (* i i) (+ 1/4 (/ (* 1/4 (- (* 2 (+ alpha beta)) (+ alpha beta))) i))) |
| 5.0ms | beta | @ | inf | (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) |
| 4.0ms | i | @ | inf | (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1)) |
| 1× | egg-herbie |
| 5 666× | lower-*.f64 |
| 5 666× | lower-*.f32 |
| 4 978× | lower-+.f64 |
| 4 978× | lower-+.f32 |
| 3 408× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 3151 | 56825 |
| 0 | 8303 | 54455 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(/ (* i (+ beta i)) (pow alpha 2)) |
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2)) |
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(/ (- (+ (* -1 (/ (+ (* i (* (+ beta i) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (+ (* (+ (* 4 beta) (* 8 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))))))) (* (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1)))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2)) |
(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1))))))) alpha)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (+ (* -1 (* beta (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 4 alpha) (* 8 i)))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))) (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
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(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
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(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
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1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(/ (* i (+ beta i)) (pow alpha 2)) |
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2)) |
(/ (- (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2)) |
(/ (- (+ (* -1 (/ (+ (* i (* (+ beta i) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (+ (* (+ (* 4 beta) (* 8 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))))))) (* (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1)))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2)) |
(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1))))))) alpha)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (+ (* -1 (* beta (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 4 alpha) (* 8 i)))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))) (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (+ (* (+ (* 4 alpha) (* 8 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (* alpha i) (pow beta 2)) |
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2)))) |
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2)))) |
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2)))) |
(/ (pow i 2) (pow beta 2)) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(/ (pow i 2) (pow beta 2)) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(/ (pow i 2) (pow beta 2)) |
(+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2))) |
(+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2))) |
(+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2))) |
(/ (* alpha i) (pow beta 2)) |
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2))))) |
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2))))) |
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2))))) |
(/ (* alpha i) (pow beta 2)) |
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2))))))) |
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2))))))) |
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2))))))) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(* alpha i) |
(* i (+ alpha i)) |
(* i (+ alpha i)) |
(* i (+ alpha i)) |
(pow i 2) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(pow i 2) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(pow i 2) |
(+ (* alpha i) (pow i 2)) |
(+ (* alpha i) (pow i 2)) |
(+ (* alpha i) (pow i 2)) |
(* alpha i) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(* alpha i) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
i |
(+ alpha i) |
(+ alpha i) |
(+ alpha i) |
alpha |
(* alpha (+ 1 (/ i alpha))) |
(* alpha (+ 1 (/ i alpha))) |
(* alpha (+ 1 (/ i alpha))) |
alpha |
(* -1 (* alpha (- (* -1 (/ i alpha)) 1))) |
(* -1 (* alpha (- (* -1 (/ i alpha)) 1))) |
(* -1 (* alpha (- (* -1 (/ i alpha)) 1))) |
alpha |
(+ alpha i) |
(+ alpha i) |
(+ alpha i) |
i |
(* i (+ 1 (/ alpha i))) |
(* i (+ 1 (/ alpha i))) |
(* i (+ 1 (/ alpha i))) |
i |
(* -1 (* i (- (* -1 (/ alpha i)) 1))) |
(* -1 (* i (- (* -1 (/ alpha i)) 1))) |
(* -1 (* i (- (* -1 (/ alpha i)) 1))) |
(* 1/4 (* i (- (* 2 (+ alpha beta)) (+ alpha beta)))) |
(* i (+ (* 1/4 i) (* 1/4 (- (* 2 (+ alpha beta)) (+ alpha beta))))) |
(* i (+ (* 1/4 i) (* 1/4 (- (* 2 (+ alpha beta)) (+ alpha beta))))) |
(* i (+ (* 1/4 i) (* 1/4 (- (* 2 (+ alpha beta)) (+ alpha beta))))) |
(* 1/4 (pow i 2)) |
(* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 (+ alpha beta)) (+ alpha beta)) i)))) |
(* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 (+ alpha beta)) (+ alpha beta)) i)))) |
(* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 (+ alpha beta)) (+ alpha beta)) i)))) |
(* 1/4 (pow i 2)) |
(* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 (+ alpha beta)) (+ alpha beta)) i)))) |
(* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 (+ alpha beta)) (+ alpha beta)) i)))) |
(* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 (+ alpha beta)) (+ alpha beta)) i)))) |
(* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 beta) beta) i)))) |
(+ (* 1/4 (* alpha i)) (* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 beta) beta) i))))) |
(+ (* 1/4 (* alpha i)) (* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 beta) beta) i))))) |
(+ (* 1/4 (* alpha i)) (* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 beta) beta) i))))) |
(* 1/4 (* alpha i)) |
(* alpha (+ (* 1/4 i) (/ (* (pow i 2) (+ 1/4 (* 1/4 (- (* 2 (/ beta i)) (/ beta i))))) alpha))) |
(* alpha (+ (* 1/4 i) (/ (* (pow i 2) (+ 1/4 (* 1/4 (- (* 2 (/ beta i)) (/ beta i))))) alpha))) |
(* alpha (+ (* 1/4 i) (/ (* (pow i 2) (+ 1/4 (* 1/4 (- (* 2 (/ beta i)) (/ beta i))))) alpha))) |
(* 1/4 (* alpha i)) |
(* -1 (* alpha (+ (* -1 (/ (* (pow i 2) (+ 1/4 (* 1/4 (- (* 2 (/ beta i)) (/ beta i))))) alpha)) (* -1/4 i)))) |
(* -1 (* alpha (+ (* -1 (/ (* (pow i 2) (+ 1/4 (* 1/4 (- (* 2 (/ beta i)) (/ beta i))))) alpha)) (* -1/4 i)))) |
(* -1 (* alpha (+ (* -1 (/ (* (pow i 2) (+ 1/4 (* 1/4 (- (* 2 (/ beta i)) (/ beta i))))) alpha)) (* -1/4 i)))) |
(* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 alpha) alpha) i)))) |
(+ (* 1/4 (* beta i)) (* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 alpha) alpha) i))))) |
(+ (* 1/4 (* beta i)) (* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 alpha) alpha) i))))) |
(+ (* 1/4 (* beta i)) (* (pow i 2) (+ 1/4 (* 1/4 (/ (- (* 2 alpha) alpha) i))))) |
(* 1/4 (* beta i)) |
(* beta (+ (* 1/4 i) (/ (* (pow i 2) (+ 1/4 (* 1/4 (- (* 2 (/ alpha i)) (/ alpha i))))) beta))) |
(* beta (+ (* 1/4 i) (/ (* (pow i 2) (+ 1/4 (* 1/4 (- (* 2 (/ alpha i)) (/ alpha i))))) beta))) |
(* beta (+ (* 1/4 i) (/ (* (pow i 2) (+ 1/4 (* 1/4 (- (* 2 (/ alpha i)) (/ alpha i))))) beta))) |
(* 1/4 (* beta i)) |
(* -1 (* beta (+ (* -1 (/ (* (pow i 2) (+ 1/4 (* 1/4 (- (* 2 (/ alpha i)) (/ alpha i))))) beta)) (* -1/4 i)))) |
(* -1 (* beta (+ (* -1 (/ (* (pow i 2) (+ 1/4 (* 1/4 (- (* 2 (/ alpha i)) (/ alpha i))))) beta)) (* -1/4 i)))) |
(* -1 (* beta (+ (* -1 (/ (* (pow i 2) (+ 1/4 (* 1/4 (- (* 2 (/ alpha i)) (/ alpha i))))) beta)) (* -1/4 i)))) |
(- (* 2 beta) beta) |
(- (+ alpha (* 2 beta)) beta) |
(- (+ alpha (* 2 beta)) beta) |
(- (+ alpha (* 2 beta)) beta) |
alpha |
(* alpha (- (+ 1 (* 2 (/ beta alpha))) (/ beta alpha))) |
(* alpha (- (+ 1 (* 2 (/ beta alpha))) (/ beta alpha))) |
(* alpha (- (+ 1 (* 2 (/ beta alpha))) (/ beta alpha))) |
alpha |
(* -1 (* alpha (- (* -1 (/ (- (* 2 beta) beta) alpha)) 1))) |
(* -1 (* alpha (- (* -1 (/ (- (* 2 beta) beta) alpha)) 1))) |
(* -1 (* alpha (- (* -1 (/ (- (* 2 beta) beta) alpha)) 1))) |
(- (* 2 alpha) alpha) |
(- (+ beta (* 2 alpha)) alpha) |
(- (+ beta (* 2 alpha)) alpha) |
(- (+ beta (* 2 alpha)) alpha) |
beta |
(* beta (- (+ 1 (* 2 (/ alpha beta))) (/ alpha beta))) |
(* beta (- (+ 1 (* 2 (/ alpha beta))) (/ alpha beta))) |
(* beta (- (+ 1 (* 2 (/ alpha beta))) (/ alpha beta))) |
beta |
(* -1 (* beta (- (* -1 (/ (- (* 2 alpha) alpha) beta)) 1))) |
(* -1 (* beta (- (* -1 (/ (- (* 2 alpha) alpha) beta)) 1))) |
(* -1 (* beta (- (* -1 (/ (- (* 2 alpha) alpha) beta)) 1))) |
(+ 1/4 (* 1/4 (/ (- (* 2 beta) beta) i))) |
(+ 1/4 (+ (* 1/4 (/ alpha i)) (* 1/4 (/ (- (* 2 beta) beta) i)))) |
(+ 1/4 (+ (* 1/4 (/ alpha i)) (* 1/4 (/ (- (* 2 beta) beta) i)))) |
(+ 1/4 (+ (* 1/4 (/ alpha i)) (* 1/4 (/ (- (* 2 beta) beta) i)))) |
(* 1/4 (/ alpha i)) |
(* alpha (+ (* 1/4 (/ (- (* 2 (/ beta i)) (/ beta i)) alpha)) (+ (* 1/4 (/ 1 alpha)) (* 1/4 (/ 1 i))))) |
(* alpha (+ (* 1/4 (/ (- (* 2 (/ beta i)) (/ beta i)) alpha)) (+ (* 1/4 (/ 1 alpha)) (* 1/4 (/ 1 i))))) |
(* alpha (+ (* 1/4 (/ (- (* 2 (/ beta i)) (/ beta i)) alpha)) (+ (* 1/4 (/ 1 alpha)) (* 1/4 (/ 1 i))))) |
(* 1/4 (/ alpha i)) |
(* -1 (* alpha (- (* -1 (/ (+ 1/4 (* 1/4 (- (* 2 (/ beta i)) (/ beta i)))) alpha)) (* 1/4 (/ 1 i))))) |
(* -1 (* alpha (- (* -1 (/ (+ 1/4 (* 1/4 (- (* 2 (/ beta i)) (/ beta i)))) alpha)) (* 1/4 (/ 1 i))))) |
(* -1 (* alpha (- (* -1 (/ (+ 1/4 (* 1/4 (- (* 2 (/ beta i)) (/ beta i)))) alpha)) (* 1/4 (/ 1 i))))) |
(+ 1/4 (* 1/4 (/ (- (* 2 alpha) alpha) i))) |
(+ 1/4 (+ (* 1/4 (/ beta i)) (* 1/4 (/ (- (* 2 alpha) alpha) i)))) |
(+ 1/4 (+ (* 1/4 (/ beta i)) (* 1/4 (/ (- (* 2 alpha) alpha) i)))) |
(+ 1/4 (+ (* 1/4 (/ beta i)) (* 1/4 (/ (- (* 2 alpha) alpha) i)))) |
(* 1/4 (/ beta i)) |
(* beta (+ (* 1/4 (/ (- (* 2 (/ alpha i)) (/ alpha i)) beta)) (+ (* 1/4 (/ 1 beta)) (* 1/4 (/ 1 i))))) |
(* beta (+ (* 1/4 (/ (- (* 2 (/ alpha i)) (/ alpha i)) beta)) (+ (* 1/4 (/ 1 beta)) (* 1/4 (/ 1 i))))) |
(* beta (+ (* 1/4 (/ (- (* 2 (/ alpha i)) (/ alpha i)) beta)) (+ (* 1/4 (/ 1 beta)) (* 1/4 (/ 1 i))))) |
(* 1/4 (/ beta i)) |
(* -1 (* beta (- (* -1 (/ (+ 1/4 (* 1/4 (- (* 2 (/ alpha i)) (/ alpha i)))) beta)) (* 1/4 (/ 1 i))))) |
(* -1 (* beta (- (* -1 (/ (+ 1/4 (* 1/4 (- (* 2 (/ alpha i)) (/ alpha i)))) beta)) (* 1/4 (/ 1 i))))) |
(* -1 (* beta (- (* -1 (/ (+ 1/4 (* 1/4 (- (* 2 (/ alpha i)) (/ alpha i)))) beta)) (* 1/4 (/ 1 i))))) |
(* 1/4 (/ (- (* 2 (+ alpha beta)) (+ alpha beta)) i)) |
(/ (+ (* 1/4 i) (* 1/4 (- (* 2 (+ alpha beta)) (+ alpha beta)))) i) |
(/ (+ (* 1/4 i) (* 1/4 (- (* 2 (+ alpha beta)) (+ alpha beta)))) i) |
(/ (+ (* 1/4 i) (* 1/4 (- (* 2 (+ alpha beta)) (+ alpha beta)))) i) |
1/4 |
(+ 1/4 (* 1/4 (/ (- (* 2 (+ alpha beta)) (+ alpha beta)) i))) |
(+ 1/4 (* 1/4 (/ (- (* 2 (+ alpha beta)) (+ alpha beta)) i))) |
(+ 1/4 (* 1/4 (/ (- (* 2 (+ alpha beta)) (+ alpha beta)) i))) |
1/4 |
(+ 1/4 (* 1/4 (/ (- (* 2 (+ alpha beta)) (+ alpha beta)) i))) |
(+ 1/4 (* 1/4 (/ (- (* 2 (+ alpha beta)) (+ alpha beta)) i))) |
(+ 1/4 (* 1/4 (/ (- (* 2 (+ alpha beta)) (+ alpha beta)) i))) |
(- (pow (+ beta (* 2 i)) 2) 1) |
(- (+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1) |
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1) |
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha))))) |
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2)))) |
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2)))) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha)))) |
(- (pow (+ alpha (* 2 i)) 2) 1) |
(- (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) |
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1) |
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta))))) |
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2)))) |
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2)))) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta)))) |
(- (pow (+ alpha beta) 2) 1) |
(- (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) 1) |
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1) |
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2)))) |
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2)))) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i)))) |
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(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
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1/16 |
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1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(/ (* i (+ beta i)) (pow alpha 2)) |
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2)) |
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1))))))) alpha)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (+ (* -1 (* beta (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 4 alpha) (* 8 i)))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))) (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (+ (* (+ (* 4 alpha) (* 8 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(* alpha beta) |
(+ (* alpha beta) (* i (+ alpha beta))) |
(+ (* alpha beta) (* i (+ alpha (+ beta i)))) |
(+ (* alpha beta) (* i (+ alpha (+ beta i)))) |
(pow i 2) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i)))) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2)))))) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2)))))) |
(pow i 2) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i)))) |
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i)))) |
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i)))) |
(* i (+ beta i)) |
(+ (* alpha (+ beta i)) (* i (+ beta i))) |
(+ (* alpha (+ beta i)) (* i (+ beta i))) |
(+ (* alpha (+ beta i)) (* i (+ beta i))) |
(* alpha (+ beta i)) |
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha)))) |
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha)))) |
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha)))) |
(* -1 (* alpha (+ (* -1 beta) (* -1 i)))) |
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))) |
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))) |
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))) |
(* i (+ alpha i)) |
(+ (* beta (+ alpha i)) (* i (+ alpha i))) |
(+ (* beta (+ alpha i)) (* i (+ alpha i))) |
(+ (* beta (+ alpha i)) (* i (+ alpha i))) |
(* beta (+ alpha i)) |
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta)))) |
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta)))) |
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta)))) |
(* -1 (* beta (+ (* -1 alpha) (* -1 i)))) |
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta)))))) |
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta)))))) |
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta)))))) |
(/ (* alpha beta) (- (pow (+ alpha beta) 2) 1)) |
(+ (* i (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(+ (* i (- (+ (* i (- (/ 1 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1)))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(+ (* i (- (+ (* i (- (+ (* -1 (* i (+ (* 4 (/ (* (+ alpha beta) (- (/ 1 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (- (pow (+ alpha beta) 2) 1)))))) (/ 1 (- (pow (+ alpha beta) 2) 1))) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1)))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1))) |
1/4 |
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
(- (+ 1/4 (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
(- (+ 1/4 (+ (* -1 (/ (+ (* -1 (* (pow (+ alpha beta) 2) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))))) (* 1/4 (* (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))) (- (pow (+ alpha beta) 2) 1)))) (pow i 4))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (+ (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3)))) |
1/4 |
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
(- (+ 1/4 (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
(- (+ 1/4 (+ (* -1 (/ (- (+ (* -1 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) i)) (* 1/4 (/ (* (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))) (- (pow (+ alpha beta) 2) 1)) i))) (* -1 (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
(/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1)) |
(+ (* alpha (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1))) |
(+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (- (pow (+ beta (* 2 i)) 2) 1))))) (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1))) |
(+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (- (pow (+ beta (* 2 i)) 2) 1)))) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ i (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (+ (/ (* i (+ beta i)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (- (pow (+ beta (* 2 i)) 2) 1))))) (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1))) |
(/ (+ beta i) alpha) |
(/ (- (+ beta (+ i (/ (* i (+ beta i)) alpha))) (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha)))) (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))))))) (* (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (- (pow (+ beta (* 2 i)) 2) 1))) (pow alpha 3))) (/ (* i (+ beta i)) alpha)))) (+ (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha) |
(* -1 (/ (+ (* -1 beta) (* -1 i)) alpha)) |
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha)) |
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha)) (+ (* i (+ beta i)) (/ (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)) alpha))) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha)) |
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ beta (* 2 i)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha)) (/ (* (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) (- (pow (+ beta (* 2 i)) 2) 1)) alpha)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha)) (* i (+ beta i))) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha)) |
(/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1)) |
(+ (* beta (- (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1))) |
(+ (* beta (- (+ (* -1 (* beta (+ (/ (* i (+ alpha i)) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (- (pow (+ alpha (* 2 i)) 2) 1))))) (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1))) |
(+ (* beta (- (+ (* beta (- (* beta (- (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)) (+ (* -1 (/ (* (+ (* 2 alpha) (* 4 i)) (+ (/ (* i (+ alpha i)) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (- (pow (+ alpha (* 2 i)) 2) 1)))) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)) (/ i (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (+ (/ (* i (+ alpha i)) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (- (pow (+ alpha (* 2 i)) 2) 1))))) (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1))) |
(/ (+ alpha i) beta) |
(/ (- (+ alpha (+ i (/ (* i (+ alpha i)) beta))) (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta)) beta) |
(/ (- (+ alpha (+ i (+ (* -1 (/ (+ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta)))) (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta)) beta) |
(/ (- (+ alpha (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))))) (* (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (- (pow (+ alpha (* 2 i)) 2) 1))) (pow beta 3))) (/ (* i (+ alpha i)) beta)))) (+ (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta) |
(* -1 (/ (+ (* -1 alpha) (* -1 i)) beta)) |
(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)))) beta)) |
(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)) (+ (* i (+ alpha i)) (/ (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) beta))) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)))) beta)) |
(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ alpha (* 2 i)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))) beta)) (/ (* (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) (- (pow (+ alpha (* 2 i)) 2) 1)) beta)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))) beta)) (* i (+ alpha i))) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)))) beta)) |
(+ alpha beta) |
(+ alpha (+ beta i)) |
(+ alpha (+ beta i)) |
(+ alpha (+ beta i)) |
i |
(* i (+ 1 (+ (/ alpha i) (/ beta i)))) |
(* i (+ 1 (+ (/ alpha i) (/ beta i)))) |
(* i (+ 1 (+ (/ alpha i) (/ beta i)))) |
i |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 1))) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 1))) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 1))) |
(+ beta i) |
(+ alpha (+ beta i)) |
(+ alpha (+ beta i)) |
(+ alpha (+ beta i)) |
alpha |
(* alpha (+ 1 (+ (/ beta alpha) (/ i alpha)))) |
(* alpha (+ 1 (+ (/ beta alpha) (/ i alpha)))) |
(* alpha (+ 1 (+ (/ beta alpha) (/ i alpha)))) |
alpha |
(* -1 (* alpha (- (* -1 (/ (+ beta i) alpha)) 1))) |
(* -1 (* alpha (- (* -1 (/ (+ beta i) alpha)) 1))) |
(* -1 (* alpha (- (* -1 (/ (+ beta i) alpha)) 1))) |
(+ alpha i) |
(+ alpha (+ beta i)) |
(+ alpha (+ beta i)) |
(+ alpha (+ beta i)) |
beta |
(* beta (+ 1 (+ (/ alpha beta) (/ i beta)))) |
(* beta (+ 1 (+ (/ alpha beta) (/ i beta)))) |
(* beta (+ 1 (+ (/ alpha beta) (/ i beta)))) |
beta |
(* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1))) |
(* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1))) |
(* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1))) |
(/ (* alpha (* beta i)) (* (+ 1 (+ alpha beta)) (* (+ alpha beta) (- (+ alpha beta) 1)))) |
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(/ (* i (+ beta i)) (pow alpha 2)) |
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2)) |
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
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1/4 |
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1/4 |
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(/ (* i (+ beta i)) (* (+ 1 (+ beta (* 2 i))) (+ beta (* 2 i)))) |
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(/ i alpha) |
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(/ i alpha) |
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(/ (* i (+ alpha i)) (* (+ 1 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) |
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(/ i beta) |
(/ (- (+ i (/ (* i (+ alpha i)) beta)) (/ (* i (+ 1 (+ (* 2 alpha) (* 4 i)))) beta)) beta) |
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(/ (* alpha beta) (* (+ alpha beta) (- (+ alpha beta) 1))) |
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1/4 |
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1/4 |
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(/ (+ beta i) alpha) |
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(/ (+ alpha i) beta) |
(/ (- (+ alpha (+ i (/ (* i (+ alpha i)) beta))) (/ (* (+ alpha i) (- (+ (* 2 alpha) (* 4 i)) 1)) beta)) beta) |
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(* -1 (/ (+ (* -1 alpha) (* -1 i)) beta)) |
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(pow beta 2) |
(pow beta 2) |
(pow beta 2) |
(pow beta 2) |
(pow beta 2) |
(pow beta 2) |
(pow beta 2) |
(pow beta 2) |
(pow beta 2) |
(pow beta 2) |
(pow beta 2) |
(pow beta 2) |
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
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1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(/ (* i (+ beta i)) (pow alpha 2)) |
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2)) |
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(/ (- (+ (* -1 (/ (+ (* i (* (+ beta i) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (+ (* (+ (* 4 beta) (* 8 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))))))) (* (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1)))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2)) |
(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1))))))) alpha)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (+ (* -1 (* beta (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 4 alpha) (* 8 i)))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))) (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (+ (* (+ (* 4 alpha) (* 8 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (* alpha (* beta i)) (+ alpha beta)) |
(* i (+ (* i (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (+ (* 2 (/ beta (pow (+ alpha beta) 2))) (* i (- (/ 1 (pow (+ alpha beta) 2)) (+ (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (pow (+ alpha beta) 2))) (* 4 (/ (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta))))) (+ alpha beta)))))))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(* 1/4 (pow i 2)) |
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (+ alpha beta) i)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)))))) |
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 3))) (+ (* 1/4 (/ (+ alpha beta) i)) (+ (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/16 (pow (+ alpha beta) 2)) (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))))) (pow i 3)))))))) |
(* 1/4 (pow i 2)) |
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* 1/4 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)) (* -1/16 (/ (pow (+ alpha beta) 2) i)))) i)))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) (* 1/4 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) i)) (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)))) i))) i)))) |
(/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2)) |
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
(+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
(+ (* alpha (- (+ (* alpha (- (+ (* alpha (- (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 6)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (pow (+ beta (* 2 i)) 2))))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
(* i (+ beta i)) |
(- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha)) |
(- (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))))) |
(- (+ (* -1 (/ (+ (* (+ (* 2 beta) (* 4 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))))) |
(* -1 (* i (+ (* -1 beta) (* -1 i)))) |
(+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) |
(+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) |
(+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i)))))))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) alpha))) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2)) |
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))) |
(+ (* beta (- (+ (* beta (- (+ (* beta (- (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 6)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (pow (+ alpha (* 2 i)) 2))))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))) |
(* i (+ alpha i)) |
(- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta)) |
(- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))))) |
(- (+ (* -1 (/ (+ (* (+ (* 2 alpha) (* 4 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))))) |
(* -1 (* i (+ (* -1 alpha) (* -1 i)))) |
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) |
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) |
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i)))))))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) beta))) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) |
(pow (+ beta (* 2 i)) 2) |
(+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) |
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha))))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(pow (+ alpha (* 2 i)) 2) |
(+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta))))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(pow (+ alpha beta) 2) |
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(/ i (+ alpha beta)) |
(* i (+ (* -3 (/ i (pow (+ alpha beta) 2))) (/ 1 (+ alpha beta)))) |
(* i (+ (* i (- (* 8 (/ i (pow (+ alpha beta) 3))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta)))) |
(* i (+ (* i (- (* i (+ (* -20 (/ i (pow (+ alpha beta) 4))) (* 8 (/ 1 (pow (+ alpha beta) 3))))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta)))) |
1/4 |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(- (+ 1/4 (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(- (+ 1/4 (* -1 (/ (+ (* -1/64 (pow (+ alpha beta) 4)) (* 1/16 (pow (+ alpha beta) 4))) (pow i 4)))) (+ (* -1/16 (/ (pow (+ alpha beta) 3) (pow i 3))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))) |
1/4 |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(+ 1/4 (+ (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3))))) |
(+ 1/4 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (pow (+ alpha beta) 4)) (* 1/64 (pow (+ alpha beta) 4))) i)) (* -1/16 (pow (+ alpha beta) 3))) (pow i 3))) (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) |
(+ (* alpha (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) |
(+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) |
(+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 6)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)))) (pow (+ beta (* 2 i)) 2))) (/ i (pow (+ beta (* 2 i)) 4))))) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) |
(/ i alpha) |
(/ (- (+ i (/ (* i (+ beta i)) alpha)) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
(/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha))) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
(/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 3))) (/ (* i (+ beta i)) alpha))) (+ (/ (* i (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* i (pow (+ beta (* 2 i)) 2)) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha) |
(/ i alpha) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -1 (/ (* i (pow (+ beta (* 2 i)) 2)) alpha)) (* i (+ beta i)))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ beta (* 2 i)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (* i (+ beta i))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha)) |
(/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) |
(+ (* beta (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) |
(+ (* beta (- (+ (* -1 (* beta (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2))))) (/ i (pow (+ alpha (* 2 i)) 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) |
(+ (* beta (- (+ (* beta (- (* beta (- (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 6)) (+ (* -1 (/ (* (+ (* 2 alpha) (* 4 i)) (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)))) (pow (+ alpha (* 2 i)) 2))) (/ i (pow (+ alpha (* 2 i)) 4))))) (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2))))) (/ i (pow (+ alpha (* 2 i)) 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) |
(/ i beta) |
(/ (- (+ i (/ (* i (+ alpha i)) beta)) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta) |
(/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta))) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta) |
(/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 3))) (/ (* i (+ alpha i)) beta))) (+ (/ (* i (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* i (pow (+ alpha (* 2 i)) 2)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta) |
(/ i beta) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -1 (/ (* i (pow (+ alpha (* 2 i)) 2)) beta)) (* i (+ alpha i)))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ alpha (* 2 i)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (* i (+ alpha i))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta)) |
(pow (+ alpha beta) 2) |
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(pow (+ beta (* 2 i)) 2) |
(+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) |
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha))))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(pow (+ alpha (* 2 i)) 2) |
(+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta))))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(/ (* alpha beta) (+ alpha beta)) |
(+ (* i (- 1 (* 2 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta))) |
(+ (* i (- (+ 1 (* i (- (/ 1 (+ alpha beta)) (* 2 (/ (- 1 (* 2 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (* 2 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta))) |
(+ (* i (- (+ 1 (* i (- (+ (* -2 (/ (* i (- (/ 1 (+ alpha beta)) (* 2 (/ (- 1 (* 2 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta))))) (+ alpha beta))) (/ 1 (+ alpha beta))) (* 2 (/ (- 1 (* 2 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (* 2 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta))) |
(* 1/2 i) |
(* i (- (+ 1/2 (* 1/2 (/ (+ alpha beta) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(* i (- (+ 1/2 (+ (* 1/2 (/ (* alpha beta) (pow i 2))) (* 1/2 (/ (+ alpha beta) i)))) (+ (* 1/4 (/ (+ alpha beta) i)) (* 1/2 (/ (* (+ alpha beta) (- (* 1/2 (+ alpha beta)) (* 1/4 (+ alpha beta)))) (pow i 2)))))) |
(* i (- (+ 1/2 (+ (* -1/2 (/ (* (+ alpha beta) (- (* 1/2 (* alpha beta)) (* 1/2 (* (+ alpha beta) (- (* 1/2 (+ alpha beta)) (* 1/4 (+ alpha beta))))))) (pow i 3))) (+ (* 1/2 (/ (* alpha beta) (pow i 2))) (* 1/2 (/ (+ alpha beta) i))))) (+ (* 1/4 (/ (+ alpha beta) i)) (* 1/2 (/ (* (+ alpha beta) (- (* 1/2 (+ alpha beta)) (* 1/4 (+ alpha beta)))) (pow i 2)))))) |
(* 1/2 i) |
(* -1 (* i (- (* -1 (/ (- (* 1/2 (+ alpha beta)) (* 1/4 (+ alpha beta))) i)) 1/2))) |
(* -1 (* i (- (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* alpha beta)) (* -1/2 (* (+ alpha beta) (- (* 1/2 (+ alpha beta)) (* 1/4 (+ alpha beta)))))) i)) (* 1/2 (+ alpha beta))) (* 1/4 (+ alpha beta))) i)) 1/2))) |
(* -1 (* i (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/2 (* alpha beta)) (* -1/2 (/ (* (+ alpha beta) (- (* -1/2 (* alpha beta)) (* -1/2 (* (+ alpha beta) (- (* 1/2 (+ alpha beta)) (* 1/4 (+ alpha beta))))))) i))) (* -1/2 (* (+ alpha beta) (- (* 1/2 (+ alpha beta)) (* 1/4 (+ alpha beta)))))) i)) (* 1/2 (+ alpha beta))) (* 1/4 (+ alpha beta))) i)) 1/2))) |
(/ (* i (+ beta i)) (+ beta (* 2 i))) |
(+ (* alpha (- (+ (/ beta (+ beta (* 2 i))) (/ i (+ beta (* 2 i)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))) (/ (* i (+ beta i)) (+ beta (* 2 i)))) |
(+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 3)) (+ (/ beta (pow (+ beta (* 2 i)) 2)) (/ i (pow (+ beta (* 2 i)) 2))))) (+ (/ beta (+ beta (* 2 i))) (/ i (+ beta (* 2 i))))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))) (/ (* i (+ beta i)) (+ beta (* 2 i)))) |
(+ (* alpha (- (+ (* alpha (- (+ (* alpha (- (+ (/ beta (pow (+ beta (* 2 i)) 3)) (/ i (pow (+ beta (* 2 i)) 3))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 3))) (+ (/ beta (pow (+ beta (* 2 i)) 2)) (/ i (pow (+ beta (* 2 i)) 2))))) (+ (/ beta (+ beta (* 2 i))) (/ i (+ beta (* 2 i))))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))) (/ (* i (+ beta i)) (+ beta (* 2 i)))) |
(+ beta i) |
(- (+ beta (+ i (/ (* i (+ beta i)) alpha))) (/ (* (+ beta i) (+ beta (* 2 i))) alpha)) |
(- (+ beta (+ i (+ (* -1 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* (+ beta i) (+ beta (* 2 i))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha)))) (/ (* (+ beta i) (+ beta (* 2 i))) alpha)) |
(- (+ beta (+ i (+ (/ (* i (+ beta i)) alpha) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* (+ beta i) (+ beta (* 2 i))))) (pow alpha 3))))) (+ (/ (* (+ beta i) (+ beta (* 2 i))) alpha) (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* (+ beta i) (+ beta (* 2 i))))) (pow alpha 2)))) |
(* -1 (+ (* -1 beta) (* -1 i))) |
(+ (* -1 (+ (* -1 beta) (* -1 i))) (* -1 (/ (- (* -1 (* i (+ beta i))) (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))) alpha))) |
(+ (* -1 (+ (* -1 beta) (* -1 i))) (* -1 (/ (- (+ (* -1 (* i (+ beta i))) (* -1 (/ (* (+ beta (* 2 i)) (- (* -1 (* i (+ beta i))) (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha))) (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))) alpha))) |
(+ (* -1 (+ (* -1 beta) (* -1 i))) (* -1 (/ (- (+ (* -1 (* i (+ beta i))) (* -1 (/ (- (* -1 (/ (* (pow (+ beta (* 2 i)) 2) (- (* -1 (* i (+ beta i))) (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)) (* -1 (* (+ beta (* 2 i)) (- (* -1 (* i (+ beta i))) (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) alpha))) (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))) alpha))) |
(/ (* i (+ alpha i)) (+ alpha (* 2 i))) |
(+ (* beta (- (+ (/ alpha (+ alpha (* 2 i))) (/ i (+ alpha (* 2 i)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))) (/ (* i (+ alpha i)) (+ alpha (* 2 i)))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 3)) (+ (/ alpha (pow (+ alpha (* 2 i)) 2)) (/ i (pow (+ alpha (* 2 i)) 2))))) (+ (/ alpha (+ alpha (* 2 i))) (/ i (+ alpha (* 2 i))))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))) (/ (* i (+ alpha i)) (+ alpha (* 2 i)))) |
(+ (* beta (- (+ (* beta (- (+ (* beta (- (+ (/ alpha (pow (+ alpha (* 2 i)) 3)) (/ i (pow (+ alpha (* 2 i)) 3))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 3))) (+ (/ alpha (pow (+ alpha (* 2 i)) 2)) (/ i (pow (+ alpha (* 2 i)) 2))))) (+ (/ alpha (+ alpha (* 2 i))) (/ i (+ alpha (* 2 i))))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))) (/ (* i (+ alpha i)) (+ alpha (* 2 i)))) |
(+ alpha i) |
(- (+ alpha (+ i (/ (* i (+ alpha i)) beta))) (/ (* (+ alpha i) (+ alpha (* 2 i))) beta)) |
(- (+ alpha (+ i (+ (* -1 (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ alpha (* 2 i))))) (pow beta 2))) (/ (* i (+ alpha i)) beta)))) (/ (* (+ alpha i) (+ alpha (* 2 i))) beta)) |
(- (+ alpha (+ i (+ (/ (* i (+ alpha i)) beta) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* (+ alpha i) (+ alpha (* 2 i))))) (pow beta 3))))) (+ (/ (* (+ alpha i) (+ alpha (* 2 i))) beta) (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ alpha (* 2 i))))) (pow beta 2)))) |
(* -1 (+ (* -1 alpha) (* -1 i))) |
(+ (* -1 (+ (* -1 alpha) (* -1 i))) (* -1 (/ (- (* -1 (* i (+ alpha i))) (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))) beta))) |
(+ (* -1 (+ (* -1 alpha) (* -1 i))) (* -1 (/ (- (+ (* -1 (* i (+ alpha i))) (* -1 (/ (* (+ alpha (* 2 i)) (- (* -1 (* i (+ alpha i))) (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta))) (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))) beta))) |
(+ (* -1 (+ (* -1 alpha) (* -1 i))) (* -1 (/ (- (+ (* -1 (* i (+ alpha i))) (* -1 (/ (- (* -1 (/ (* (pow (+ alpha (* 2 i)) 2) (- (* -1 (* i (+ alpha i))) (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)) (* -1 (* (+ alpha (* 2 i)) (- (* -1 (* i (+ alpha i))) (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) beta))) (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))) beta))) |
i |
(* i (+ 1 (* -1 (/ i (+ alpha beta))))) |
(* i (+ 1 (* i (- (* 2 (/ i (pow (+ alpha beta) 2))) (/ 1 (+ alpha beta)))))) |
(* i (+ 1 (* i (- (* i (+ (* -4 (/ i (pow (+ alpha beta) 3))) (* 2 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta)))))) |
(* 1/2 i) |
(* i (- (+ 1/2 (* 1/2 (/ (+ alpha beta) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(* i (- (+ 1/2 (+ (* -1/2 (/ (* (+ alpha beta) (- (* 1/2 (+ alpha beta)) (* 1/4 (+ alpha beta)))) (pow i 2))) (* 1/2 (/ (+ alpha beta) i)))) (* 1/4 (/ (+ alpha beta) i)))) |
(* i (- (+ 1/2 (+ (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/2 (+ alpha beta)) (* 1/4 (+ alpha beta)))) (pow i 3))) (* 1/2 (/ (+ alpha beta) i)))) (+ (* 1/4 (/ (+ alpha beta) i)) (* 1/2 (/ (* (+ alpha beta) (- (* 1/2 (+ alpha beta)) (* 1/4 (+ alpha beta)))) (pow i 2)))))) |
(* 1/2 i) |
(* -1 (* i (- (* -1/2 (/ (+ alpha beta) i)) (+ 1/2 (* -1/4 (/ (+ alpha beta) i)))))) |
(* -1 (* i (- (* -1 (/ (+ (* -1 (- (* -1/2 (+ alpha beta)) (* -1/4 (+ alpha beta)))) (* 1/2 (/ (* (+ alpha beta) (- (* -1/2 (+ alpha beta)) (* -1/4 (+ alpha beta)))) i))) i)) 1/2))) |
(* -1 (* i (- (* -1 (/ (+ (* -1 (- (* -1/2 (+ alpha beta)) (* -1/4 (+ alpha beta)))) (* -1 (/ (+ (* -1/2 (* (+ alpha beta) (- (* -1/2 (+ alpha beta)) (* -1/4 (+ alpha beta))))) (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* -1/2 (+ alpha beta)) (* -1/4 (+ alpha beta)))) i))) i))) i)) 1/2))) |
(/ (* i (+ beta i)) (+ beta (* 2 i))) |
(+ (* alpha (- (/ i (+ beta (* 2 i))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))) (/ (* i (+ beta i)) (+ beta (* 2 i)))) |
(+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 3)) (/ i (pow (+ beta (* 2 i)) 2)))) (/ i (+ beta (* 2 i)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))) (/ (* i (+ beta i)) (+ beta (* 2 i)))) |
(+ (* alpha (- (+ (* alpha (- (+ (* alpha (- (/ i (pow (+ beta (* 2 i)) 3)) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 3))) (/ i (pow (+ beta (* 2 i)) 2)))) (/ i (+ beta (* 2 i)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))) (/ (* i (+ beta i)) (+ beta (* 2 i)))) |
i |
(- (+ i (/ (* i (+ beta i)) alpha)) (/ (* i (+ beta (* 2 i))) alpha)) |
(- (+ i (+ (* -1 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* i (+ beta (* 2 i))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha))) (/ (* i (+ beta (* 2 i))) alpha)) |
(- (+ i (+ (/ (* i (+ beta i)) alpha) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* i (+ beta (* 2 i))))) (pow alpha 3)))) (+ (/ (* i (+ beta (* 2 i))) alpha) (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* i (+ beta (* 2 i))))) (pow alpha 2)))) |
i |
(+ i (* -1 (/ (- (* -1 (* i (+ beta i))) (* -1 (* i (+ beta (* 2 i))))) alpha))) |
(+ i (* -1 (/ (- (+ (* -1 (* i (+ beta i))) (* -1 (/ (* (+ beta (* 2 i)) (- (* -1 (* i (+ beta i))) (* -1 (* i (+ beta (* 2 i)))))) alpha))) (* -1 (* i (+ beta (* 2 i))))) alpha))) |
(+ i (* -1 (/ (- (+ (* -1 (* i (+ beta i))) (* -1 (/ (- (* -1 (/ (* (pow (+ beta (* 2 i)) 2) (- (* -1 (* i (+ beta i))) (* -1 (* i (+ beta (* 2 i)))))) alpha)) (* -1 (* (+ beta (* 2 i)) (- (* -1 (* i (+ beta i))) (* -1 (* i (+ beta (* 2 i)))))))) alpha))) (* -1 (* i (+ beta (* 2 i))))) alpha))) |
(/ (* i (+ alpha i)) (+ alpha (* 2 i))) |
(+ (* beta (- (/ i (+ alpha (* 2 i))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))) (/ (* i (+ alpha i)) (+ alpha (* 2 i)))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 3)) (/ i (pow (+ alpha (* 2 i)) 2)))) (/ i (+ alpha (* 2 i)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))) (/ (* i (+ alpha i)) (+ alpha (* 2 i)))) |
(+ (* beta (- (+ (* beta (- (+ (* beta (- (/ i (pow (+ alpha (* 2 i)) 3)) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 3))) (/ i (pow (+ alpha (* 2 i)) 2)))) (/ i (+ alpha (* 2 i)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))) (/ (* i (+ alpha i)) (+ alpha (* 2 i)))) |
i |
(- (+ i (/ (* i (+ alpha i)) beta)) (/ (* i (+ alpha (* 2 i))) beta)) |
(- (+ i (+ (* -1 (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* i (+ alpha (* 2 i))))) (pow beta 2))) (/ (* i (+ alpha i)) beta))) (/ (* i (+ alpha (* 2 i))) beta)) |
(- (+ i (+ (/ (* i (+ alpha i)) beta) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* i (+ alpha (* 2 i))))) (pow beta 3)))) (+ (/ (* i (+ alpha (* 2 i))) beta) (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* i (+ alpha (* 2 i))))) (pow beta 2)))) |
i |
(+ i (* -1 (/ (- (* -1 (* i (+ alpha i))) (* -1 (* i (+ alpha (* 2 i))))) beta))) |
(+ i (* -1 (/ (- (+ (* -1 (* i (+ alpha i))) (* -1 (/ (* (+ alpha (* 2 i)) (- (* -1 (* i (+ alpha i))) (* -1 (* i (+ alpha (* 2 i)))))) beta))) (* -1 (* i (+ alpha (* 2 i))))) beta))) |
(+ i (* -1 (/ (- (+ (* -1 (* i (+ alpha i))) (* -1 (/ (- (* -1 (/ (* (pow (+ alpha (* 2 i)) 2) (- (* -1 (* i (+ alpha i))) (* -1 (* i (+ alpha (* 2 i)))))) beta)) (* -1 (* (+ alpha (* 2 i)) (- (* -1 (* i (+ alpha i))) (* -1 (* i (+ alpha (* 2 i)))))))) beta))) (* -1 (* i (+ alpha (* 2 i))))) beta))) |
| Outputs |
|---|
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(/.f64 (*.f64 alpha (*.f64 beta i)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) |
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(*.f64 i (fma.f64 i (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 (*.f64 alpha beta) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))) (/.f64 (*.f64 alpha (*.f64 beta (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) |
1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
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(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(/.f64 (*.f64 alpha (*.f64 beta i)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) |
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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#s(literal 1/4 binary64) |
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(pow alpha 2) |
(*.f64 alpha alpha) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha))))) |
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(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2)))) |
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(pow alpha 2) |
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(* 4 (pow i 2)) |
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(* 4 (pow i 2)) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) |
1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
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(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i)))) |
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(/ (* alpha beta) (- (pow (+ alpha beta) 2) 1)) |
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1/4 |
#s(literal 1/4 binary64) |
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
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1/4 |
#s(literal 1/4 binary64) |
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
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(- (+ 1/4 (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
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(- (+ 1/4 (+ (* -1 (/ (- (+ (* -1 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) i)) (* 1/4 (/ (* (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))) (- (pow (+ alpha beta) 2) 1)) i))) (* -1 (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
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(/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1)) |
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(/ (+ beta i) alpha) |
(/.f64 (+.f64 beta i) alpha) |
(/ (- (+ beta (+ i (/ (* i (+ beta i)) alpha))) (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
(/.f64 (-.f64 (+.f64 (+.f64 beta i) (/.f64 (*.f64 i (+.f64 beta i)) alpha)) (/.f64 (*.f64 (+.f64 beta i) (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i))) alpha)) alpha) |
(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha)))) (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
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(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))))))) (* (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (- (pow (+ beta (* 2 i)) 2) 1))) (pow alpha 3))) (/ (* i (+ beta i)) alpha)))) (+ (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha) |
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(* -1 (/ (+ (* -1 beta) (* -1 i)) alpha)) |
(neg.f64 (neg.f64 (/.f64 (+.f64 beta i) alpha))) |
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha)) |
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(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha)) (+ (* i (+ beta i)) (/ (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)) alpha))) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha)) |
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(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ beta (* 2 i)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha)) (/ (* (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) (- (pow (+ beta (* 2 i)) 2) 1)) alpha)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha)) (* i (+ beta i))) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha)) |
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(/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1)) |
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(+ (* beta (- (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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(/ (- (+ alpha (+ i (+ (* -1 (/ (+ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta)))) (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta)) beta) |
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(/ (- (+ alpha (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))))) (* (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (- (pow (+ alpha (* 2 i)) 2) 1))) (pow beta 3))) (/ (* i (+ alpha i)) beta)))) (+ (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta) |
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(* -1 (/ (+ (* -1 alpha) (* -1 i)) beta)) |
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(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ alpha (* 2 i)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))) beta)) (/ (* (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) (- (pow (+ alpha (* 2 i)) 2) 1)) beta)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))) beta)) (* i (+ alpha i))) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)))) beta)) |
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(+ alpha beta) |
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(+ alpha (+ beta i)) |
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(+ alpha (+ beta i)) |
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i |
(* i (+ 1 (+ (/ alpha i) (/ beta i)))) |
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(* i (+ 1 (+ (/ alpha i) (/ beta i)))) |
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(* i (+ 1 (+ (/ alpha i) (/ beta i)))) |
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i |
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(+ beta i) |
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(+.f64 alpha (+.f64 beta i)) |
(+ alpha (+ beta i)) |
(+.f64 alpha (+.f64 beta i)) |
(+ alpha (+ beta i)) |
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alpha |
(* alpha (+ 1 (+ (/ beta alpha) (/ i alpha)))) |
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(* alpha (+ 1 (+ (/ beta alpha) (/ i alpha)))) |
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(* alpha (+ 1 (+ (/ beta alpha) (/ i alpha)))) |
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alpha |
(* -1 (* alpha (- (* -1 (/ (+ beta i) alpha)) 1))) |
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(* -1 (* alpha (- (* -1 (/ (+ beta i) alpha)) 1))) |
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(* -1 (* alpha (- (* -1 (/ (+ beta i) alpha)) 1))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 (+.f64 beta i) alpha)) #s(literal -1 binary64))) |
(+ alpha i) |
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(+ alpha (+ beta i)) |
(+.f64 alpha (+.f64 beta i)) |
(+ alpha (+ beta i)) |
(+.f64 alpha (+.f64 beta i)) |
(+ alpha (+ beta i)) |
(+.f64 alpha (+.f64 beta i)) |
beta |
(* beta (+ 1 (+ (/ alpha beta) (/ i beta)))) |
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(* beta (+ 1 (+ (/ alpha beta) (/ i beta)))) |
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(* beta (+ 1 (+ (/ alpha beta) (/ i beta)))) |
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beta |
(* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1))) |
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(* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1))) |
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(* i (+ (* i (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (+ alpha beta) (- (+ alpha beta) 1)))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (* 2 (/ beta (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))) (+ (/ (* alpha (* beta (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))) (/ (* (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))))) (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (+ alpha beta) (- (+ alpha beta) 1)))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (+ (* 2 (/ beta (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (* i (- (/ 1 (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))) (+ (/ (* alpha (* beta (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))) (+ (/ (* (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (- (+ (* 2 (/ alpha (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (* 2 (/ beta (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))) (+ (/ (* alpha (* beta (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))) (/ (* (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))) (/ (* (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))))))) (+ (/ (* alpha (* beta (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))) (/ (* (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))))) (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (+ alpha beta) (- (+ alpha beta) 1)))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/256 (/ (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) i))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* -1/256 (/ (+ (* -8 (+ 1 (+ alpha beta))) (* -2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) i))) |
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(/ (- (+ (* -1 (/ (+ (* i (* (+ beta i) (+ (* (+ 1 (+ beta (* 2 i))) (+ (* (+ (* 2 beta) (* 4 i)) (- (+ beta (* 2 i)) 1)) (pow (+ beta (* 2 i)) 2))) (* (pow (+ beta (* 2 i)) 2) (- (+ beta (* 2 i)) 1))))) (+ (* (+ (* 4 beta) (* 8 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (+ (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))) 1)) (+ (* (+ (* 2 beta) (* 4 i)) (- (+ beta (* 2 i)) 1)) (pow (+ beta (* 2 i)) 2))))) (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))))))) (* (+ (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))) 1)) (+ (* (+ (* 2 beta) (* 4 i)) (- (+ beta (* 2 i)) 1)) (pow (+ beta (* 2 i)) 2))) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (+ (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))) 1)) (+ (* (+ (* 2 beta) (* 4 i)) (- (+ beta (* 2 i)) 1)) (pow (+ beta (* 2 i)) 2))))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2)) |
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
(neg.f64 (/.f64 (*.f64 i (+.f64 (neg.f64 beta) (neg.f64 i))) (*.f64 alpha alpha))) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))))))) alpha))) (pow alpha 2)) |
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(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ (* -2 (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* -1 (pow (+ beta (* 2 i)) 2)))) (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))) (* (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))))))) alpha))) (pow alpha 2)) |
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(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (* (pow (+ beta (* 2 i)) 2) (- (+ beta (* 2 i)) 1))) (* (+ 1 (+ beta (* 2 i))) (+ (* -2 (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* -1 (pow (+ beta (* 2 i)) 2))))))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (+ (/ (* (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ (* -2 (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* -1 (pow (+ beta (* 2 i)) 2)))) (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))) (* (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))))))))))) alpha) (/ (* (+ (* -1 (+ (* -2 (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* -1 (pow (+ beta (* 2 i)) 2)))) (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))))) alpha)))) (+ (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ (* -2 (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* -1 (pow (+ beta (* 2 i)) 2)))) (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))) (* (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))))))) alpha))) (pow alpha 2)) |
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (+ 1 (+ alpha (* 2 i))) (* (pow (+ alpha (* 2 i)) 2) (- (+ alpha (* 2 i)) 1)))) |
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(/ i alpha) |
(/.f64 i alpha) |
(/ (- (+ i (/ (* i (+ beta i)) alpha)) (/ (* i (+ 1 (+ (* 2 beta) (* 4 i)))) alpha)) alpha) |
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(/ i alpha) |
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(/ (* alpha beta) (* (+ alpha beta) (- (+ alpha beta) 1))) |
(/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)))) |
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1/4 |
#s(literal 1/4 binary64) |
(- (+ 1/4 (* 1/4 (/ (+ alpha beta) i))) (* 1/16 (/ (+ (* 2 (+ alpha beta)) (* 2 (- (+ alpha beta) 1))) i))) |
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1/4 |
#s(literal 1/4 binary64) |
(+ 1/4 (* -1 (/ (- (* -1/4 (+ alpha beta)) (* 1/16 (+ (* -2 (+ alpha beta)) (* -2 (- (+ alpha beta) 1))))) i))) |
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(/ (* i (+ beta i)) (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) |
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(/ (+ beta i) alpha) |
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(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* (+ beta i) (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* (- (* i (+ beta i)) (* (+ beta i) (- (+ (* 2 beta) (* 4 i)) 1))) (- (+ (* 2 beta) (* 4 i)) 1))) (pow alpha 2))) (/ (* i (+ beta i)) alpha)))) (/ (* (+ beta i) (- (+ (* 2 beta) (* 4 i)) 1)) alpha)) alpha) |
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(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* (+ beta i) (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* (- (* i (+ beta i)) (* (+ beta i) (- (+ (* 2 beta) (* 4 i)) 1))) (- (+ (* 2 beta) (* 4 i)) 1))) (- (+ (* 2 beta) (* 4 i)) 1))) (* (+ beta (* 2 i)) (* (- (* i (+ beta i)) (* (+ beta i) (- (+ (* 2 beta) (* 4 i)) 1))) (- (+ beta (* 2 i)) 1)))) (pow alpha 3))) (/ (* i (+ beta i)) alpha)))) (+ (/ (* (+ beta i) (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (pow alpha 2)) (+ (/ (* (+ beta i) (- (+ (* 2 beta) (* 4 i)) 1)) alpha) (/ (* (- (* i (+ beta i)) (* (+ beta i) (- (+ (* 2 beta) (* 4 i)) 1))) (- (+ (* 2 beta) (* 4 i)) 1)) (pow alpha 2))))) alpha) |
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(* -1 (/ (+ (* -1 beta) (* -1 i)) alpha)) |
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(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* i (+ beta i)) (+ (/ (* (+ beta (* 2 i)) (* (+ (* -1 beta) (* -1 i)) (- (+ beta (* 2 i)) 1))) alpha) (/ (* (+ (* -1 (+ beta (* 2 i))) (* -1 (- (+ beta (* 2 i)) 1))) (- (* i (+ beta i)) (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ beta (* 2 i))) (* -1 (- (+ beta (* 2 i)) 1)))))) alpha))) (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ beta (* 2 i))) (* -1 (- (+ beta (* 2 i)) 1))))) alpha)))) alpha)) |
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(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -1 (+ beta (* 2 i))) (* -1 (- (+ beta (* 2 i)) 1))) (+ (* (+ beta (* 2 i)) (* (+ (* -1 beta) (* -1 i)) (- (+ beta (* 2 i)) 1))) (* (+ (* -1 (+ beta (* 2 i))) (* -1 (- (+ beta (* 2 i)) 1))) (- (* i (+ beta i)) (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ beta (* 2 i))) (* -1 (- (+ beta (* 2 i)) 1)))))))) alpha)) (/ (* (+ beta (* 2 i)) (* (- (* i (+ beta i)) (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ beta (* 2 i))) (* -1 (- (+ beta (* 2 i)) 1))))) (- (+ beta (* 2 i)) 1))) alpha)) (+ (* (+ beta (* 2 i)) (* (+ (* -1 beta) (* -1 i)) (- (+ beta (* 2 i)) 1))) (* (+ (* -1 (+ beta (* 2 i))) (* -1 (- (+ beta (* 2 i)) 1))) (- (* i (+ beta i)) (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ beta (* 2 i))) (* -1 (- (+ beta (* 2 i)) 1)))))))) alpha)) (* i (+ beta i))) (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ beta (* 2 i))) (* -1 (- (+ beta (* 2 i)) 1))))) alpha)))) alpha)) |
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(pow beta 2) |
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(pow beta 2) |
(*.f64 beta beta) |
(pow beta 2) |
(*.f64 beta beta) |
(pow beta 2) |
(*.f64 beta beta) |
(pow beta 2) |
(*.f64 beta beta) |
(pow beta 2) |
(*.f64 beta beta) |
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(/.f64 (*.f64 alpha (*.f64 beta i)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) |
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) |
1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
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(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(/ (* alpha (* beta i)) (+ alpha beta)) |
(/.f64 (*.f64 alpha (*.f64 beta i)) (+.f64 alpha beta)) |
(* i (+ (* i (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(*.f64 i (fma.f64 i (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (*.f64 alpha beta) (+.f64 alpha beta)))) |
(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
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(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (+ (* 2 (/ beta (pow (+ alpha beta) 2))) (* i (- (/ 1 (pow (+ alpha beta) 2)) (+ (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (pow (+ alpha beta) 2))) (* 4 (/ (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta))))) (+ alpha beta)))))))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(*.f64 i (fma.f64 i (+.f64 #s(literal 1 binary64) (-.f64 (fma.f64 i (-.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 beta (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (*.f64 i (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 #s(literal 4 binary64) (+.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 beta (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (*.f64 #s(literal 4 binary64) (+.f64 (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (+.f64 alpha beta))))) (+.f64 alpha beta))))))) (*.f64 #s(literal 4 binary64) (+.f64 (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (+.f64 alpha beta))))) (/.f64 (*.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (*.f64 alpha beta) (+.f64 alpha beta)))) |
(* 1/4 (pow i 2)) |
(*.f64 #s(literal 1/4 binary64) (*.f64 i i)) |
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (-.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) i))) (/.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 alpha beta)) i))) |
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (+ alpha beta) i)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)))))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) i) (/.f64 (fma.f64 alpha beta (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i)) (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 alpha beta) i) (/.f64 (*.f64 (+.f64 alpha beta) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))) (*.f64 i i))))))) |
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 3))) (+ (* 1/4 (/ (+ alpha beta) i)) (+ (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/16 (pow (+ alpha beta) 2)) (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))))) (pow i 3)))))))) |
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(* 1/4 (pow i 2)) |
(*.f64 #s(literal 1/4 binary64) (*.f64 i i)) |
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (-.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) i))) (/.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 alpha beta)) i))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* 1/4 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)) (* -1/16 (/ (pow (+ alpha beta) 2) i)))) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (neg.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))) (/.f64 (*.f64 #s(literal 1/4 binary64) (fma.f64 (neg.f64 alpha) beta (neg.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) i)) (+.f64 (/.f64 (*.f64 (neg.f64 (+.f64 alpha beta)) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))) i) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) i))) i)))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) (* 1/4 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) i)) (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)))) i))) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (neg.f64 (/.f64 (*.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)) (/.f64 (-.f64 (+.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (fma.f64 (neg.f64 alpha) beta (neg.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (fma.f64 (neg.f64 (+.f64 alpha beta)) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 alpha (*.f64 beta (+.f64 alpha beta)))) i)) (+.f64 (neg.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 (*.f64 #s(literal 1/4 binary64) (fma.f64 (neg.f64 alpha) beta (neg.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (fma.f64 (neg.f64 (+.f64 alpha beta)) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) i)) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))))) i))) i))) i)))) |
(/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2)) |
(/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))) |
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
(fma.f64 alpha (-.f64 (/.f64 (*.f64 i (fma.f64 i (+.f64 beta i) (*.f64 (+.f64 beta i) (+.f64 beta i)))) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))) (/.f64 (*.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i))) (pow.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) #s(literal 4 binary64)))) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))))) |
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(* i (+ beta i)) |
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(pow alpha 2) |
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(pow alpha 2) |
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(fma.f64 beta (fma.f64 #s(literal 2 binary64) alpha (*.f64 #s(literal 4 binary64) i)) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(fma.f64 beta (+.f64 beta (fma.f64 #s(literal 2 binary64) alpha (*.f64 #s(literal 4 binary64) i))) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(fma.f64 beta (+.f64 beta (fma.f64 #s(literal 2 binary64) alpha (*.f64 #s(literal 4 binary64) i))) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) |
(pow beta 2) |
(*.f64 beta beta) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta))))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (/.f64 (*.f64 #s(literal 4 binary64) i) beta)))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) (*.f64 beta beta)))))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) (*.f64 beta beta)))))) |
(pow beta 2) |
(*.f64 beta beta) |
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta)))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) beta))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (neg.f64 (/.f64 (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) beta))) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (neg.f64 (/.f64 (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) beta))) beta)))) |
(pow (+ alpha beta) 2) |
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) |
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 i (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) |
(* 4 (pow i 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 i i)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (+.f64 alpha beta)) i))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i))))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i))))) |
(* 4 (pow i 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 i i)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (+.f64 alpha beta)) i))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -4 binary64) (+.f64 alpha beta) (neg.f64 (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i))) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -4 binary64) (+.f64 alpha beta) (neg.f64 (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i))) i)))) |
(/ i (+ alpha beta)) |
(/.f64 i (+.f64 alpha beta)) |
(* i (+ (* -3 (/ i (pow (+ alpha beta) 2))) (/ 1 (+ alpha beta)))) |
(*.f64 i (fma.f64 #s(literal -3 binary64) (/.f64 i (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 #s(literal 1 binary64) (+.f64 alpha beta)))) |
(* i (+ (* i (- (* 8 (/ i (pow (+ alpha beta) 3))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta)))) |
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(* i (+ (* i (- (* i (+ (* -20 (/ i (pow (+ alpha beta) 4))) (* 8 (/ 1 (pow (+ alpha beta) 3))))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta)))) |
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1/4 |
#s(literal 1/4 binary64) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))) |
(- (+ 1/4 (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (*.f64 i (*.f64 i i))) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)))) |
(- (+ 1/4 (* -1 (/ (+ (* -1/64 (pow (+ alpha beta) 4)) (* 1/16 (pow (+ alpha beta) 4))) (pow i 4)))) (+ (* -1/16 (/ (pow (+ alpha beta) 3) (pow i 3))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(-.f64 (+.f64 #s(literal 1/4 binary64) (neg.f64 (/.f64 (*.f64 (pow.f64 (+.f64 alpha beta) #s(literal 4 binary64)) #s(literal 3/64 binary64)) (pow.f64 i #s(literal 4 binary64))))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i (*.f64 i i))) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)))) |
1/4 |
#s(literal 1/4 binary64) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))) |
(+ 1/4 (+ (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3))))) |
(+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (*.f64 i (*.f64 i i))))) |
(+ 1/4 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (pow (+ alpha beta) 4)) (* 1/64 (pow (+ alpha beta) 4))) i)) (* -1/16 (pow (+ alpha beta) 3))) (pow i 3))) (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(+.f64 #s(literal 1/4 binary64) (+.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (*.f64 (pow.f64 (+.f64 alpha beta) #s(literal 4 binary64)) #s(literal -3/64 binary64)) i)) (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (*.f64 i (*.f64 i i)))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)))) |
(/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) |
(/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))) |
(+ (* alpha (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) |
(fma.f64 alpha (-.f64 (/.f64 i (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))) (/.f64 (*.f64 (*.f64 i (+.f64 beta i)) (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i))) (pow.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) #s(literal 4 binary64)))) (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))))) |
(+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) |
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(+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 6)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)))) (pow (+ beta (* 2 i)) 2))) (/ i (pow (+ beta (* 2 i)) 4))))) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) |
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(/ i alpha) |
(/.f64 i alpha) |
(/ (- (+ i (/ (* i (+ beta i)) alpha)) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
(/.f64 (-.f64 (+.f64 i (/.f64 (*.f64 i (+.f64 beta i)) alpha)) (/.f64 (*.f64 i (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i))) alpha)) alpha) |
(/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha))) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
(/.f64 (+.f64 i (-.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 i (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i)) (*.f64 i (-.f64 (+.f64 beta i) (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i)))))) (*.f64 alpha alpha))) (/.f64 (*.f64 i (+.f64 beta i)) alpha)) (/.f64 (*.f64 i (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i))) alpha))) alpha) |
(/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 3))) (/ (* i (+ beta i)) alpha))) (+ (/ (* i (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* i (pow (+ beta (* 2 i)) 2)) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha) |
(/.f64 (+.f64 i (-.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i)) (fma.f64 i (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i)) (*.f64 i (-.f64 (+.f64 beta i) (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i)))))))) (*.f64 (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 i (-.f64 (+.f64 beta i) (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i)))))) (*.f64 alpha (*.f64 alpha alpha)))) (/.f64 (*.f64 i (+.f64 beta i)) alpha)) (+.f64 (/.f64 (*.f64 i (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i))) alpha) (+.f64 (/.f64 (*.f64 i (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))) (*.f64 alpha alpha)) (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i)) (*.f64 i (-.f64 (+.f64 beta i) (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i))))) (*.f64 alpha alpha)))))) alpha) |
(/ i alpha) |
(/.f64 i alpha) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha)) |
(neg.f64 (/.f64 (+.f64 (neg.f64 i) (neg.f64 (/.f64 (fma.f64 i (+.f64 beta i) (*.f64 #s(literal -2 binary64) (*.f64 i (+.f64 beta (*.f64 #s(literal 2 binary64) i))))) alpha))) alpha)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -1 (/ (* i (pow (+ beta (* 2 i)) 2)) alpha)) (* i (+ beta i)))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha)) |
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(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ beta (* 2 i)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (* i (+ beta i))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha)) |
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(/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) |
(/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) |
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(/ i beta) |
(/.f64 i beta) |
(/ (- (+ i (/ (* i (+ alpha i)) beta)) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta) |
(/.f64 (+.f64 i (-.f64 (/.f64 (*.f64 i (+.f64 alpha i)) beta) (/.f64 (*.f64 i (fma.f64 #s(literal 2 binary64) alpha (*.f64 #s(literal 4 binary64) i))) beta))) beta) |
(/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta))) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta) |
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(/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 3))) (/ (* i (+ alpha i)) beta))) (+ (/ (* i (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* i (pow (+ alpha (* 2 i)) 2)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta) |
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(/ i beta) |
(/.f64 i beta) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta)) |
(neg.f64 (/.f64 (+.f64 (neg.f64 i) (neg.f64 (/.f64 (fma.f64 i (+.f64 alpha i) (*.f64 #s(literal -2 binary64) (*.f64 i (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) beta))) beta)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -1 (/ (* i (pow (+ alpha (* 2 i)) 2)) beta)) (* i (+ alpha i)))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta)) |
(neg.f64 (/.f64 (+.f64 (neg.f64 i) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (fma.f64 i (+.f64 alpha i) (*.f64 #s(literal -2 binary64) (*.f64 i (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))))) beta) (-.f64 (+.f64 (/.f64 (*.f64 (neg.f64 i) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) beta) (*.f64 i (+.f64 alpha i))) (*.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) beta))) beta)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ alpha (* 2 i)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (* i (+ alpha i))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta)) |
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(pow (+ alpha beta) 2) |
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) |
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 i (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) |
(* 4 (pow i 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 i i)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (+.f64 alpha beta)) i))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i))))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i))))) |
(* 4 (pow i 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 i i)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (+.f64 alpha beta)) i))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
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(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -4 binary64) (+.f64 alpha beta) (neg.f64 (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i))) i)))) |
(pow (+ beta (* 2 i)) 2) |
(*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))) |
(+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) |
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(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
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(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
(fma.f64 alpha (+.f64 alpha (fma.f64 #s(literal 2 binary64) beta (*.f64 #s(literal 4 binary64) i))) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))) |
(pow alpha 2) |
(*.f64 alpha alpha) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha))))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (/.f64 (*.f64 #s(literal 4 binary64) i) alpha)))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) (/.f64 (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 alpha alpha)))))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) (/.f64 (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 alpha alpha)))))) |
(pow alpha 2) |
(*.f64 alpha alpha) |
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha)))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 beta (*.f64 #s(literal 2 binary64) i))) alpha))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (neg.f64 (/.f64 (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))) alpha))) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (neg.f64 (/.f64 (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))) alpha))) alpha)))) |
(pow (+ alpha (* 2 i)) 2) |
(*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) |
(+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) |
(fma.f64 beta (fma.f64 #s(literal 2 binary64) alpha (*.f64 #s(literal 4 binary64) i)) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(fma.f64 beta (+.f64 beta (fma.f64 #s(literal 2 binary64) alpha (*.f64 #s(literal 4 binary64) i))) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(fma.f64 beta (+.f64 beta (fma.f64 #s(literal 2 binary64) alpha (*.f64 #s(literal 4 binary64) i))) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) |
(pow beta 2) |
(*.f64 beta beta) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta))))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (/.f64 (*.f64 #s(literal 4 binary64) i) beta)))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
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(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
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(pow beta 2) |
(*.f64 beta beta) |
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta)))) |
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(* 1/2 i) |
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(* 1/2 i) |
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(+ beta i) |
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(* -1 (+ (* -1 beta) (* -1 i))) |
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(-.f64 (+.f64 (+.f64 alpha i) (+.f64 (neg.f64 (/.f64 (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (-.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (+.f64 alpha i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) (*.f64 beta beta))) (/.f64 (*.f64 i (+.f64 alpha i)) beta))) (/.f64 (*.f64 (+.f64 alpha i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) beta)) |
(- (+ alpha (+ i (+ (/ (* i (+ alpha i)) beta) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* (+ alpha i) (+ alpha (* 2 i))))) (pow beta 3))))) (+ (/ (* (+ alpha i) (+ alpha (* 2 i))) beta) (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ alpha (* 2 i))))) (pow beta 2)))) |
(+.f64 alpha (-.f64 (+.f64 (+.f64 i (/.f64 (*.f64 i (+.f64 alpha i)) beta)) (/.f64 (*.f64 (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) (-.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (+.f64 alpha i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) (*.f64 beta (*.f64 beta beta)))) (+.f64 (/.f64 (*.f64 (+.f64 alpha i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) beta) (/.f64 (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (-.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (+.f64 alpha i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) (*.f64 beta beta))))) |
(* -1 (+ (* -1 alpha) (* -1 i))) |
(neg.f64 (+.f64 (neg.f64 alpha) (neg.f64 i))) |
(+ (* -1 (+ (* -1 alpha) (* -1 i))) (* -1 (/ (- (* -1 (* i (+ alpha i))) (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))) beta))) |
(+.f64 (neg.f64 (+.f64 (neg.f64 alpha) (neg.f64 i))) (neg.f64 (/.f64 (-.f64 (neg.f64 (*.f64 i (+.f64 alpha i))) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 (neg.f64 alpha) (neg.f64 i)))) beta))) |
(+ (* -1 (+ (* -1 alpha) (* -1 i))) (* -1 (/ (- (+ (* -1 (* i (+ alpha i))) (* -1 (/ (* (+ alpha (* 2 i)) (- (* -1 (* i (+ alpha i))) (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta))) (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))) beta))) |
(+.f64 (neg.f64 (+.f64 (neg.f64 alpha) (neg.f64 i))) (neg.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 i) (+.f64 alpha i) (/.f64 (*.f64 (neg.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) (-.f64 (neg.f64 (*.f64 i (+.f64 alpha i))) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 (neg.f64 alpha) (neg.f64 i))))) beta)) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 (neg.f64 alpha) (neg.f64 i)))) beta))) |
(+ (* -1 (+ (* -1 alpha) (* -1 i))) (* -1 (/ (- (+ (* -1 (* i (+ alpha i))) (* -1 (/ (- (* -1 (/ (* (pow (+ alpha (* 2 i)) 2) (- (* -1 (* i (+ alpha i))) (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)) (* -1 (* (+ alpha (* 2 i)) (- (* -1 (* i (+ alpha i))) (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) beta))) (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))) beta))) |
(+.f64 (neg.f64 (+.f64 (neg.f64 alpha) (neg.f64 i))) (neg.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 i) (+.f64 alpha i) (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (*.f64 (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) (-.f64 (neg.f64 (*.f64 i (+.f64 alpha i))) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 (neg.f64 alpha) (neg.f64 i))))) beta)) (*.f64 (neg.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) (-.f64 (neg.f64 (*.f64 i (+.f64 alpha i))) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 (neg.f64 alpha) (neg.f64 i)))))) beta))) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 (neg.f64 alpha) (neg.f64 i)))) beta))) |
i |
(* i (+ 1 (* -1 (/ i (+ alpha beta))))) |
(*.f64 i (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 i (+.f64 alpha beta))))) |
(* i (+ 1 (* i (- (* 2 (/ i (pow (+ alpha beta) 2))) (/ 1 (+ alpha beta)))))) |
(*.f64 i (+.f64 #s(literal 1 binary64) (*.f64 i (-.f64 (/.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 #s(literal 1 binary64) (+.f64 alpha beta)))))) |
(* i (+ 1 (* i (- (* i (+ (* -4 (/ i (pow (+ alpha beta) 3))) (* 2 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta)))))) |
(*.f64 i (+.f64 #s(literal 1 binary64) (*.f64 i (fma.f64 i (fma.f64 #s(literal -4 binary64) (/.f64 i (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 alpha beta))))))) |
(* 1/2 i) |
(*.f64 #s(literal 1/2 binary64) i) |
(* i (- (+ 1/2 (* 1/2 (/ (+ alpha beta) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(*.f64 i (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/4 binary64)) i))) |
(* i (- (+ 1/2 (+ (* -1/2 (/ (* (+ alpha beta) (- (* 1/2 (+ alpha beta)) (* 1/4 (+ alpha beta)))) (pow i 2))) (* 1/2 (/ (+ alpha beta) i)))) (* 1/4 (/ (+ alpha beta) i)))) |
(*.f64 i (+.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal 1/4 binary64))) (*.f64 i i)) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 alpha beta) i))) (/.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 alpha beta)) i)))) |
(* i (- (+ 1/2 (+ (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/2 (+ alpha beta)) (* 1/4 (+ alpha beta)))) (pow i 3))) (* 1/2 (/ (+ alpha beta) i)))) (+ (* 1/4 (/ (+ alpha beta) i)) (* 1/2 (/ (* (+ alpha beta) (- (* 1/2 (+ alpha beta)) (* 1/4 (+ alpha beta)))) (pow i 2)))))) |
(*.f64 i (+.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal 1/4 binary64))) (*.f64 i (*.f64 i i))) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 alpha beta) i))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 alpha beta) i) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal 1/4 binary64))) (*.f64 i i)))))) |
(* 1/2 i) |
(*.f64 #s(literal 1/2 binary64) i) |
(* -1 (* i (- (* -1/2 (/ (+ alpha beta) i)) (+ 1/2 (* -1/4 (/ (+ alpha beta) i)))))) |
(*.f64 (neg.f64 i) (-.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 alpha beta)) i) #s(literal 1/2 binary64)) (*.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 alpha beta) i)))) |
(* -1 (* i (- (* -1 (/ (+ (* -1 (- (* -1/2 (+ alpha beta)) (* -1/4 (+ alpha beta)))) (* 1/2 (/ (* (+ alpha beta) (- (* -1/2 (+ alpha beta)) (* -1/4 (+ alpha beta)))) i))) i)) 1/2))) |
(*.f64 (neg.f64 i) (+.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (*.f64 (+.f64 alpha beta) #s(literal -1/4 binary64))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/4 binary64)))) i)) i)) #s(literal -1/2 binary64))) |
(* -1 (* i (- (* -1 (/ (+ (* -1 (- (* -1/2 (+ alpha beta)) (* -1/4 (+ alpha beta)))) (* -1 (/ (+ (* -1/2 (* (+ alpha beta) (- (* -1/2 (+ alpha beta)) (* -1/4 (+ alpha beta))))) (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* -1/2 (+ alpha beta)) (* -1/4 (+ alpha beta)))) i))) i))) i)) 1/2))) |
(*.f64 (neg.f64 i) (+.f64 (neg.f64 (/.f64 (*.f64 #s(literal -1 binary64) (fma.f64 (+.f64 alpha beta) #s(literal -1/4 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/4 binary64))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/4 binary64)))) i)) i))) i)) #s(literal -1/2 binary64))) |
(/ (* i (+ beta i)) (+ beta (* 2 i))) |
(/.f64 (*.f64 i (+.f64 beta i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))) |
(+ (* alpha (- (/ i (+ beta (* 2 i))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))) (/ (* i (+ beta i)) (+ beta (* 2 i)))) |
(fma.f64 alpha (-.f64 (/.f64 i (+.f64 beta (*.f64 #s(literal 2 binary64) i))) (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))))) (/.f64 (*.f64 i (+.f64 beta i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))) |
(+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 3)) (/ i (pow (+ beta (* 2 i)) 2)))) (/ i (+ beta (* 2 i)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))) (/ (* i (+ beta i)) (+ beta (* 2 i)))) |
(fma.f64 alpha (fma.f64 alpha (-.f64 (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))))) (/.f64 i (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))))) (-.f64 (/.f64 i (+.f64 beta (*.f64 #s(literal 2 binary64) i))) (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))))) (/.f64 (*.f64 i (+.f64 beta i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))) |
(+ (* alpha (- (+ (* alpha (- (+ (* alpha (- (/ i (pow (+ beta (* 2 i)) 3)) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 3))) (/ i (pow (+ beta (* 2 i)) 2)))) (/ i (+ beta (* 2 i)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))) (/ (* i (+ beta i)) (+ beta (* 2 i)))) |
(fma.f64 alpha (fma.f64 alpha (fma.f64 alpha (-.f64 (/.f64 i (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))))) (/.f64 (*.f64 i (+.f64 beta i)) (pow.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) #s(literal 4 binary64)))) (-.f64 (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))))) (/.f64 i (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))))) (-.f64 (/.f64 i (+.f64 beta (*.f64 #s(literal 2 binary64) i))) (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))))) (/.f64 (*.f64 i (+.f64 beta i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))) |
i |
(- (+ i (/ (* i (+ beta i)) alpha)) (/ (* i (+ beta (* 2 i))) alpha)) |
(-.f64 (+.f64 i (/.f64 (*.f64 i (+.f64 beta i)) alpha)) (/.f64 (*.f64 i (+.f64 beta (*.f64 #s(literal 2 binary64) i))) alpha)) |
(- (+ i (+ (* -1 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* i (+ beta (* 2 i))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha))) (/ (* i (+ beta (* 2 i))) alpha)) |
(+.f64 i (-.f64 (+.f64 (neg.f64 (/.f64 (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (*.f64 i (-.f64 (+.f64 beta i) (+.f64 beta (*.f64 #s(literal 2 binary64) i))))) (*.f64 alpha alpha))) (/.f64 (*.f64 i (+.f64 beta i)) alpha)) (/.f64 (*.f64 i (+.f64 beta (*.f64 #s(literal 2 binary64) i))) alpha))) |
(- (+ i (+ (/ (* i (+ beta i)) alpha) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* i (+ beta (* 2 i))))) (pow alpha 3)))) (+ (/ (* i (+ beta (* 2 i))) alpha) (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* i (+ beta (* 2 i))))) (pow alpha 2)))) |
(-.f64 (+.f64 (+.f64 i (/.f64 (*.f64 i (+.f64 beta i)) alpha)) (/.f64 (*.f64 (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 i (-.f64 (+.f64 beta i) (+.f64 beta (*.f64 #s(literal 2 binary64) i))))) (*.f64 alpha (*.f64 alpha alpha)))) (+.f64 (/.f64 (*.f64 i (+.f64 beta (*.f64 #s(literal 2 binary64) i))) alpha) (/.f64 (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (*.f64 i (-.f64 (+.f64 beta i) (+.f64 beta (*.f64 #s(literal 2 binary64) i))))) (*.f64 alpha alpha)))) |
i |
(+ i (* -1 (/ (- (* -1 (* i (+ beta i))) (* -1 (* i (+ beta (* 2 i))))) alpha))) |
(+.f64 i (neg.f64 (/.f64 (*.f64 #s(literal -1 binary64) (*.f64 i (-.f64 (+.f64 beta i) (+.f64 beta (*.f64 #s(literal 2 binary64) i))))) alpha))) |
(+ i (* -1 (/ (- (+ (* -1 (* i (+ beta i))) (* -1 (/ (* (+ beta (* 2 i)) (- (* -1 (* i (+ beta i))) (* -1 (* i (+ beta (* 2 i)))))) alpha))) (* -1 (* i (+ beta (* 2 i))))) alpha))) |
(+.f64 i (neg.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 i) (+.f64 beta i) (/.f64 (*.f64 (neg.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal -1 binary64) (*.f64 i (-.f64 (+.f64 beta i) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))))) alpha)) (*.f64 (neg.f64 i) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))) alpha))) |
(+ i (* -1 (/ (- (+ (* -1 (* i (+ beta i))) (* -1 (/ (- (* -1 (/ (* (pow (+ beta (* 2 i)) 2) (- (* -1 (* i (+ beta i))) (* -1 (* i (+ beta (* 2 i)))))) alpha)) (* -1 (* (+ beta (* 2 i)) (- (* -1 (* i (+ beta i))) (* -1 (* i (+ beta (* 2 i)))))))) alpha))) (* -1 (* i (+ beta (* 2 i))))) alpha))) |
(+.f64 i (neg.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 i) (+.f64 beta i) (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (*.f64 (*.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal -1 binary64) (*.f64 i (-.f64 (+.f64 beta i) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))))) alpha)) (*.f64 (neg.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal -1 binary64) (*.f64 i (-.f64 (+.f64 beta i) (+.f64 beta (*.f64 #s(literal 2 binary64) i))))))) alpha))) (*.f64 (neg.f64 i) (+.f64 beta (*.f64 #s(literal 2 binary64) i)))) alpha))) |
(/ (* i (+ alpha i)) (+ alpha (* 2 i))) |
(/.f64 (*.f64 i (+.f64 alpha i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) |
(+ (* beta (- (/ i (+ alpha (* 2 i))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))) (/ (* i (+ alpha i)) (+ alpha (* 2 i)))) |
(fma.f64 beta (-.f64 (/.f64 i (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) (/.f64 (*.f64 i (+.f64 alpha i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 3)) (/ i (pow (+ alpha (* 2 i)) 2)))) (/ i (+ alpha (* 2 i)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))) (/ (* i (+ alpha i)) (+ alpha (* 2 i)))) |
(fma.f64 beta (-.f64 (fma.f64 beta (-.f64 (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) (/.f64 i (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) (/.f64 i (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) (/.f64 (*.f64 i (+.f64 alpha i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) |
(+ (* beta (- (+ (* beta (- (+ (* beta (- (/ i (pow (+ alpha (* 2 i)) 3)) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 3))) (/ i (pow (+ alpha (* 2 i)) 2)))) (/ i (+ alpha (* 2 i)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))) (/ (* i (+ alpha i)) (+ alpha (* 2 i)))) |
(fma.f64 beta (fma.f64 beta (fma.f64 beta (-.f64 (/.f64 i (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) (/.f64 (*.f64 i (+.f64 alpha i)) (pow.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) #s(literal 4 binary64)))) (-.f64 (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) (/.f64 i (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))))) (-.f64 (/.f64 i (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))))) (/.f64 (*.f64 i (+.f64 alpha i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) |
i |
(- (+ i (/ (* i (+ alpha i)) beta)) (/ (* i (+ alpha (* 2 i))) beta)) |
(-.f64 (+.f64 i (/.f64 (*.f64 i (+.f64 alpha i)) beta)) (/.f64 (*.f64 i (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) beta)) |
(- (+ i (+ (* -1 (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* i (+ alpha (* 2 i))))) (pow beta 2))) (/ (* i (+ alpha i)) beta))) (/ (* i (+ alpha (* 2 i))) beta)) |
(+.f64 i (-.f64 (+.f64 (neg.f64 (/.f64 (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (*.f64 i (-.f64 (+.f64 alpha i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) (*.f64 beta beta))) (/.f64 (*.f64 i (+.f64 alpha i)) beta)) (/.f64 (*.f64 i (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) beta))) |
(- (+ i (+ (/ (* i (+ alpha i)) beta) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* i (+ alpha (* 2 i))))) (pow beta 3)))) (+ (/ (* i (+ alpha (* 2 i))) beta) (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* i (+ alpha (* 2 i))))) (pow beta 2)))) |
(-.f64 (+.f64 (+.f64 i (/.f64 (*.f64 i (+.f64 alpha i)) beta)) (/.f64 (*.f64 (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) (*.f64 i (-.f64 (+.f64 alpha i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) (*.f64 beta (*.f64 beta beta)))) (+.f64 (/.f64 (*.f64 i (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) beta) (/.f64 (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (*.f64 i (-.f64 (+.f64 alpha i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) (*.f64 beta beta)))) |
i |
(+ i (* -1 (/ (- (* -1 (* i (+ alpha i))) (* -1 (* i (+ alpha (* 2 i))))) beta))) |
(+.f64 i (neg.f64 (/.f64 (*.f64 #s(literal -1 binary64) (*.f64 i (-.f64 (+.f64 alpha i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))) beta))) |
(+ i (* -1 (/ (- (+ (* -1 (* i (+ alpha i))) (* -1 (/ (* (+ alpha (* 2 i)) (- (* -1 (* i (+ alpha i))) (* -1 (* i (+ alpha (* 2 i)))))) beta))) (* -1 (* i (+ alpha (* 2 i))))) beta))) |
(+.f64 i (neg.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 i) (+.f64 alpha i) (/.f64 (*.f64 (neg.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal -1 binary64) (*.f64 i (-.f64 (+.f64 alpha i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))))) beta)) (*.f64 (neg.f64 i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) beta))) |
(+ i (* -1 (/ (- (+ (* -1 (* i (+ alpha i))) (* -1 (/ (- (* -1 (/ (* (pow (+ alpha (* 2 i)) 2) (- (* -1 (* i (+ alpha i))) (* -1 (* i (+ alpha (* 2 i)))))) beta)) (* -1 (* (+ alpha (* 2 i)) (- (* -1 (* i (+ alpha i))) (* -1 (* i (+ alpha (* 2 i)))))))) beta))) (* -1 (* i (+ alpha (* 2 i))))) beta))) |
(+.f64 i (neg.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 i) (+.f64 alpha i) (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (*.f64 (*.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i)) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal -1 binary64) (*.f64 i (-.f64 (+.f64 alpha i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))))) beta)) (*.f64 (neg.f64 (+.f64 alpha (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal -1 binary64) (*.f64 i (-.f64 (+.f64 alpha i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i))))))) beta))) (*.f64 (neg.f64 i) (+.f64 alpha (*.f64 #s(literal 2 binary64) i)))) beta))) |
| 4 796× | lower-/.f32 |
| 4 778× | lower-/.f64 |
| 3 804× | lower-*.f32 |
| 3 780× | lower-*.f64 |
| 2 964× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 57 | 592 |
| 0 | 93 | 490 |
| 1 | 495 | 490 |
| 2 | 4647 | 490 |
| 0 | 8414 | 486 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta))) |
(/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta)) |
(*.f64 i (+.f64 alpha i)) |
(+.f64 alpha i) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) |
(-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)) |
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)) |
(-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) |
(*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) |
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) |
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) |
(+.f64 i (+.f64 alpha beta)) |
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) |
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) |
(/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) |
(*.f64 beta beta) |
(/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
#s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)))) |
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) |
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) |
(*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) |
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) |
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) |
| Outputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 i alpha)) (*.f64 beta beta))) |
(exp.f64 (*.f64 (log.f64 (*.f64 beta (/.f64 beta (*.f64 i (+.f64 i alpha))))) #s(literal -1 binary64))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (*.f64 beta beta))) (/.f64 (*.f64 i (+.f64 i alpha)) (neg.f64 (*.f64 beta beta)))) |
(neg.f64 (/.f64 (*.f64 i (+.f64 i alpha)) (neg.f64 (*.f64 beta beta)))) |
(neg.f64 (/.f64 (neg.f64 (*.f64 i (+.f64 i alpha))) (*.f64 beta beta))) |
(/.f64 #s(literal 1 binary64) (*.f64 beta (/.f64 beta (*.f64 i (+.f64 i alpha))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 beta (/.f64 beta (*.f64 i (+.f64 i alpha)))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 beta (/.f64 (*.f64 i (+.f64 i alpha)) beta))) |
(/.f64 (*.f64 i (+.f64 i alpha)) (*.f64 beta beta)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 beta (/.f64 beta (*.f64 i (+.f64 i alpha)))))) |
(/.f64 (neg.f64 (*.f64 i (+.f64 i alpha))) (neg.f64 (*.f64 beta beta))) |
(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta) |
(/.f64 (neg.f64 (neg.f64 (*.f64 i (+.f64 i alpha)))) (neg.f64 (neg.f64 (*.f64 beta beta)))) |
(/.f64 (neg.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta)) (neg.f64 beta)) |
(/.f64 (*.f64 (*.f64 i (+.f64 i alpha)) #s(literal 1 binary64)) (*.f64 beta beta)) |
(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta) |
(pow.f64 (*.f64 beta (/.f64 beta (*.f64 i (+.f64 i alpha)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (*.f64 beta (/.f64 beta (*.f64 i (+.f64 i alpha)))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 beta (/.f64 (*.f64 i (+.f64 i alpha)) beta)) #s(literal -1 binary64)) |
(*.f64 i (/.f64 (+.f64 i alpha) (*.f64 beta beta))) |
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 i (+.f64 i alpha)) (*.f64 beta beta))) |
(*.f64 (+.f64 i alpha) (*.f64 i (/.f64 #s(literal 1 binary64) (*.f64 beta beta)))) |
(*.f64 (+.f64 i alpha) (/.f64 i (*.f64 beta beta))) |
(*.f64 (*.f64 i (+.f64 i alpha)) (/.f64 #s(literal 1 binary64) (*.f64 beta beta))) |
(*.f64 (neg.f64 (*.f64 i (+.f64 i alpha))) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 beta beta)))) |
(*.f64 (/.f64 i beta) (/.f64 (+.f64 i alpha) beta)) |
(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta)) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 beta beta)) (*.f64 i (+.f64 i alpha))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 beta beta)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 i (+.f64 i alpha))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta)) |
(*.f64 (/.f64 (+.f64 i alpha) (*.f64 beta beta)) i) |
(*.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 (*.f64 i (+.f64 i alpha)) beta)) |
(+.f64 (*.f64 i i) (*.f64 i alpha)) |
(+.f64 (*.f64 i alpha) (*.f64 i i)) |
(-.f64 (/.f64 (*.f64 (*.f64 alpha alpha) (*.f64 i i)) (-.f64 (*.f64 i alpha) (*.f64 i i))) (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (-.f64 (*.f64 i alpha) (*.f64 i i)))) |
(fma.f64 i i (*.f64 i alpha)) |
(fma.f64 i alpha (*.f64 i i)) |
(fma.f64 alpha i (*.f64 i i)) |
(fma.f64 (neg.f64 i) (neg.f64 i) (*.f64 i alpha)) |
(fma.f64 (exp.f64 (log.f64 i)) (exp.f64 (log.f64 i)) (*.f64 i alpha)) |
(/.f64 (fma.f64 (*.f64 alpha (*.f64 alpha alpha)) (*.f64 i (*.f64 i i)) (*.f64 (*.f64 i (*.f64 i i)) (*.f64 i (*.f64 i i)))) (fma.f64 (*.f64 alpha alpha) (*.f64 i i) (-.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 i alpha) (*.f64 i i))))) |
(/.f64 (-.f64 (*.f64 (*.f64 alpha alpha) (*.f64 i i)) (*.f64 (*.f64 i i) (*.f64 i i))) (-.f64 (*.f64 i alpha) (*.f64 i i))) |
(/.f64 (*.f64 i (fma.f64 i (*.f64 i i) (*.f64 alpha (*.f64 alpha alpha)))) (fma.f64 i (-.f64 i alpha) (*.f64 alpha alpha))) |
(/.f64 (*.f64 i (*.f64 (+.f64 i alpha) (-.f64 alpha i))) (-.f64 alpha i)) |
(/.f64 (*.f64 (fma.f64 i (*.f64 i i) (*.f64 alpha (*.f64 alpha alpha))) i) (fma.f64 i (-.f64 i alpha) (*.f64 alpha alpha))) |
(/.f64 (*.f64 (*.f64 (+.f64 i alpha) (-.f64 alpha i)) i) (-.f64 alpha i)) |
(*.f64 i (+.f64 i alpha)) |
(*.f64 (+.f64 i alpha) i) |
(+.f64 i alpha) |
(+.f64 alpha i) |
(-.f64 (/.f64 (*.f64 alpha alpha) (-.f64 alpha i)) (/.f64 (*.f64 i i) (-.f64 alpha i))) |
(-.f64 (/.f64 (*.f64 i i) (-.f64 i alpha)) (/.f64 (*.f64 alpha alpha) (-.f64 i alpha))) |
(fma.f64 (/.f64 #s(literal 1 binary64) i) (*.f64 i i) alpha) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 i (-.f64 i alpha) (*.f64 alpha alpha)) (fma.f64 i (*.f64 i i) (*.f64 alpha (*.f64 alpha alpha))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 alpha i) (*.f64 (+.f64 i alpha) (-.f64 alpha i)))) |
(/.f64 (fma.f64 i (*.f64 i i) (*.f64 alpha (*.f64 alpha alpha))) (fma.f64 i (-.f64 i alpha) (*.f64 alpha alpha))) |
(/.f64 (fma.f64 i (*.f64 i i) (*.f64 alpha (*.f64 alpha alpha))) (fma.f64 i i (-.f64 (*.f64 alpha alpha) (*.f64 i alpha)))) |
(/.f64 (*.f64 (+.f64 i alpha) (-.f64 alpha i)) (-.f64 alpha i)) |
(/.f64 (neg.f64 (fma.f64 i (*.f64 i i) (*.f64 alpha (*.f64 alpha alpha)))) (neg.f64 (fma.f64 i (-.f64 i alpha) (*.f64 alpha alpha)))) |
(/.f64 (neg.f64 (*.f64 (+.f64 i alpha) (-.f64 alpha i))) (neg.f64 (-.f64 alpha i))) |
(/.f64 (-.f64 (*.f64 i i) (*.f64 alpha alpha)) (-.f64 i alpha)) |
(pow.f64 (/.f64 (fma.f64 i (-.f64 i alpha) (*.f64 alpha alpha)) (fma.f64 i (*.f64 i i) (*.f64 alpha (*.f64 alpha alpha)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 alpha i) (*.f64 (+.f64 i alpha) (-.f64 alpha i))) #s(literal -1 binary64)) |
(*.f64 (fma.f64 i (*.f64 i i) (*.f64 alpha (*.f64 alpha alpha))) (/.f64 #s(literal 1 binary64) (fma.f64 i (-.f64 i alpha) (*.f64 alpha alpha)))) |
(*.f64 (*.f64 (+.f64 i alpha) (-.f64 alpha i)) (/.f64 #s(literal 1 binary64) (-.f64 alpha i))) |
(+.f64 (*.f64 i (*.f64 i #s(literal 1/4 binary64))) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)) |
(+.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i) (*.f64 i (*.f64 i #s(literal 1/4 binary64)))) |
(-.f64 (/.f64 (*.f64 (*.f64 i (*.f64 i #s(literal 1/4 binary64))) (*.f64 i (*.f64 i #s(literal 1/4 binary64)))) (-.f64 (*.f64 i (*.f64 i #s(literal 1/4 binary64))) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) (/.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)) (-.f64 (*.f64 i (*.f64 i #s(literal 1/4 binary64))) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)))) |
(fma.f64 i (*.f64 i #s(literal 1/4 binary64)) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)) |
(fma.f64 i (*.f64 i (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)) (*.f64 i (*.f64 i #s(literal 1/4 binary64)))) |
(fma.f64 (*.f64 i i) #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)) |
(fma.f64 (*.f64 i i) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i) (*.f64 i (*.f64 i #s(literal 1/4 binary64)))) |
(fma.f64 #s(literal 1/4 binary64) (*.f64 i i) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)) |
(fma.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)) i) (*.f64 i i)) (*.f64 i (*.f64 i #s(literal 1/4 binary64)))) |
(fma.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i (*.f64 i (*.f64 i #s(literal 1/4 binary64)))) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i) (*.f64 i i) (*.f64 i (*.f64 i #s(literal 1/4 binary64)))) |
(fma.f64 (*.f64 i (*.f64 i #s(literal 1/4 binary64))) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)) i) (*.f64 i (*.f64 i #s(literal 1/4 binary64)))) |
(fma.f64 (*.f64 #s(literal 1/4 binary64) i) i (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)) |
(fma.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i) i) i (*.f64 i (*.f64 i #s(literal 1/4 binary64)))) |
(fma.f64 (*.f64 (*.f64 i i) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))) (/.f64 #s(literal 1 binary64) i) (*.f64 i (*.f64 i #s(literal 1/4 binary64)))) |
(/.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 i (*.f64 i i)) (*.f64 i (*.f64 i i))) (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))))) (*.f64 i (*.f64 i i)))) (fma.f64 (*.f64 i (*.f64 i #s(literal 1/4 binary64))) (*.f64 i (*.f64 i #s(literal 1/4 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)) (*.f64 (*.f64 i (*.f64 i #s(literal 1/4 binary64))) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))))) |
(/.f64 (-.f64 (*.f64 (*.f64 i (*.f64 i #s(literal 1/4 binary64))) (*.f64 i (*.f64 i #s(literal 1/4 binary64)))) (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) (-.f64 (*.f64 i (*.f64 i #s(literal 1/4 binary64))) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) |
(/.f64 (*.f64 (*.f64 i i) (+.f64 #s(literal 1/64 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))))) (*.f64 i (*.f64 i i))))) (fma.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i) (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i) #s(literal 1/4 binary64)) #s(literal 1/16 binary64))) |
(/.f64 (*.f64 (*.f64 i i) (-.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))) (*.f64 i i)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) |
(/.f64 (*.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))))) (*.f64 i (*.f64 i i)))) (*.f64 i i)) (fma.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i) (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i) #s(literal 1/4 binary64)) #s(literal 1/16 binary64))) |
(/.f64 (*.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))) (*.f64 i i))) (*.f64 i i)) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) |
(*.f64 i (*.f64 i (fma.f64 (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)) (/.f64 #s(literal 1/4 binary64) i) #s(literal 1/4 binary64)))) |
(*.f64 (*.f64 i i) (fma.f64 (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)) (/.f64 #s(literal 1/4 binary64) i) #s(literal 1/4 binary64))) |
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)) (/.f64 #s(literal 1/4 binary64) i) #s(literal 1/4 binary64)) (*.f64 i i)) |
(*.f64 (*.f64 i (fma.f64 (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)) (/.f64 #s(literal 1/4 binary64) i) #s(literal 1/4 binary64))) i) |
(+.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (neg.f64 (+.f64 alpha beta))) |
(+.f64 (neg.f64 (+.f64 alpha beta)) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) |
(+.f64 (*.f64 alpha #s(literal 2 binary64)) (fma.f64 beta #s(literal 2 binary64) (neg.f64 (+.f64 alpha beta)))) |
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(*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 8 binary64)))) (fma.f64 (*.f64 i i) #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64))))))) |
(*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 8 binary64)))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 (*.f64 i #s(literal 2 binary64)) (-.f64 (*.f64 i #s(literal 2 binary64)) (+.f64 alpha beta))))) |
(*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (-.f64 (*.f64 (*.f64 i i) #s(literal 4 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (-.f64 (*.f64 i #s(literal 2 binary64)) (+.f64 alpha beta))) |
(*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i i) #s(literal 4 binary64)))) (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (fma.f64 (*.f64 alpha beta) (*.f64 alpha (*.f64 beta (*.f64 alpha beta))) (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 i (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (+.f64 i (+.f64 alpha beta)))))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (-.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 alpha beta)) (*.f64 alpha (*.f64 beta (*.f64 alpha beta)))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (fma.f64 (*.f64 alpha beta) (*.f64 alpha (*.f64 beta (*.f64 alpha beta))) (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 i (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (+.f64 i (+.f64 alpha beta)))))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 alpha beta) (-.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (*.f64 i (*.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i (+.f64 i (+.f64 alpha beta)))))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (-.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 alpha beta) (*.f64 i (+.f64 i (+.f64 alpha beta)))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (-.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 alpha beta)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 alpha beta)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 i (+.f64 i (+.f64 alpha beta))))) #s(literal -1 binary64))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (neg.f64 i)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) |
(neg.f64 (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (neg.f64 i)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 i (+.f64 i (+.f64 alpha beta))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 i (+.f64 i (+.f64 alpha beta)))) #s(literal 1 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 i (+.f64 i (+.f64 alpha beta)))))) |
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) |
(/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (neg.f64 i)) (neg.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) |
(/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) #s(literal 1 binary64)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) |
(/.f64 (neg.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (neg.f64 i))) (neg.f64 (neg.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))))) |
(pow.f64 (/.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 i (+.f64 i (+.f64 alpha beta)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 i (+.f64 i (+.f64 alpha beta)))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(*.f64 i (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) |
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) |
(*.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 i (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) |
(*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 #s(literal 1 binary64) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) |
(*.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (neg.f64 i)) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))))) |
(*.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) i) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (*.f64 i (+.f64 i (+.f64 alpha beta)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 i (+.f64 i (+.f64 alpha beta)))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 8 binary64)))) (fma.f64 (*.f64 i i) #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64))))))) |
(*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 8 binary64)))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 (*.f64 i #s(literal 2 binary64)) (-.f64 (*.f64 i #s(literal 2 binary64)) (+.f64 alpha beta))))) |
(*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (-.f64 (*.f64 (*.f64 i i) #s(literal 4 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (-.f64 (*.f64 i #s(literal 2 binary64)) (+.f64 alpha beta))) |
(*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i i) #s(literal 4 binary64)))) (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64))))) |
Compiled 154 121 to 6 576 computations (95.7% saved)
32 alts after pruning (31 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 2 070 | 27 | 2 097 |
| Fresh | 10 | 4 | 14 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 0 | 0 |
| Total | 2 084 | 32 | 2 116 |
| Status | Accuracy | Program |
|---|---|---|
| 37.5% | (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (fma.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i (*.f64 i (*.f64 i #s(literal 1/4 binary64))))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))) | |
| 37.5% | (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (fma.f64 (*.f64 #s(literal 1/4 binary64) i) i (*.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | |
| 37.5% | (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i (fma.f64 (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)) (/.f64 #s(literal 1/4 binary64) i) #s(literal 1/4 binary64))) i)) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | |
| 37.5% | (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)))) #s(approx (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1) (fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))) | |
| 41.9% | (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) #s(approx (+ 1/4 (/ (* 1/4 (- (* 2 (+ alpha beta)) (+ alpha beta))) i)) #s(literal 1/4 binary64)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | |
| 18.0% | (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | |
| 42.5% | (*.f64 (/.f64 (fma.f64 (+.f64 alpha beta) i (fma.f64 i i (*.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) | |
| 42.5% | (*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) #s(approx (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) (fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) | |
| 42.3% | (*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (*.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 i (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))))) | |
| ▶ | 33.9% | (*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) |
| 42.5% | (*.f64 (/.f64 (fma.f64 i i (fma.f64 i (+.f64 alpha beta) (*.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) | |
| 20.7% | (*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (/.f64 #s(approx (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+.f64 alpha i)) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) | |
| 22.7% | (*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (*.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) #s(literal -1 binary64))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 #s(literal 1 binary64) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))))) | |
| 34.6% | (*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) #s(approx (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1)) #s(literal 1/4 binary64))) | |
| 26.6% | (*.f64 (/.f64 #s(approx (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (*.f64 beta (+.f64 (+.f64 alpha i) (/.f64 (*.f64 i (+.f64 alpha i)) beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) | |
| 41.8% | (*.f64 #s(approx (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) -1)) (/.f64 (*.f64 i (+.f64 beta i)) (fma.f64 (+.f64 beta (*.f64 #s(literal 2 binary64) i)) (+.f64 beta (*.f64 #s(literal 2 binary64) i)) #s(literal -1 binary64)))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) | |
| 36.7% | (*.f64 #s(approx (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) -1)) #s(literal 1/4 binary64)) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) | |
| 42.3% | (*.f64 i (*.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))))) | |
| 12.4% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (fma.f64 i (+.f64 alpha i) (*.f64 i (-.f64 (/.f64 (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (*.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))) | |
| 22.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)) | |
| 27.1% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)) | |
| ▶ | 14.5% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) |
| 13.8% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 i i)) (*.f64 beta beta))) | |
| ▶ | 11.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) |
| 21.7% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(literal 1 binary64) (*.f64 beta (/.f64 beta (*.f64 i (+.f64 i alpha)))))) | |
| 64.0% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (-.f64 #s(literal 1/16 binary64) (/.f64 (neg.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) #s(literal -1/8 binary64) (/.f64 (-.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 alpha (*.f64 beta (+.f64 alpha beta)))) i) (+.f64 (fma.f64 #s(literal 1/16 binary64) (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta))) (*.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64))))) (*.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/256 binary64)))) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 #s(literal 1/16 binary64) (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta))) (*.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64))))) (*.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/256 binary64)))) i) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64)))) i) (/.f64 (*.f64 #s(literal -1/256 binary64) (*.f64 #s(literal -4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) i)))) i)))) i))) | |
| 15.0% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) (*.f64 beta beta)) i)) | |
| 27.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))) | |
| ▶ | 22.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta))) |
| 14.6% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 beta beta)) (*.f64 i (+.f64 i alpha)))) | |
| ✓ | 74.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
| ▶ | 81.1% | #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i))) |
Compiled 2 497 to 976 computations (60.9% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) | |
| cost-diff | 0 | (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) | |
| cost-diff | 0 | (*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) | |
| cost-diff | 128 | (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))) | |
| cost-diff | 0 | (*.f64 i i) | |
| cost-diff | 0 | (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) | |
| cost-diff | 0 | (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) | |
| cost-diff | 0 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) | |
| cost-diff | 0 | (*.f64 i (+.f64 i alpha)) | |
| cost-diff | 0 | (/.f64 (*.f64 i (+.f64 i alpha)) beta) | |
| cost-diff | 0 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta))) | |
| cost-diff | 704 | (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta)) | |
| cost-diff | 0 | (*.f64 alpha i) | |
| cost-diff | 0 | #s(approx (* i (+ alpha i)) (*.f64 alpha i)) | |
| cost-diff | 0 | (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta)) | |
| cost-diff | 0 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) | |
| cost-diff | 128 | (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) | |
| cost-diff | 192 | (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)))) | |
| cost-diff | 320 | (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) | |
| cost-diff | 704 | (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) |
| 8 870× | lower-fma.f32 |
| 8 856× | lower-fma.f64 |
| 5 460× | lower-*.f32 |
| 5 424× | lower-*.f64 |
| 3 952× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 89 | 877 |
| 0 | 139 | 849 |
| 1 | 381 | 838 |
| 2 | 1338 | 799 |
| 3 | 6378 | 795 |
| 0 | 8084 | 773 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i))) |
(-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i)) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) |
#s(literal 1/16 binary64) |
(/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i) |
(*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) |
(*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) |
#s(literal 2 binary64) |
(+.f64 alpha beta) |
alpha |
beta |
i |
(/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i) |
(*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) |
#s(literal 1/256 binary64) |
(fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)))) |
(fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) |
#s(literal 4 binary64) |
(+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(*.f64 #s(literal 8 binary64) (+.f64 alpha beta)) |
#s(literal 8 binary64) |
(+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))) |
(*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) |
(/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta)) |
#s(approx (* i (+ alpha i)) (*.f64 alpha i)) |
(*.f64 alpha i) |
alpha |
i |
(*.f64 beta beta) |
beta |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta))) |
(*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta)) |
(/.f64 (*.f64 i (+.f64 i alpha)) beta) |
(*.f64 i (+.f64 i alpha)) |
i |
(+.f64 i alpha) |
alpha |
beta |
(/.f64 #s(literal 1 binary64) beta) |
#s(literal 1 binary64) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) |
(/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) |
(*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) |
(*.f64 i i) |
i |
(*.f64 (+.f64 beta i) (+.f64 beta i)) |
(+.f64 beta i) |
beta |
(*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) |
(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) |
(fma.f64 i #s(literal 2 binary64) beta) |
#s(literal 2 binary64) |
(fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) |
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) |
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) |
i |
(+.f64 i (+.f64 alpha beta)) |
(+.f64 alpha beta) |
alpha |
beta |
(*.f64 alpha beta) |
(fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) |
(fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) |
#s(literal 2 binary64) |
#s(literal -1 binary64) |
#s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)))) |
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))) |
#s(literal 1/4 binary64) |
(/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) |
(*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) |
#s(literal -1/16 binary64) |
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) |
(*.f64 i i) |
| Outputs |
|---|
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i))) |
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (fma.f64 (fma.f64 #s(literal 8 binary64) (+.f64 alpha (+.f64 beta #s(literal 1 binary64))) (fma.f64 (+.f64 alpha beta) #s(literal 24 binary64) #s(literal -8 binary64))) (/.f64 #s(literal -1/256 binary64) i) (fma.f64 (+.f64 alpha beta) (/.f64 #s(literal 1/8 binary64) i) #s(literal 1/16 binary64)))) |
(-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i)) |
(fma.f64 (fma.f64 #s(literal 8 binary64) (+.f64 alpha (+.f64 beta #s(literal 1 binary64))) (fma.f64 (+.f64 alpha beta) #s(literal 24 binary64) #s(literal -8 binary64))) (/.f64 #s(literal -1/256 binary64) i) (fma.f64 (+.f64 alpha beta) (/.f64 #s(literal 1/8 binary64) i) #s(literal 1/16 binary64))) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) |
(fma.f64 (+.f64 alpha beta) (/.f64 #s(literal 1/8 binary64) i) #s(literal 1/16 binary64)) |
#s(literal 1/16 binary64) |
(/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i) |
(/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) i) |
(*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) |
(*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) |
(*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) |
#s(literal 2 binary64) |
(+.f64 alpha beta) |
alpha |
beta |
i |
(/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i) |
(/.f64 (fma.f64 (+.f64 alpha beta) #s(literal 1/32 binary64) (fma.f64 #s(literal 1/256 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 24 binary64) #s(literal -8 binary64)) #s(literal 1/32 binary64))) i) |
(*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) |
(fma.f64 (+.f64 alpha beta) #s(literal 1/32 binary64) (fma.f64 #s(literal 1/256 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 24 binary64) #s(literal -8 binary64)) #s(literal 1/32 binary64))) |
#s(literal 1/256 binary64) |
(fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)))) |
(fma.f64 #s(literal 8 binary64) (+.f64 alpha (+.f64 beta #s(literal 1 binary64))) (fma.f64 (+.f64 alpha beta) #s(literal 24 binary64) #s(literal -8 binary64))) |
(fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) |
(fma.f64 (+.f64 alpha beta) #s(literal 12 binary64) #s(literal -4 binary64)) |
#s(literal 4 binary64) |
(+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) |
(+.f64 #s(literal -1 binary64) (+.f64 alpha beta)) |
#s(literal -1 binary64) |
(*.f64 #s(literal 8 binary64) (+.f64 alpha beta)) |
(*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) |
#s(literal 8 binary64) |
(+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))) |
(fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) #s(literal 8 binary64)) |
(*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) |
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 i alpha)) (*.f64 beta beta))) |
(/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta)) |
(/.f64 #s(approx (* i (+ alpha i)) (*.f64 i alpha)) (*.f64 beta beta)) |
#s(approx (* i (+ alpha i)) (*.f64 alpha i)) |
#s(approx (* i (+ alpha i)) (*.f64 i alpha)) |
(*.f64 alpha i) |
(*.f64 i alpha) |
alpha |
i |
(*.f64 beta beta) |
beta |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta))) |
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (/.f64 (*.f64 i (+.f64 i alpha)) (*.f64 beta beta))) |
(*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta)) |
(/.f64 (*.f64 i (+.f64 i alpha)) (*.f64 beta beta)) |
(/.f64 (*.f64 i (+.f64 i alpha)) beta) |
(*.f64 (+.f64 i alpha) (/.f64 i beta)) |
(*.f64 i (+.f64 i alpha)) |
i |
(+.f64 i alpha) |
alpha |
beta |
(/.f64 #s(literal 1 binary64) beta) |
#s(literal 1 binary64) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) |
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (/.f64 (*.f64 i (*.f64 i (*.f64 (+.f64 i beta) (+.f64 i beta)))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) |
(/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) |
(/.f64 (*.f64 i (*.f64 i (*.f64 (+.f64 i beta) (+.f64 i beta)))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) |
(*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) |
(*.f64 i (*.f64 i (*.f64 (+.f64 i beta) (+.f64 i beta)))) |
(*.f64 i i) |
i |
(*.f64 (+.f64 beta i) (+.f64 beta i)) |
(*.f64 (+.f64 i beta) (+.f64 i beta)) |
(+.f64 beta i) |
(+.f64 i beta) |
beta |
(*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) |
(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) |
(fma.f64 i #s(literal 2 binary64) beta) |
#s(literal 2 binary64) |
(fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) |
(*.f64 (/.f64 (fma.f64 i (+.f64 i alpha) (*.f64 beta (+.f64 i alpha))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (/.f64 #s(literal -1/16 binary64) (*.f64 i i))) #s(literal 1/4 binary64)))) |
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) |
(/.f64 (fma.f64 i (+.f64 i alpha) (*.f64 beta (+.f64 i alpha))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) |
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) |
(fma.f64 i (+.f64 i alpha) (*.f64 beta (+.f64 i alpha))) |
i |
(+.f64 i (+.f64 alpha beta)) |
(+.f64 alpha beta) |
alpha |
beta |
(*.f64 alpha beta) |
(fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) |
(fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) |
(fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
#s(literal 2 binary64) |
#s(literal -1 binary64) |
#s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)))) |
#s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (/.f64 #s(literal -1/16 binary64) (*.f64 i i))) #s(literal 1/4 binary64))) |
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))) |
(fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (/.f64 #s(literal -1/16 binary64) (*.f64 i i))) #s(literal 1/4 binary64)) |
#s(literal 1/4 binary64) |
(/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) |
(*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (/.f64 #s(literal -1/16 binary64) (*.f64 i i))) |
(*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) |
(*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64))) |
#s(literal -1/16 binary64) |
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) |
(*.f64 i i) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.08984375 | (*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) | |
| accuracy | 15.74780048387187 | (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) | |
| accuracy | 16.25289308675801 | #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)))) | |
| accuracy | 37.7579555123497 | (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) | |
| accuracy | 0.0703125 | (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) | |
| accuracy | 0.07421875 | (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) | |
| accuracy | 1.6495458610298008 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) | |
| accuracy | 53.187418570578934 | (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) | |
| accuracy | 0.00390625 | (*.f64 i (+.f64 i alpha)) | |
| accuracy | 3.1352828453674344 | (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta)) | |
| accuracy | 7.755555846572081 | (/.f64 (*.f64 i (+.f64 i alpha)) beta) | |
| accuracy | 46.552331073904746 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta))) | |
| accuracy | 0 | (*.f64 alpha i) | |
| accuracy | 15.734599367425485 | (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta)) | |
| accuracy | 46.552331073904746 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) | |
| accuracy | 59.34234634629779 | #s(approx (* i (+ alpha i)) (*.f64 alpha i)) | |
| accuracy | 0.21197349452482545 | (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) | |
| accuracy | 14.55303242253887 | (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i)) | |
| accuracy | 16.497107014582685 | #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i))) | |
| accuracy | 26.35487685492712 | (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)))) |
| 191.0ms | 163× | 1 | valid |
| 47.0ms | 80× | 0 | valid |
| 16.0ms | 13× | 2 | valid |
Compiled 789 to 82 computations (89.6% saved)
ival-mult: 82.0ms (42.8% of total)ival-add: 43.0ms (22.5% of total)ival-div: 36.0ms (18.8% of total)adjust: 26.0ms (13.6% of total)ival-sub: 4.0ms (2.1% of total)exact: 1.0ms (0.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ()) |
#s(alt (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)))) (patch (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)))) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (patch (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) (patch #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta)) (patch (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta)) #<representation binary64>) () ()) |
#s(alt #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (patch #s(approx (* i (+ alpha i)) (*.f64 alpha i)) #<representation binary64>) () ()) |
#s(alt (*.f64 alpha i) (patch (*.f64 alpha i) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta)) (patch (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta))) (patch #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta))) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 i (+.f64 i alpha)) beta) (patch (/.f64 (*.f64 i (+.f64 i alpha)) beta) #<representation binary64>) () ()) |
#s(alt (*.f64 i (+.f64 i alpha)) (patch (*.f64 i (+.f64 i alpha)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) (patch #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (patch (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) #<representation binary64>) () ()) |
#s(alt (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (patch (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) #<representation binary64>) () ()) |
#s(alt (*.f64 i i) (patch (*.f64 i i) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))) (patch (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) (patch (*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (patch (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (patch (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) #<representation binary64>) () ()) |
#s(alt #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i))) (patch #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i))) #<representation binary64>) () ()) |
#s(alt (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i)) (patch (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) (patch (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) #<representation binary64>) () ()) |
#s(alt (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) (patch (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)))) (patch #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)))) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) (patch (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (+ (* 4 (- beta 1)) (* 8 beta)) (taylor 0 alpha) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 4 (- beta 1)) (+ (* 8 beta) (* 12 alpha))) (taylor 0 alpha) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 4 (- beta 1)) (+ (* 8 beta) (* 12 alpha))) (taylor 0 alpha) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 4 (- beta 1)) (+ (* 8 beta) (* 12 alpha))) (taylor 0 alpha) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* 12 alpha) (taylor inf alpha) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ 12 (+ (* 4 (/ (- beta 1) alpha)) (* 8 (/ beta alpha))))) (taylor inf alpha) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ 12 (+ (* 4 (/ (- beta 1) alpha)) (* 8 (/ beta alpha))))) (taylor inf alpha) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ 12 (+ (* 4 (/ (- beta 1) alpha)) (* 8 (/ beta alpha))))) (taylor inf alpha) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* 12 alpha) (taylor -inf alpha) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* alpha (- (* -1 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) 12))) (taylor -inf alpha) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* alpha (- (* -1 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) 12))) (taylor -inf alpha) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* alpha (- (* -1 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) 12))) (taylor -inf alpha) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 4 (- alpha 1)) (* 8 alpha)) (taylor 0 beta) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 4 (- alpha 1)) (+ (* 8 alpha) (* 12 beta))) (taylor 0 beta) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 4 (- alpha 1)) (+ (* 8 alpha) (* 12 beta))) (taylor 0 beta) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 4 (- alpha 1)) (+ (* 8 alpha) (* 12 beta))) (taylor 0 beta) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* 12 beta) (taylor inf beta) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* beta (+ 12 (+ (* 4 (/ (- alpha 1) beta)) (* 8 (/ alpha beta))))) (taylor inf beta) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* beta (+ 12 (+ (* 4 (/ (- alpha 1) beta)) (* 8 (/ alpha beta))))) (taylor inf beta) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* beta (+ 12 (+ (* 4 (/ (- alpha 1) beta)) (* 8 (/ alpha beta))))) (taylor inf beta) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* 12 beta) (taylor -inf beta) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* beta (- (* -1 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) 12))) (taylor -inf beta) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* beta (- (* -1 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) 12))) (taylor -inf beta) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* beta (- (* -1 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) 12))) (taylor -inf beta) (#s(alt (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (patch (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 beta) (taylor 0 alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/8 alpha) (* 1/8 beta)) (taylor 0 alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/8 alpha) (* 1/8 beta)) (taylor 0 alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/8 alpha) (* 1/8 beta)) (taylor 0 alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 alpha) (taylor inf alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) (taylor inf alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) (taylor inf alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) (taylor inf alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 alpha) (taylor -inf alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
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#s(alt (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (taylor 0 i) (#s(alt (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) (patch (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (taylor 0 i) (#s(alt (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) (patch (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (taylor 0 i) (#s(alt (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) (patch (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (taylor 0 i) (#s(alt (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) (patch (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (taylor inf i) (#s(alt (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) (patch (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (taylor inf i) (#s(alt (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) (patch (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (taylor inf i) (#s(alt (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) (patch (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (taylor inf i) (#s(alt (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) (patch (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (taylor -inf i) (#s(alt (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) (patch (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (taylor -inf i) (#s(alt (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) (patch (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (taylor -inf i) (#s(alt (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) (patch (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (taylor -inf i) (#s(alt (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) (patch (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) #<representation binary64>) () ())) ()) |
198 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 13.0ms | alpha | @ | -inf | (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8))) |
| 5.0ms | alpha | @ | inf | (- (+ 1/16 (/ (* 1/16 (* 2 (+ alpha beta))) i)) (/ (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) i)) |
| 3.0ms | beta | @ | 0 | (/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))) |
| 3.0ms | i | @ | inf | (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) |
| 2.0ms | i | @ | 0 | (/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))) |
| 1× | egg-herbie |
| 6 422× | lower-*.f64 |
| 6 422× | lower-*.f32 |
| 5 688× | lower-fma.f64 |
| 5 688× | lower-fma.f32 |
| 4 758× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 2268 | 48093 |
| 1 | 7831 | 48075 |
| 0 | 8152 | 43795 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (* 4 (- beta 1)) (* 8 beta)) |
(+ (* 4 (- beta 1)) (+ (* 8 beta) (* 12 alpha))) |
(+ (* 4 (- beta 1)) (+ (* 8 beta) (* 12 alpha))) |
(+ (* 4 (- beta 1)) (+ (* 8 beta) (* 12 alpha))) |
(* 12 alpha) |
(* alpha (+ 12 (+ (* 4 (/ (- beta 1) alpha)) (* 8 (/ beta alpha))))) |
(* alpha (+ 12 (+ (* 4 (/ (- beta 1) alpha)) (* 8 (/ beta alpha))))) |
(* alpha (+ 12 (+ (* 4 (/ (- beta 1) alpha)) (* 8 (/ beta alpha))))) |
(* 12 alpha) |
(* -1 (* alpha (- (* -1 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) 12))) |
(* -1 (* alpha (- (* -1 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) 12))) |
(* -1 (* alpha (- (* -1 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) 12))) |
(+ (* 4 (- alpha 1)) (* 8 alpha)) |
(+ (* 4 (- alpha 1)) (+ (* 8 alpha) (* 12 beta))) |
(+ (* 4 (- alpha 1)) (+ (* 8 alpha) (* 12 beta))) |
(+ (* 4 (- alpha 1)) (+ (* 8 alpha) (* 12 beta))) |
(* 12 beta) |
(* beta (+ 12 (+ (* 4 (/ (- alpha 1) beta)) (* 8 (/ alpha beta))))) |
(* beta (+ 12 (+ (* 4 (/ (- alpha 1) beta)) (* 8 (/ alpha beta))))) |
(* beta (+ 12 (+ (* 4 (/ (- alpha 1) beta)) (* 8 (/ alpha beta))))) |
(* 12 beta) |
(* -1 (* beta (- (* -1 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) 12))) |
(* -1 (* beta (- (* -1 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) 12))) |
(* -1 (* beta (- (* -1 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) 12))) |
(* 1/8 beta) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(* 1/8 alpha) |
(* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) |
(* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) |
(* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) |
(* 1/8 alpha) |
(* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) |
(* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) |
(* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) |
(* 1/8 alpha) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(* 1/8 beta) |
(* beta (+ 1/8 (* 1/8 (/ alpha beta)))) |
(* beta (+ 1/8 (* 1/8 (/ alpha beta)))) |
(* beta (+ 1/8 (* 1/8 (/ alpha beta)))) |
(* 1/8 beta) |
(* -1 (* beta (- (* -1/8 (/ alpha beta)) 1/8))) |
(* -1 (* beta (- (* -1/8 (/ alpha beta)) 1/8))) |
(* -1 (* beta (- (* -1/8 (/ alpha beta)) 1/8))) |
(+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) |
(+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (+ (* 8 beta) (* 32 alpha)))) |
(+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (+ (* 8 beta) (* 32 alpha)))) |
(+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (+ (* 8 beta) (* 32 alpha)))) |
(* 32 alpha) |
(* alpha (+ 32 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) (+ (* 8 (/ beta alpha)) (* 8 (/ 1 alpha)))))) |
(* alpha (+ 32 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) (+ (* 8 (/ beta alpha)) (* 8 (/ 1 alpha)))))) |
(* alpha (+ 32 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) (+ (* 8 (/ beta alpha)) (* 8 (/ 1 alpha)))))) |
(* 32 alpha) |
(* -1 (* alpha (- (* -1 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)) 32))) |
(* -1 (* alpha (- (* -1 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)) 32))) |
(* -1 (* alpha (- (* -1 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)) 32))) |
(+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) |
(+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (+ (* 8 alpha) (* 32 beta)))) |
(+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (+ (* 8 alpha) (* 32 beta)))) |
(+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (+ (* 8 alpha) (* 32 beta)))) |
(* 32 beta) |
(* beta (+ 32 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) (+ (* 8 (/ alpha beta)) (* 8 (/ 1 beta)))))) |
(* beta (+ 32 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) (+ (* 8 (/ alpha beta)) (* 8 (/ 1 beta)))))) |
(* beta (+ 32 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) (+ (* 8 (/ alpha beta)) (* 8 (/ 1 beta)))))) |
(* 32 beta) |
(* -1 (* beta (- (* -1 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)) 32))) |
(* -1 (* beta (- (* -1 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)) 32))) |
(* -1 (* beta (- (* -1 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)) 32))) |
(+ 1/16 (* 1/8 (/ beta i))) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(* 1/8 (/ alpha i)) |
(* alpha (+ (* 1/8 (/ beta (* alpha i))) (+ (* 1/16 (/ 1 alpha)) (* 1/8 (/ 1 i))))) |
(* alpha (+ (* 1/8 (/ beta (* alpha i))) (+ (* 1/16 (/ 1 alpha)) (* 1/8 (/ 1 i))))) |
(* alpha (+ (* 1/8 (/ beta (* alpha i))) (+ (* 1/16 (/ 1 alpha)) (* 1/8 (/ 1 i))))) |
(* 1/8 (/ alpha i)) |
(* -1 (* alpha (- (* -1 (/ (+ 1/16 (* 1/8 (/ beta i))) alpha)) (* 1/8 (/ 1 i))))) |
(* -1 (* alpha (- (* -1 (/ (+ 1/16 (* 1/8 (/ beta i))) alpha)) (* 1/8 (/ 1 i))))) |
(* -1 (* alpha (- (* -1 (/ (+ 1/16 (* 1/8 (/ beta i))) alpha)) (* 1/8 (/ 1 i))))) |
(+ 1/16 (* 1/8 (/ alpha i))) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(* 1/8 (/ beta i)) |
(* beta (+ (* 1/8 (/ alpha (* beta i))) (+ (* 1/16 (/ 1 beta)) (* 1/8 (/ 1 i))))) |
(* beta (+ (* 1/8 (/ alpha (* beta i))) (+ (* 1/16 (/ 1 beta)) (* 1/8 (/ 1 i))))) |
(* beta (+ (* 1/8 (/ alpha (* beta i))) (+ (* 1/16 (/ 1 beta)) (* 1/8 (/ 1 i))))) |
(* 1/8 (/ beta i)) |
(* -1 (* beta (- (* -1 (/ (+ 1/16 (* 1/8 (/ alpha i))) beta)) (* 1/8 (/ 1 i))))) |
(* -1 (* beta (- (* -1 (/ (+ 1/16 (* 1/8 (/ alpha i))) beta)) (* 1/8 (/ 1 i))))) |
(* -1 (* beta (- (* -1 (/ (+ 1/16 (* 1/8 (/ alpha i))) beta)) (* 1/8 (/ 1 i))))) |
(* 1/8 (/ (+ alpha beta) i)) |
(/ (+ (* 1/16 i) (* 1/8 (+ alpha beta))) i) |
(/ (+ (* 1/16 i) (* 1/8 (+ alpha beta))) i) |
(/ (+ (* 1/16 i) (* 1/8 (+ alpha beta))) i) |
1/16 |
(+ 1/16 (* 1/8 (/ (+ alpha beta) i))) |
(+ 1/16 (* 1/8 (/ (+ alpha beta) i))) |
(+ 1/16 (* 1/8 (/ (+ alpha beta) i))) |
1/16 |
(+ 1/16 (* 1/8 (/ (+ alpha beta) i))) |
(+ 1/16 (* 1/8 (/ (+ alpha beta) i))) |
(+ 1/16 (* 1/8 (/ (+ alpha beta) i))) |
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i)) (* -1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i)))) i))) |
(+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i))))) i))) i))) |
(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) |
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(/ (* i (+ beta i)) (pow alpha 2)) |
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
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(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1))))))) alpha)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (+ (* (+ (* 4 alpha) (* 8 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (* alpha i) (pow beta 2)) |
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2)))) |
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2)))) |
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2)))) |
(/ (pow i 2) (pow beta 2)) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(/ (pow i 2) (pow beta 2)) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(/ (pow i 2) (pow beta 2)) |
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(/ (* alpha i) (pow beta 2)) |
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2))))) |
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2))))) |
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2))))) |
(/ (* alpha i) (pow beta 2)) |
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2))))))) |
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2))))))) |
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2))))))) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
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(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(* alpha i) |
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(* i (+ alpha i)) |
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(pow i 2) |
(* (pow i 2) (+ 1 (/ alpha i))) |
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(* (pow i 2) (+ 1 (/ alpha i))) |
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(* alpha i) |
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(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(* alpha i) |
(* alpha i) |
(* alpha i) |
(* alpha i) |
(* alpha i) |
(* alpha i) |
(* alpha i) |
(* alpha i) |
(* alpha i) |
(* alpha i) |
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(* alpha i) |
(* alpha i) |
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(/ (* alpha i) (pow beta 2)) |
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1/16 |
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1/16 |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(/ (* i (+ beta i)) (pow alpha 2)) |
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2)) |
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(/ (- (+ (* -1 (/ (+ (* i (* (+ beta i) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (+ (* (+ (* 4 beta) (* 8 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))))))) (* (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1)))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2)) |
(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1))))))) alpha)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (+ (* -1 (* beta (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 4 alpha) (* 8 i)))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))) (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (+ (* (+ (* 4 alpha) (* 8 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (* alpha i) beta) |
(* i (+ (/ alpha beta) (/ i beta))) |
(* i (+ (/ alpha beta) (/ i beta))) |
(* i (+ (/ alpha beta) (/ i beta))) |
(/ (pow i 2) beta) |
(* (pow i 2) (+ (/ 1 beta) (/ alpha (* beta i)))) |
(* (pow i 2) (+ (/ 1 beta) (/ alpha (* beta i)))) |
(* (pow i 2) (+ (/ 1 beta) (/ alpha (* beta i)))) |
(/ (pow i 2) beta) |
(* (pow i 2) (+ (/ 1 beta) (/ alpha (* beta i)))) |
(* (pow i 2) (+ (/ 1 beta) (/ alpha (* beta i)))) |
(* (pow i 2) (+ (/ 1 beta) (/ alpha (* beta i)))) |
(/ (pow i 2) beta) |
(+ (/ (* alpha i) beta) (/ (pow i 2) beta)) |
(+ (/ (* alpha i) beta) (/ (pow i 2) beta)) |
(+ (/ (* alpha i) beta) (/ (pow i 2) beta)) |
(/ (* alpha i) beta) |
(* alpha (+ (/ i beta) (/ (pow i 2) (* alpha beta)))) |
(* alpha (+ (/ i beta) (/ (pow i 2) (* alpha beta)))) |
(* alpha (+ (/ i beta) (/ (pow i 2) (* alpha beta)))) |
(/ (* alpha i) beta) |
(* -1 (* alpha (+ (* -1 (/ i beta)) (* -1 (/ (pow i 2) (* alpha beta)))))) |
(* -1 (* alpha (+ (* -1 (/ i beta)) (* -1 (/ (pow i 2) (* alpha beta)))))) |
(* -1 (* alpha (+ (* -1 (/ i beta)) (* -1 (/ (pow i 2) (* alpha beta)))))) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(* alpha i) |
(* i (+ alpha i)) |
(* i (+ alpha i)) |
(* i (+ alpha i)) |
(pow i 2) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(pow i 2) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(pow i 2) |
(+ (* alpha i) (pow i 2)) |
(+ (* alpha i) (pow i 2)) |
(+ (* alpha i) (pow i 2)) |
(* alpha i) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(* alpha i) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i)) (* -1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i)))) i))) |
(+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i))))) i))) i))) |
(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) |
(+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) |
(+ (* alpha (- (+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))) (- (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 4 beta) (* 8 i)))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))))) (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) |
(/ (* i (+ beta i)) (pow alpha 2)) |
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2)) |
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(/ (- (+ (* -1 (/ (+ (* i (* (+ beta i) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (+ (* (+ (* 4 beta) (* 8 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))))))) (* (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1)))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2)) |
(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1))))))) alpha)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (+ (* -1 (* beta (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 4 alpha) (* 8 i)))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))) (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (+ (* (+ (* 4 alpha) (* 8 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (pow i 2) (- (pow beta 2) 1)) |
(* (pow i 2) (+ (* -1 (* i (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1)))) |
(* (pow i 2) (+ (* i (- (* -1 (* i (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))))) (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1)))) |
(* (pow i 2) (+ (* i (- (* i (- (* -1 (* i (+ (* -1 (/ (* (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* -1 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (* 32 (/ 1 (* beta (pow (- (pow beta 2) 1) 2)))))))) (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))))) (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1)))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (pow beta 2) (pow i 2)))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
(- (+ 1/16 (+ (* -1 (/ (+ (* 1/256 (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* 2 (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))))) (pow i 3))) (* 1/16 (/ (pow beta 2) (pow i 2))))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
(- (+ 1/16 (+ (* -1 (/ (+ (* -2 (* beta (+ (* 1/256 (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* 2 (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))))))) (+ (* 1/256 (* (pow beta 2) (- (pow beta 2) 1))) (* 1/16 (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))))) (pow i 4))) (* 1/16 (/ (pow beta 2) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2))) (* 2 (/ (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))) (pow i 3)))))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (pow beta 2) (pow i 2)))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
(- (+ 1/16 (+ (* -2 (/ (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))) (pow i 3))) (+ (* 1/256 (/ (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3))) (pow i 3))) (* 1/16 (/ (pow beta 2) (pow i 2)))))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
(- (+ 1/16 (+ (* -1 (/ (- (+ (* 1/256 (/ (* (pow beta 2) (- (pow beta 2) 1)) i)) (+ (* 1/16 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))) i)) (* 2 (/ (* beta (+ (* -2 (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) (* 1/256 (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3)))))) i)))) (+ (* -2 (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) (* 1/256 (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3)))))) (pow i 3))) (* 1/16 (/ (pow beta 2) (pow i 2))))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
(* 1/4 (/ (pow i 2) (- (* 4 (pow i 2)) 1))) |
(+ (* 1/4 (/ (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (- (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2)))))) |
(+ (* 1/4 (/ (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (- (+ (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* beta (- (* 1/4 (/ 1 (- (* 4 (pow i 2)) 1))) (+ (* 1/16 (/ (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1) (pow (- (* 4 (pow i 2)) 1) 2))) (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2))))) (* (pow i 2) (- (* 4 (pow i 2)) 1)))))))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2)))))) |
(+ (* 1/4 (/ (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (- (+ (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* beta (- (+ (* -1 (* beta (+ (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/4 (/ 1 (- (* 4 (pow i 2)) 1))) (+ (* 1/16 (/ (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1) (pow (- (* 4 (pow i 2)) 1) 2))) (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2))))) (* (pow i 2) (- (* 4 (pow i 2)) 1))))))) (* (pow i 2) (- (* 4 (pow i 2)) 1)))) (+ (* 1/4 (/ (* (- (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2)))) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (* (pow i 2) (- (* 4 (pow i 2)) 1)))) (* 1/2 (/ i (pow (- (* 4 (pow i 2)) 1) 2))))))) (* 1/4 (/ 1 (- (* 4 (pow i 2)) 1)))) (+ (* 1/16 (/ (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1) (pow (- (* 4 (pow i 2)) 1) 2))) (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2))))) (* (pow i 2) (- (* 4 (pow i 2)) 1)))))))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2)))))) |
(/ (pow i 2) (pow beta 2)) |
(/ (- (+ (* 2 (/ (pow i 3) beta)) (pow i 2)) (* 8 (/ (pow i 3) beta))) (pow beta 2)) |
(/ (- (+ (* 2 (/ (pow i 3) beta)) (+ (/ (pow i 4) (pow beta 2)) (pow i 2))) (+ (* 8 (/ (* i (- (* 2 (pow i 3)) (* 8 (pow i 3)))) (pow beta 2))) (+ (* 8 (/ (pow i 3) beta)) (/ (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (pow beta 2))))) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* 8 (* i (- (pow i 4) (+ (* 8 (* i (- (* 2 (pow i 3)) (* 8 (pow i 3))))) (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))))) (+ (* (- (* 2 (pow i 3)) (* 8 (pow i 3))) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (* (pow i 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))))) (pow beta 3))) (+ (* 2 (/ (pow i 3) beta)) (+ (/ (pow i 4) (pow beta 2)) (pow i 2)))) (+ (* 8 (/ (* i (- (* 2 (pow i 3)) (* 8 (pow i 3)))) (pow beta 2))) (+ (* 8 (/ (pow i 3) beta)) (/ (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (pow beta 2))))) (pow beta 2)) |
(/ (pow i 2) (pow beta 2)) |
(/ (+ (* -1 (/ (- (* -2 (pow i 3)) (* -8 (pow i 3))) beta)) (pow i 2)) (pow beta 2)) |
(/ (+ (* -1 (/ (- (+ (* -2 (pow i 3)) (* -1 (/ (- (pow i 4) (+ (* -8 (* i (- (* -2 (pow i 3)) (* -8 (pow i 3))))) (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))) beta))) (* -8 (pow i 3))) beta)) (pow i 2)) (pow beta 2)) |
(/ (+ (* -1 (/ (- (+ (* -2 (pow i 3)) (* -1 (/ (- (+ (* -8 (/ (* i (- (pow i 4) (+ (* -8 (* i (- (* -2 (pow i 3)) (* -8 (pow i 3))))) (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))))) beta)) (+ (/ (* (- (* -2 (pow i 3)) (* -8 (pow i 3))) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) beta) (+ (/ (* (pow i 2) (+ (* -16 (pow i 3)) (* -4 (* i (- (* 4 (pow i 2)) 1))))) beta) (pow i 4)))) (+ (* -8 (* i (- (* -2 (pow i 3)) (* -8 (pow i 3))))) (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))) beta))) (* -8 (pow i 3))) beta)) (pow i 2)) (pow beta 2)) |
(* (pow beta 2) (pow i 2)) |
(* (pow i 2) (+ (* 2 (* beta i)) (pow beta 2))) |
(* (pow i 2) (+ (* i (+ i (* 2 beta))) (pow beta 2))) |
(* (pow i 2) (+ (* i (+ i (* 2 beta))) (pow beta 2))) |
(pow i 4) |
(* (pow i 4) (+ 1 (* 2 (/ beta i)))) |
(* (pow i 4) (+ 1 (+ (* 2 (/ beta i)) (/ (pow beta 2) (pow i 2))))) |
(* (pow i 4) (+ 1 (+ (* 2 (/ beta i)) (/ (pow beta 2) (pow i 2))))) |
(pow i 4) |
(* (pow i 4) (+ 1 (* 2 (/ beta i)))) |
(* (pow i 4) (+ 1 (* -1 (/ (+ (* -2 beta) (* -1 (/ (pow beta 2) i))) i)))) |
(* (pow i 4) (+ 1 (* -1 (/ (+ (* -2 beta) (* -1 (/ (pow beta 2) i))) i)))) |
(pow i 4) |
(+ (* 2 (* beta (pow i 3))) (pow i 4)) |
(+ (* beta (+ (* 2 (pow i 3)) (* beta (pow i 2)))) (pow i 4)) |
(+ (* beta (+ (* 2 (pow i 3)) (* beta (pow i 2)))) (pow i 4)) |
(* (pow beta 2) (pow i 2)) |
(* (pow beta 2) (+ (* 2 (/ (pow i 3) beta)) (pow i 2))) |
(* (pow beta 2) (+ (* 2 (/ (pow i 3) beta)) (+ (/ (pow i 4) (pow beta 2)) (pow i 2)))) |
(* (pow beta 2) (+ (* 2 (/ (pow i 3) beta)) (+ (/ (pow i 4) (pow beta 2)) (pow i 2)))) |
(* (pow beta 2) (pow i 2)) |
(* (pow beta 2) (+ (* 2 (/ (pow i 3) beta)) (pow i 2))) |
(* (pow beta 2) (+ (* -1 (/ (+ (* -2 (pow i 3)) (* -1 (/ (pow i 4) beta))) beta)) (pow i 2))) |
(* (pow beta 2) (+ (* -1 (/ (+ (* -2 (pow i 3)) (* -1 (/ (pow i 4) beta))) beta)) (pow i 2))) |
(pow i 2) |
(pow i 2) |
(pow i 2) |
(pow i 2) |
(pow i 2) |
(pow i 2) |
(pow i 2) |
(pow i 2) |
(pow i 2) |
(pow i 2) |
(pow i 2) |
(pow i 2) |
(+ 1/4 (* -1/16 (/ (pow beta 2) (pow i 2)))) |
(+ 1/4 (+ (* -1/8 (/ (* alpha beta) (pow i 2))) (* -1/16 (/ (pow beta 2) (pow i 2))))) |
(+ 1/4 (+ (* -1/16 (/ (pow beta 2) (pow i 2))) (* alpha (+ (* -1/8 (/ beta (pow i 2))) (* -1/16 (/ alpha (pow i 2))))))) |
(+ 1/4 (+ (* -1/16 (/ (pow beta 2) (pow i 2))) (* alpha (+ (* -1/8 (/ beta (pow i 2))) (* -1/16 (/ alpha (pow i 2))))))) |
(* -1/16 (/ (pow alpha 2) (pow i 2))) |
(* (pow alpha 2) (- (* -1/8 (/ beta (* alpha (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow alpha 2) (- (+ (* -1/8 (/ beta (* alpha (pow i 2)))) (+ (* -1/16 (/ (pow beta 2) (* (pow alpha 2) (pow i 2)))) (/ 1/4 (pow alpha 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow alpha 2) (- (+ (* -1/8 (/ beta (* alpha (pow i 2)))) (+ (* -1/16 (/ (pow beta 2) (* (pow alpha 2) (pow i 2)))) (/ 1/4 (pow alpha 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(* -1/16 (/ (pow alpha 2) (pow i 2))) |
(* (pow alpha 2) (- (* -1/8 (/ beta (* alpha (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ (+ 1/4 (* -1/16 (/ (pow beta 2) (pow i 2)))) alpha)) (* 1/8 (/ beta (pow i 2)))) alpha)) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ (+ 1/4 (* -1/16 (/ (pow beta 2) (pow i 2)))) alpha)) (* 1/8 (/ beta (pow i 2)))) alpha)) (* 1/16 (/ 1 (pow i 2))))) |
(+ 1/4 (* -1/16 (/ (pow alpha 2) (pow i 2)))) |
(+ 1/4 (+ (* -1/8 (/ (* alpha beta) (pow i 2))) (* -1/16 (/ (pow alpha 2) (pow i 2))))) |
(+ 1/4 (+ (* -1/16 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1/8 (/ alpha (pow i 2))) (* -1/16 (/ beta (pow i 2))))))) |
(+ 1/4 (+ (* -1/16 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1/8 (/ alpha (pow i 2))) (* -1/16 (/ beta (pow i 2))))))) |
(* -1/16 (/ (pow beta 2) (pow i 2))) |
(* (pow beta 2) (- (* -1/8 (/ alpha (* beta (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow beta 2) (- (+ (* -1/8 (/ alpha (* beta (pow i 2)))) (+ (* -1/16 (/ (pow alpha 2) (* (pow beta 2) (pow i 2)))) (/ 1/4 (pow beta 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow beta 2) (- (+ (* -1/8 (/ alpha (* beta (pow i 2)))) (+ (* -1/16 (/ (pow alpha 2) (* (pow beta 2) (pow i 2)))) (/ 1/4 (pow beta 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(* -1/16 (/ (pow beta 2) (pow i 2))) |
(* (pow beta 2) (- (* -1/8 (/ alpha (* beta (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow beta 2) (- (* -1 (/ (+ (* -1 (/ (+ 1/4 (* -1/16 (/ (pow alpha 2) (pow i 2)))) beta)) (* 1/8 (/ alpha (pow i 2)))) beta)) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow beta 2) (- (* -1 (/ (+ (* -1 (/ (+ 1/4 (* -1/16 (/ (pow alpha 2) (pow i 2)))) beta)) (* 1/8 (/ alpha (pow i 2)))) beta)) (* 1/16 (/ 1 (pow i 2))))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/ (+ (* -1/16 (pow (+ alpha beta) 2)) (* 1/4 (pow i 2))) (pow i 2)) |
(/ (+ (* -1/16 (pow (+ alpha beta) 2)) (* 1/4 (pow i 2))) (pow i 2)) |
(/ (+ (* -1/16 (pow (+ alpha beta) 2)) (* 1/4 (pow i 2))) (pow i 2)) |
1/4 |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
1/4 |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i)) (* -1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i)))) i))) |
(+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i))))) i))) i))) |
(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) |
(+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) |
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(/ (* i (+ beta i)) (pow alpha 2)) |
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2)) |
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
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(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (+ (* (+ (* 4 alpha) (* 8 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (* alpha beta) (- (pow (+ alpha beta) 2) 1)) |
(+ (* i (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(+ (* i (- (+ (* i (- (/ 1 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1)))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(+ (* i (- (+ (* i (- (+ (* -1 (* i (+ (* 4 (/ (* (+ alpha beta) (- (/ 1 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (- (pow (+ alpha beta) 2) 1)))))) (/ 1 (- (pow (+ alpha beta) 2) 1))) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1)))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1))) |
1/4 |
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
(- (+ 1/4 (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
(- (+ 1/4 (+ (* -1 (/ (+ (* -1 (* (pow (+ alpha beta) 2) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))))) (* 1/4 (* (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))) (- (pow (+ alpha beta) 2) 1)))) (pow i 4))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (+ (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3)))) |
1/4 |
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
(- (+ 1/4 (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
(- (+ 1/4 (+ (* -1 (/ (- (+ (* -1 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) i)) (* 1/4 (/ (* (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))) (- (pow (+ alpha beta) 2) 1)) i))) (* -1 (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
(/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1)) |
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(/ (+ beta i) alpha) |
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(* -1 (/ (+ (* -1 beta) (* -1 i)) alpha)) |
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(/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1)) |
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(/ (+ alpha i) beta) |
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(* -1 (/ (+ (* -1 alpha) (* -1 i)) beta)) |
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(* alpha beta) |
(+ (* alpha beta) (* i (+ alpha beta))) |
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(+ (* alpha beta) (* i (+ alpha (+ beta i)))) |
(pow i 2) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i)))) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2)))))) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2)))))) |
(pow i 2) |
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(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i)))) |
(* i (+ beta i)) |
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(* alpha (+ beta i)) |
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(* i (+ alpha i)) |
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(/ (* alpha (* beta i)) (* (+ 1 (+ alpha beta)) (* (+ alpha beta) (- (+ alpha beta) 1)))) |
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1/16 |
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1/16 |
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(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (+ (* -1 (+ 1 (+ alpha (* 2 i)))) (* -1 (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1))))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (+ (* -1 (+ (* -2 (* (+ alpha (* 2 i)) (- (+ alpha (* 2 i)) 1))) (* -1 (pow (+ alpha (* 2 i)) 2)))) (* (+ 1 (+ alpha (* 2 i))) (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1)))))) (* (+ (* -1 (+ 1 (+ alpha (* 2 i)))) (* -1 (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (+ (* -1 (+ 1 (+ alpha (* 2 i)))) (* -1 (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1)))))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (+ (* -1 (+ 1 (+ alpha (* 2 i)))) (* -1 (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1))))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* i (* (+ (* -1 alpha) (* -1 i)) (+ (* -1 (* (pow (+ alpha (* 2 i)) 2) (- (+ alpha (* 2 i)) 1))) (* (+ 1 (+ alpha (* 2 i))) (+ (* -2 (* (+ alpha (* 2 i)) (- (+ alpha (* 2 i)) 1))) (* -1 (pow (+ alpha (* 2 i)) 2))))))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (+ (/ (* (+ (* -1 (+ 1 (+ alpha (* 2 i)))) (* -1 (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1))) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (+ (* -1 (+ (* -2 (* (+ alpha (* 2 i)) (- (+ alpha (* 2 i)) 1))) (* -1 (pow (+ alpha (* 2 i)) 2)))) (* (+ 1 (+ alpha (* 2 i))) (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1)))))) (* (+ (* -1 (+ 1 (+ alpha (* 2 i)))) (* -1 (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (+ (* -1 (+ 1 (+ alpha (* 2 i)))) (* -1 (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1))))))))))) beta) (/ (* (+ (* -1 (+ (* -2 (* (+ alpha (* 2 i)) (- (+ alpha (* 2 i)) 1))) (* -1 (pow (+ alpha (* 2 i)) 2)))) (* (+ 1 (+ alpha (* 2 i))) (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (+ (* -1 (+ 1 (+ alpha (* 2 i)))) (* -1 (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1)))))))) beta)))) (+ (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (+ (* -1 (+ (* -2 (* (+ alpha (* 2 i)) (- (+ alpha (* 2 i)) 1))) (* -1 (pow (+ alpha (* 2 i)) 2)))) (* (+ 1 (+ alpha (* 2 i))) (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1)))))) (* (+ (* -1 (+ 1 (+ alpha (* 2 i)))) (* -1 (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (+ (* -1 (+ 1 (+ alpha (* 2 i)))) (* -1 (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1)))))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (+ (* -1 (+ 1 (+ alpha (* 2 i)))) (* -1 (- (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 1))))))) beta))) (pow beta 2)) |
(- (+ 1/16 (* 1/8 (/ beta i))) (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) i))) |
(- (+ 1/16 (* 1/8 (/ beta i))) (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) i))) |
(- (+ 1/16 (* 1/8 (/ beta i))) (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) i))) |
(- (+ 1/16 (* 1/8 (/ beta i))) (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) i))) |
(- (+ 1/16 (* 1/8 (/ beta i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))))) |
(- (+ 1/16 (* 1/8 (/ beta i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))))) |
(- (+ 1/16 (* 1/8 (/ beta i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))))) |
(- (+ 1/16 (* 1/8 (/ beta i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))))) |
(- (+ 1/16 (* 1/8 (/ beta i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))))) |
(- (+ 1/16 (* 1/8 (/ beta i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))))) |
(- (+ 1/16 (* 1/8 (/ beta i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))))) |
(- (+ 1/16 (* 1/8 (/ beta i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))))) |
(- (+ 1/16 (* 1/8 (/ alpha i))) (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) i))) |
(- (+ 1/16 (* 1/8 (/ alpha i))) (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) i))) |
(- (+ 1/16 (* 1/8 (/ alpha i))) (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) i))) |
(- (+ 1/16 (* 1/8 (/ alpha i))) (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) i))) |
(- (+ 1/16 (* 1/8 (/ alpha i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))))) |
(- (+ 1/16 (* 1/8 (/ alpha i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))))) |
(- (+ 1/16 (* 1/8 (/ alpha i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))))) |
(- (+ 1/16 (* 1/8 (/ alpha i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))))) |
(- (+ 1/16 (* 1/8 (/ alpha i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))))) |
(- (+ 1/16 (* 1/8 (/ alpha i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))))) |
(- (+ 1/16 (* 1/8 (/ alpha i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))))) |
(- (+ 1/16 (* 1/8 (/ alpha i))) (* 1/256 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))))) |
(/ (- (* 1/8 (+ alpha beta)) (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))))) i) |
(/ (- (+ (* 1/16 i) (* 1/8 (+ alpha beta))) (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))))) i) |
(/ (- (+ (* 1/16 i) (* 1/8 (+ alpha beta))) (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))))) i) |
(/ (- (+ (* 1/16 i) (* 1/8 (+ alpha beta))) (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))))) i) |
1/16 |
(- (+ 1/16 (* 1/8 (/ (+ alpha beta) i))) (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i))) |
(- (+ 1/16 (* 1/8 (/ (+ alpha beta) i))) (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i))) |
(- (+ 1/16 (* 1/8 (/ (+ alpha beta) i))) (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i))) |
1/16 |
(+ 1/16 (* -1 (/ (- (* -1/8 (+ alpha beta)) (* -1/256 (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))))) i))) |
(+ 1/16 (* -1 (/ (- (* -1/8 (+ alpha beta)) (* -1/256 (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))))) i))) |
(+ 1/16 (* -1 (/ (- (* -1/8 (+ alpha beta)) (* -1/256 (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))))) i))) |
(* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta)))) |
(+ (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta)))) (* 1/8 alpha)) |
(+ (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta)))) (* 1/8 alpha)) |
(+ (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta)))) (* 1/8 alpha)) |
(* 1/8 alpha) |
(* alpha (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)))) |
(* alpha (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)))) |
(* alpha (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)))) |
(* 1/8 alpha) |
(* -1 (* alpha (- (* -1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)) 1/8))) |
(* -1 (* alpha (- (* -1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)) 1/8))) |
(* -1 (* alpha (- (* -1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)) 1/8))) |
(* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha)))) |
(+ (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha)))) (* 1/8 beta)) |
(+ (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha)))) (* 1/8 beta)) |
(+ (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha)))) (* 1/8 beta)) |
(* 1/8 beta) |
(* beta (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)))) |
(* beta (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)))) |
(* beta (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)))) |
(* 1/8 beta) |
(* -1 (* beta (- (* -1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)) 1/8))) |
(* -1 (* beta (- (* -1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)) 1/8))) |
(* -1 (* beta (- (* -1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)) 1/8))) |
(* (pow beta 2) (- (pow beta 2) 1)) |
(+ (* i (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* (pow beta 2) (- (pow beta 2) 1))) |
(+ (* i (+ (* 4 (* beta (- (pow beta 2) 1))) (+ (* 4 (pow beta 3)) (* i (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) (* (pow beta 2) (- (pow beta 2) 1))) |
(+ (* i (+ (* 4 (* beta (- (pow beta 2) 1))) (+ (* 4 (pow beta 3)) (* i (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (+ (* 16 (pow beta 2)) (* 32 (* beta i))))))))) (* (pow beta 2) (- (pow beta 2) 1))) |
(* 16 (pow i 4)) |
(* (pow i 4) (+ 16 (* 32 (/ beta i)))) |
(* (pow i 4) (+ 16 (+ (* 4 (/ (- (pow beta 2) 1) (pow i 2))) (+ (* 4 (/ (pow beta 2) (pow i 2))) (+ (* 16 (/ (pow beta 2) (pow i 2))) (* 32 (/ beta i))))))) |
(* (pow i 4) (+ 16 (+ (* 4 (/ (* beta (- (pow beta 2) 1)) (pow i 3))) (+ (* 4 (/ (- (pow beta 2) 1) (pow i 2))) (+ (* 4 (/ (pow beta 2) (pow i 2))) (+ (* 4 (/ (pow beta 3) (pow i 3))) (+ (* 16 (/ (pow beta 2) (pow i 2))) (* 32 (/ beta i))))))))) |
(* 16 (pow i 4)) |
(* (pow i 4) (+ 16 (* 32 (/ beta i)))) |
(* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 beta) (* -1 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) i))) i)))) |
(* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 beta) (* -1 (/ (+ (* -1 (/ (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3))) i)) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))) i))) i)))) |
(* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) |
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))))) |
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (+ (* 16 (pow i 3)) (* beta (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))))) |
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (+ (* 16 (pow i 3)) (* beta (- (+ (* 8 (* beta i)) (+ (* 8 (pow i 2)) (* 16 (pow i 2)))) 1)))))) |
(pow beta 4) |
(* (pow beta 4) (+ 1 (* 8 (/ i beta)))) |
(* (pow beta 4) (- (+ 1 (+ (* 8 (/ i beta)) (+ (* 8 (/ (pow i 2) (pow beta 2))) (* 16 (/ (pow i 2) (pow beta 2)))))) (/ 1 (pow beta 2)))) |
(* (pow beta 4) (- (+ 1 (+ (* 4 (/ (* i (- (* 4 (pow i 2)) 1)) (pow beta 3))) (+ (* 8 (/ i beta)) (+ (* 8 (/ (pow i 2) (pow beta 2))) (+ (* 16 (/ (pow i 2) (pow beta 2))) (* 16 (/ (pow i 3) (pow beta 3)))))))) (/ 1 (pow beta 2)))) |
(pow beta 4) |
(* (pow beta 4) (+ 1 (* 8 (/ i beta)))) |
(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -8 i) (* -1 (/ (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1) beta))) beta)))) |
(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -8 i) (* -1 (/ (- (+ (* -1 (/ (+ (* -16 (pow i 3)) (* -4 (* i (- (* 4 (pow i 2)) 1)))) beta)) (+ (* 8 (pow i 2)) (* 16 (pow i 2)))) 1) beta))) beta)))) |
(/ i (+ alpha beta)) |
(* i (+ (* -3 (/ i (pow (+ alpha beta) 2))) (/ 1 (+ alpha beta)))) |
(* i (+ (* i (- (* 8 (/ i (pow (+ alpha beta) 3))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta)))) |
(* i (+ (* i (- (* i (+ (* -20 (/ i (pow (+ alpha beta) 4))) (* 8 (/ 1 (pow (+ alpha beta) 3))))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta)))) |
1/4 |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(- (+ 1/4 (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(- (+ 1/4 (* -1 (/ (+ (* -1/64 (pow (+ alpha beta) 4)) (* 1/16 (pow (+ alpha beta) 4))) (pow i 4)))) (+ (* -1/16 (/ (pow (+ alpha beta) 3) (pow i 3))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))) |
1/4 |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(+ 1/4 (+ (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3))))) |
(+ 1/4 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (pow (+ alpha beta) 4)) (* 1/64 (pow (+ alpha beta) 4))) i)) (* -1/16 (pow (+ alpha beta) 3))) (pow i 3))) (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) |
(+ (* alpha (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) |
(+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) |
(+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 6)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)))) (pow (+ beta (* 2 i)) 2))) (/ i (pow (+ beta (* 2 i)) 4))))) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) |
(/ i alpha) |
(/ (- (+ i (/ (* i (+ beta i)) alpha)) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
(/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha))) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
(/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 3))) (/ (* i (+ beta i)) alpha))) (+ (/ (* i (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* i (pow (+ beta (* 2 i)) 2)) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha) |
(/ i alpha) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -1 (/ (* i (pow (+ beta (* 2 i)) 2)) alpha)) (* i (+ beta i)))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ beta (* 2 i)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (* i (+ beta i))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha)) |
(/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) |
(+ (* beta (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) |
(+ (* beta (- (+ (* -1 (* beta (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2))))) (/ i (pow (+ alpha (* 2 i)) 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) |
(+ (* beta (- (+ (* beta (- (* beta (- (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 6)) (+ (* -1 (/ (* (+ (* 2 alpha) (* 4 i)) (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)))) (pow (+ alpha (* 2 i)) 2))) (/ i (pow (+ alpha (* 2 i)) 4))))) (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2))))) (/ i (pow (+ alpha (* 2 i)) 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) |
(/ i beta) |
(/ (- (+ i (/ (* i (+ alpha i)) beta)) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta) |
(/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta))) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta) |
(/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 3))) (/ (* i (+ alpha i)) beta))) (+ (/ (* i (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* i (pow (+ alpha (* 2 i)) 2)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta) |
(/ i beta) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -1 (/ (* i (pow (+ alpha (* 2 i)) 2)) beta)) (* i (+ alpha i)))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ alpha (* 2 i)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (* i (+ alpha i))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta)) |
(* -1/16 (/ (pow beta 2) (pow i 2))) |
(+ (* -1/8 (/ (* alpha beta) (pow i 2))) (* -1/16 (/ (pow beta 2) (pow i 2)))) |
(+ (* -1/16 (/ (pow beta 2) (pow i 2))) (* alpha (+ (* -1/8 (/ beta (pow i 2))) (* -1/16 (/ alpha (pow i 2)))))) |
(+ (* -1/16 (/ (pow beta 2) (pow i 2))) (* alpha (+ (* -1/8 (/ beta (pow i 2))) (* -1/16 (/ alpha (pow i 2)))))) |
(* -1/16 (/ (pow alpha 2) (pow i 2))) |
(* (pow alpha 2) (- (* -1/8 (/ beta (* alpha (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow alpha 2) (- (+ (* -1/8 (/ beta (* alpha (pow i 2)))) (* -1/16 (/ (pow beta 2) (* (pow alpha 2) (pow i 2))))) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow alpha 2) (- (+ (* -1/8 (/ beta (* alpha (pow i 2)))) (* -1/16 (/ (pow beta 2) (* (pow alpha 2) (pow i 2))))) (* 1/16 (/ 1 (pow i 2))))) |
(* -1/16 (/ (pow alpha 2) (pow i 2))) |
(* (pow alpha 2) (- (* -1/8 (/ beta (* alpha (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow alpha 2) (- (* -1 (/ (+ (* 1/16 (/ (pow beta 2) (* alpha (pow i 2)))) (* 1/8 (/ beta (pow i 2)))) alpha)) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow alpha 2) (- (* -1 (/ (+ (* 1/16 (/ (pow beta 2) (* alpha (pow i 2)))) (* 1/8 (/ beta (pow i 2)))) alpha)) (* 1/16 (/ 1 (pow i 2))))) |
(* -1/16 (/ (pow alpha 2) (pow i 2))) |
(+ (* -1/8 (/ (* alpha beta) (pow i 2))) (* -1/16 (/ (pow alpha 2) (pow i 2)))) |
(+ (* -1/16 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1/8 (/ alpha (pow i 2))) (* -1/16 (/ beta (pow i 2)))))) |
(+ (* -1/16 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1/8 (/ alpha (pow i 2))) (* -1/16 (/ beta (pow i 2)))))) |
(* -1/16 (/ (pow beta 2) (pow i 2))) |
(* (pow beta 2) (- (* -1/8 (/ alpha (* beta (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow beta 2) (- (+ (* -1/8 (/ alpha (* beta (pow i 2)))) (* -1/16 (/ (pow alpha 2) (* (pow beta 2) (pow i 2))))) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow beta 2) (- (+ (* -1/8 (/ alpha (* beta (pow i 2)))) (* -1/16 (/ (pow alpha 2) (* (pow beta 2) (pow i 2))))) (* 1/16 (/ 1 (pow i 2))))) |
(* -1/16 (/ (pow beta 2) (pow i 2))) |
(* (pow beta 2) (- (* -1/8 (/ alpha (* beta (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow beta 2) (- (* -1 (/ (+ (* 1/16 (/ (pow alpha 2) (* beta (pow i 2)))) (* 1/8 (/ alpha (pow i 2)))) beta)) (* 1/16 (/ 1 (pow i 2))))) |
(* (pow beta 2) (- (* -1 (/ (+ (* 1/16 (/ (pow alpha 2) (* beta (pow i 2)))) (* 1/8 (/ alpha (pow i 2)))) beta)) (* 1/16 (/ 1 (pow i 2))))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
| Outputs |
|---|
(+ (* 4 (- beta 1)) (* 8 beta)) |
(fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) |
(+ (* 4 (- beta 1)) (+ (* 8 beta) (* 12 alpha))) |
(fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (fma.f64 beta #s(literal 8 binary64) (*.f64 #s(literal 12 binary64) alpha))) |
(+ (* 4 (- beta 1)) (+ (* 8 beta) (* 12 alpha))) |
(fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (fma.f64 beta #s(literal 8 binary64) (*.f64 #s(literal 12 binary64) alpha))) |
(+ (* 4 (- beta 1)) (+ (* 8 beta) (* 12 alpha))) |
(fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (fma.f64 beta #s(literal 8 binary64) (*.f64 #s(literal 12 binary64) alpha))) |
(* 12 alpha) |
(*.f64 #s(literal 12 binary64) alpha) |
(* alpha (+ 12 (+ (* 4 (/ (- beta 1) alpha)) (* 8 (/ beta alpha))))) |
(*.f64 alpha (+.f64 #s(literal 12 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 beta #s(literal -1 binary64)) alpha) (*.f64 #s(literal 8 binary64) (/.f64 beta alpha))))) |
(* alpha (+ 12 (+ (* 4 (/ (- beta 1) alpha)) (* 8 (/ beta alpha))))) |
(*.f64 alpha (+.f64 #s(literal 12 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 beta #s(literal -1 binary64)) alpha) (*.f64 #s(literal 8 binary64) (/.f64 beta alpha))))) |
(* alpha (+ 12 (+ (* 4 (/ (- beta 1) alpha)) (* 8 (/ beta alpha))))) |
(*.f64 alpha (+.f64 #s(literal 12 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 beta #s(literal -1 binary64)) alpha) (*.f64 #s(literal 8 binary64) (/.f64 beta alpha))))) |
(* 12 alpha) |
(*.f64 #s(literal 12 binary64) alpha) |
(* -1 (* alpha (- (* -1 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) 12))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) alpha)) #s(literal -12 binary64))) |
(* -1 (* alpha (- (* -1 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) 12))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) alpha)) #s(literal -12 binary64))) |
(* -1 (* alpha (- (* -1 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) 12))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) alpha)) #s(literal -12 binary64))) |
(+ (* 4 (- alpha 1)) (* 8 alpha)) |
(fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) |
(+ (* 4 (- alpha 1)) (+ (* 8 alpha) (* 12 beta))) |
(fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (fma.f64 beta #s(literal 12 binary64) (*.f64 #s(literal 8 binary64) alpha))) |
(+ (* 4 (- alpha 1)) (+ (* 8 alpha) (* 12 beta))) |
(fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (fma.f64 beta #s(literal 12 binary64) (*.f64 #s(literal 8 binary64) alpha))) |
(+ (* 4 (- alpha 1)) (+ (* 8 alpha) (* 12 beta))) |
(fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (fma.f64 beta #s(literal 12 binary64) (*.f64 #s(literal 8 binary64) alpha))) |
(* 12 beta) |
(*.f64 beta #s(literal 12 binary64)) |
(* beta (+ 12 (+ (* 4 (/ (- alpha 1) beta)) (* 8 (/ alpha beta))))) |
(*.f64 beta (+.f64 #s(literal 12 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha #s(literal -1 binary64)) beta) (/.f64 (*.f64 #s(literal 8 binary64) alpha) beta)))) |
(* beta (+ 12 (+ (* 4 (/ (- alpha 1) beta)) (* 8 (/ alpha beta))))) |
(*.f64 beta (+.f64 #s(literal 12 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha #s(literal -1 binary64)) beta) (/.f64 (*.f64 #s(literal 8 binary64) alpha) beta)))) |
(* beta (+ 12 (+ (* 4 (/ (- alpha 1) beta)) (* 8 (/ alpha beta))))) |
(*.f64 beta (+.f64 #s(literal 12 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha #s(literal -1 binary64)) beta) (/.f64 (*.f64 #s(literal 8 binary64) alpha) beta)))) |
(* 12 beta) |
(*.f64 beta #s(literal 12 binary64)) |
(* -1 (* beta (- (* -1 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) 12))) |
(*.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) beta)) #s(literal -12 binary64))) |
(* -1 (* beta (- (* -1 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) 12))) |
(*.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) beta)) #s(literal -12 binary64))) |
(* -1 (* beta (- (* -1 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) 12))) |
(*.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) beta)) #s(literal -12 binary64))) |
(* 1/8 beta) |
(*.f64 beta #s(literal 1/8 binary64)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 beta alpha)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 beta alpha)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 beta alpha)) |
(* 1/8 alpha) |
(*.f64 alpha #s(literal 1/8 binary64)) |
(* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) |
(*.f64 alpha (fma.f64 (/.f64 beta alpha) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) |
(* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) |
(*.f64 alpha (fma.f64 (/.f64 beta alpha) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) |
(* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) |
(*.f64 alpha (fma.f64 (/.f64 beta alpha) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) |
(* 1/8 alpha) |
(*.f64 alpha #s(literal 1/8 binary64)) |
(* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) |
(*.f64 (neg.f64 alpha) (fma.f64 (/.f64 beta alpha) #s(literal -1/8 binary64) #s(literal -1/8 binary64))) |
(* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) |
(*.f64 (neg.f64 alpha) (fma.f64 (/.f64 beta alpha) #s(literal -1/8 binary64) #s(literal -1/8 binary64))) |
(* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) |
(*.f64 (neg.f64 alpha) (fma.f64 (/.f64 beta alpha) #s(literal -1/8 binary64) #s(literal -1/8 binary64))) |
(* 1/8 alpha) |
(*.f64 alpha #s(literal 1/8 binary64)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 beta alpha)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 beta alpha)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 beta alpha)) |
(* 1/8 beta) |
(*.f64 beta #s(literal 1/8 binary64)) |
(* beta (+ 1/8 (* 1/8 (/ alpha beta)))) |
(*.f64 beta (fma.f64 (/.f64 alpha beta) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) |
(* beta (+ 1/8 (* 1/8 (/ alpha beta)))) |
(*.f64 beta (fma.f64 (/.f64 alpha beta) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) |
(* beta (+ 1/8 (* 1/8 (/ alpha beta)))) |
(*.f64 beta (fma.f64 (/.f64 alpha beta) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) |
(* 1/8 beta) |
(*.f64 beta #s(literal 1/8 binary64)) |
(* -1 (* beta (- (* -1/8 (/ alpha beta)) 1/8))) |
(neg.f64 (*.f64 beta (fma.f64 (/.f64 alpha beta) #s(literal -1/8 binary64) #s(literal -1/8 binary64)))) |
(* -1 (* beta (- (* -1/8 (/ alpha beta)) 1/8))) |
(neg.f64 (*.f64 beta (fma.f64 (/.f64 alpha beta) #s(literal -1/8 binary64) #s(literal -1/8 binary64)))) |
(* -1 (* beta (- (* -1/8 (/ alpha beta)) 1/8))) |
(neg.f64 (*.f64 beta (fma.f64 (/.f64 alpha beta) #s(literal -1/8 binary64) #s(literal -1/8 binary64)))) |
(+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) |
(+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) #s(literal 2 binary64) (*.f64 beta #s(literal 8 binary64)))) |
(+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (+ (* 8 beta) (* 32 alpha)))) |
(+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) #s(literal 2 binary64) (fma.f64 beta #s(literal 8 binary64) (*.f64 alpha #s(literal 32 binary64))))) |
(+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (+ (* 8 beta) (* 32 alpha)))) |
(+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) #s(literal 2 binary64) (fma.f64 beta #s(literal 8 binary64) (*.f64 alpha #s(literal 32 binary64))))) |
(+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (+ (* 8 beta) (* 32 alpha)))) |
(+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) #s(literal 2 binary64) (fma.f64 beta #s(literal 8 binary64) (*.f64 alpha #s(literal 32 binary64))))) |
(* 32 alpha) |
(*.f64 alpha #s(literal 32 binary64)) |
(* alpha (+ 32 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) (+ (* 8 (/ beta alpha)) (* 8 (/ 1 alpha)))))) |
(*.f64 alpha (+.f64 #s(literal 32 binary64) (fma.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) alpha) #s(literal 2 binary64) (fma.f64 #s(literal 8 binary64) (/.f64 beta alpha) (/.f64 #s(literal 8 binary64) alpha))))) |
(* alpha (+ 32 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) (+ (* 8 (/ beta alpha)) (* 8 (/ 1 alpha)))))) |
(*.f64 alpha (+.f64 #s(literal 32 binary64) (fma.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) alpha) #s(literal 2 binary64) (fma.f64 #s(literal 8 binary64) (/.f64 beta alpha) (/.f64 #s(literal 8 binary64) alpha))))) |
(* alpha (+ 32 (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) alpha)) (+ (* 8 (/ beta alpha)) (* 8 (/ 1 alpha)))))) |
(*.f64 alpha (+.f64 #s(literal 32 binary64) (fma.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) alpha) #s(literal 2 binary64) (fma.f64 #s(literal 8 binary64) (/.f64 beta alpha) (/.f64 #s(literal 8 binary64) alpha))))) |
(* 32 alpha) |
(*.f64 alpha #s(literal 32 binary64)) |
(* -1 (* alpha (- (* -1 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)) 32))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 (+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) #s(literal 2 binary64) (*.f64 beta #s(literal 8 binary64)))) alpha)) #s(literal -32 binary64))) |
(* -1 (* alpha (- (* -1 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)) 32))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 (+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) #s(literal 2 binary64) (*.f64 beta #s(literal 8 binary64)))) alpha)) #s(literal -32 binary64))) |
(* -1 (* alpha (- (* -1 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)) 32))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 (+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 beta #s(literal -1 binary64)) (*.f64 beta #s(literal 8 binary64))) #s(literal 2 binary64) (*.f64 beta #s(literal 8 binary64)))) alpha)) #s(literal -32 binary64))) |
(+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) |
(+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) #s(literal 2 binary64) (*.f64 #s(literal 8 binary64) alpha))) |
(+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (+ (* 8 alpha) (* 32 beta)))) |
(+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) #s(literal 2 binary64) (fma.f64 #s(literal 8 binary64) alpha (*.f64 beta #s(literal 32 binary64))))) |
(+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (+ (* 8 alpha) (* 32 beta)))) |
(+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) #s(literal 2 binary64) (fma.f64 #s(literal 8 binary64) alpha (*.f64 beta #s(literal 32 binary64))))) |
(+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (+ (* 8 alpha) (* 32 beta)))) |
(+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) #s(literal 2 binary64) (fma.f64 #s(literal 8 binary64) alpha (*.f64 beta #s(literal 32 binary64))))) |
(* 32 beta) |
(*.f64 beta #s(literal 32 binary64)) |
(* beta (+ 32 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) (+ (* 8 (/ alpha beta)) (* 8 (/ 1 beta)))))) |
(*.f64 beta (+.f64 #s(literal 32 binary64) (fma.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) beta) #s(literal 2 binary64) (fma.f64 #s(literal 8 binary64) (/.f64 alpha beta) (/.f64 #s(literal 8 binary64) beta))))) |
(* beta (+ 32 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) (+ (* 8 (/ alpha beta)) (* 8 (/ 1 beta)))))) |
(*.f64 beta (+.f64 #s(literal 32 binary64) (fma.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) beta) #s(literal 2 binary64) (fma.f64 #s(literal 8 binary64) (/.f64 alpha beta) (/.f64 #s(literal 8 binary64) beta))))) |
(* beta (+ 32 (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) beta)) (+ (* 8 (/ alpha beta)) (* 8 (/ 1 beta)))))) |
(*.f64 beta (+.f64 #s(literal 32 binary64) (fma.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) beta) #s(literal 2 binary64) (fma.f64 #s(literal 8 binary64) (/.f64 alpha beta) (/.f64 #s(literal 8 binary64) beta))))) |
(* 32 beta) |
(*.f64 beta #s(literal 32 binary64)) |
(* -1 (* beta (- (* -1 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)) 32))) |
(*.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 (+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) #s(literal 2 binary64) (*.f64 #s(literal 8 binary64) alpha))) beta)) #s(literal -32 binary64))) |
(* -1 (* beta (- (* -1 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)) 32))) |
(*.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 (+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) #s(literal 2 binary64) (*.f64 #s(literal 8 binary64) alpha))) beta)) #s(literal -32 binary64))) |
(* -1 (* beta (- (* -1 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)) 32))) |
(*.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 (+.f64 #s(literal 8 binary64) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) alpha)) #s(literal 2 binary64) (*.f64 #s(literal 8 binary64) alpha))) beta)) #s(literal -32 binary64))) |
(+ 1/16 (* 1/8 (/ beta i))) |
(fma.f64 #s(literal 1/8 binary64) (/.f64 beta i) #s(literal 1/16 binary64)) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(fma.f64 #s(literal 1/8 binary64) (+.f64 (/.f64 beta i) (/.f64 alpha i)) #s(literal 1/16 binary64)) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(fma.f64 #s(literal 1/8 binary64) (+.f64 (/.f64 beta i) (/.f64 alpha i)) #s(literal 1/16 binary64)) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(fma.f64 #s(literal 1/8 binary64) (+.f64 (/.f64 beta i) (/.f64 alpha i)) #s(literal 1/16 binary64)) |
(* 1/8 (/ alpha i)) |
(/.f64 (*.f64 alpha #s(literal 1/8 binary64)) i) |
(* alpha (+ (* 1/8 (/ beta (* alpha i))) (+ (* 1/16 (/ 1 alpha)) (* 1/8 (/ 1 i))))) |
(*.f64 alpha (+.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 beta (*.f64 alpha i)) (/.f64 #s(literal 1/16 binary64) alpha)) (/.f64 #s(literal 1/8 binary64) i))) |
(* alpha (+ (* 1/8 (/ beta (* alpha i))) (+ (* 1/16 (/ 1 alpha)) (* 1/8 (/ 1 i))))) |
(*.f64 alpha (+.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 beta (*.f64 alpha i)) (/.f64 #s(literal 1/16 binary64) alpha)) (/.f64 #s(literal 1/8 binary64) i))) |
(* alpha (+ (* 1/8 (/ beta (* alpha i))) (+ (* 1/16 (/ 1 alpha)) (* 1/8 (/ 1 i))))) |
(*.f64 alpha (+.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 beta (*.f64 alpha i)) (/.f64 #s(literal 1/16 binary64) alpha)) (/.f64 #s(literal 1/8 binary64) i))) |
(* 1/8 (/ alpha i)) |
(/.f64 (*.f64 alpha #s(literal 1/8 binary64)) i) |
(* -1 (* alpha (- (* -1 (/ (+ 1/16 (* 1/8 (/ beta i))) alpha)) (* 1/8 (/ 1 i))))) |
(*.f64 (neg.f64 alpha) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 beta i) #s(literal 1/16 binary64)) alpha)) (/.f64 #s(literal 1/8 binary64) i))) |
(* -1 (* alpha (- (* -1 (/ (+ 1/16 (* 1/8 (/ beta i))) alpha)) (* 1/8 (/ 1 i))))) |
(*.f64 (neg.f64 alpha) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 beta i) #s(literal 1/16 binary64)) alpha)) (/.f64 #s(literal 1/8 binary64) i))) |
(* -1 (* alpha (- (* -1 (/ (+ 1/16 (* 1/8 (/ beta i))) alpha)) (* 1/8 (/ 1 i))))) |
(*.f64 (neg.f64 alpha) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 beta i) #s(literal 1/16 binary64)) alpha)) (/.f64 #s(literal 1/8 binary64) i))) |
(+ 1/16 (* 1/8 (/ alpha i))) |
(fma.f64 #s(literal 1/8 binary64) (/.f64 alpha i) #s(literal 1/16 binary64)) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(fma.f64 #s(literal 1/8 binary64) (+.f64 (/.f64 beta i) (/.f64 alpha i)) #s(literal 1/16 binary64)) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(fma.f64 #s(literal 1/8 binary64) (+.f64 (/.f64 beta i) (/.f64 alpha i)) #s(literal 1/16 binary64)) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(fma.f64 #s(literal 1/8 binary64) (+.f64 (/.f64 beta i) (/.f64 alpha i)) #s(literal 1/16 binary64)) |
(* 1/8 (/ beta i)) |
(/.f64 (*.f64 beta #s(literal 1/8 binary64)) i) |
(* beta (+ (* 1/8 (/ alpha (* beta i))) (+ (* 1/16 (/ 1 beta)) (* 1/8 (/ 1 i))))) |
(*.f64 beta (+.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 alpha (*.f64 beta i)) (/.f64 #s(literal 1/16 binary64) beta)) (/.f64 #s(literal 1/8 binary64) i))) |
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#s(literal 1/16 binary64) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
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(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
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(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1))))))) alpha)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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1/16 |
#s(literal 1/16 binary64) |
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
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(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
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(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1))))))) alpha)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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alpha))))) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))))) (fma.f64 (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))))) (/.f64 (-.f64 (fma.f64 alpha (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 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(+.f64 beta alpha) #s(literal -1 binary64)))))) (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal 20 binary64)))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))))) (-.f64 (fma.f64 alpha (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))))) (/.f64 (*.f64 beta alpha) (*.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))))) |
1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 beta alpha)) (*.f64 #s(literal -1/8 binary64) (+.f64 beta alpha))) i)) |
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
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(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 beta alpha)) (*.f64 #s(literal -1/8 binary64) (+.f64 beta alpha))) i)) |
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(/ (pow i 2) (- (pow beta 2) 1)) |
(/.f64 (*.f64 i i) (fma.f64 beta beta #s(literal -1 binary64))) |
(* (pow i 2) (+ (* -1 (* i (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1)))) |
(*.f64 (*.f64 i i) (fma.f64 (neg.f64 i) (fma.f64 #s(literal 4 binary64) (/.f64 beta (*.f64 (fma.f64 beta beta #s(literal -1 binary64)) (fma.f64 beta beta #s(literal -1 binary64)))) (/.f64 #s(literal 2 binary64) (*.f64 beta (fma.f64 beta beta #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 beta beta #s(literal -1 binary64))))) |
(* (pow i 2) (+ (* i (- (* -1 (* i (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))))) (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1)))) |
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(* (pow i 2) (+ (* i (- (* i (- (* -1 (* i (+ (* -1 (/ (* (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* -1 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (* 32 (/ 1 (* beta (pow (- (pow beta 2) 1) 2)))))))) (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))))) (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1)))) |
(*.f64 (*.f64 i i) (fma.f64 i (fma.f64 i (fma.f64 (neg.f64 i) (+.f64 (neg.f64 (*.f64 (+.f64 (neg.f64 (/.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (/.f64 beta (*.f64 (fma.f64 beta beta #s(literal -1 binary64)) (fma.f64 beta beta #s(literal -1 binary64)))) (/.f64 #s(literal 2 binary64) (*.f64 beta (fma.f64 beta beta #s(literal -1 binary64))))) (*.f64 #s(literal 4 binary64) (fma.f64 beta (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 beta (*.f64 beta beta))))) (*.f64 (*.f64 beta beta) (fma.f64 beta beta #s(literal -1 binary64))))) (+.f64 (/.f64 #s(literal 3 binary64) (*.f64 (*.f64 beta beta) (fma.f64 beta beta #s(literal -1 binary64)))) (/.f64 #s(literal 20 binary64) (*.f64 (fma.f64 beta beta #s(literal -1 binary64)) (fma.f64 beta beta #s(literal -1 binary64)))))) (/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 beta (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 beta (*.f64 beta beta)))) (*.f64 (*.f64 beta beta) (fma.f64 beta beta #s(literal -1 binary64)))))) (+.f64 (neg.f64 (/.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (/.f64 beta (*.f64 (fma.f64 beta beta #s(literal -1 binary64)) (fma.f64 beta beta #s(literal -1 binary64)))) (/.f64 #s(literal 2 binary64) (*.f64 beta (fma.f64 beta beta #s(literal -1 binary64))))) (fma.f64 (*.f64 beta beta) #s(literal 20 binary64) (*.f64 #s(literal 4 binary64) (fma.f64 beta beta #s(literal -1 binary64))))) (*.f64 (*.f64 beta beta) (fma.f64 beta beta #s(literal -1 binary64))))) (/.f64 #s(literal 32 binary64) (*.f64 beta (*.f64 (fma.f64 beta beta #s(literal -1 binary64)) (fma.f64 beta beta #s(literal -1 binary64))))))) (neg.f64 (+.f64 (neg.f64 (/.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (/.f64 beta (*.f64 (fma.f64 beta beta #s(literal -1 binary64)) (fma.f64 beta beta #s(literal -1 binary64)))) (/.f64 #s(literal 2 binary64) (*.f64 beta (fma.f64 beta beta #s(literal -1 binary64))))) (*.f64 #s(literal 4 binary64) (fma.f64 beta (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 beta (*.f64 beta beta))))) (*.f64 (*.f64 beta beta) (fma.f64 beta beta #s(literal -1 binary64))))) (+.f64 (/.f64 #s(literal 3 binary64) (*.f64 (*.f64 beta beta) (fma.f64 beta beta #s(literal -1 binary64)))) (/.f64 #s(literal 20 binary64) (*.f64 (fma.f64 beta beta #s(literal -1 binary64)) (fma.f64 beta beta #s(literal -1 binary64)))))))) (neg.f64 (fma.f64 #s(literal 4 binary64) (/.f64 beta (*.f64 (fma.f64 beta beta #s(literal -1 binary64)) (fma.f64 beta beta #s(literal -1 binary64)))) (/.f64 #s(literal 2 binary64) (*.f64 beta (fma.f64 beta beta #s(literal -1 binary64))))))) (/.f64 #s(literal 1 binary64) (fma.f64 beta beta #s(literal -1 binary64))))) |
1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (pow beta 2) (pow i 2)))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
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(- (+ 1/16 (+ (* -1 (/ (+ (* 1/256 (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* 2 (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))))) (pow i 3))) (* 1/16 (/ (pow beta 2) (pow i 2))))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
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(- (+ 1/16 (+ (* -1 (/ (+ (* -2 (* beta (+ (* 1/256 (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* 2 (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))))))) (+ (* 1/256 (* (pow beta 2) (- (pow beta 2) 1))) (* 1/16 (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))))) (pow i 4))) (* 1/16 (/ (pow beta 2) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2))) (* 2 (/ (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))) (pow i 3)))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (pow beta 2) (pow i 2)))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
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(- (+ 1/16 (+ (* -2 (/ (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))) (pow i 3))) (+ (* 1/256 (/ (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3))) (pow i 3))) (* 1/16 (/ (pow beta 2) (pow i 2)))))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
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(* 1/4 (/ (pow i 2) (- (* 4 (pow i 2)) 1))) |
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(pow i 2) |
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(pow i 2) |
(*.f64 i i) |
(pow i 2) |
(*.f64 i i) |
(pow i 2) |
(*.f64 i i) |
(pow i 2) |
(*.f64 i i) |
(pow i 2) |
(*.f64 i i) |
(pow i 2) |
(*.f64 i i) |
(pow i 2) |
(*.f64 i i) |
(+ 1/4 (* -1/16 (/ (pow beta 2) (pow i 2)))) |
(fma.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) #s(literal -1/16 binary64) #s(literal 1/4 binary64)) |
(+ 1/4 (+ (* -1/8 (/ (* alpha beta) (pow i 2))) (* -1/16 (/ (pow beta 2) (pow i 2))))) |
(+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 beta alpha) (*.f64 i i)) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 beta beta)) (*.f64 i i)))) |
(+ 1/4 (+ (* -1/16 (/ (pow beta 2) (pow i 2))) (* alpha (+ (* -1/8 (/ beta (pow i 2))) (* -1/16 (/ alpha (pow i 2))))))) |
(+.f64 #s(literal 1/4 binary64) (fma.f64 alpha (fma.f64 #s(literal -1/8 binary64) (/.f64 beta (*.f64 i i)) (*.f64 #s(literal -1/16 binary64) (/.f64 alpha (*.f64 i i)))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 beta beta)) (*.f64 i i)))) |
(+ 1/4 (+ (* -1/16 (/ (pow beta 2) (pow i 2))) (* alpha (+ (* -1/8 (/ beta (pow i 2))) (* -1/16 (/ alpha (pow i 2))))))) |
(+.f64 #s(literal 1/4 binary64) (fma.f64 alpha (fma.f64 #s(literal -1/8 binary64) (/.f64 beta (*.f64 i i)) (*.f64 #s(literal -1/16 binary64) (/.f64 alpha (*.f64 i i)))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 beta beta)) (*.f64 i i)))) |
(* -1/16 (/ (pow alpha 2) (pow i 2))) |
(/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 alpha alpha)) (*.f64 i i)) |
(* (pow alpha 2) (- (* -1/8 (/ beta (* alpha (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 alpha alpha) (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) beta) (*.f64 alpha (*.f64 i i))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow alpha 2) (- (+ (* -1/8 (/ beta (* alpha (pow i 2)))) (+ (* -1/16 (/ (pow beta 2) (* (pow alpha 2) (pow i 2)))) (/ 1/4 (pow alpha 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 alpha alpha) (-.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 beta (*.f64 alpha (*.f64 i i))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 beta beta) (*.f64 (*.f64 i i) (*.f64 alpha alpha))) (/.f64 #s(literal 1/4 binary64) (*.f64 alpha alpha)))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow alpha 2) (- (+ (* -1/8 (/ beta (* alpha (pow i 2)))) (+ (* -1/16 (/ (pow beta 2) (* (pow alpha 2) (pow i 2)))) (/ 1/4 (pow alpha 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 alpha alpha) (-.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 beta (*.f64 alpha (*.f64 i i))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 beta beta) (*.f64 (*.f64 i i) (*.f64 alpha alpha))) (/.f64 #s(literal 1/4 binary64) (*.f64 alpha alpha)))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* -1/16 (/ (pow alpha 2) (pow i 2))) |
(/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 alpha alpha)) (*.f64 i i)) |
(* (pow alpha 2) (- (* -1/8 (/ beta (* alpha (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 alpha alpha) (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) beta) (*.f64 alpha (*.f64 i i))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ (+ 1/4 (* -1/16 (/ (pow beta 2) (pow i 2)))) alpha)) (* 1/8 (/ beta (pow i 2)))) alpha)) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 alpha alpha) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 beta (*.f64 i i)) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) #s(literal -1/16 binary64) #s(literal 1/4 binary64)) alpha))) alpha)) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ (+ 1/4 (* -1/16 (/ (pow beta 2) (pow i 2)))) alpha)) (* 1/8 (/ beta (pow i 2)))) alpha)) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 alpha alpha) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 beta (*.f64 i i)) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) #s(literal -1/16 binary64) #s(literal 1/4 binary64)) alpha))) alpha)) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(+ 1/4 (* -1/16 (/ (pow alpha 2) (pow i 2)))) |
(fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 alpha alpha) (*.f64 i i)) #s(literal 1/4 binary64)) |
(+ 1/4 (+ (* -1/8 (/ (* alpha beta) (pow i 2))) (* -1/16 (/ (pow alpha 2) (pow i 2))))) |
(+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 beta alpha) (*.f64 i i)) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 alpha alpha)) (*.f64 i i)))) |
(+ 1/4 (+ (* -1/16 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1/8 (/ alpha (pow i 2))) (* -1/16 (/ beta (pow i 2))))))) |
(+.f64 #s(literal 1/4 binary64) (fma.f64 beta (fma.f64 #s(literal -1/8 binary64) (/.f64 alpha (*.f64 i i)) (*.f64 #s(literal -1/16 binary64) (/.f64 beta (*.f64 i i)))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 alpha alpha)) (*.f64 i i)))) |
(+ 1/4 (+ (* -1/16 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1/8 (/ alpha (pow i 2))) (* -1/16 (/ beta (pow i 2))))))) |
(+.f64 #s(literal 1/4 binary64) (fma.f64 beta (fma.f64 #s(literal -1/8 binary64) (/.f64 alpha (*.f64 i i)) (*.f64 #s(literal -1/16 binary64) (/.f64 beta (*.f64 i i)))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 alpha alpha)) (*.f64 i i)))) |
(* -1/16 (/ (pow beta 2) (pow i 2))) |
(/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 beta beta)) (*.f64 i i)) |
(* (pow beta 2) (- (* -1/8 (/ alpha (* beta (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 beta beta) (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) alpha) (*.f64 beta (*.f64 i i))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow beta 2) (- (+ (* -1/8 (/ alpha (* beta (pow i 2)))) (+ (* -1/16 (/ (pow alpha 2) (* (pow beta 2) (pow i 2)))) (/ 1/4 (pow beta 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 beta beta) (-.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 alpha (*.f64 beta (*.f64 i i))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 alpha alpha) (*.f64 (*.f64 i i) (*.f64 beta beta))) (/.f64 #s(literal 1/4 binary64) (*.f64 beta beta)))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow beta 2) (- (+ (* -1/8 (/ alpha (* beta (pow i 2)))) (+ (* -1/16 (/ (pow alpha 2) (* (pow beta 2) (pow i 2)))) (/ 1/4 (pow beta 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 beta beta) (-.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 alpha (*.f64 beta (*.f64 i i))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 alpha alpha) (*.f64 (*.f64 i i) (*.f64 beta beta))) (/.f64 #s(literal 1/4 binary64) (*.f64 beta beta)))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* -1/16 (/ (pow beta 2) (pow i 2))) |
(/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 beta beta)) (*.f64 i i)) |
(* (pow beta 2) (- (* -1/8 (/ alpha (* beta (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 beta beta) (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) alpha) (*.f64 beta (*.f64 i i))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow beta 2) (- (* -1 (/ (+ (* -1 (/ (+ 1/4 (* -1/16 (/ (pow alpha 2) (pow i 2)))) beta)) (* 1/8 (/ alpha (pow i 2)))) beta)) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 beta beta) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 alpha (*.f64 i i)) (neg.f64 (/.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 alpha alpha) (*.f64 i i)) #s(literal 1/4 binary64)) beta))) beta)) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow beta 2) (- (* -1 (/ (+ (* -1 (/ (+ 1/4 (* -1/16 (/ (pow alpha 2) (pow i 2)))) beta)) (* 1/8 (/ alpha (pow i 2)))) beta)) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 beta beta) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 alpha (*.f64 i i)) (neg.f64 (/.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 alpha alpha) (*.f64 i i)) #s(literal 1/4 binary64)) beta))) beta)) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)) |
(/ (+ (* -1/16 (pow (+ alpha beta) 2)) (* 1/4 (pow i 2))) (pow i 2)) |
(/.f64 (fma.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64) (*.f64 (*.f64 i i) #s(literal 1/4 binary64))) (*.f64 i i)) |
(/ (+ (* -1/16 (pow (+ alpha beta) 2)) (* 1/4 (pow i 2))) (pow i 2)) |
(/.f64 (fma.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64) (*.f64 (*.f64 i i) #s(literal 1/4 binary64))) (*.f64 i i)) |
(/ (+ (* -1/16 (pow (+ alpha beta) 2)) (* 1/4 (pow i 2))) (pow i 2)) |
(/.f64 (fma.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64) (*.f64 (*.f64 i i) #s(literal 1/4 binary64))) (*.f64 i i)) |
1/4 |
#s(literal 1/4 binary64) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i)) #s(literal 1/4 binary64)) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i)) #s(literal 1/4 binary64)) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i)) #s(literal 1/4 binary64)) |
1/4 |
#s(literal 1/4 binary64) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i)) #s(literal 1/4 binary64)) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i)) #s(literal 1/4 binary64)) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i)) #s(literal 1/4 binary64)) |
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(/.f64 (*.f64 alpha (*.f64 beta i)) (*.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) |
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
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(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i)) (* -1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i)))) i))) |
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(+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i))))) i))) i))) |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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1/4 |
#s(literal 1/4 binary64) |
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
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(- (+ 1/4 (+ (* -1 (/ (+ (* -1 (* (pow (+ alpha beta) 2) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))))) (* 1/4 (* (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))) (- (pow (+ alpha beta) 2) 1)))) (pow i 4))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (+ (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3)))) |
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1/4 |
#s(literal 1/4 binary64) |
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
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(- (+ 1/4 (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
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(- (+ 1/4 (+ (* -1 (/ (- (+ (* -1 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) i)) (* 1/4 (/ (* (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))) (- (pow (+ alpha beta) 2) 1)) i))) (* -1 (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2)))) |
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(/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1)) |
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(+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (- (pow (+ beta (* 2 i)) 2) 1)))) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ i (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (+ (/ (* i (+ beta i)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (- (pow (+ beta (* 2 i)) 2) 1))))) (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(/ (+ beta i) alpha) |
(/.f64 (+.f64 beta i) alpha) |
(/ (- (+ beta (+ i (/ (* i (+ beta i)) alpha))) (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
(/.f64 (+.f64 beta (-.f64 (fma.f64 i (/.f64 (+.f64 beta i) alpha) i) (*.f64 (+.f64 beta i) (/.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))) alpha)))) alpha) |
(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha)))) (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
(/.f64 (-.f64 (+.f64 (+.f64 beta i) (fma.f64 i (/.f64 (+.f64 beta i) alpha) (neg.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))) (-.f64 (*.f64 i (+.f64 beta i)) (*.f64 (+.f64 beta i) (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))))) (*.f64 (+.f64 beta i) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) (*.f64 alpha alpha))))) (*.f64 (+.f64 beta i) (/.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))) alpha))) alpha) |
(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))))))) (* (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (- (pow (+ beta (* 2 i)) 2) 1))) (pow alpha 3))) (/ (* i (+ beta i)) alpha)))) (+ (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha) |
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(* -1 (/ (+ (* -1 beta) (* -1 i)) alpha)) |
(neg.f64 (/.f64 (+.f64 (neg.f64 beta) (neg.f64 i)) alpha)) |
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha)) |
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(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha)) (+ (* i (+ beta i)) (/ (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)) alpha))) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha)) |
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(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ beta (* 2 i)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha)) (/ (* (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) (- (pow (+ beta (* 2 i)) 2) 1)) alpha)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha)) (* i (+ beta i))) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha)) |
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(/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1)) |
(/.f64 (*.f64 i (+.f64 alpha i)) (fma.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha) #s(literal -1 binary64))) |
(+ (* beta (- (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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(+ (* beta (- (+ (* -1 (* beta (+ (/ (* i (+ alpha i)) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (- (pow (+ alpha (* 2 i)) 2) 1))))) (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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(+ (* beta (- (+ (* beta (- (* beta (- (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)) (+ (* -1 (/ (* (+ (* 2 alpha) (* 4 i)) (+ (/ (* i (+ alpha i)) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (- (pow (+ alpha (* 2 i)) 2) 1)))) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)) (/ i (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (+ (/ (* i (+ alpha i)) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (- (pow (+ alpha (* 2 i)) 2) 1))))) (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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(/ (+ alpha i) beta) |
(/.f64 (+.f64 alpha i) beta) |
(/ (- (+ alpha (+ i (/ (* i (+ alpha i)) beta))) (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta)) beta) |
(/.f64 (-.f64 (+.f64 alpha (fma.f64 i (/.f64 (+.f64 alpha i) beta) i)) (/.f64 (*.f64 (+.f64 alpha i) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64)))) beta)) beta) |
(/ (- (+ alpha (+ i (+ (* -1 (/ (+ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta)))) (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta)) beta) |
(/.f64 (-.f64 (+.f64 (+.f64 alpha i) (fma.f64 i (/.f64 (+.f64 alpha i) beta) (neg.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) (-.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (+.f64 alpha i) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))))) (*.f64 (+.f64 alpha i) (fma.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha) #s(literal -1 binary64)))) (*.f64 beta beta))))) (/.f64 (*.f64 (+.f64 alpha i) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64)))) beta)) beta) |
(/ (- (+ alpha (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))))) (* (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (- (pow (+ alpha (* 2 i)) 2) 1))) (pow beta 3))) (/ (* i (+ alpha i)) beta)))) (+ (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta) |
(/.f64 (-.f64 (+.f64 (+.f64 alpha i) (fma.f64 i (/.f64 (+.f64 alpha i) beta) (neg.f64 (/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha) #s(literal -1 binary64)) (-.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (+.f64 alpha i) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))))) (neg.f64 (*.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) (-.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (+.f64 alpha i) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))))) (*.f64 (+.f64 alpha i) (fma.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha) #s(literal -1 binary64))))))) (*.f64 beta (*.f64 beta beta)))))) (fma.f64 (+.f64 alpha i) (/.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) beta) (fma.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) (/.f64 (-.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (+.f64 alpha i) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))))) (*.f64 beta beta)) (*.f64 (+.f64 alpha i) (/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha) #s(literal -1 binary64)) (*.f64 beta beta)))))) beta) |
(* -1 (/ (+ (* -1 alpha) (* -1 i)) beta)) |
(neg.f64 (/.f64 (+.f64 (neg.f64 i) (neg.f64 alpha)) beta)) |
(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)))) beta)) |
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(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)) (+ (* i (+ alpha i)) (/ (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) beta))) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)))) beta)) |
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(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ alpha (* 2 i)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))) beta)) (/ (* (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) (- (pow (+ alpha (* 2 i)) 2) 1)) beta)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))) beta)) (* i (+ alpha i))) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)))) beta)) |
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(* alpha beta) |
(*.f64 beta alpha) |
(+ (* alpha beta) (* i (+ alpha beta))) |
(fma.f64 beta alpha (*.f64 i (+.f64 beta alpha))) |
(+ (* alpha beta) (* i (+ alpha (+ beta i)))) |
(fma.f64 beta alpha (*.f64 i (+.f64 alpha (+.f64 beta i)))) |
(+ (* alpha beta) (* i (+ alpha (+ beta i)))) |
(fma.f64 beta alpha (*.f64 i (+.f64 alpha (+.f64 beta i)))) |
(pow i 2) |
(*.f64 i i) |
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i)))) |
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(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2)))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/256 (/ (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) i))) |
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(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (pow i 3))) (+ (* 1/256 (/ (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) (pow i 2))) (+ (* 1/256 (/ (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) i)) (+ (* 1/16 (/ (* (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/256 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta))))))) (pow i 3))) (+ (* 1/16 (/ (* (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/256 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta))))))) (pow i 2))) (* 1/16 (/ (* (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))))) (* 1/16 (* (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/256 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta))))))))))) (pow i 3))))))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* -1/256 (/ (+ (* -8 (+ 1 (+ alpha beta))) (* -2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) i))) |
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(/.f64 (*.f64 i (+.f64 beta i)) (*.f64 alpha alpha)) |
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(/ (- (+ (* -1 (/ (+ (* i (* (+ beta i) (+ (* (+ 1 (+ beta (* 2 i))) (+ (* (+ (* 2 beta) (* 4 i)) (- (+ beta (* 2 i)) 1)) (pow (+ beta (* 2 i)) 2))) (* (pow (+ beta (* 2 i)) 2) (- (+ beta (* 2 i)) 1))))) (+ (* (+ (* 4 beta) (* 8 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (+ (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))) 1)) (+ (* (+ (* 2 beta) (* 4 i)) (- (+ beta (* 2 i)) 1)) (pow (+ beta (* 2 i)) 2))))) (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))))))) (* (+ (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))) 1)) (+ (* (+ (* 2 beta) (* 4 i)) (- (+ beta (* 2 i)) 1)) (pow (+ beta (* 2 i)) 2))) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (+ (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))) 1)) (+ (* (+ (* 2 beta) (* 4 i)) (- (+ beta (* 2 i)) 1)) (pow (+ beta (* 2 i)) 2))))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2)) |
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
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(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (* (pow (+ beta (* 2 i)) 2) (- (+ beta (* 2 i)) 1))) (* (+ 1 (+ beta (* 2 i))) (+ (* -2 (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* -1 (pow (+ beta (* 2 i)) 2))))))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (+ (/ (* (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ (* -2 (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* -1 (pow (+ beta (* 2 i)) 2)))) (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))) (* (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))))))))))) alpha) (/ (* (+ (* -1 (+ (* -2 (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* -1 (pow (+ beta (* 2 i)) 2)))) (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))))) alpha)))) (+ (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ (* -2 (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* -1 (pow (+ beta (* 2 i)) 2)))) (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))) (* (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))))))) alpha))) (pow alpha 2)) |
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (+ 1 (+ alpha (* 2 i))) (* (pow (+ alpha (* 2 i)) 2) (- (+ alpha (* 2 i)) 1)))) |
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#s(literal 1/16 binary64) |
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1/16 |
#s(literal 1/16 binary64) |
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(* 1/8 alpha) |
(*.f64 alpha #s(literal 1/8 binary64)) |
(* alpha (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)))) |
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(* alpha (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)))) |
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(* 1/8 alpha) |
(*.f64 alpha #s(literal 1/8 binary64)) |
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(* 1/8 beta) |
(*.f64 beta #s(literal 1/8 binary64)) |
(* beta (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)))) |
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(* beta (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)))) |
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(* 1/8 beta) |
(*.f64 beta #s(literal 1/8 binary64)) |
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(* -1 (* beta (- (* -1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)) 1/8))) |
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(* (pow beta 2) (- (pow beta 2) 1)) |
(*.f64 (*.f64 beta beta) (fma.f64 beta beta #s(literal -1 binary64))) |
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(* 16 (pow i 4)) |
(*.f64 #s(literal 16 binary64) (pow.f64 i #s(literal 4 binary64))) |
(* (pow i 4) (+ 16 (* 32 (/ beta i)))) |
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(* 16 (pow i 4)) |
(*.f64 #s(literal 16 binary64) (pow.f64 i #s(literal 4 binary64))) |
(* (pow i 4) (+ 16 (* 32 (/ beta i)))) |
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(fma.f64 #s(literal 4 binary64) (*.f64 (*.f64 i i) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))) (*.f64 beta (fma.f64 #s(literal 4 binary64) (*.f64 i (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))) (*.f64 #s(literal 16 binary64) (*.f64 i (*.f64 i i)))))) |
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (+ (* 16 (pow i 3)) (* beta (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))))) |
(fma.f64 beta (fma.f64 #s(literal 4 binary64) (*.f64 i (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))) (fma.f64 beta (fma.f64 (*.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64)) (*.f64 #s(literal 16 binary64) (*.f64 i (*.f64 i i))))) (*.f64 (*.f64 #s(literal 4 binary64) (*.f64 i i)) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64)))) |
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (+ (* 16 (pow i 3)) (* beta (- (+ (* 8 (* beta i)) (+ (* 8 (pow i 2)) (* 16 (pow i 2)))) 1)))))) |
(fma.f64 #s(literal 4 binary64) (*.f64 (*.f64 i i) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))) (*.f64 beta (fma.f64 #s(literal 4 binary64) (*.f64 i (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))) (fma.f64 beta (fma.f64 #s(literal 8 binary64) (*.f64 beta i) (fma.f64 (*.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64))) (*.f64 #s(literal 16 binary64) (*.f64 i (*.f64 i i))))))) |
(pow beta 4) |
(pow.f64 beta #s(literal 4 binary64)) |
(* (pow beta 4) (+ 1 (* 8 (/ i beta)))) |
(*.f64 (pow.f64 beta #s(literal 4 binary64)) (fma.f64 #s(literal 8 binary64) (/.f64 i beta) #s(literal 1 binary64))) |
(* (pow beta 4) (- (+ 1 (+ (* 8 (/ i beta)) (+ (* 8 (/ (pow i 2) (pow beta 2))) (* 16 (/ (pow i 2) (pow beta 2)))))) (/ 1 (pow beta 2)))) |
(*.f64 (pow.f64 beta #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) #s(literal 24 binary64) (/.f64 (*.f64 #s(literal 8 binary64) i) beta)) (/.f64 #s(literal 1 binary64) (*.f64 beta beta))))) |
(* (pow beta 4) (- (+ 1 (+ (* 4 (/ (* i (- (* 4 (pow i 2)) 1)) (pow beta 3))) (+ (* 8 (/ i beta)) (+ (* 8 (/ (pow i 2) (pow beta 2))) (+ (* 16 (/ (pow i 2) (pow beta 2))) (* 16 (/ (pow i 3) (pow beta 3)))))))) (/ 1 (pow beta 2)))) |
(*.f64 (pow.f64 beta #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (*.f64 i (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))) (*.f64 beta (*.f64 beta beta))) (fma.f64 #s(literal 8 binary64) (/.f64 i beta) (fma.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) #s(literal 24 binary64) (/.f64 (*.f64 #s(literal 16 binary64) (*.f64 i (*.f64 i i))) (*.f64 beta (*.f64 beta beta)))))) (/.f64 #s(literal 1 binary64) (*.f64 beta beta))))) |
(pow beta 4) |
(pow.f64 beta #s(literal 4 binary64)) |
(* (pow beta 4) (+ 1 (* 8 (/ i beta)))) |
(*.f64 (pow.f64 beta #s(literal 4 binary64)) (fma.f64 #s(literal 8 binary64) (/.f64 i beta) #s(literal 1 binary64))) |
(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -8 i) (* -1 (/ (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1) beta))) beta)))) |
(*.f64 (pow.f64 beta #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 i #s(literal -8 binary64) (neg.f64 (/.f64 (fma.f64 (*.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64)) beta))) beta)))) |
(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -8 i) (* -1 (/ (- (+ (* -1 (/ (+ (* -16 (pow i 3)) (* -4 (* i (- (* 4 (pow i 2)) 1)))) beta)) (+ (* 8 (pow i 2)) (* 16 (pow i 2)))) 1) beta))) beta)))) |
(*.f64 (pow.f64 beta #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 i #s(literal -8 binary64) (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (*.f64 i (*.f64 i i)) #s(literal -16 binary64) (*.f64 #s(literal -4 binary64) (*.f64 i (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))))) beta)) (fma.f64 (*.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64))) beta))) beta)))) |
(/ i (+ alpha beta)) |
(/.f64 i (+.f64 beta alpha)) |
(* i (+ (* -3 (/ i (pow (+ alpha beta) 2))) (/ 1 (+ alpha beta)))) |
(*.f64 i (fma.f64 #s(literal -3 binary64) (/.f64 i (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (/.f64 #s(literal 1 binary64) (+.f64 beta alpha)))) |
(* i (+ (* i (- (* 8 (/ i (pow (+ alpha beta) 3))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta)))) |
(*.f64 i (fma.f64 i (-.f64 (/.f64 (*.f64 #s(literal 8 binary64) i) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))) (/.f64 #s(literal 3 binary64) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))) (/.f64 #s(literal 1 binary64) (+.f64 beta alpha)))) |
(* i (+ (* i (- (* i (+ (* -20 (/ i (pow (+ alpha beta) 4))) (* 8 (/ 1 (pow (+ alpha beta) 3))))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta)))) |
(*.f64 i (fma.f64 i (fma.f64 i (fma.f64 #s(literal -20 binary64) (/.f64 i (pow.f64 (+.f64 beta alpha) #s(literal 4 binary64))) (/.f64 #s(literal 8 binary64) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))))) (neg.f64 (/.f64 #s(literal 3 binary64) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))))) (/.f64 #s(literal 1 binary64) (+.f64 beta alpha)))) |
1/4 |
#s(literal 1/4 binary64) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i)) #s(literal 1/4 binary64)) |
(- (+ 1/4 (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(+.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 i (*.f64 i i))) #s(literal 1/4 binary64)) (/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i))) |
(- (+ 1/4 (* -1 (/ (+ (* -1/64 (pow (+ alpha beta) 4)) (* 1/16 (pow (+ alpha beta) 4))) (pow i 4)))) (+ (* -1/16 (/ (pow (+ alpha beta) 3) (pow i 3))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(+.f64 #s(literal 1/4 binary64) (-.f64 (neg.f64 (/.f64 (*.f64 (pow.f64 (+.f64 beta alpha) #s(literal 4 binary64)) #s(literal 3/64 binary64)) (pow.f64 i #s(literal 4 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i)) (*.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 i (*.f64 i i))))))) |
1/4 |
#s(literal 1/4 binary64) |
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))) |
(fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i)) #s(literal 1/4 binary64)) |
(+ 1/4 (+ (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3))))) |
(+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 i (*.f64 i i))) (/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)))) |
(+ 1/4 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (pow (+ alpha beta) 4)) (* 1/64 (pow (+ alpha beta) 4))) i)) (* -1/16 (pow (+ alpha beta) 3))) (pow i 3))) (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i)) (neg.f64 (/.f64 (fma.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) #s(literal -1/16 binary64) (neg.f64 (/.f64 (*.f64 (pow.f64 (+.f64 beta alpha) #s(literal 4 binary64)) #s(literal -3/64 binary64)) i))) (*.f64 i (*.f64 i i)))))) |
(/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) |
(/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) |
(+ (* alpha (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) |
(fma.f64 alpha (-.f64 (/.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 (*.f64 i (+.f64 beta i)) (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal 4 binary64)))) (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) |
(+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) |
(fma.f64 alpha (fma.f64 (neg.f64 alpha) (fma.f64 i (/.f64 (+.f64 beta i) (pow.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal 4 binary64))) (/.f64 (*.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))) (-.f64 (/.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 (*.f64 i (+.f64 beta i)) (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal 4 binary64))))) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) (-.f64 (/.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 (*.f64 i (+.f64 beta i)) (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal 4 binary64))))) (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) |
(+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 6)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)))) (pow (+ beta (* 2 i)) 2))) (/ i (pow (+ beta (* 2 i)) 4))))) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) |
(fma.f64 alpha (-.f64 (fma.f64 alpha (-.f64 (*.f64 alpha (-.f64 (/.f64 (*.f64 (*.f64 i (+.f64 beta i)) (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal 6 binary64))) (+.f64 (neg.f64 (/.f64 (*.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))) (fma.f64 i (/.f64 (+.f64 beta i) (pow.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal 4 binary64))) (/.f64 (*.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))) (-.f64 (/.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 (*.f64 i (+.f64 beta i)) (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal 4 binary64))))) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))))) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) (/.f64 i (pow.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal 4 binary64)))))) (fma.f64 i (/.f64 (+.f64 beta i) (pow.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal 4 binary64))) (/.f64 (*.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))) (-.f64 (/.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 (*.f64 i (+.f64 beta i)) (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal 4 binary64))))) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))))) (/.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) (/.f64 (*.f64 (*.f64 i (+.f64 beta i)) (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal 4 binary64)))) (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) |
(/ i alpha) |
(/.f64 i alpha) |
(/ (- (+ i (/ (* i (+ beta i)) alpha)) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
(/.f64 (-.f64 (fma.f64 i (/.f64 (+.f64 beta i) alpha) i) (/.f64 (*.f64 i (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64)))) alpha)) alpha) |
(/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha))) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha) |
(/.f64 (+.f64 i (-.f64 (fma.f64 i (/.f64 (+.f64 beta i) alpha) (neg.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))) (*.f64 i (-.f64 (+.f64 beta i) (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))))) (*.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) (*.f64 alpha alpha)))) (/.f64 (*.f64 i (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64)))) alpha))) alpha) |
(/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 3))) (/ (* i (+ beta i)) alpha))) (+ (/ (* i (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* i (pow (+ beta (* 2 i)) 2)) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha) |
(/.f64 (+.f64 i (-.f64 (fma.f64 i (/.f64 (+.f64 beta i) alpha) (neg.f64 (/.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 i (-.f64 (+.f64 beta i) (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))))) (neg.f64 (*.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))) (*.f64 i (-.f64 (+.f64 beta i) (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))))) (*.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))))))) (*.f64 alpha (*.f64 alpha alpha))))) (fma.f64 i (/.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))) alpha) (fma.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))) (/.f64 (*.f64 i (-.f64 (+.f64 beta i) (fma.f64 #s(literal 4 binary64) i (*.f64 beta #s(literal 2 binary64))))) (*.f64 alpha alpha)) (/.f64 (*.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 alpha alpha)))))) alpha) |
(/ i alpha) |
(/.f64 i alpha) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha)) |
(neg.f64 (/.f64 (+.f64 (neg.f64 i) (neg.f64 (/.f64 (fma.f64 i (+.f64 beta i) (*.f64 #s(literal -2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i beta)))) alpha))) alpha)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -1 (/ (* i (pow (+ beta (* 2 i)) 2)) alpha)) (* i (+ beta i)))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha)) |
(neg.f64 (/.f64 (+.f64 (neg.f64 i) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 i (+.f64 beta i) (*.f64 #s(literal -2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i beta))))) alpha) (-.f64 (fma.f64 i (+.f64 beta i) (neg.f64 (/.f64 (*.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) alpha))) (*.f64 #s(literal 2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i beta))))) alpha))) alpha)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ beta (* 2 i)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (* i (+ beta i))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha)) |
(neg.f64 (/.f64 (+.f64 (neg.f64 i) (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 (*.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 i (+.f64 beta i) (*.f64 #s(literal -2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i beta)))) (*.f64 (neg.f64 i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))))) alpha) (-.f64 (/.f64 (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 i (+.f64 beta i) (*.f64 #s(literal -2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i beta))))) alpha) (fma.f64 (*.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 i (+.f64 beta i) (*.f64 #s(literal -2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i beta)))) (*.f64 (neg.f64 i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))))) alpha)) (fma.f64 i (+.f64 beta i) (*.f64 #s(literal -2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i beta))))) alpha))) alpha)) |
(/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) |
(/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha))) |
(+ (* beta (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) |
(fma.f64 beta (-.f64 (/.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha))) (/.f64 (*.f64 (*.f64 i (+.f64 alpha i)) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i alpha) #s(literal 4 binary64)))) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha)))) |
(+ (* beta (- (+ (* -1 (* beta (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2))))) (/ i (pow (+ alpha (* 2 i)) 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) |
(fma.f64 beta (-.f64 (fma.f64 (neg.f64 beta) (fma.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha))) (/.f64 (*.f64 (*.f64 i (+.f64 alpha i)) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i alpha) #s(literal 4 binary64)))) (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha))) (/.f64 (*.f64 i (+.f64 alpha i)) (pow.f64 (fma.f64 #s(literal 2 binary64) i alpha) #s(literal 4 binary64)))) (/.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha)))) (/.f64 (*.f64 (*.f64 i (+.f64 alpha i)) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i alpha) #s(literal 4 binary64)))) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha)))) |
(+ (* beta (- (+ (* beta (- (* beta (- (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 6)) (+ (* -1 (/ (* (+ (* 2 alpha) (* 4 i)) (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)))) (pow (+ alpha (* 2 i)) 2))) (/ i (pow (+ alpha (* 2 i)) 4))))) (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2))))) (/ i (pow (+ alpha (* 2 i)) 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) |
(fma.f64 beta (-.f64 (fma.f64 beta (-.f64 (*.f64 beta (-.f64 (/.f64 (*.f64 (*.f64 i (+.f64 alpha i)) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i alpha) #s(literal 6 binary64))) (+.f64 (neg.f64 (/.f64 (*.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha))) (/.f64 (*.f64 (*.f64 i (+.f64 alpha i)) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i alpha) #s(literal 4 binary64)))) (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha))) (/.f64 (*.f64 i (+.f64 alpha i)) (pow.f64 (fma.f64 #s(literal 2 binary64) i alpha) #s(literal 4 binary64))))) (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha)))) (/.f64 i (pow.f64 (fma.f64 #s(literal 2 binary64) i alpha) #s(literal 4 binary64)))))) (fma.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha))) (/.f64 (*.f64 (*.f64 i (+.f64 alpha i)) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i alpha) #s(literal 4 binary64)))) (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha))) (/.f64 (*.f64 i (+.f64 alpha i)) (pow.f64 (fma.f64 #s(literal 2 binary64) i alpha) #s(literal 4 binary64))))) (/.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha)))) (/.f64 (*.f64 (*.f64 i (+.f64 alpha i)) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) i alpha) #s(literal 4 binary64)))) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha)))) |
(/ i beta) |
(/.f64 i beta) |
(/ (- (+ i (/ (* i (+ alpha i)) beta)) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta) |
(/.f64 (-.f64 (fma.f64 i (/.f64 (+.f64 alpha i) beta) i) (/.f64 (*.f64 i (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64)))) beta)) beta) |
(/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta))) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta) |
(/.f64 (+.f64 i (-.f64 (fma.f64 i (/.f64 (+.f64 alpha i) beta) (neg.f64 (/.f64 (fma.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha)) (*.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) (*.f64 i (-.f64 (+.f64 alpha i) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))))))) (*.f64 beta beta)))) (/.f64 (*.f64 i (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64)))) beta))) beta) |
(/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 3))) (/ (* i (+ alpha i)) beta))) (+ (/ (* i (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* i (pow (+ alpha (* 2 i)) 2)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta) |
(/.f64 (+.f64 i (-.f64 (fma.f64 i (/.f64 (+.f64 alpha i) beta) (neg.f64 (/.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha)) (*.f64 i (-.f64 (+.f64 alpha i) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))))) (neg.f64 (*.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) (fma.f64 i (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha)) (*.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) (*.f64 i (-.f64 (+.f64 alpha i) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64)))))))))) (*.f64 beta (*.f64 beta beta))))) (fma.f64 i (/.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) beta) (fma.f64 (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))) (/.f64 (*.f64 i (-.f64 (+.f64 alpha i) (fma.f64 #s(literal 4 binary64) i (*.f64 alpha #s(literal 2 binary64))))) (*.f64 beta beta)) (*.f64 i (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha)) (*.f64 beta beta))))))) beta) |
(/ i beta) |
(/.f64 i beta) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta)) |
(neg.f64 (/.f64 (+.f64 (neg.f64 i) (neg.f64 (/.f64 (fma.f64 i (+.f64 alpha i) (*.f64 #s(literal -2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i alpha)))) beta))) beta)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -1 (/ (* i (pow (+ alpha (* 2 i)) 2)) beta)) (* i (+ alpha i)))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta)) |
(neg.f64 (/.f64 (+.f64 (neg.f64 i) (neg.f64 (/.f64 (+.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 i (+.f64 alpha i) (*.f64 #s(literal -2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i alpha))))) beta) (fma.f64 i (+.f64 alpha i) (/.f64 (*.f64 (neg.f64 i) (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha))) beta))) (*.f64 #s(literal -2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i alpha)))) beta))) beta)) |
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ alpha (* 2 i)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (* i (+ alpha i))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta)) |
(neg.f64 (/.f64 (+.f64 (neg.f64 i) (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal -2 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 i (+.f64 alpha i) (*.f64 #s(literal -2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i alpha))))) (*.f64 (neg.f64 i) (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha))))) beta) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha)) (/.f64 (fma.f64 i (+.f64 alpha i) (*.f64 #s(literal -2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i alpha)))) beta)) (fma.f64 #s(literal -2 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 i (+.f64 alpha i) (*.f64 #s(literal -2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i alpha))))) (*.f64 (neg.f64 i) (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (fma.f64 #s(literal 2 binary64) i alpha)))))) beta)) (fma.f64 i (+.f64 alpha i) (*.f64 #s(literal -2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i alpha))))) beta))) beta)) |
(* -1/16 (/ (pow beta 2) (pow i 2))) |
(/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 beta beta)) (*.f64 i i)) |
(+ (* -1/8 (/ (* alpha beta) (pow i 2))) (* -1/16 (/ (pow beta 2) (pow i 2)))) |
(fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 beta alpha) (*.f64 i i)) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 beta beta)) (*.f64 i i))) |
(+ (* -1/16 (/ (pow beta 2) (pow i 2))) (* alpha (+ (* -1/8 (/ beta (pow i 2))) (* -1/16 (/ alpha (pow i 2)))))) |
(fma.f64 alpha (fma.f64 #s(literal -1/8 binary64) (/.f64 beta (*.f64 i i)) (*.f64 #s(literal -1/16 binary64) (/.f64 alpha (*.f64 i i)))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 beta beta)) (*.f64 i i))) |
(+ (* -1/16 (/ (pow beta 2) (pow i 2))) (* alpha (+ (* -1/8 (/ beta (pow i 2))) (* -1/16 (/ alpha (pow i 2)))))) |
(fma.f64 alpha (fma.f64 #s(literal -1/8 binary64) (/.f64 beta (*.f64 i i)) (*.f64 #s(literal -1/16 binary64) (/.f64 alpha (*.f64 i i)))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 beta beta)) (*.f64 i i))) |
(* -1/16 (/ (pow alpha 2) (pow i 2))) |
(/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 alpha alpha)) (*.f64 i i)) |
(* (pow alpha 2) (- (* -1/8 (/ beta (* alpha (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 alpha alpha) (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) beta) (*.f64 alpha (*.f64 i i))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow alpha 2) (- (+ (* -1/8 (/ beta (* alpha (pow i 2)))) (* -1/16 (/ (pow beta 2) (* (pow alpha 2) (pow i 2))))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 alpha alpha) (-.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 beta (*.f64 alpha (*.f64 i i))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 beta beta)) (*.f64 (*.f64 i i) (*.f64 alpha alpha)))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow alpha 2) (- (+ (* -1/8 (/ beta (* alpha (pow i 2)))) (* -1/16 (/ (pow beta 2) (* (pow alpha 2) (pow i 2))))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 alpha alpha) (-.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 beta (*.f64 alpha (*.f64 i i))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 beta beta)) (*.f64 (*.f64 i i) (*.f64 alpha alpha)))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* -1/16 (/ (pow alpha 2) (pow i 2))) |
(/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 alpha alpha)) (*.f64 i i)) |
(* (pow alpha 2) (- (* -1/8 (/ beta (* alpha (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 alpha alpha) (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) beta) (*.f64 alpha (*.f64 i i))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow alpha 2) (- (* -1 (/ (+ (* 1/16 (/ (pow beta 2) (* alpha (pow i 2)))) (* 1/8 (/ beta (pow i 2)))) alpha)) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 alpha alpha) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 beta (*.f64 i i)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 beta beta)) (*.f64 alpha (*.f64 i i)))) alpha)) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow alpha 2) (- (* -1 (/ (+ (* 1/16 (/ (pow beta 2) (* alpha (pow i 2)))) (* 1/8 (/ beta (pow i 2)))) alpha)) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 alpha alpha) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 beta (*.f64 i i)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 beta beta)) (*.f64 alpha (*.f64 i i)))) alpha)) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* -1/16 (/ (pow alpha 2) (pow i 2))) |
(/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 alpha alpha)) (*.f64 i i)) |
(+ (* -1/8 (/ (* alpha beta) (pow i 2))) (* -1/16 (/ (pow alpha 2) (pow i 2)))) |
(fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 beta alpha) (*.f64 i i)) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 alpha alpha)) (*.f64 i i))) |
(+ (* -1/16 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1/8 (/ alpha (pow i 2))) (* -1/16 (/ beta (pow i 2)))))) |
(fma.f64 beta (fma.f64 #s(literal -1/8 binary64) (/.f64 alpha (*.f64 i i)) (*.f64 #s(literal -1/16 binary64) (/.f64 beta (*.f64 i i)))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 alpha alpha)) (*.f64 i i))) |
(+ (* -1/16 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1/8 (/ alpha (pow i 2))) (* -1/16 (/ beta (pow i 2)))))) |
(fma.f64 beta (fma.f64 #s(literal -1/8 binary64) (/.f64 alpha (*.f64 i i)) (*.f64 #s(literal -1/16 binary64) (/.f64 beta (*.f64 i i)))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 alpha alpha)) (*.f64 i i))) |
(* -1/16 (/ (pow beta 2) (pow i 2))) |
(/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 beta beta)) (*.f64 i i)) |
(* (pow beta 2) (- (* -1/8 (/ alpha (* beta (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 beta beta) (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) alpha) (*.f64 beta (*.f64 i i))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow beta 2) (- (+ (* -1/8 (/ alpha (* beta (pow i 2)))) (* -1/16 (/ (pow alpha 2) (* (pow beta 2) (pow i 2))))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 beta beta) (-.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 alpha (*.f64 beta (*.f64 i i))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 alpha alpha)) (*.f64 (*.f64 i i) (*.f64 beta beta)))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow beta 2) (- (+ (* -1/8 (/ alpha (* beta (pow i 2)))) (* -1/16 (/ (pow alpha 2) (* (pow beta 2) (pow i 2))))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 beta beta) (-.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 alpha (*.f64 beta (*.f64 i i))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 alpha alpha)) (*.f64 (*.f64 i i) (*.f64 beta beta)))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* -1/16 (/ (pow beta 2) (pow i 2))) |
(/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 beta beta)) (*.f64 i i)) |
(* (pow beta 2) (- (* -1/8 (/ alpha (* beta (pow i 2)))) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 beta beta) (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) alpha) (*.f64 beta (*.f64 i i))) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow beta 2) (- (* -1 (/ (+ (* 1/16 (/ (pow alpha 2) (* beta (pow i 2)))) (* 1/8 (/ alpha (pow i 2)))) beta)) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 beta beta) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 alpha (*.f64 i i)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 alpha alpha)) (*.f64 beta (*.f64 i i)))) beta)) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* (pow beta 2) (- (* -1 (/ (+ (* 1/16 (/ (pow alpha 2) (* beta (pow i 2)))) (* 1/8 (/ alpha (pow i 2)))) beta)) (* 1/16 (/ 1 (pow i 2))))) |
(*.f64 (*.f64 beta beta) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 alpha (*.f64 i i)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 alpha alpha)) (*.f64 beta (*.f64 i i)))) beta)) (/.f64 #s(literal 1/16 binary64) (*.f64 i i)))) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)) |
(* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) |
(/.f64 (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal -1/16 binary64)) (*.f64 i i)) |
| 4 322× | lower-*.f32 |
| 4 286× | lower-*.f64 |
| 3 674× | lower-/.f32 |
| 3 658× | lower-/.f64 |
| 3 380× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 89 | 694 |
| 0 | 139 | 585 |
| 1 | 752 | 562 |
| 2 | 7273 | 562 |
| 0 | 8011 | 548 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) |
(*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) |
(fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)))) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) |
(/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta)) |
#s(approx (* i (+ alpha i)) (*.f64 alpha i)) |
(*.f64 alpha i) |
(*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta))) |
(/.f64 (*.f64 i (+.f64 i alpha)) beta) |
(*.f64 i (+.f64 i alpha)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) |
(/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) |
(*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) |
(*.f64 i i) |
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))) |
(*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) |
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) |
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) |
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i))) |
(-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i)) |
(*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) |
(*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) |
#s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)))) |
(/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i)) |
| Outputs |
|---|
(+.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64))) |
(+.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))) |
(+.f64 (*.f64 alpha #s(literal 8 binary64)) (fma.f64 beta #s(literal 8 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)))) |
(+.f64 (*.f64 #s(literal 4 binary64) (+.f64 alpha beta)) (+.f64 #s(literal -4 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)))) |
(+.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (*.f64 #s(literal 4 binary64) (+.f64 alpha beta))) #s(literal -4 binary64)) |
(+.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (*.f64 alpha #s(literal 8 binary64))) (*.f64 beta #s(literal 8 binary64))) |
(-.f64 (/.f64 (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)) (+.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 #s(literal -8 binary64) (+.f64 alpha beta)))) (/.f64 (*.f64 (+.f64 alpha beta) (*.f64 #s(literal 64 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 #s(literal -8 binary64) (+.f64 alpha beta))))) |
(fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) (+.f64 #s(literal -4 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)))) |
(fma.f64 #s(literal 4 binary64) (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))) |
(fma.f64 alpha #s(literal 8 binary64) (fma.f64 beta #s(literal 8 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)))) |
(fma.f64 (+.f64 alpha beta) #s(literal 4 binary64) (+.f64 #s(literal -4 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)))) |
(fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64))) |
(fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 4 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))) |
(fma.f64 #s(literal 8 binary64) alpha (fma.f64 beta #s(literal 8 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)))) |
(fma.f64 #s(literal 8 binary64) (+.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (-.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64))) (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64))) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 512 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 #s(literal -8 binary64) (+.f64 alpha beta))) (-.f64 (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)) (*.f64 (+.f64 alpha beta) (*.f64 #s(literal 64 binary64) (+.f64 alpha beta)))))) |
(/.f64 (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 512 binary64))) (fma.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (-.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64))) (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)))) |
(/.f64 (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 512 binary64))) (fma.f64 (+.f64 alpha beta) (*.f64 #s(literal 64 binary64) (+.f64 alpha beta)) (-.f64 (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)) (*.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)) (*.f64 (+.f64 alpha beta) (*.f64 #s(literal 64 binary64) (+.f64 alpha beta)))) (+.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 #s(literal -8 binary64) (+.f64 alpha beta)))) |
(/.f64 (neg.f64 (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 512 binary64)))) (neg.f64 (fma.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (-.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64))) (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)) (*.f64 (+.f64 alpha beta) (*.f64 #s(literal 64 binary64) (+.f64 alpha beta))))) (neg.f64 (+.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 #s(literal -8 binary64) (+.f64 alpha beta))))) |
(/.f64 (-.f64 (*.f64 (+.f64 alpha beta) (*.f64 #s(literal 64 binary64) (+.f64 alpha beta))) (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64))) (-.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)))) |
(pow.f64 (/.f64 (fma.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (-.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64))) (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64))) (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 512 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 #s(literal -8 binary64) (+.f64 alpha beta))) (-.f64 (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)) (*.f64 (+.f64 alpha beta) (*.f64 #s(literal 64 binary64) (+.f64 alpha beta))))) #s(literal -1 binary64)) |
(*.f64 (fma.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 512 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (-.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64))) (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64))))) |
(*.f64 (-.f64 (*.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) (+.f64 alpha (+.f64 beta #s(literal -1 binary64)))) #s(literal 16 binary64)) (*.f64 (+.f64 alpha beta) (*.f64 #s(literal 64 binary64) (+.f64 alpha beta)))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha beta) #s(literal -4 binary64)) (*.f64 #s(literal -8 binary64) (+.f64 alpha beta))))) |
(+.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 alpha #s(literal 2 binary64))) (*.f64 #s(literal 1/16 binary64) (*.f64 beta #s(literal 2 binary64)))) |
(+.f64 (*.f64 #s(literal 1/8 binary64) alpha) (*.f64 #s(literal 1/8 binary64) beta)) |
(+.f64 (*.f64 #s(literal 1/8 binary64) beta) (*.f64 #s(literal 1/8 binary64) alpha)) |
(+.f64 (*.f64 (*.f64 alpha #s(literal 2 binary64)) #s(literal 1/16 binary64)) (*.f64 (*.f64 beta #s(literal 2 binary64)) #s(literal 1/16 binary64))) |
(+.f64 (*.f64 alpha #s(literal 1/8 binary64)) (*.f64 beta #s(literal 1/8 binary64))) |
(+.f64 (*.f64 beta #s(literal 1/8 binary64)) (*.f64 alpha #s(literal 1/8 binary64))) |
(fma.f64 alpha #s(literal 1/8 binary64) (*.f64 beta #s(literal 1/8 binary64))) |
(fma.f64 beta #s(literal 1/8 binary64) (*.f64 alpha #s(literal 1/8 binary64))) |
(fma.f64 #s(literal 1/16 binary64) (*.f64 alpha #s(literal 2 binary64)) (*.f64 #s(literal 1/16 binary64) (*.f64 beta #s(literal 2 binary64)))) |
(fma.f64 (*.f64 alpha #s(literal 2 binary64)) #s(literal 1/16 binary64) (*.f64 (*.f64 beta #s(literal 2 binary64)) #s(literal 1/16 binary64))) |
(fma.f64 #s(literal 1/8 binary64) alpha (*.f64 #s(literal 1/8 binary64) beta)) |
(fma.f64 #s(literal 1/8 binary64) beta (*.f64 #s(literal 1/8 binary64) alpha)) |
(/.f64 (*.f64 #s(literal 1/8 binary64) (fma.f64 alpha (*.f64 alpha alpha) (*.f64 beta (*.f64 beta beta)))) (fma.f64 beta (-.f64 beta alpha) (*.f64 alpha alpha))) |
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 alpha beta) (-.f64 alpha beta))) (-.f64 alpha beta)) |
(*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) |
(*.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 alpha beta) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 (+.f64 alpha beta) #s(literal 1/16 binary64))) |
(*.f64 (*.f64 (+.f64 alpha beta) #s(literal 2 binary64)) #s(literal 1/16 binary64)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 alpha beta)) |
(*.f64 (*.f64 #s(literal 1/16 binary64) (+.f64 alpha beta)) #s(literal 2 binary64)) |
(+.f64 #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 16 binary64))))) |
(+.f64 (*.f64 (+.f64 alpha beta) #s(literal 8 binary64)) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) |
(+.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) #s(literal 8 binary64)) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 16 binary64)))) |
(+.f64 (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 16 binary64))) (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) #s(literal 8 binary64))) |
(+.f64 (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64)) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) #s(literal 8 binary64)))) |
(+.f64 (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64))) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))) |
(+.f64 (+.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) #s(literal 8 binary64)) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64))) (*.f64 (+.f64 alpha beta) #s(literal 16 binary64))) |
(+.f64 (+.f64 (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 16 binary64))) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))) #s(literal 8 binary64)) |
(+.f64 (+.f64 (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64))) (*.f64 alpha #s(literal 8 binary64))) (*.f64 beta #s(literal 8 binary64))) |
(-.f64 (/.f64 (*.f64 (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 16 binary64))) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 16 binary64)))) (-.f64 (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 16 binary64))) (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) #s(literal 8 binary64)))) (/.f64 (*.f64 (*.f64 (+.f64 (+.f64 alpha beta) #s(literal 1 binary64)) (+.f64 (+.f64 alpha beta) #s(literal 1 binary64))) #s(literal 64 binary64)) (-.f64 (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 16 binary64))) (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) #s(literal 8 binary64))))) |
(fma.f64 #s(literal 4 binary64) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 2 binary64)) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) #s(literal 8 binary64)))) |
(fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) |
(fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) #s(literal 8 binary64)))) |
(fma.f64 #s(literal 8 binary64) (+.f64 alpha beta) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) |
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(/.f64 (*.f64 (*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) (-.f64 (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 16 binary64))) (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) #s(literal 8 binary64)))) #s(literal 1/256 binary64)) (-.f64 (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 16 binary64))) (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) #s(literal 8 binary64)))) |
(*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) #s(literal 1/256 binary64)) |
(*.f64 #s(literal 1/256 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64))))) |
(+.f64 (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) |
(+.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) |
(+.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i beta)))) (*.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)) (*.f64 beta (fma.f64 #s(literal 2 binary64) i beta)))) |
(+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i beta))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))) (*.f64 (*.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) |
(fma.f64 #s(literal -1 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) #s(literal -1 binary64) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)) (*.f64 beta (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 (*.f64 #s(literal 2 binary64) (*.f64 i (fma.f64 #s(literal 2 binary64) i beta))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)) (*.f64 (*.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) |
(fma.f64 (*.f64 #s(literal -1 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta) (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (-.f64 (*.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) (*.f64 (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) (*.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))))) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal -1 binary64))) (-.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal -1 binary64))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal 1 binary64))) |
(/.f64 (*.f64 (fma.f64 beta (*.f64 beta beta) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i)))) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) (fma.f64 beta (-.f64 beta (*.f64 #s(literal 2 binary64) i)) (*.f64 #s(literal 4 binary64) (*.f64 i i)))) |
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 i i)) (*.f64 beta beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) (-.f64 (*.f64 #s(literal 2 binary64) i) beta)) |
(/.f64 (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (-.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))))) |
(/.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal 1 binary64))) |
(*.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) |
(*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) |
(*.f64 (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (+.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) |
(*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) i beta)) |
(*.f64 (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (+.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))) |
#s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (/.f64 #s(literal -1/16 binary64) (*.f64 i i)) #s(literal 1/4 binary64))) |
(neg.f64 (/.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64))) (neg.f64 (*.f64 i i)))) |
(neg.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 i i) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 i i) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 i i) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64)))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 i (/.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64))) i))) |
(/.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64))) (*.f64 i i)) |
(/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (neg.f64 (*.f64 i i))) |
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64))) i) i) |
(/.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64))) #s(literal 1 binary64)) (*.f64 i i)) |
(/.f64 (neg.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (neg.f64 (neg.f64 (*.f64 i i)))) |
(/.f64 (neg.f64 (/.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64))) i)) (neg.f64 i)) |
(/.f64 (*.f64 (/.f64 #s(literal -1/16 binary64) i) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) i) |
(pow.f64 (/.f64 (*.f64 i i) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 (*.f64 i i) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 i (/.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64))) i)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (/.f64 #s(literal -1/16 binary64) (*.f64 i i)))) |
(*.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i))) |
(*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal -1/16 binary64) (/.f64 #s(literal 1 binary64) (*.f64 i i)))) |
(*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (/.f64 #s(literal -1/16 binary64) (*.f64 i i))) |
(*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 i i))) |
(*.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 i i)))) |
(*.f64 (/.f64 #s(literal -1/16 binary64) i) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i)) |
(*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i) (/.f64 #s(literal -1/16 binary64) i)) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 i i)) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64)))) |
(*.f64 (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64)) (*.f64 (+.f64 alpha beta) (/.f64 #s(literal 1 binary64) (*.f64 i i)))) |
(*.f64 (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64)) (/.f64 (+.f64 alpha beta) (*.f64 i i))) |
(*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64))) i) (/.f64 #s(literal 1 binary64) i)) |
(*.f64 (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i)) #s(literal -1/16 binary64)) |
(*.f64 (/.f64 (*.f64 (+.f64 alpha beta) #s(literal -1/16 binary64)) i) (/.f64 (+.f64 alpha beta) i)) |
Compiled 87 474 to 3 976 computations (95.5% saved)
32 alts after pruning (31 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 339 | 19 | 1 358 |
| Fresh | 14 | 12 | 26 |
| Picked | 5 | 0 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 358 | 32 | 1 390 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 18.0% | (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
| 42.5% | (*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) #s(approx (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) (fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) | |
| 33.9% | (*.f64 (/.f64 (fma.f64 i i (fma.f64 (+.f64 alpha beta) i (*.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) | |
| 42.5% | (*.f64 (/.f64 (fma.f64 i i (fma.f64 i (+.f64 alpha beta) (*.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) | |
| 22.7% | (*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (*.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) #s(literal -1 binary64))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 #s(literal 1 binary64) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))))) | |
| 26.6% | (*.f64 (/.f64 #s(approx (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (*.f64 beta (+.f64 (+.f64 alpha i) (/.f64 (*.f64 i (+.f64 alpha i)) beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) | |
| 33.9% | (*.f64 #s(approx (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) -1)) (/.f64 (*.f64 i (+.f64 beta i)) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) | |
| 67.5% | (*.f64 #s(approx (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) -1)) #s(literal 1/4 binary64)) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) | |
| 42.3% | (*.f64 i (*.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))))) | |
| ▶ | 22.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)) |
| 12.6% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) beta) beta)) | |
| ▶ | 38.3% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) |
| 27.1% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)) | |
| 14.4% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i (*.f64 (+.f64 beta i) (+.f64 beta i))) i) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) | |
| 13.8% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 i i)) (*.f64 beta beta))) | |
| 21.7% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 beta (*.f64 i (+.f64 alpha i))) beta))) | |
| 15.0% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) (*.f64 beta beta)) i)) | |
| 27.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))) | |
| 41.8% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i (+.f64 beta i)) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))))) | |
| 20.0% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(approx (* i (+ i alpha)) (*.f64 i i)) beta) (/.f64 #s(literal 1 binary64) beta))) | |
| 22.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 beta (*.f64 i (+.f64 alpha i)))) (/.f64 #s(literal 1 binary64) beta))) | |
| 14.6% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 beta beta)) (*.f64 i (+.f64 i alpha)))) | |
| 27.1% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (*.f64 (+.f64 alpha i) (*.f64 i (/.f64 #s(literal 1 binary64) beta))) (/.f64 #s(literal 1 binary64) beta))) | |
| 16.9% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (*.f64 i (*.f64 i (+.f64 beta i))) (*.f64 (+.f64 beta i) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))))))) | |
| 10.6% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))) (/.f64 (fma.f64 i i (neg.f64 (/.f64 (*.f64 (*.f64 i (*.f64 i i)) #s(literal 6 binary64)) beta))) (*.f64 beta beta)))) | |
| 34.4% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))) (/.f64 (*.f64 (*.f64 i i) #s(literal 1/4 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))))) | |
| 67.7% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))) (+.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 beta beta) (*.f64 i i)) #s(literal 1/16 binary64)) (*.f64 #s(literal -1/256 binary64) (/.f64 (fma.f64 (*.f64 beta beta) #s(literal 20 binary64) (*.f64 #s(literal 4 binary64) (fma.f64 beta beta #s(literal -1 binary64)))) (*.f64 i i)))))) | |
| ▶ | 11.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) |
| ✓ | 74.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
| 73.7% | #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (/.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64))) (pow.f64 (/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) #s(literal -1/256 binary64)) i) #s(literal 3 binary64))) (fma.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (-.f64 (*.f64 (/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) #s(literal -1/256 binary64)) i) (/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) #s(literal -1/256 binary64)) i)) (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) #s(literal -1/256 binary64)) i)))))) | |
| ▶ | 81.5% | #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
| 79.1% | #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 #s(approx (+ 1/16 (/ (* 1/16 (* 2 (+ alpha beta))) i)) (*.f64 (neg.f64 beta) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 alpha i) #s(literal 1/16 binary64)) beta)) (/.f64 #s(literal 1/8 binary64) i)))) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i))) |
Compiled 2 067 to 842 computations (59.3% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) | |
| cost-diff | 0 | (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) | |
| cost-diff | 0 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) | |
| cost-diff | 384 | (/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))) | |
| cost-diff | 0 | #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) | |
| cost-diff | 0 | (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | |
| cost-diff | 128 | (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) | |
| cost-diff | 128 | (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) | |
| cost-diff | 0 | (*.f64 i (+.f64 i alpha)) | |
| cost-diff | 0 | (/.f64 (*.f64 i (+.f64 i alpha)) beta) | |
| cost-diff | 0 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)) | |
| cost-diff | 384 | (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta) | |
| cost-diff | 0 | (/.f64 i (*.f64 beta beta)) | |
| cost-diff | 0 | (*.f64 alpha (/.f64 i (*.f64 beta beta))) | |
| cost-diff | 0 | #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta)))) | |
| cost-diff | 0 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) | |
| cost-diff | 0 | (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)) | |
| cost-diff | 0 | #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) | |
| cost-diff | 128 | (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) | |
| cost-diff | 320 | (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) |
| 7 832× | lower-fma.f32 |
| 7 828× | lower-fma.f64 |
| 5 690× | lower-*.f32 |
| 5 666× | lower-*.f64 |
| 3 294× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 87 | 792 |
| 0 | 120 | 755 |
| 1 | 316 | 745 |
| 2 | 1082 | 721 |
| 3 | 5121 | 721 |
| 4 | 7808 | 721 |
| 0 | 8020 | 694 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
(-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) |
#s(literal 1/16 binary64) |
(/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i) |
(*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) |
(*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) |
#s(literal 2 binary64) |
(+.f64 alpha beta) |
alpha |
beta |
i |
(/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i) |
#s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) |
(*.f64 beta #s(literal 1/8 binary64)) |
#s(literal 1/8 binary64) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) |
#s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta)))) |
(*.f64 alpha (/.f64 i (*.f64 beta beta))) |
alpha |
(/.f64 i (*.f64 beta beta)) |
i |
(*.f64 beta beta) |
beta |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)) |
(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta) |
(/.f64 (*.f64 i (+.f64 i alpha)) beta) |
(*.f64 i (+.f64 i alpha)) |
i |
(+.f64 i alpha) |
alpha |
beta |
(/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
#s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) |
(*.f64 i (+.f64 alpha i)) |
i |
(+.f64 alpha i) |
alpha |
(-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) |
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) |
(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) |
(+.f64 alpha beta) |
beta |
(*.f64 #s(literal 2 binary64) i) |
#s(literal 2 binary64) |
#s(literal 1 binary64) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) |
(/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))) |
(*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) |
(/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) |
(*.f64 i i) |
i |
(*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) |
(fma.f64 #s(literal 2 binary64) i beta) |
#s(literal 2 binary64) |
beta |
(*.f64 (+.f64 beta i) (+.f64 beta i)) |
(+.f64 beta i) |
(fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
| Outputs |
|---|
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (-.f64 (fma.f64 (+.f64 alpha beta) (/.f64 #s(literal 1/8 binary64) i) #s(literal 1/16 binary64)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
(-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)) |
(-.f64 (fma.f64 (+.f64 alpha beta) (/.f64 #s(literal 1/8 binary64) i) #s(literal 1/16 binary64)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) |
(fma.f64 (+.f64 alpha beta) (/.f64 #s(literal 1/8 binary64) i) #s(literal 1/16 binary64)) |
#s(literal 1/16 binary64) |
(/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i) |
(/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) i) |
(*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) |
(*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) |
(*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) |
(*.f64 (+.f64 alpha beta) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(+.f64 alpha beta) |
alpha |
beta |
i |
(/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i) |
#s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) |
(*.f64 beta #s(literal 1/8 binary64)) |
#s(literal 1/8 binary64) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (/.f64 (*.f64 i alpha) (*.f64 beta beta)))) |
#s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta)))) |
#s(approx (/ (* i (+ alpha i)) (* beta beta)) (/.f64 (*.f64 i alpha) (*.f64 beta beta))) |
(*.f64 alpha (/.f64 i (*.f64 beta beta))) |
(/.f64 (*.f64 i alpha) (*.f64 beta beta)) |
alpha |
(/.f64 i (*.f64 beta beta)) |
i |
(*.f64 beta beta) |
beta |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 i alpha)) (*.f64 beta beta))) |
(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta) |
(/.f64 (*.f64 i (+.f64 i alpha)) (*.f64 beta beta)) |
(/.f64 (*.f64 i (+.f64 i alpha)) beta) |
(*.f64 i (+.f64 i alpha)) |
i |
(+.f64 i alpha) |
alpha |
beta |
(/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 i alpha))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) |
#s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) |
#s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 i alpha))) |
(*.f64 i (+.f64 alpha i)) |
(*.f64 i (+.f64 i alpha)) |
i |
(+.f64 alpha i) |
(+.f64 i alpha) |
alpha |
(-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) |
(fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) |
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) |
(*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) |
(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(+.f64 alpha beta) |
beta |
(*.f64 #s(literal 2 binary64) i) |
(*.f64 i #s(literal 2 binary64)) |
#s(literal 2 binary64) |
#s(literal 1 binary64) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (*.f64 i i) (*.f64 (+.f64 i beta) (/.f64 (+.f64 i beta) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))))) |
(/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))) |
(*.f64 (*.f64 i i) (*.f64 (+.f64 i beta) (/.f64 (+.f64 i beta) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))) |
(*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) |
(/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 i beta) (+.f64 i beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) |
(/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) |
(/.f64 (*.f64 i i) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) |
(*.f64 i i) |
i |
(*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) |
(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) |
(fma.f64 #s(literal 2 binary64) i beta) |
(fma.f64 i #s(literal 2 binary64) beta) |
#s(literal 2 binary64) |
beta |
(*.f64 (+.f64 beta i) (+.f64 beta i)) |
(*.f64 (+.f64 i beta) (+.f64 i beta)) |
(+.f64 beta i) |
(+.f64 i beta) |
(fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)) |
(fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 1.6495458610298008 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) | |
| accuracy | 9.30747731785824 | (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) | |
| accuracy | 32.82852340916933 | (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) | |
| accuracy | 32.82966422018866 | (/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))) | |
| accuracy | 0.00390625 | (*.f64 i (+.f64 alpha i)) | |
| accuracy | 0.01953125 | (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) | |
| accuracy | 18.540716972370557 | #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) | |
| accuracy | 33.079017936929866 | (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) | |
| accuracy | 0.00390625 | (*.f64 i (+.f64 i alpha)) | |
| accuracy | 3.1313765953674344 | (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta) | |
| accuracy | 7.755555846572081 | (/.f64 (*.f64 i (+.f64 i alpha)) beta) | |
| accuracy | 46.552331073904746 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)) | |
| accuracy | 7.197989653206004 | (/.f64 i (*.f64 beta beta)) | |
| accuracy | 10.222044982790027 | (*.f64 alpha (/.f64 i (*.f64 beta beta))) | |
| accuracy | 46.552331073904746 | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) | |
| accuracy | 55.37404332948529 | #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta)))) | |
| accuracy | 0.01171875 | (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i) | |
| accuracy | 14.55303242253887 | (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)) | |
| accuracy | 14.868646161740479 | #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) | |
| accuracy | 16.497107014582685 | #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
| 211.0ms | 156× | 1 | valid |
| 59.0ms | 91× | 0 | valid |
| 19.0ms | 9× | 2 | valid |
Compiled 672 to 73 computations (89.1% saved)
ival-mult: 85.0ms (46.2% of total)ival-add: 45.0ms (24.4% of total)ival-div: 27.0ms (14.7% of total)adjust: 23.0ms (12.5% of total)ival-sub: 3.0ms (1.6% of total)exact: 1.0ms (0.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (patch (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) #<representation binary64>) () ()) |
#s(alt #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) (patch #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) #<representation binary64>) () ()) |
#s(alt (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)) (patch (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) (patch #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta)))) (patch #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta)))) #<representation binary64>) () ()) |
#s(alt (*.f64 alpha (/.f64 i (*.f64 beta beta))) (patch (*.f64 alpha (/.f64 i (*.f64 beta beta))) #<representation binary64>) () ()) |
#s(alt (/.f64 i (*.f64 beta beta)) (patch (/.f64 i (*.f64 beta beta)) #<representation binary64>) () ()) |
#s(alt (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta) (patch (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)) (patch #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 i (+.f64 i alpha)) beta) (patch (/.f64 (*.f64 i (+.f64 i alpha)) beta) #<representation binary64>) () ()) |
#s(alt (*.f64 i (+.f64 i alpha)) (patch (*.f64 i (+.f64 i alpha)) #<representation binary64>) () ()) |
#s(alt (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) (patch (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (patch (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) (patch (/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) (patch #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))) (patch (/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) (patch #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (patch (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (patch (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) #<representation binary64>) () ()) |
#s(alt #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) (patch #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i) (patch (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i) #<representation binary64>) () ()) |
#s(alt (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) (patch (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #<representation binary64>) () ()) |
#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 1/8 beta) (taylor 0 alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/8 alpha) (* 1/8 beta)) (taylor 0 alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/8 alpha) (* 1/8 beta)) (taylor 0 alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/8 alpha) (* 1/8 beta)) (taylor 0 alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 alpha) (taylor inf alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) (taylor inf alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) (taylor inf alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) (taylor inf alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 alpha) (taylor -inf alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) (taylor -inf alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) (taylor -inf alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) (taylor -inf alpha) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 alpha) (taylor 0 beta) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/8 alpha) (* 1/8 beta)) (taylor 0 beta) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/8 alpha) (* 1/8 beta)) (taylor 0 beta) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* 1/8 alpha) (* 1/8 beta)) (taylor 0 beta) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 beta) (taylor inf beta) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* beta (+ 1/8 (* 1/8 (/ alpha beta)))) (taylor inf beta) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* beta (+ 1/8 (* 1/8 (/ alpha beta)))) (taylor inf beta) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* beta (+ 1/8 (* 1/8 (/ alpha beta)))) (taylor inf beta) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 beta) (taylor -inf beta) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* beta (- (* -1/8 (/ alpha beta)) 1/8))) (taylor -inf beta) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* beta (- (* -1/8 (/ alpha beta)) 1/8))) (taylor -inf beta) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* beta (- (* -1/8 (/ alpha beta)) 1/8))) (taylor -inf beta) (#s(alt (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) (patch (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/16 (* 1/8 (/ beta i))) (taylor 0 alpha) (#s(alt (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (patch (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) (taylor 0 alpha) (#s(alt (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (patch (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) (taylor 0 alpha) (#s(alt (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (patch (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) (taylor 0 alpha) (#s(alt (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (patch (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (/ alpha i)) (taylor inf alpha) (#s(alt (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (patch (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ (* 1/8 (/ beta (* alpha i))) (+ (* 1/16 (/ 1 alpha)) (* 1/8 (/ 1 i))))) (taylor inf alpha) (#s(alt (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (patch (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ (* 1/8 (/ beta (* alpha i))) (+ (* 1/16 (/ 1 alpha)) (* 1/8 (/ 1 i))))) (taylor inf alpha) (#s(alt (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (patch (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ (* 1/8 (/ beta (* alpha i))) (+ (* 1/16 (/ 1 alpha)) (* 1/8 (/ 1 i))))) (taylor inf alpha) (#s(alt (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (patch (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/8 (/ alpha i)) (taylor -inf alpha) (#s(alt (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (patch (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* alpha (- (* -1 (/ (+ 1/16 (* 1/8 (/ beta i))) alpha)) (* 1/8 (/ 1 i))))) (taylor -inf alpha) (#s(alt (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (patch (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) #<representation binary64>) () ())) ()) |
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#s(alt (* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) (taylor inf i) (#s(alt (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) (patch (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) (taylor inf i) (#s(alt (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) (patch (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #<representation binary64>) () ())) ()) |
#s(alt (* 4 (pow i 2)) (taylor -inf i) (#s(alt (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) (patch (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) (taylor -inf i) (#s(alt (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) (patch (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) (taylor -inf i) (#s(alt (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) (patch (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) (taylor -inf i) (#s(alt (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) (patch (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #<representation binary64>) () ())) ()) |
#s(alt (* alpha i) (taylor 0 i) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* i (+ alpha i)) (taylor 0 i) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* i (+ alpha i)) (taylor 0 i) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* i (+ alpha i)) (taylor 0 i) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (pow i 2) (taylor inf i) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow i 2) (+ 1 (/ alpha i))) (taylor inf i) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow i 2) (+ 1 (/ alpha i))) (taylor inf i) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow i 2) (+ 1 (/ alpha i))) (taylor inf i) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (pow i 2) (taylor -inf i) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow i 2) (+ 1 (/ alpha i))) (taylor -inf i) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow i 2) (+ 1 (/ alpha i))) (taylor -inf i) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow i 2) (+ 1 (/ alpha i))) (taylor -inf i) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (pow i 2) (taylor 0 alpha) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* alpha i) (pow i 2)) (taylor 0 alpha) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* alpha i) (pow i 2)) (taylor 0 alpha) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* alpha i) (pow i 2)) (taylor 0 alpha) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* alpha i) (taylor inf alpha) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ i (/ (pow i 2) alpha))) (taylor inf alpha) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ i (/ (pow i 2) alpha))) (taylor inf alpha) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* alpha (+ i (/ (pow i 2) alpha))) (taylor inf alpha) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* alpha i) (taylor -inf alpha) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) (taylor -inf alpha) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) (taylor -inf alpha) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) (taylor -inf alpha) (#s(alt (*.f64 i (+.f64 alpha i)) (patch (*.f64 i (+.f64 alpha i)) #<representation binary64>) () ())) ()) |
192 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | beta | @ | inf | (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) |
| 1.0ms | i | @ | 0 | (/ (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) i) |
| 1.0ms | i | @ | inf | (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) |
| 1.0ms | alpha | @ | inf | (* alpha (/ i (* beta beta))) |
| 1.0ms | i | @ | -inf | (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) |
| 1× | egg-herbie |
| 7 852× | lower-*.f64 |
| 7 852× | lower-*.f32 |
| 6 934× | lower-fma.f64 |
| 6 934× | lower-fma.f32 |
| 4 312× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 2108 | 47035 |
| 1 | 7391 | 47003 |
| 0 | 9110 | 42805 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/8 beta) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(* 1/8 alpha) |
(* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) |
(* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) |
(* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) |
(* 1/8 alpha) |
(* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) |
(* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) |
(* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) |
(* 1/8 alpha) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(* 1/8 beta) |
(* beta (+ 1/8 (* 1/8 (/ alpha beta)))) |
(* beta (+ 1/8 (* 1/8 (/ alpha beta)))) |
(* beta (+ 1/8 (* 1/8 (/ alpha beta)))) |
(* 1/8 beta) |
(* -1 (* beta (- (* -1/8 (/ alpha beta)) 1/8))) |
(* -1 (* beta (- (* -1/8 (/ alpha beta)) 1/8))) |
(* -1 (* beta (- (* -1/8 (/ alpha beta)) 1/8))) |
(+ 1/16 (* 1/8 (/ beta i))) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(* 1/8 (/ alpha i)) |
(* alpha (+ (* 1/8 (/ beta (* alpha i))) (+ (* 1/16 (/ 1 alpha)) (* 1/8 (/ 1 i))))) |
(* alpha (+ (* 1/8 (/ beta (* alpha i))) (+ (* 1/16 (/ 1 alpha)) (* 1/8 (/ 1 i))))) |
(* alpha (+ (* 1/8 (/ beta (* alpha i))) (+ (* 1/16 (/ 1 alpha)) (* 1/8 (/ 1 i))))) |
(* 1/8 (/ alpha i)) |
(* -1 (* alpha (- (* -1 (/ (+ 1/16 (* 1/8 (/ beta i))) alpha)) (* 1/8 (/ 1 i))))) |
(* -1 (* alpha (- (* -1 (/ (+ 1/16 (* 1/8 (/ beta i))) alpha)) (* 1/8 (/ 1 i))))) |
(* -1 (* alpha (- (* -1 (/ (+ 1/16 (* 1/8 (/ beta i))) alpha)) (* 1/8 (/ 1 i))))) |
(+ 1/16 (* 1/8 (/ alpha i))) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(+ 1/16 (+ (* 1/8 (/ alpha i)) (* 1/8 (/ beta i)))) |
(* 1/8 (/ beta i)) |
(* beta (+ (* 1/8 (/ alpha (* beta i))) (+ (* 1/16 (/ 1 beta)) (* 1/8 (/ 1 i))))) |
(* beta (+ (* 1/8 (/ alpha (* beta i))) (+ (* 1/16 (/ 1 beta)) (* 1/8 (/ 1 i))))) |
(* beta (+ (* 1/8 (/ alpha (* beta i))) (+ (* 1/16 (/ 1 beta)) (* 1/8 (/ 1 i))))) |
(* 1/8 (/ beta i)) |
(* -1 (* beta (- (* -1 (/ (+ 1/16 (* 1/8 (/ alpha i))) beta)) (* 1/8 (/ 1 i))))) |
(* -1 (* beta (- (* -1 (/ (+ 1/16 (* 1/8 (/ alpha i))) beta)) (* 1/8 (/ 1 i))))) |
(* -1 (* beta (- (* -1 (/ (+ 1/16 (* 1/8 (/ alpha i))) beta)) (* 1/8 (/ 1 i))))) |
(* 1/8 (/ (+ alpha beta) i)) |
(/ (+ (* 1/16 i) (* 1/8 (+ alpha beta))) i) |
(/ (+ (* 1/16 i) (* 1/8 (+ alpha beta))) i) |
(/ (+ (* 1/16 i) (* 1/8 (+ alpha beta))) i) |
1/16 |
(+ 1/16 (* 1/8 (/ (+ alpha beta) i))) |
(+ 1/16 (* 1/8 (/ (+ alpha beta) i))) |
(+ 1/16 (* 1/8 (/ (+ alpha beta) i))) |
1/16 |
(+ 1/16 (* 1/8 (/ (+ alpha beta) i))) |
(+ 1/16 (* 1/8 (/ (+ alpha beta) i))) |
(+ 1/16 (* 1/8 (/ (+ alpha beta) i))) |
(/ (* alpha (* beta i)) (* (+ 1 (+ alpha beta)) (* (+ alpha beta) (- (+ alpha beta) 1)))) |
(* i (+ (* i (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (+ alpha beta) (- (+ alpha beta) 1)))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (* 2 (/ beta (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))) (+ (/ (* alpha (* beta (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))) (/ (* (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))))) (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (+ alpha beta) (- (+ alpha beta) 1)))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (+ (* 2 (/ beta (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (* i (- (/ 1 (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))) (+ (/ (* alpha (* beta (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))) (+ (/ (* (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (- (+ (* 2 (/ alpha (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (* 2 (/ beta (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))) (+ (/ (* alpha (* beta (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))) (/ (* (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))) (/ (* (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))))))) (+ (/ (* alpha (* beta (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))) (/ (* (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))))) (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (+ alpha beta) (- (+ alpha beta) 1)))))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/256 (/ (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) i))) |
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) (pow i 2))) (+ (* 1/256 (/ (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) i)) (* 1/16 (/ (* (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/256 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta))))))) (pow i 2)))))) |
(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (pow i 3))) (+ (* 1/256 (/ (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) (pow i 2))) (+ (* 1/256 (/ (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) i)) (+ (* 1/16 (/ (* (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/256 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta))))))) (pow i 3))) (+ (* 1/16 (/ (* (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/256 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta))))))) (pow i 2))) (* 1/16 (/ (* (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))))) (* 1/16 (* (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/256 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta))))))))))) (pow i 3))))))))) |
1/16 |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(/ (* i (+ beta i)) (pow alpha 2)) |
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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(/ (* i (+ alpha i)) (pow beta 2)) |
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(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (* alpha i) (pow beta 2)) |
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2)))) |
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2)))) |
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(/ (pow i 2) (pow beta 2)) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i)))) |
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1/16 |
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1/16 |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(/ (* i (+ beta i)) (pow alpha 2)) |
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2)) |
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(/ (- (+ (* -1 (/ (+ (* i (* (+ beta i) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (+ (* (+ (* 4 beta) (* 8 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))))))) (* (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1)))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2)) |
(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1))))))) alpha)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (+ (* -1 (* beta (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 4 alpha) (* 8 i)))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))) (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (+ (* (+ (* 4 alpha) (* 8 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (* alpha i) beta) |
(* i (+ (/ alpha beta) (/ i beta))) |
(* i (+ (/ alpha beta) (/ i beta))) |
(* i (+ (/ alpha beta) (/ i beta))) |
(/ (pow i 2) beta) |
(* (pow i 2) (+ (/ 1 beta) (/ alpha (* beta i)))) |
(* (pow i 2) (+ (/ 1 beta) (/ alpha (* beta i)))) |
(* (pow i 2) (+ (/ 1 beta) (/ alpha (* beta i)))) |
(/ (pow i 2) beta) |
(* (pow i 2) (+ (/ 1 beta) (/ alpha (* beta i)))) |
(* (pow i 2) (+ (/ 1 beta) (/ alpha (* beta i)))) |
(* (pow i 2) (+ (/ 1 beta) (/ alpha (* beta i)))) |
(/ (pow i 2) beta) |
(+ (/ (* alpha i) beta) (/ (pow i 2) beta)) |
(+ (/ (* alpha i) beta) (/ (pow i 2) beta)) |
(+ (/ (* alpha i) beta) (/ (pow i 2) beta)) |
(/ (* alpha i) beta) |
(* alpha (+ (/ i beta) (/ (pow i 2) (* alpha beta)))) |
(* alpha (+ (/ i beta) (/ (pow i 2) (* alpha beta)))) |
(* alpha (+ (/ i beta) (/ (pow i 2) (* alpha beta)))) |
(/ (* alpha i) beta) |
(* -1 (* alpha (+ (* -1 (/ i beta)) (* -1 (/ (pow i 2) (* alpha beta)))))) |
(* -1 (* alpha (+ (* -1 (/ i beta)) (* -1 (/ (pow i 2) (* alpha beta)))))) |
(* -1 (* alpha (+ (* -1 (/ i beta)) (* -1 (/ (pow i 2) (* alpha beta)))))) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(/ (* i (+ alpha i)) beta) |
(* alpha i) |
(* i (+ alpha i)) |
(* i (+ alpha i)) |
(* i (+ alpha i)) |
(pow i 2) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(pow i 2) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(pow i 2) |
(+ (* alpha i) (pow i 2)) |
(+ (* alpha i) (pow i 2)) |
(+ (* alpha i) (pow i 2)) |
(* alpha i) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(* alpha i) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(- (pow (+ beta (* 2 i)) 2) 1) |
(- (+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1) |
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1) |
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha))))) |
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2)))) |
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2)))) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha)))) |
(- (pow (+ alpha (* 2 i)) 2) 1) |
(- (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) |
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1) |
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta))))) |
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2)))) |
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2)))) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta)))) |
(- (pow (+ alpha beta) 2) 1) |
(- (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) 1) |
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1) |
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2)))) |
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2)))) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i)))) |
(+ beta (* 2 i)) |
(+ alpha (+ beta (* 2 i))) |
(+ alpha (+ beta (* 2 i))) |
(+ alpha (+ beta (* 2 i))) |
alpha |
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha)))) |
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha)))) |
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha)))) |
alpha |
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1))) |
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1))) |
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1))) |
(+ alpha (* 2 i)) |
(+ alpha (+ beta (* 2 i))) |
(+ alpha (+ beta (* 2 i))) |
(+ alpha (+ beta (* 2 i))) |
beta |
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta)))) |
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta)))) |
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta)))) |
beta |
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1))) |
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1))) |
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1))) |
(+ alpha beta) |
(+ alpha (+ beta (* 2 i))) |
(+ alpha (+ beta (* 2 i))) |
(+ alpha (+ beta (* 2 i))) |
(* 2 i) |
(* i (+ 2 (+ (/ alpha i) (/ beta i)))) |
(* i (+ 2 (+ (/ alpha i) (/ beta i)))) |
(* i (+ 2 (+ (/ alpha i) (/ beta i)))) |
(* 2 i) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2))) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2))) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2))) |
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i)) (* -1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i)))) i))) |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(/ (* i (+ beta i)) (pow alpha 2)) |
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2)) |
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(/ (- (+ (* -1 (/ (+ (* i (* (+ beta i) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (+ (* (+ (* 4 beta) (* 8 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))))))) (* (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1)))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2)) |
(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1))))))) alpha)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (+ (* -1 (* beta (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 4 alpha) (* 8 i)))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))) (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (+ (* (+ (* 4 alpha) (* 8 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (* alpha (* beta i)) (+ alpha beta)) |
(* i (+ (* i (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (+ (* 2 (/ beta (pow (+ alpha beta) 2))) (* i (- (/ 1 (pow (+ alpha beta) 2)) (+ (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (pow (+ alpha beta) 2))) (* 4 (/ (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta))))) (+ alpha beta)))))))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
(* 1/4 (pow i 2)) |
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (+ alpha beta) i)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)))))) |
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 3))) (+ (* 1/4 (/ (+ alpha beta) i)) (+ (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/16 (pow (+ alpha beta) 2)) (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))))) (pow i 3)))))))) |
(* 1/4 (pow i 2)) |
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* 1/4 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)) (* -1/16 (/ (pow (+ alpha beta) 2) i)))) i)))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) (* 1/4 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) i)) (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)))) i))) i)))) |
(/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2)) |
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
(+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
(+ (* alpha (- (+ (* alpha (- (+ (* alpha (- (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 6)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (pow (+ beta (* 2 i)) 2))))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
(* i (+ beta i)) |
(- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha)) |
(- (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))))) |
(- (+ (* -1 (/ (+ (* (+ (* 2 beta) (* 4 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))))) |
(* -1 (* i (+ (* -1 beta) (* -1 i)))) |
(+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) |
(+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) |
(+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i)))))))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) alpha))) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2)) |
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))) |
(+ (* beta (- (+ (* beta (- (+ (* beta (- (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 6)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (pow (+ alpha (* 2 i)) 2))))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))) |
(* i (+ alpha i)) |
(- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta)) |
(- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))))) |
(- (+ (* -1 (/ (+ (* (+ (* 2 alpha) (* 4 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))))) |
(* -1 (* i (+ (* -1 alpha) (* -1 i)))) |
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) |
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) |
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i)))))))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) beta))) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) |
(/ (pow i 2) (- (pow beta 2) 1)) |
(* (pow i 2) (+ (* -1 (* i (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1)))) |
(* (pow i 2) (+ (* i (- (* -1 (* i (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))))) (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1)))) |
(* (pow i 2) (+ (* i (- (* i (- (* -1 (* i (+ (* -1 (/ (* (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* -1 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (* 32 (/ 1 (* beta (pow (- (pow beta 2) 1) 2)))))))) (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))))) (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1)))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (pow beta 2) (pow i 2)))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
(- (+ 1/16 (+ (* -1 (/ (+ (* 1/256 (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* 2 (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))))) (pow i 3))) (* 1/16 (/ (pow beta 2) (pow i 2))))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
(- (+ 1/16 (+ (* -1 (/ (+ (* -2 (* beta (+ (* 1/256 (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* 2 (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))))))) (+ (* 1/256 (* (pow beta 2) (- (pow beta 2) 1))) (* 1/16 (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))))) (pow i 4))) (* 1/16 (/ (pow beta 2) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2))) (* 2 (/ (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))) (pow i 3)))))) |
1/16 |
(- (+ 1/16 (* 1/16 (/ (pow beta 2) (pow i 2)))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
(- (+ 1/16 (+ (* -2 (/ (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))) (pow i 3))) (+ (* 1/256 (/ (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3))) (pow i 3))) (* 1/16 (/ (pow beta 2) (pow i 2)))))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
(- (+ 1/16 (+ (* -1 (/ (- (+ (* 1/256 (/ (* (pow beta 2) (- (pow beta 2) 1)) i)) (+ (* 1/16 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))) i)) (* 2 (/ (* beta (+ (* -2 (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) (* 1/256 (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3)))))) i)))) (+ (* -2 (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) (* 1/256 (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3)))))) (pow i 3))) (* 1/16 (/ (pow beta 2) (pow i 2))))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
(* 1/4 (/ (pow i 2) (- (* 4 (pow i 2)) 1))) |
(+ (* 1/4 (/ (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (- (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2)))))) |
(+ (* 1/4 (/ (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (- (+ (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* beta (- (* 1/4 (/ 1 (- (* 4 (pow i 2)) 1))) (+ (* 1/16 (/ (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1) (pow (- (* 4 (pow i 2)) 1) 2))) (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2))))) (* (pow i 2) (- (* 4 (pow i 2)) 1)))))))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2)))))) |
(+ (* 1/4 (/ (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (- (+ (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* beta (- (+ (* -1 (* beta (+ (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/4 (/ 1 (- (* 4 (pow i 2)) 1))) (+ (* 1/16 (/ (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1) (pow (- (* 4 (pow i 2)) 1) 2))) (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2))))) (* (pow i 2) (- (* 4 (pow i 2)) 1))))))) (* (pow i 2) (- (* 4 (pow i 2)) 1)))) (+ (* 1/4 (/ (* (- (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2)))) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (* (pow i 2) (- (* 4 (pow i 2)) 1)))) (* 1/2 (/ i (pow (- (* 4 (pow i 2)) 1) 2))))))) (* 1/4 (/ 1 (- (* 4 (pow i 2)) 1)))) (+ (* 1/16 (/ (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1) (pow (- (* 4 (pow i 2)) 1) 2))) (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/2 (/ i (- (* 4 (pow i 2)) 1))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2))))) (* (pow i 2) (- (* 4 (pow i 2)) 1)))))))) (* 1/16 (/ (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (pow (- (* 4 (pow i 2)) 1) 2)))))) |
(/ (pow i 2) (pow beta 2)) |
(/ (- (+ (* 2 (/ (pow i 3) beta)) (pow i 2)) (* 8 (/ (pow i 3) beta))) (pow beta 2)) |
(/ (- (+ (* 2 (/ (pow i 3) beta)) (+ (/ (pow i 4) (pow beta 2)) (pow i 2))) (+ (* 8 (/ (* i (- (* 2 (pow i 3)) (* 8 (pow i 3)))) (pow beta 2))) (+ (* 8 (/ (pow i 3) beta)) (/ (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (pow beta 2))))) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* 8 (* i (- (pow i 4) (+ (* 8 (* i (- (* 2 (pow i 3)) (* 8 (pow i 3))))) (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))))) (+ (* (- (* 2 (pow i 3)) (* 8 (pow i 3))) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (* (pow i 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))))) (pow beta 3))) (+ (* 2 (/ (pow i 3) beta)) (+ (/ (pow i 4) (pow beta 2)) (pow i 2)))) (+ (* 8 (/ (* i (- (* 2 (pow i 3)) (* 8 (pow i 3)))) (pow beta 2))) (+ (* 8 (/ (pow i 3) beta)) (/ (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (pow beta 2))))) (pow beta 2)) |
(/ (pow i 2) (pow beta 2)) |
(/ (+ (* -1 (/ (- (* -2 (pow i 3)) (* -8 (pow i 3))) beta)) (pow i 2)) (pow beta 2)) |
(/ (+ (* -1 (/ (- (+ (* -2 (pow i 3)) (* -1 (/ (- (pow i 4) (+ (* -8 (* i (- (* -2 (pow i 3)) (* -8 (pow i 3))))) (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))) beta))) (* -8 (pow i 3))) beta)) (pow i 2)) (pow beta 2)) |
(/ (+ (* -1 (/ (- (+ (* -2 (pow i 3)) (* -1 (/ (- (+ (* -8 (/ (* i (- (pow i 4) (+ (* -8 (* i (- (* -2 (pow i 3)) (* -8 (pow i 3))))) (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))))) beta)) (+ (/ (* (- (* -2 (pow i 3)) (* -8 (pow i 3))) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) beta) (+ (/ (* (pow i 2) (+ (* -16 (pow i 3)) (* -4 (* i (- (* 4 (pow i 2)) 1))))) beta) (pow i 4)))) (+ (* -8 (* i (- (* -2 (pow i 3)) (* -8 (pow i 3))))) (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))) beta))) (* -8 (pow i 3))) beta)) (pow i 2)) (pow beta 2)) |
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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1/16 |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
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(/ (* i (+ beta i)) (pow alpha 2)) |
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2)) |
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(/ (- (+ (* -1 (/ (+ (* i (* (+ beta i) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (+ (* (+ (* 4 beta) (* 8 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))))))) (* (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1)))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2)) |
(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2))) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1))))))) alpha)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2)) |
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(+ (* beta (- (+ (* beta (- (+ (* -1 (* beta (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 4 alpha) (* 8 i)))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))) (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) |
(/ (* i (+ alpha i)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2)) |
(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (+ (* (+ (* 4 alpha) (* 8 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2)) |
(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
(pow i 2) |
(* (pow i 2) (+ 1 (* -2 (/ i beta)))) |
(* (pow i 2) (+ 1 (* i (- (* 5 (/ i (pow beta 2))) (* 2 (/ 1 beta)))))) |
(* (pow i 2) (+ 1 (* i (- (* i (+ (* -12 (/ i (pow beta 3))) (* 5 (/ 1 (pow beta 2))))) (* 2 (/ 1 beta)))))) |
(* 1/4 (pow i 2)) |
(* (pow i 2) (- (+ 1/4 (* 1/2 (/ beta i))) (* 1/4 (/ beta i)))) |
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (pow beta 2) (pow i 2))) (* 1/2 (/ beta i)))) (+ (* 1/16 (/ (pow beta 2) (pow i 2))) (+ (* 1/4 (/ beta i)) (/ (* beta (- (* 1/2 beta) (* 1/4 beta))) (pow i 2)))))) |
(* (pow i 2) (- (+ 1/4 (+ (* -1 (/ (+ (* 1/4 (* (pow beta 2) (- (* 1/2 beta) (* 1/4 beta)))) (* beta (- (* 1/4 (pow beta 2)) (+ (* 1/16 (pow beta 2)) (* beta (- (* 1/2 beta) (* 1/4 beta))))))) (pow i 3))) (+ (* 1/4 (/ (pow beta 2) (pow i 2))) (* 1/2 (/ beta i))))) (+ (* 1/16 (/ (pow beta 2) (pow i 2))) (+ (* 1/4 (/ beta i)) (/ (* beta (- (* 1/2 beta) (* 1/4 beta))) (pow i 2)))))) |
(* 1/4 (pow i 2)) |
(* (pow i 2) (+ 1/4 (* -1 (/ (- (* -1/2 beta) (* -1/4 beta)) i)))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (pow beta 2)) (+ (* -1 (* beta (- (* -1/2 beta) (* -1/4 beta)))) (* 1/16 (pow beta 2)))) i)) (* -1/2 beta)) (* -1/4 beta)) i)))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* beta (- (* 1/4 (pow beta 2)) (+ (* -1 (* beta (- (* -1/2 beta) (* -1/4 beta)))) (* 1/16 (pow beta 2))))) i)) (+ (* 1/4 (/ (* (pow beta 2) (- (* -1/2 beta) (* -1/4 beta))) i)) (* 1/4 (pow beta 2)))) (+ (* -1 (* beta (- (* -1/2 beta) (* -1/4 beta)))) (* 1/16 (pow beta 2)))) i)) (* -1/2 beta)) (* -1/4 beta)) i)))) |
(* 1/4 (pow i 2)) |
(+ (* 1/4 (pow i 2)) (* beta (- (* 1/2 i) (* 1/4 i)))) |
(+ (* 1/4 (pow i 2)) (* beta (- (+ (* -1/16 beta) (* 1/2 i)) (* 1/4 i)))) |
(+ (* 1/4 (pow i 2)) (* beta (- (+ (* 1/2 i) (* beta (- (* beta (- (* 1/16 (/ 1 i)) (* 1/4 (/ (- (* 1/2 i) (* 1/4 i)) (pow i 2))))) 1/16))) (* 1/4 i)))) |
(pow i 2) |
(- (+ (* 2 (/ (pow i 3) beta)) (pow i 2)) (* 4 (/ (pow i 3) beta))) |
(- (+ (* 2 (/ (pow i 3) beta)) (+ (/ (pow i 4) (pow beta 2)) (pow i 2))) (+ (* 4 (/ (* i (- (* 2 (pow i 3)) (* 4 (pow i 3)))) (pow beta 2))) (+ (* 4 (/ (pow i 3) beta)) (* 4 (/ (pow i 4) (pow beta 2)))))) |
(- (+ (* -1 (/ (+ (* 4 (* i (- (pow i 4) (+ (* 4 (* i (- (* 2 (pow i 3)) (* 4 (pow i 3))))) (* 4 (pow i 4)))))) (* 4 (* (pow i 2) (- (* 2 (pow i 3)) (* 4 (pow i 3)))))) (pow beta 3))) (+ (* 2 (/ (pow i 3) beta)) (+ (/ (pow i 4) (pow beta 2)) (pow i 2)))) (+ (* 4 (/ (* i (- (* 2 (pow i 3)) (* 4 (pow i 3)))) (pow beta 2))) (+ (* 4 (/ (pow i 3) beta)) (* 4 (/ (pow i 4) (pow beta 2)))))) |
(pow i 2) |
(+ (* -1 (/ (- (* -2 (pow i 3)) (* -4 (pow i 3))) beta)) (pow i 2)) |
(+ (* -1 (/ (- (+ (* -2 (pow i 3)) (* -1 (/ (- (pow i 4) (+ (* -4 (* i (- (* -2 (pow i 3)) (* -4 (pow i 3))))) (* 4 (pow i 4)))) beta))) (* -4 (pow i 3))) beta)) (pow i 2)) |
(+ (* -1 (/ (- (+ (* -2 (pow i 3)) (* -1 (/ (- (+ (* -4 (/ (* i (- (pow i 4) (+ (* -4 (* i (- (* -2 (pow i 3)) (* -4 (pow i 3))))) (* 4 (pow i 4))))) beta)) (+ (* 4 (/ (* (pow i 2) (- (* -2 (pow i 3)) (* -4 (pow i 3)))) beta)) (pow i 4))) (+ (* -4 (* i (- (* -2 (pow i 3)) (* -4 (pow i 3))))) (* 4 (pow i 4)))) beta))) (* -4 (pow i 3))) beta)) (pow i 2)) |
(/ (pow i 2) (pow beta 2)) |
(* (pow i 2) (+ (* -4 (/ i (pow beta 3))) (/ 1 (pow beta 2)))) |
(* (pow i 2) (+ (* i (- (* 12 (/ i (pow beta 4))) (* 4 (/ 1 (pow beta 3))))) (/ 1 (pow beta 2)))) |
(* (pow i 2) (+ (* i (- (* i (+ (* -32 (/ i (pow beta 5))) (* 12 (/ 1 (pow beta 4))))) (* 4 (/ 1 (pow beta 3))))) (/ 1 (pow beta 2)))) |
1/4 |
(+ 1/4 (* -1/4 (/ beta i))) |
(- (+ 1/4 (* -1 (/ (+ (* -1/4 (pow beta 2)) (* 1/16 (pow beta 2))) (pow i 2)))) (* 1/4 (/ beta i))) |
(- (+ 1/4 (* -1 (/ (+ (* -1 (* beta (+ (* -1/4 (pow beta 2)) (* 1/16 (pow beta 2))))) (* -1/16 (pow beta 3))) (pow i 3)))) (+ (* -1/4 (/ (pow beta 2) (pow i 2))) (+ (* 1/16 (/ (pow beta 2) (pow i 2))) (* 1/4 (/ beta i))))) |
1/4 |
(+ 1/4 (* -1/4 (/ beta i))) |
(+ 1/4 (* -1 (/ (- (+ (* -1/4 (/ (pow beta 2) i)) (* 1/16 (/ (pow beta 2) i))) (* -1/4 beta)) i))) |
(+ 1/4 (* -1 (/ (- (* -1 (/ (- (+ (* 1/16 (/ (pow beta 3) i)) (/ (* beta (+ (* -1/4 (pow beta 2)) (* 1/16 (pow beta 2)))) i)) (+ (* -1/4 (pow beta 2)) (* 1/16 (pow beta 2)))) i)) (* -1/4 beta)) i))) |
1/4 |
(+ 1/4 (* -1/4 (/ beta i))) |
(+ 1/4 (* beta (- (* 3/16 (/ beta (pow i 2))) (* 1/4 (/ 1 i))))) |
(+ 1/4 (* beta (- (* beta (+ (* -1/8 (/ beta (pow i 3))) (* 3/16 (/ 1 (pow i 2))))) (* 1/4 (/ 1 i))))) |
(/ (pow i 2) (pow beta 2)) |
(/ (+ (* -4 (/ (pow i 3) beta)) (pow i 2)) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* -16 (pow i 4)) (* 4 (pow i 4))) (pow beta 2))) (pow i 2)) (* 4 (/ (pow i 3) beta))) (pow beta 2)) |
(/ (- (+ (* -1 (/ (+ (* -16 (pow i 5)) (* -4 (* i (+ (* -16 (pow i 4)) (* 4 (pow i 4)))))) (pow beta 3))) (pow i 2)) (+ (* -16 (/ (pow i 4) (pow beta 2))) (+ (* 4 (/ (pow i 3) beta)) (* 4 (/ (pow i 4) (pow beta 2)))))) (pow beta 2)) |
(/ (pow i 2) (pow beta 2)) |
(/ (+ (* -4 (/ (pow i 3) beta)) (pow i 2)) (pow beta 2)) |
(/ (+ (* -1 (/ (- (+ (* -16 (/ (pow i 4) beta)) (* 4 (/ (pow i 4) beta))) (* -4 (pow i 3))) beta)) (pow i 2)) (pow beta 2)) |
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* 4 (/ (* i (+ (* -16 (pow i 4)) (* 4 (pow i 4)))) beta)) (* 16 (/ (pow i 5) beta))) (+ (* -16 (pow i 4)) (* 4 (pow i 4)))) beta)) (* -4 (pow i 3))) beta)) (pow i 2)) (pow beta 2)) |
(* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta)))) |
(+ (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta)))) (* 1/8 alpha)) |
(+ (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta)))) (* 1/8 alpha)) |
(+ (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta)))) (* 1/8 alpha)) |
(* 1/8 alpha) |
(* alpha (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)))) |
(* alpha (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)))) |
(* alpha (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)))) |
(* 1/8 alpha) |
(* -1 (* alpha (- (* -1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)) 1/8))) |
(* -1 (* alpha (- (* -1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)) 1/8))) |
(* -1 (* alpha (- (* -1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) alpha)) 1/8))) |
(* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha)))) |
(+ (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha)))) (* 1/8 beta)) |
(+ (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha)))) (* 1/8 beta)) |
(+ (* 1/256 (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha)))) (* 1/8 beta)) |
(* 1/8 beta) |
(* beta (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)))) |
(* beta (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)))) |
(* beta (+ 1/8 (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)))) |
(* 1/8 beta) |
(* -1 (* beta (- (* -1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)) 1/8))) |
(* -1 (* beta (- (* -1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)) 1/8))) |
(* -1 (* beta (- (* -1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) beta)) 1/8))) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) i)) |
(+ (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) i)) (* 1/8 (/ alpha i))) |
(+ (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) i)) (* 1/8 (/ alpha i))) |
(+ (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- beta 1)) (* 8 beta))) (* 8 beta))) i)) (* 1/8 (/ alpha i))) |
(* 1/8 (/ alpha i)) |
(* alpha (+ (* 1/256 (/ (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))) alpha)) (* 1/8 (/ 1 i)))) |
(* alpha (+ (* 1/256 (/ (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))) alpha)) (* 1/8 (/ 1 i)))) |
(* alpha (+ (* 1/256 (/ (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))) alpha)) (* 1/8 (/ 1 i)))) |
(* 1/8 (/ alpha i)) |
(* -1 (* alpha (- (* -1/256 (/ (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))) alpha)) (* 1/8 (/ 1 i))))) |
(* -1 (* alpha (- (* -1/256 (/ (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))) alpha)) (* 1/8 (/ 1 i))))) |
(* -1 (* alpha (- (* -1/256 (/ (+ (* 2 (/ (+ (* 4 (- beta 1)) (* 8 beta)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ beta i)))) alpha)) (* 1/8 (/ 1 i))))) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) i)) |
(+ (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) i)) (* 1/8 (/ beta i))) |
(+ (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) i)) (* 1/8 (/ beta i))) |
(+ (* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- alpha 1)) (* 8 alpha))) (* 8 alpha))) i)) (* 1/8 (/ beta i))) |
(* 1/8 (/ beta i)) |
(* beta (+ (* 1/256 (/ (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))) beta)) (* 1/8 (/ 1 i)))) |
(* beta (+ (* 1/256 (/ (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))) beta)) (* 1/8 (/ 1 i)))) |
(* beta (+ (* 1/256 (/ (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))) beta)) (* 1/8 (/ 1 i)))) |
(* 1/8 (/ beta i)) |
(* -1 (* beta (- (* -1/256 (/ (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))) beta)) (* 1/8 (/ 1 i))))) |
(* -1 (* beta (- (* -1/256 (/ (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))) beta)) (* 1/8 (/ 1 i))))) |
(* -1 (* beta (- (* -1/256 (/ (+ (* 2 (/ (+ (* 4 (- alpha 1)) (* 8 alpha)) i)) (+ (* 8 (/ 1 i)) (* 8 (/ alpha i)))) beta)) (* 1/8 (/ 1 i))))) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(pow (+ beta (* 2 i)) 2) |
(+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) |
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha))))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(pow alpha 2) |
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(pow (+ alpha (* 2 i)) 2) |
(+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta))))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(pow beta 2) |
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(pow (+ alpha beta) 2) |
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(* 4 (pow i 2)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(* alpha i) |
(* i (+ alpha i)) |
(* i (+ alpha i)) |
(* i (+ alpha i)) |
(pow i 2) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(pow i 2) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(pow i 2) |
(+ (* alpha i) (pow i 2)) |
(+ (* alpha i) (pow i 2)) |
(+ (* alpha i) (pow i 2)) |
(* alpha i) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(* alpha i) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
| Outputs |
|---|
(* 1/8 beta) |
(*.f64 #s(literal 1/8 binary64) beta) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 beta alpha)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 beta alpha)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 beta alpha)) |
(* 1/8 alpha) |
(*.f64 #s(literal 1/8 binary64) alpha) |
(* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) |
(*.f64 alpha (fma.f64 #s(literal 1/8 binary64) (/.f64 beta alpha) #s(literal 1/8 binary64))) |
(* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) |
(*.f64 alpha (fma.f64 #s(literal 1/8 binary64) (/.f64 beta alpha) #s(literal 1/8 binary64))) |
(* alpha (+ 1/8 (* 1/8 (/ beta alpha)))) |
(*.f64 alpha (fma.f64 #s(literal 1/8 binary64) (/.f64 beta alpha) #s(literal 1/8 binary64))) |
(* 1/8 alpha) |
(*.f64 #s(literal 1/8 binary64) alpha) |
(* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) |
(neg.f64 (*.f64 alpha (fma.f64 (/.f64 beta alpha) #s(literal -1/8 binary64) #s(literal -1/8 binary64)))) |
(* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) |
(neg.f64 (*.f64 alpha (fma.f64 (/.f64 beta alpha) #s(literal -1/8 binary64) #s(literal -1/8 binary64)))) |
(* -1 (* alpha (- (* -1/8 (/ beta alpha)) 1/8))) |
(neg.f64 (*.f64 alpha (fma.f64 (/.f64 beta alpha) #s(literal -1/8 binary64) #s(literal -1/8 binary64)))) |
(* 1/8 alpha) |
(*.f64 #s(literal 1/8 binary64) alpha) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 beta alpha)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 beta alpha)) |
(+ (* 1/8 alpha) (* 1/8 beta)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 beta alpha)) |
(* 1/8 beta) |
(*.f64 #s(literal 1/8 binary64) beta) |
(* beta (+ 1/8 (* 1/8 (/ alpha beta)))) |
(*.f64 beta (fma.f64 #s(literal 1/8 binary64) (/.f64 alpha beta) #s(literal 1/8 binary64))) |
(* beta (+ 1/8 (* 1/8 (/ alpha beta)))) |
(*.f64 beta (fma.f64 #s(literal 1/8 binary64) (/.f64 alpha beta) #s(literal 1/8 binary64))) |
(* beta (+ 1/8 (* 1/8 (/ alpha beta)))) |
(*.f64 beta (fma.f64 #s(literal 1/8 binary64) (/.f64 alpha beta) #s(literal 1/8 binary64))) |
(* 1/8 beta) |
(*.f64 #s(literal 1/8 binary64) beta) |
(* -1 (* beta (- (* -1/8 (/ alpha beta)) 1/8))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (* 2 (/ beta (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))) (+ (/ (* alpha (* beta (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))) (/ (* (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))))) (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (+ alpha beta) (- (+ alpha beta) 1)))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (+ (* 2 (/ beta (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (* i (- (/ 1 (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))) (+ (/ (* alpha (* beta (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))) (+ (/ (* (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (- (+ (* 2 (/ alpha (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (* 2 (/ beta (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))) (+ (/ (* alpha (* beta (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))) (/ (* (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))) (/ (* (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))))))) (+ (/ (* alpha (* beta (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))) (/ (* (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (- (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))))))) (+ (/ 1 (* (+ 1 (+ alpha beta)) (- (+ alpha beta) 1))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1)))))) (/ (* alpha (* beta (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))))) (* (pow (+ 1 (+ alpha beta)) 2) (* (pow (+ alpha beta) 3) (pow (- (+ alpha beta) 1) 2)))))) (/ (* alpha beta) (* (+ 1 (+ alpha beta)) (* (+ alpha beta) (- (+ alpha beta) 1)))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/256 (/ (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) i))) |
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(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) (pow i 2))) (+ (* 1/256 (/ (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) i)) (* 1/16 (/ (* (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/256 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta))))))) (pow i 2)))))) |
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(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 2 (* (pow (+ alpha beta) 2) (- (+ alpha beta) 1))) (* (+ 1 (+ alpha beta)) (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1)))))) (pow i 3))) (+ (* 1/256 (/ (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) (pow i 2))) (+ (* 1/256 (/ (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) i)) (+ (* 1/16 (/ (* (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/256 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta))))))) (pow i 3))) (+ (* 1/16 (/ (* (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/256 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta))))))) (pow i 2))) (* 1/16 (/ (* (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 2 (+ (* 2 (pow (+ alpha beta) 2)) (* 4 (* (+ alpha beta) (- (+ alpha beta) 1))))) (* (+ 1 (+ alpha beta)) (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))))) (* 1/16 (* (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/256 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ 1 (+ alpha beta))))))))))) (pow i 3))))))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* -1/256 (/ (+ (* -8 (+ 1 (+ alpha beta))) (* -2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta))))) i))) |
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(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (* (pow (+ beta (* 2 i)) 2) (- (+ beta (* 2 i)) 1))) (* (+ 1 (+ beta (* 2 i))) (+ (* -2 (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* -1 (pow (+ beta (* 2 i)) 2))))))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (+ (/ (* (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ (* -2 (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* -1 (pow (+ beta (* 2 i)) 2)))) (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))) (* (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))))))))))) alpha) (/ (* (+ (* -1 (+ (* -2 (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* -1 (pow (+ beta (* 2 i)) 2)))) (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))))) alpha)))) (+ (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ (* -2 (* (+ beta (* 2 i)) (- (+ beta (* 2 i)) 1))) (* -1 (pow (+ beta (* 2 i)) 2)))) (* (+ 1 (+ beta (* 2 i))) (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))) (* (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1)))))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (+ (* -1 (+ 1 (+ beta (* 2 i)))) (* -1 (- (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) 1))))))) alpha))) (pow alpha 2)) |
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (+ 1 (+ alpha (* 2 i))) (* (pow (+ alpha (* 2 i)) 2) (- (+ alpha (* 2 i)) 1)))) |
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(+.f64 beta alpha) #s(literal -1 binary64)))))) (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (fma.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal 20 binary64) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))))) (-.f64 (fma.f64 alpha (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))))) (/.f64 (*.f64 beta alpha) (*.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))))) |
1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 beta alpha)) (*.f64 #s(literal -1/8 binary64) (+.f64 beta alpha))) i)) |
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
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(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i)) (* -1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i)))) i))) |
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(+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i))))) i))) i))) |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
(/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) |
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) |
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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(+.f64 beta alpha) #s(literal -1 binary64)))))) (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (fma.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal 20 binary64) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))))) (-.f64 (fma.f64 alpha (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))))) (/.f64 (*.f64 beta alpha) (*.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))))) |
1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 beta alpha)) (*.f64 #s(literal -1/8 binary64) (+.f64 beta alpha))) i)) |
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
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(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i)) (* -1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i)))) i))) |
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(+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i))))) i))) i))) |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) |
(/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) |
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) |
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2)))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (/.f64 beta alpha) #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 alpha alpha)))) (/.f64 #s(literal 1 binary64) (*.f64 alpha alpha))))) |
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2)))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (/.f64 beta alpha) #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 alpha alpha)))) (/.f64 #s(literal 1 binary64) (*.f64 alpha alpha))))) |
(pow alpha 2) |
(*.f64 alpha alpha) |
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha)))) |
(*.f64 (*.f64 alpha alpha) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha) #s(literal 1 binary64))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha)))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta) (neg.f64 (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) alpha))) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha)))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta) (neg.f64 (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) alpha))) alpha)))) |
(- (pow (+ alpha (* 2 i)) 2) 1) |
(fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)) |
(- (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) |
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))) |
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1) |
(fma.f64 beta (+.f64 beta (fma.f64 alpha #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))) |
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1) |
(fma.f64 beta (+.f64 beta (fma.f64 alpha #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))) |
(pow beta 2) |
(*.f64 beta beta) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta))))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (fma.f64 (/.f64 alpha beta) #s(literal 2 binary64) (/.f64 (*.f64 i #s(literal 4 binary64)) beta)))) |
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2)))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (/.f64 alpha beta) #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 beta beta)))) (/.f64 #s(literal 1 binary64) (*.f64 beta beta))))) |
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2)))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (/.f64 alpha beta) #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 beta beta)))) (/.f64 #s(literal 1 binary64) (*.f64 beta beta))))) |
(pow beta 2) |
(*.f64 beta beta) |
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta)))) |
(*.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta) #s(literal 1 binary64))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta)))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha) (neg.f64 (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)) beta))) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta)))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha) (neg.f64 (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)) beta))) beta)))) |
(- (pow (+ alpha beta) 2) 1) |
(fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) |
(- (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) 1) |
(fma.f64 #s(literal 4 binary64) (*.f64 i (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))) |
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1) |
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 beta alpha))) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))) |
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1) |
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 beta alpha))) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))) |
(* 4 (pow i 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 i i)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (fma.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 4 binary64) #s(literal 4 binary64))) |
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (-.f64 (fma.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 4 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i))) (/.f64 #s(literal 1 binary64) (*.f64 i i))))) |
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (-.f64 (fma.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 4 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i))) (/.f64 #s(literal 1 binary64) (*.f64 i i))))) |
(* 4 (pow i 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 i i)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (fma.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 4 binary64) #s(literal 4 binary64))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (neg.f64 (/.f64 (fma.f64 (+.f64 beta alpha) #s(literal -4 binary64) (neg.f64 (/.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) i))) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (neg.f64 (/.f64 (fma.f64 (+.f64 beta alpha) #s(literal -4 binary64) (neg.f64 (/.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) i))) i)))) |
(+ beta (* 2 i)) |
(fma.f64 i #s(literal 2 binary64) beta) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
alpha |
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha)))) |
(*.f64 alpha (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (/.f64 beta alpha)))) |
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha)))) |
(*.f64 alpha (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (/.f64 beta alpha)))) |
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha)))) |
(*.f64 alpha (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (/.f64 beta alpha)))) |
alpha |
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha)) #s(literal -1 binary64))) |
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha)) #s(literal -1 binary64))) |
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha)) #s(literal -1 binary64))) |
(+ alpha (* 2 i)) |
(fma.f64 i #s(literal 2 binary64) alpha) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
beta |
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta)))) |
(*.f64 beta (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 i beta) (/.f64 alpha beta)))) |
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta)))) |
(*.f64 beta (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 i beta) (/.f64 alpha beta)))) |
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta)))) |
(*.f64 beta (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 i beta) (/.f64 alpha beta)))) |
beta |
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1))) |
(*.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta)) #s(literal -1 binary64))) |
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1))) |
(*.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta)) #s(literal -1 binary64))) |
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1))) |
(*.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta)) #s(literal -1 binary64))) |
(+ alpha beta) |
(+.f64 beta alpha) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(+ alpha (+ beta (* 2 i))) |
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) |
(* 2 i) |
(*.f64 i #s(literal 2 binary64)) |
(* i (+ 2 (+ (/ alpha i) (/ beta i)))) |
(*.f64 i (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 alpha i)) (/.f64 beta i))) |
(* i (+ 2 (+ (/ alpha i) (/ beta i)))) |
(*.f64 i (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 alpha i)) (/.f64 beta i))) |
(* i (+ 2 (+ (/ alpha i) (/ beta i)))) |
(*.f64 i (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 alpha i)) (/.f64 beta i))) |
(* 2 i) |
(*.f64 i #s(literal 2 binary64)) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2))) |
(*.f64 (neg.f64 i) (+.f64 (neg.f64 (/.f64 (+.f64 beta alpha) i)) #s(literal -2 binary64))) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2))) |
(*.f64 (neg.f64 i) (+.f64 (neg.f64 (/.f64 (+.f64 beta alpha) i)) #s(literal -2 binary64))) |
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2))) |
(*.f64 (neg.f64 i) (+.f64 (neg.f64 (/.f64 (+.f64 beta alpha) i)) #s(literal -2 binary64))) |
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) |
(/.f64 (*.f64 alpha (*.f64 beta i)) (*.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) |
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(*.f64 i (fma.f64 i (-.f64 (fma.f64 alpha (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))))) (/.f64 (*.f64 beta alpha) (*.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))))) |
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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alpha))))) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))))) (fma.f64 (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))))) (/.f64 (-.f64 (fma.f64 alpha (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 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(+.f64 beta alpha) #s(literal -1 binary64)))))) (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (fma.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal 20 binary64) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))))) (-.f64 (fma.f64 alpha (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))))) (/.f64 (*.f64 beta alpha) (*.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))))) |
1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 beta alpha)) (*.f64 #s(literal -1/8 binary64) (+.f64 beta alpha))) i)) |
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
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(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
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(+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i)) (* -1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i)))) i))) |
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) |
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(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2))) |
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(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
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(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2)) |
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(/ (* alpha (* beta i)) (+ alpha beta)) |
(/.f64 (*.f64 alpha (*.f64 beta i)) (+.f64 beta alpha)) |
(* i (+ (* i (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
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(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
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(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (+ (* 2 (/ beta (pow (+ alpha beta) 2))) (* i (- (/ 1 (pow (+ alpha beta) 2)) (+ (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (pow (+ alpha beta) 2))) (* 4 (/ (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta))))) (+ alpha beta)))))))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta)))) |
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(* 1/4 (pow i 2)) |
(*.f64 (*.f64 i i) #s(literal 1/4 binary64)) |
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i)))) |
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(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (+ alpha beta) i)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)))))) |
(*.f64 (*.f64 i i) (-.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 beta alpha)) i) (/.f64 (fma.f64 beta alpha (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 i i))) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i)) (fma.f64 (+.f64 beta alpha) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 beta alpha)) (+.f64 beta alpha))) (*.f64 i i)) (/.f64 (*.f64 (+.f64 beta alpha) #s(literal 1/4 binary64)) i))))) |
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 3))) (+ (* 1/4 (/ (+ alpha beta) i)) (+ (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/16 (pow (+ alpha beta) 2)) (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))))) (pow i 3)))))))) |
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(* 1/4 (pow i 2)) |
(*.f64 (*.f64 i i) #s(literal 1/4 binary64)) |
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 beta alpha)) (+.f64 beta alpha))) i))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* 1/4 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)) (* -1/16 (/ (pow (+ alpha beta) 2) i)))) i)))) |
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(* (pow i 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) (* 1/4 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) i)) (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)))) i))) i)))) |
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(/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2)) |
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(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
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(+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
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(+ (* alpha (- (+ (* alpha (- (+ (* alpha (- (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 6)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (pow (+ beta (* 2 i)) 2))))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))) |
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(* i (+ beta i)) |
(*.f64 i (+.f64 beta i)) |
(- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha)) |
(-.f64 (fma.f64 i (/.f64 (fma.f64 i (+.f64 beta i) (*.f64 (+.f64 beta i) (+.f64 beta i))) alpha) (*.f64 i (+.f64 beta i))) (/.f64 (*.f64 (*.f64 i (+.f64 beta i)) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) alpha)) |
(- (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))))) |
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(- (+ (* -1 (/ (+ (* (+ (* 2 beta) (* 4 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))))) |
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(* -1 (* i (+ (* -1 beta) (* -1 i)))) |
(*.f64 (neg.f64 i) (+.f64 (neg.f64 beta) (neg.f64 i))) |
(+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) |
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(/ (pow i 2) (- (pow beta 2) 1)) |
(/.f64 (*.f64 i i) (fma.f64 beta beta #s(literal -1 binary64))) |
(* (pow i 2) (+ (* -1 (* i (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1)))) |
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(* (pow i 2) (+ (* i (- (* -1 (* i (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))))) (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1)))) |
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(* (pow i 2) (+ (* i (- (* i (- (* -1 (* i (+ (* -1 (/ (* (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* -1 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (* 32 (/ 1 (* beta (pow (- (pow beta 2) 1) 2)))))))) (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))))) (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1)))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (pow beta 2) (pow i 2)))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2)))) |
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1/16 |
#s(literal 1/16 binary64) |
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(* 1/4 (/ (pow i 2) (- (* 4 (pow i 2)) 1))) |
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(/ (pow i 2) (pow beta 2)) |
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(/ (- (+ (* -1 (/ (+ (* 8 (* i (- (pow i 4) (+ (* 8 (* i (- (* 2 (pow i 3)) (* 8 (pow i 3))))) (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))))) (+ (* (- (* 2 (pow i 3)) (* 8 (pow i 3))) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (* (pow i 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))))) (pow beta 3))) (+ (* 2 (/ (pow i 3) beta)) (+ (/ (pow i 4) (pow beta 2)) (pow i 2)))) (+ (* 8 (/ (* i (- (* 2 (pow i 3)) (* 8 (pow i 3)))) (pow beta 2))) (+ (* 8 (/ (pow i 3) beta)) (/ (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (pow beta 2))))) (pow beta 2)) |
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(/ (+ (* -1 (/ (- (+ (* -2 (pow i 3)) (* -1 (/ (- (+ (* -8 (/ (* i (- (pow i 4) (+ (* -8 (* i (- (* -2 (pow i 3)) (* -8 (pow i 3))))) (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))))) beta)) (+ (/ (* (- (* -2 (pow i 3)) (* -8 (pow i 3))) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) beta) (+ (/ (* (pow i 2) (+ (* -16 (pow i 3)) (* -4 (* i (- (* 4 (pow i 2)) 1))))) beta) (pow i 4)))) (+ (* -8 (* i (- (* -2 (pow i 3)) (* -8 (pow i 3))))) (* (pow i 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))) beta))) (* -8 (pow i 3))) beta)) (pow i 2)) (pow beta 2)) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) |
(*.f64 i (fma.f64 i (fma.f64 i (-.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))) (*.f64 i (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (fma.f64 #s(literal 32 binary64) (/.f64 (*.f64 beta alpha) (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))) (fma.f64 (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))))) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))))) (fma.f64 (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))))) (/.f64 (-.f64 (fma.f64 alpha (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))))) (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (fma.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal 20 binary64) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))))) (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 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alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))))))) (fma.f64 (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))))) (/.f64 (-.f64 (fma.f64 alpha (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))))) (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (fma.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) #s(literal 20 binary64) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))))) (-.f64 (fma.f64 alpha (/.f64 beta (*.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))) (/.f64 (*.f64 (*.f64 beta alpha) (*.f64 #s(literal 4 binary64) (fma.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))))) (*.f64 (*.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (*.f64 (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64))))))) (/.f64 (*.f64 beta alpha) (*.f64 (+.f64 beta alpha) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) #s(literal -1 binary64)))))) |
1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 beta alpha)) (*.f64 #s(literal -1/8 binary64) (+.f64 beta alpha))) i)) |
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2)))))) |
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(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3))))))))) |
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1/16 |
#s(literal 1/16 binary64) |
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i))) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 beta alpha)) (*.f64 #s(literal -1/8 binary64) (+.f64 beta alpha))) i)) |
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(pow i 2) |
(*.f64 i i) |
(* (pow i 2) (+ 1 (* -2 (/ i beta)))) |
(*.f64 (*.f64 i i) (fma.f64 #s(literal -2 binary64) (/.f64 i beta) #s(literal 1 binary64))) |
(* (pow i 2) (+ 1 (* i (- (* 5 (/ i (pow beta 2))) (* 2 (/ 1 beta)))))) |
(*.f64 (*.f64 i i) (fma.f64 i (-.f64 (*.f64 (/.f64 i (*.f64 beta beta)) #s(literal 5 binary64)) (/.f64 #s(literal 2 binary64) beta)) #s(literal 1 binary64))) |
(* (pow i 2) (+ 1 (* i (- (* i (+ (* -12 (/ i (pow beta 3))) (* 5 (/ 1 (pow beta 2))))) (* 2 (/ 1 beta)))))) |
(*.f64 (*.f64 i i) (fma.f64 i (fma.f64 i (fma.f64 #s(literal -12 binary64) (/.f64 i (*.f64 beta (*.f64 beta beta))) (/.f64 #s(literal 5 binary64) (*.f64 beta beta))) (neg.f64 (/.f64 #s(literal 2 binary64) beta))) #s(literal 1 binary64))) |
(* 1/4 (pow i 2)) |
(*.f64 (*.f64 i i) #s(literal 1/4 binary64)) |
(* (pow i 2) (- (+ 1/4 (* 1/2 (/ beta i))) (* 1/4 (/ beta i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 beta #s(literal 1/4 binary64)) i))) |
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (pow beta 2) (pow i 2))) (* 1/2 (/ beta i)))) (+ (* 1/16 (/ (pow beta 2) (pow i 2))) (+ (* 1/4 (/ beta i)) (/ (* beta (- (* 1/2 beta) (* 1/4 beta))) (pow i 2)))))) |
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(* (pow i 2) (- (+ 1/4 (+ (* -1 (/ (+ (* 1/4 (* (pow beta 2) (- (* 1/2 beta) (* 1/4 beta)))) (* beta (- (* 1/4 (pow beta 2)) (+ (* 1/16 (pow beta 2)) (* beta (- (* 1/2 beta) (* 1/4 beta))))))) (pow i 3))) (+ (* 1/4 (/ (pow beta 2) (pow i 2))) (* 1/2 (/ beta i))))) (+ (* 1/16 (/ (pow beta 2) (pow i 2))) (+ (* 1/4 (/ beta i)) (/ (* beta (- (* 1/2 beta) (* 1/4 beta))) (pow i 2)))))) |
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(* 1/4 (pow i 2)) |
(*.f64 (*.f64 i i) #s(literal 1/4 binary64)) |
(* (pow i 2) (+ 1/4 (* -1 (/ (- (* -1/2 beta) (* -1/4 beta)) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 1/4 binary64) (neg.f64 (/.f64 (*.f64 beta #s(literal -1/4 binary64)) i)))) |
(* (pow i 2) (+ 1/4 (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (pow beta 2)) (+ (* -1 (* beta (- (* -1/2 beta) (* -1/4 beta)))) (* 1/16 (pow beta 2)))) i)) (* -1/2 beta)) (* -1/4 beta)) i)))) |
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(* (pow i 2) (+ 1/4 (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* beta (- (* 1/4 (pow beta 2)) (+ (* -1 (* beta (- (* -1/2 beta) (* -1/4 beta)))) (* 1/16 (pow beta 2))))) i)) (+ (* 1/4 (/ (* (pow beta 2) (- (* -1/2 beta) (* -1/4 beta))) i)) (* 1/4 (pow beta 2)))) (+ (* -1 (* beta (- (* -1/2 beta) (* -1/4 beta)))) (* 1/16 (pow beta 2)))) i)) (* -1/2 beta)) (* -1/4 beta)) i)))) |
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(* 1/4 (pow i 2)) |
(*.f64 (*.f64 i i) #s(literal 1/4 binary64)) |
(+ (* 1/4 (pow i 2)) (* beta (- (* 1/2 i) (* 1/4 i)))) |
(fma.f64 beta (*.f64 i #s(literal 1/4 binary64)) (*.f64 (*.f64 i i) #s(literal 1/4 binary64))) |
(+ (* 1/4 (pow i 2)) (* beta (- (+ (* -1/16 beta) (* 1/2 i)) (* 1/4 i)))) |
(fma.f64 beta (fma.f64 beta #s(literal -1/16 binary64) (*.f64 i #s(literal 1/4 binary64))) (*.f64 (*.f64 i i) #s(literal 1/4 binary64))) |
(+ (* 1/4 (pow i 2)) (* beta (- (+ (* 1/2 i) (* beta (- (* beta (- (* 1/16 (/ 1 i)) (* 1/4 (/ (- (* 1/2 i) (* 1/4 i)) (pow i 2))))) 1/16))) (* 1/4 i)))) |
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(pow i 2) |
(*.f64 i i) |
(- (+ (* 2 (/ (pow i 3) beta)) (pow i 2)) (* 4 (/ (pow i 3) beta))) |
(+.f64 (fma.f64 i i (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 i (*.f64 i i)) beta))) (/.f64 (*.f64 (*.f64 i (*.f64 i i)) #s(literal -4 binary64)) beta)) |
(- (+ (* 2 (/ (pow i 3) beta)) (+ (/ (pow i 4) (pow beta 2)) (pow i 2))) (+ (* 4 (/ (* i (- (* 2 (pow i 3)) (* 4 (pow i 3)))) (pow beta 2))) (+ (* 4 (/ (pow i 3) beta)) (* 4 (/ (pow i 4) (pow beta 2)))))) |
(-.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 i (*.f64 i i)) beta) (fma.f64 i i (/.f64 (pow.f64 i #s(literal 4 binary64)) (*.f64 beta beta)))) (fma.f64 #s(literal 4 binary64) (+.f64 (/.f64 (*.f64 i (*.f64 i i)) beta) (/.f64 (pow.f64 i #s(literal 4 binary64)) (*.f64 beta beta))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 i (*.f64 (*.f64 i (*.f64 i i)) #s(literal -2 binary64)))) (*.f64 beta beta)))) |
(- (+ (* -1 (/ (+ (* 4 (* i (- (pow i 4) (+ (* 4 (* i (- (* 2 (pow i 3)) (* 4 (pow i 3))))) (* 4 (pow i 4)))))) (* 4 (* (pow i 2) (- (* 2 (pow i 3)) (* 4 (pow i 3)))))) (pow beta 3))) (+ (* 2 (/ (pow i 3) beta)) (+ (/ (pow i 4) (pow beta 2)) (pow i 2)))) (+ (* 4 (/ (* i (- (* 2 (pow i 3)) (* 4 (pow i 3)))) (pow beta 2))) (+ (* 4 (/ (pow i 3) beta)) (* 4 (/ (pow i 4) (pow beta 2)))))) |
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(pow i 2) |
(*.f64 i i) |
(+ (* -1 (/ (- (* -2 (pow i 3)) (* -4 (pow i 3))) beta)) (pow i 2)) |
(fma.f64 i i (neg.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 i (*.f64 i i)) beta)))) |
(+ (* -1 (/ (- (+ (* -2 (pow i 3)) (* -1 (/ (- (pow i 4) (+ (* -4 (* i (- (* -2 (pow i 3)) (* -4 (pow i 3))))) (* 4 (pow i 4)))) beta))) (* -4 (pow i 3))) beta)) (pow i 2)) |
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(+ (* -1 (/ (- (+ (* -2 (pow i 3)) (* -1 (/ (- (+ (* -4 (/ (* i (- (pow i 4) (+ (* -4 (* i (- (* -2 (pow i 3)) (* -4 (pow i 3))))) (* 4 (pow i 4))))) beta)) (+ (* 4 (/ (* (pow i 2) (- (* -2 (pow i 3)) (* -4 (pow i 3)))) beta)) (pow i 4))) (+ (* -4 (* i (- (* -2 (pow i 3)) (* -4 (pow i 3))))) (* 4 (pow i 4)))) beta))) (* -4 (pow i 3))) beta)) (pow i 2)) |
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(/ (pow i 2) (pow beta 2)) |
(/.f64 (*.f64 i i) (*.f64 beta beta)) |
(* (pow i 2) (+ (* -4 (/ i (pow beta 3))) (/ 1 (pow beta 2)))) |
(*.f64 (*.f64 i i) (fma.f64 #s(literal -4 binary64) (/.f64 i (*.f64 beta (*.f64 beta beta))) (/.f64 #s(literal 1 binary64) (*.f64 beta beta)))) |
(* (pow i 2) (+ (* i (- (* 12 (/ i (pow beta 4))) (* 4 (/ 1 (pow beta 3))))) (/ 1 (pow beta 2)))) |
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(* (pow i 2) (+ (* i (- (* i (+ (* -32 (/ i (pow beta 5))) (* 12 (/ 1 (pow beta 4))))) (* 4 (/ 1 (pow beta 3))))) (/ 1 (pow beta 2)))) |
(*.f64 (*.f64 i i) (fma.f64 i (fma.f64 i (fma.f64 #s(literal -32 binary64) (/.f64 i (pow.f64 beta #s(literal 5 binary64))) (/.f64 #s(literal 12 binary64) (pow.f64 beta #s(literal 4 binary64)))) (neg.f64 (/.f64 #s(literal 4 binary64) (*.f64 beta (*.f64 beta beta))))) (/.f64 #s(literal 1 binary64) (*.f64 beta beta)))) |
1/4 |
#s(literal 1/4 binary64) |
(+ 1/4 (* -1/4 (/ beta i))) |
(fma.f64 (/.f64 beta i) #s(literal -1/4 binary64) #s(literal 1/4 binary64)) |
(- (+ 1/4 (* -1 (/ (+ (* -1/4 (pow beta 2)) (* 1/16 (pow beta 2))) (pow i 2)))) (* 1/4 (/ beta i))) |
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(- (+ 1/4 (* -1 (/ (+ (* -1 (* beta (+ (* -1/4 (pow beta 2)) (* 1/16 (pow beta 2))))) (* -1/16 (pow beta 3))) (pow i 3)))) (+ (* -1/4 (/ (pow beta 2) (pow i 2))) (+ (* 1/16 (/ (pow beta 2) (pow i 2))) (* 1/4 (/ beta i))))) |
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1/4 |
#s(literal 1/4 binary64) |
(+ 1/4 (* -1/4 (/ beta i))) |
(fma.f64 (/.f64 beta i) #s(literal -1/4 binary64) #s(literal 1/4 binary64)) |
(+ 1/4 (* -1 (/ (- (+ (* -1/4 (/ (pow beta 2) i)) (* 1/16 (/ (pow beta 2) i))) (* -1/4 beta)) i))) |
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(+ 1/4 (* -1 (/ (- (* -1 (/ (- (+ (* 1/16 (/ (pow beta 3) i)) (/ (* beta (+ (* -1/4 (pow beta 2)) (* 1/16 (pow beta 2)))) i)) (+ (* -1/4 (pow beta 2)) (* 1/16 (pow beta 2)))) i)) (* -1/4 beta)) i))) |
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1/4 |
#s(literal 1/4 binary64) |
(+ 1/4 (* -1/4 (/ beta i))) |
(fma.f64 (/.f64 beta i) #s(literal -1/4 binary64) #s(literal 1/4 binary64)) |
(+ 1/4 (* beta (- (* 3/16 (/ beta (pow i 2))) (* 1/4 (/ 1 i))))) |
(fma.f64 beta (-.f64 (*.f64 #s(literal 3/16 binary64) (/.f64 beta (*.f64 i i))) (/.f64 #s(literal 1/4 binary64) i)) #s(literal 1/4 binary64)) |
(+ 1/4 (* beta (- (* beta (+ (* -1/8 (/ beta (pow i 3))) (* 3/16 (/ 1 (pow i 2))))) (* 1/4 (/ 1 i))))) |
(fma.f64 beta (fma.f64 beta (fma.f64 #s(literal -1/8 binary64) (/.f64 beta (*.f64 i (*.f64 i i))) (/.f64 #s(literal 3/16 binary64) (*.f64 i i))) (neg.f64 (/.f64 #s(literal 1/4 binary64) i))) #s(literal 1/4 binary64)) |
(/ (pow i 2) (pow beta 2)) |
(/.f64 (*.f64 i i) (*.f64 beta beta)) |
(/ (+ (* -4 (/ (pow i 3) beta)) (pow i 2)) (pow beta 2)) |
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(*.f64 (neg.f64 beta) (fma.f64 #s(literal -1/256 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal 4 binary64) (+.f64 alpha #s(literal -1 binary64)) (*.f64 alpha #s(literal 8 binary64))) i) (fma.f64 (/.f64 alpha i) #s(literal 8 binary64) (/.f64 #s(literal 8 binary64) i))) beta) (neg.f64 (/.f64 #s(literal 1/8 binary64) i)))) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 (+.f64 beta alpha) #s(literal 8 binary64) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 4 binary64))) (*.f64 (+.f64 beta alpha) #s(literal 8 binary64))))) i) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 (+.f64 beta alpha) #s(literal 8 binary64) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 4 binary64))) (*.f64 (+.f64 beta alpha) #s(literal 8 binary64))))) i) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 (+.f64 beta alpha) #s(literal 8 binary64) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 4 binary64))) (*.f64 (+.f64 beta alpha) #s(literal 8 binary64))))) i) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 (+.f64 beta alpha) #s(literal 8 binary64) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 4 binary64))) (*.f64 (+.f64 beta alpha) #s(literal 8 binary64))))) i) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 (+.f64 beta alpha) #s(literal 8 binary64) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 4 binary64))) (*.f64 (+.f64 beta alpha) #s(literal 8 binary64))))) i) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 (+.f64 beta alpha) #s(literal 8 binary64) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 4 binary64))) (*.f64 (+.f64 beta alpha) #s(literal 8 binary64))))) i) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 (+.f64 beta alpha) #s(literal 8 binary64) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 4 binary64))) (*.f64 (+.f64 beta alpha) #s(literal 8 binary64))))) i) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 (+.f64 beta alpha) #s(literal 8 binary64) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 4 binary64))) (*.f64 (+.f64 beta alpha) #s(literal 8 binary64))))) i) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 (+.f64 beta alpha) #s(literal 8 binary64) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 4 binary64))) (*.f64 (+.f64 beta alpha) #s(literal 8 binary64))))) i) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 (+.f64 beta alpha) #s(literal 8 binary64) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 4 binary64))) (*.f64 (+.f64 beta alpha) #s(literal 8 binary64))))) i) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 (+.f64 beta alpha) #s(literal 8 binary64) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 4 binary64))) (*.f64 (+.f64 beta alpha) #s(literal 8 binary64))))) i) |
(* 1/256 (/ (+ 8 (+ (* 2 (+ (* 4 (- (+ alpha beta) 1)) (* 8 (+ alpha beta)))) (* 8 (+ alpha beta)))) i)) |
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 (+.f64 beta alpha) #s(literal 8 binary64) (*.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 4 binary64))) (*.f64 (+.f64 beta alpha) #s(literal 8 binary64))))) i) |
(pow (+ beta (* 2 i)) 2) |
(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) |
(+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) |
(fma.f64 alpha (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) |
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
(fma.f64 alpha (+.f64 alpha (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) |
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) |
(fma.f64 alpha (+.f64 alpha (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) |
(pow alpha 2) |
(*.f64 alpha alpha) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha))))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (fma.f64 (/.f64 beta alpha) #s(literal 2 binary64) (/.f64 (*.f64 i #s(literal 4 binary64)) alpha)))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (fma.f64 (/.f64 beta alpha) #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 alpha alpha)))))) |
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (fma.f64 (/.f64 beta alpha) #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 alpha alpha)))))) |
(pow alpha 2) |
(*.f64 alpha alpha) |
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha)))) |
(*.f64 (*.f64 alpha alpha) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha) #s(literal 1 binary64))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta) (/.f64 (neg.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) alpha)) alpha)))) |
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha)))) |
(*.f64 (*.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta) (/.f64 (neg.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) alpha)) alpha)))) |
(pow (+ alpha (* 2 i)) 2) |
(*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) |
(+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) |
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))) (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(fma.f64 beta (+.f64 beta (fma.f64 alpha #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))) |
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) |
(fma.f64 beta (+.f64 beta (fma.f64 alpha #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))) |
(pow beta 2) |
(*.f64 beta beta) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta))))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (fma.f64 (/.f64 alpha beta) #s(literal 2 binary64) (/.f64 (*.f64 i #s(literal 4 binary64)) beta)))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (fma.f64 (/.f64 alpha beta) #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 beta beta)))))) |
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (fma.f64 (/.f64 alpha beta) #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 beta beta)))))) |
(pow beta 2) |
(*.f64 beta beta) |
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta)))) |
(*.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta) #s(literal 1 binary64))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha) (neg.f64 (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) beta))) beta)))) |
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta)))) |
(*.f64 (*.f64 beta beta) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha) (neg.f64 (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) beta))) beta)))) |
(pow (+ alpha beta) 2) |
(*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) |
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) |
(fma.f64 #s(literal 4 binary64) (*.f64 i (+.f64 beta alpha)) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 beta alpha))) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) |
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) |
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 beta alpha))) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha))) |
(* 4 (pow i 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 i i)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (fma.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 4 binary64) #s(literal 4 binary64))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (fma.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 4 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i))))) |
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2))))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (fma.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 4 binary64) (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 i i))))) |
(* 4 (pow i 2)) |
(*.f64 #s(literal 4 binary64) (*.f64 i i)) |
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i)))) |
(*.f64 (*.f64 i i) (fma.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 4 binary64) #s(literal 4 binary64))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (neg.f64 (/.f64 (fma.f64 (+.f64 beta alpha) #s(literal -4 binary64) (neg.f64 (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) i))) i)))) |
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i)))) |
(*.f64 (*.f64 i i) (+.f64 #s(literal 4 binary64) (neg.f64 (/.f64 (fma.f64 (+.f64 beta alpha) #s(literal -4 binary64) (neg.f64 (/.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) i))) i)))) |
(* alpha i) |
(*.f64 alpha i) |
(* i (+ alpha i)) |
(*.f64 i (+.f64 alpha i)) |
(* i (+ alpha i)) |
(*.f64 i (+.f64 alpha i)) |
(* i (+ alpha i)) |
(*.f64 i (+.f64 alpha i)) |
(pow i 2) |
(*.f64 i i) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(*.f64 (*.f64 i i) (+.f64 (/.f64 alpha i) #s(literal 1 binary64))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(*.f64 (*.f64 i i) (+.f64 (/.f64 alpha i) #s(literal 1 binary64))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(*.f64 (*.f64 i i) (+.f64 (/.f64 alpha i) #s(literal 1 binary64))) |
(pow i 2) |
(*.f64 i i) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(*.f64 (*.f64 i i) (+.f64 (/.f64 alpha i) #s(literal 1 binary64))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(*.f64 (*.f64 i i) (+.f64 (/.f64 alpha i) #s(literal 1 binary64))) |
(* (pow i 2) (+ 1 (/ alpha i))) |
(*.f64 (*.f64 i i) (+.f64 (/.f64 alpha i) #s(literal 1 binary64))) |
(pow i 2) |
(*.f64 i i) |
(+ (* alpha i) (pow i 2)) |
(*.f64 i (+.f64 alpha i)) |
(+ (* alpha i) (pow i 2)) |
(*.f64 i (+.f64 alpha i)) |
(+ (* alpha i) (pow i 2)) |
(*.f64 i (+.f64 alpha i)) |
(* alpha i) |
(*.f64 alpha i) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(*.f64 alpha (+.f64 i (/.f64 (*.f64 i i) alpha))) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(*.f64 alpha (+.f64 i (/.f64 (*.f64 i i) alpha))) |
(* alpha (+ i (/ (pow i 2) alpha))) |
(*.f64 alpha (+.f64 i (/.f64 (*.f64 i i) alpha))) |
(* alpha i) |
(*.f64 alpha i) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 i) (neg.f64 (/.f64 (*.f64 i i) alpha)))) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 i) (neg.f64 (/.f64 (*.f64 i i) alpha)))) |
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha))))) |
(*.f64 (neg.f64 alpha) (+.f64 (neg.f64 i) (neg.f64 (/.f64 (*.f64 i i) alpha)))) |
| 5 132× | lower-*.f32 |
| 5 108× | lower-*.f64 |
| 4 056× | lower-fma.f32 |
| 4 052× | lower-fma.f64 |
| 3 298× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 87 | 700 |
| 0 | 120 | 583 |
| 1 | 666 | 556 |
| 2 | 6404 | 556 |
| 0 | 8506 | 537 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) |
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
(-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) |
#s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta)))) |
(*.f64 alpha (/.f64 i (*.f64 beta beta))) |
(/.f64 i (*.f64 beta beta)) |
(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)) |
(/.f64 (*.f64 i (+.f64 i alpha)) beta) |
(*.f64 i (+.f64 i alpha)) |
(-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)) |
(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) |
(/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
#s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) |
(/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) |
(/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) |
#s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) |
(/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i) |
(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) |
(*.f64 i (+.f64 alpha i)) |
| Outputs |
|---|
(+.f64 (*.f64 beta #s(literal 1/8 binary64)) (*.f64 #s(literal 1/8 binary64) alpha)) |
(+.f64 (*.f64 beta #s(literal 1/8 binary64)) (*.f64 alpha #s(literal 1/8 binary64))) |
(+.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) alpha)) (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) beta))) |
(+.f64 (*.f64 #s(literal 1/8 binary64) alpha) (*.f64 beta #s(literal 1/8 binary64))) |
(+.f64 (*.f64 (*.f64 #s(literal 2 binary64) alpha) #s(literal 1/16 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) beta) #s(literal 1/16 binary64))) |
(+.f64 (*.f64 alpha #s(literal 1/8 binary64)) (*.f64 beta #s(literal 1/8 binary64))) |
(fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) alpha) (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) beta))) |
(fma.f64 alpha #s(literal 1/8 binary64) (*.f64 beta #s(literal 1/8 binary64))) |
(fma.f64 beta #s(literal 1/8 binary64) (*.f64 #s(literal 1/8 binary64) alpha)) |
(fma.f64 beta #s(literal 1/8 binary64) (*.f64 alpha #s(literal 1/8 binary64))) |
(fma.f64 #s(literal 1/8 binary64) alpha (*.f64 beta #s(literal 1/8 binary64))) |
(fma.f64 #s(literal 1/8 binary64) beta (*.f64 #s(literal 1/8 binary64) alpha)) |
(fma.f64 #s(literal 1/8 binary64) beta (*.f64 alpha #s(literal 1/8 binary64))) |
(fma.f64 (*.f64 #s(literal 2 binary64) alpha) #s(literal 1/16 binary64) (*.f64 (*.f64 #s(literal 2 binary64) beta) #s(literal 1/16 binary64))) |
(/.f64 (*.f64 #s(literal 1/8 binary64) (fma.f64 alpha (*.f64 alpha alpha) (*.f64 beta (*.f64 beta beta)))) (fma.f64 alpha alpha (*.f64 beta (-.f64 beta alpha)))) |
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 alpha beta) (-.f64 alpha beta))) (-.f64 alpha beta)) |
(*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) |
(*.f64 #s(literal 2 binary64) (*.f64 (+.f64 alpha beta) #s(literal 1/16 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1/16 binary64)) |
(*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) |
(*.f64 #s(literal 1/8 binary64) (+.f64 alpha beta)) |
(*.f64 (*.f64 #s(literal 1/16 binary64) (+.f64 alpha beta)) #s(literal 2 binary64)) |
(+.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i))) |
(+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) #s(literal 1/16 binary64)) |
(-.f64 (/.f64 #s(literal 1/256 binary64) (-.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)))) (/.f64 (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64))) (*.f64 i i)) (-.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i))))) |
(fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) i) #s(literal 1/16 binary64)) |
(fma.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1 binary64) i)) #s(literal 1/16 binary64)) |
(fma.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (/.f64 #s(literal 1/16 binary64) i) #s(literal 1/16 binary64)) |
(fma.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) i) #s(literal 1/16 binary64)) |
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) #s(literal 1/16 binary64)) |
(fma.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 alpha beta) (/.f64 #s(literal 1 binary64) i)) #s(literal 1/16 binary64)) |
(fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) |
(fma.f64 (*.f64 #s(literal -1/8 binary64) (+.f64 alpha beta)) (/.f64 #s(literal 1 binary64) (neg.f64 i)) #s(literal 1/16 binary64)) |
(fma.f64 (/.f64 #s(literal 1 binary64) i) (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) #s(literal 1/16 binary64)) |
(fma.f64 (/.f64 #s(literal 1 binary64) i) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64))) #s(literal -1 binary64)) #s(literal 1/16 binary64)) |
(fma.f64 (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) i) #s(literal 1/16 binary64) #s(literal 1/16 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) (-.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) #s(literal 1/16 binary64)) #s(literal 1/256 binary64)) (+.f64 #s(literal 1/4096 binary64) (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1/512 binary64)) (*.f64 i (*.f64 i i)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i))) (-.f64 #s(literal 1/256 binary64) (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64))) (*.f64 i i))))) |
(/.f64 (+.f64 #s(literal 1/4096 binary64) (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1/512 binary64)) (*.f64 i (*.f64 i i)))) (fma.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) (-.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) #s(literal 1/16 binary64)) #s(literal 1/256 binary64))) |
(/.f64 (+.f64 #s(literal 1/4096 binary64) (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1/512 binary64)) (*.f64 i (*.f64 i i)))) (+.f64 (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64))) (*.f64 i i)) (-.f64 #s(literal 1/256 binary64) (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)))))) |
(/.f64 (-.f64 #s(literal 1/256 binary64) (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64))) (*.f64 i i))) (-.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)))) |
(/.f64 (neg.f64 (+.f64 #s(literal 1/4096 binary64) (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1/512 binary64)) (*.f64 i (*.f64 i i))))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) (-.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) #s(literal 1/16 binary64)) #s(literal 1/256 binary64)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/256 binary64) (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64))) (*.f64 i i)))) (neg.f64 (-.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i))))) |
(/.f64 (-.f64 (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64))) (*.f64 i i)) #s(literal 1/256 binary64)) (-.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) #s(literal 1/16 binary64))) |
(pow.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) (-.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) #s(literal 1/16 binary64)) #s(literal 1/256 binary64)) (+.f64 #s(literal 1/4096 binary64) (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1/512 binary64)) (*.f64 i (*.f64 i i))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i))) (-.f64 #s(literal 1/256 binary64) (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64))) (*.f64 i i)))) #s(literal -1 binary64)) |
(*.f64 (+.f64 #s(literal 1/4096 binary64) (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1/512 binary64)) (*.f64 i (*.f64 i i)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) (-.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) #s(literal 1/16 binary64)) #s(literal 1/256 binary64)))) |
(*.f64 (-.f64 #s(literal 1/256 binary64) (/.f64 (*.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64))) (*.f64 i i))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (+.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64)))) i))) |
(+.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64)))) i)) |
(+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) (neg.f64 i)))) |
(+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
(+.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) (neg.f64 i))) |
(+.f64 (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) (neg.f64 i)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64))) |
(+.f64 (/.f64 (-.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64)))) i) #s(literal 1/16 binary64)) |
(-.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)) |
(-.f64 (/.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)))) (fma.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (*.f64 (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i) (+.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))))) (/.f64 (*.f64 (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i) (/.f64 (*.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64)))) (*.f64 i i))) (fma.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (*.f64 (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i) (+.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)))))) |
(-.f64 (/.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64))) (+.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) (/.f64 (/.f64 (*.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64)))) (*.f64 i i)) (+.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)))) |
(fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) i) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) (neg.f64 i)))) |
(fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) i) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
(fma.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1 binary64) i)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) (neg.f64 i)))) |
(fma.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1 binary64) i)) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
(fma.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (/.f64 #s(literal 1/16 binary64) i) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) (neg.f64 i)))) |
(fma.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (/.f64 #s(literal 1/16 binary64) i) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
(fma.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) i) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) (neg.f64 i)))) |
(fma.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) i) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) (neg.f64 i)))) |
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i)) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
(fma.f64 #s(literal -1 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64))) |
(fma.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 alpha beta) (/.f64 #s(literal 1 binary64) i)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) (neg.f64 i)))) |
(fma.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 alpha beta) (/.f64 #s(literal 1 binary64) i)) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
(fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) (neg.f64 i)))) |
(fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
(fma.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) i)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64))) |
(fma.f64 (*.f64 #s(literal -1/8 binary64) (+.f64 alpha beta)) (/.f64 #s(literal 1 binary64) (neg.f64 i)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) (neg.f64 i)))) |
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#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i (+.f64 beta i)) (*.f64 i (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))))) |
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(+.f64 (*.f64 beta (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (+.f64 beta i))) (*.f64 i (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (+.f64 beta i)))) |
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#s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) |
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(/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i) |
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(pow.f64 (/.f64 (/.f64 i #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)) |
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(+.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 #s(literal 2 binary64) (*.f64 i (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))))) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 i (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) |
(+.f64 (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) alpha) (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta))) |
(+.f64 (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i alpha)) (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) beta)) |
(+.f64 (*.f64 alpha (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) |
(+.f64 (*.f64 (fma.f64 #s(literal 2 binary64) i alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 beta (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) |
(exp.f64 (*.f64 (log.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 2 binary64))) |
(fma.f64 #s(literal 2 binary64) (*.f64 i (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 alpha (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 i (*.f64 #s(literal 2 binary64) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 #s(literal 2 binary64) (*.f64 i (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))))) |
(fma.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) alpha (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta))) |
(fma.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) (*.f64 i (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))))) |
(fma.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 #s(literal 2 binary64) i) (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i alpha) (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) beta)) |
(fma.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 (fma.f64 #s(literal 2 binary64) i alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 beta (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) #s(literal 2 binary64)) i (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) |
(fma.f64 (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) i) #s(literal 2 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) |
(/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i)))) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i))))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal 4 binary64) (*.f64 i i))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal 4 binary64) (*.f64 i i))))) |
(/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i)))) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i))))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal 4 binary64) (*.f64 i i))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 (*.f64 #s(literal 2 binary64) i) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)))))) |
(/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i)))) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i))))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 (*.f64 #s(literal 2 binary64) i) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal 4 binary64) (*.f64 i i))))) |
(/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i)))) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i))))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 (*.f64 #s(literal 2 binary64) i) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 (*.f64 #s(literal 2 binary64) i) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)))))) |
(/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i)))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 i i)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal 4 binary64) (*.f64 i i))) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)))) |
(/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i)))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 i i)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 (*.f64 #s(literal 2 binary64) i) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)))) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)))) |
(/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i)))) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 4 binary64) (*.f64 i i)))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal 4 binary64) (*.f64 i i))) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))))) |
(/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i)))) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 4 binary64) (*.f64 i i)))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 (*.f64 #s(literal 2 binary64) i) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)))) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))))) |
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 i i)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i))))) (*.f64 (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal 4 binary64) (*.f64 i i))))) |
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 i i)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i))))) (*.f64 (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 (*.f64 #s(literal 2 binary64) i) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)))))) |
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 i i)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 i i)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (*.f64 (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)))) |
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 i i)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 4 binary64) (*.f64 i i)))) (*.f64 (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 4 binary64) (*.f64 i i))) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i))))) (*.f64 (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal 4 binary64) (*.f64 i i))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 4 binary64) (*.f64 i i))) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i))))) (*.f64 (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 (*.f64 #s(literal 2 binary64) i) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 4 binary64) (*.f64 i i))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 i i)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (*.f64 (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta)))) |
(/.f64 (*.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 4 binary64) (*.f64 i i))) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 4 binary64) (*.f64 i i)))) (*.f64 (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))))) |
(/.f64 (fma.f64 (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) (*.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i))))) (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 i (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) (*.f64 #s(literal 2 binary64) (*.f64 i (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))))) (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 #s(literal 2 binary64) (*.f64 i (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 i (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) (*.f64 #s(literal 2 binary64) (*.f64 i (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))))) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 #s(literal 2 binary64) (*.f64 i (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))))) |
(/.f64 (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i))))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal 4 binary64) (*.f64 i i)))) |
(/.f64 (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i))))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 (*.f64 #s(literal 2 binary64) i) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta))))) |
(/.f64 (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 i i)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta))) |
(/.f64 (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 4 binary64) (*.f64 i i)))) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i)))) |
(/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i)))) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal 4 binary64) (*.f64 i i)))) |
(/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i)))) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 (*.f64 #s(literal 2 binary64) i) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta))))) |
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 i i)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta))) |
(/.f64 (*.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 4 binary64) (*.f64 i i))) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i)))) |
(pow.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) #s(literal 2 binary64)) |
(*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) |
(*.f64 #s(literal 1 binary64) (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))) |
(*.f64 (*.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) |
(*.f64 (pow.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) #s(literal 1 binary64)) (pow.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i)))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i))) (*.f64 #s(literal 4 binary64) (*.f64 i i)))) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 8 binary64) (*.f64 i (*.f64 i i)))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 (*.f64 #s(literal 2 binary64) i) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta))))) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 i i)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 2 binary64) i) (+.f64 alpha beta))) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 #s(literal 4 binary64) (*.f64 i i))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 alpha (-.f64 beta (*.f64 #s(literal 2 binary64) i)))) #s(literal 2 binary64))) |
(+.f64 (*.f64 i i) (*.f64 alpha i)) |
(+.f64 (*.f64 alpha i) (*.f64 i i)) |
(fma.f64 alpha i (*.f64 i i)) |
(fma.f64 i alpha (*.f64 i i)) |
(fma.f64 i i (*.f64 alpha i)) |
(fma.f64 (pow.f64 i #s(literal 1 binary64)) (pow.f64 i #s(literal 1 binary64)) (*.f64 alpha i)) |
(/.f64 (fma.f64 (*.f64 i (*.f64 i i)) (*.f64 i (*.f64 i i)) (*.f64 (*.f64 i (*.f64 i i)) (*.f64 alpha (*.f64 alpha alpha)))) (fma.f64 (*.f64 i i) (*.f64 i i) (-.f64 (*.f64 (*.f64 alpha i) (*.f64 alpha i)) (*.f64 (*.f64 i i) (*.f64 alpha i))))) |
(/.f64 (fma.f64 (*.f64 i (*.f64 i i)) (*.f64 alpha (*.f64 alpha alpha)) (*.f64 (*.f64 i (*.f64 i i)) (*.f64 i (*.f64 i i)))) (fma.f64 (*.f64 alpha i) (*.f64 alpha i) (-.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 alpha i) (*.f64 i i))))) |
(/.f64 (-.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 alpha i) (*.f64 alpha i))) (*.f64 i (-.f64 i alpha))) |
(/.f64 (-.f64 (*.f64 (*.f64 alpha i) (*.f64 alpha i)) (*.f64 (*.f64 i i) (*.f64 i i))) (-.f64 (*.f64 alpha i) (*.f64 i i))) |
(/.f64 (*.f64 i (fma.f64 alpha (*.f64 alpha alpha) (*.f64 i (*.f64 i i)))) (fma.f64 alpha (-.f64 alpha i) (*.f64 i i))) |
(/.f64 (*.f64 i (fma.f64 alpha (*.f64 alpha alpha) (*.f64 i (*.f64 i i)))) (fma.f64 alpha alpha (*.f64 i (-.f64 i alpha)))) |
(/.f64 (*.f64 i (*.f64 (+.f64 alpha i) (-.f64 i alpha))) (-.f64 i alpha)) |
(/.f64 (*.f64 i (*.f64 (+.f64 alpha i) (-.f64 alpha i))) (-.f64 alpha i)) |
(/.f64 (*.f64 (fma.f64 alpha (*.f64 alpha alpha) (*.f64 i (*.f64 i i))) i) (fma.f64 alpha (-.f64 alpha i) (*.f64 i i))) |
(/.f64 (*.f64 (fma.f64 alpha (*.f64 alpha alpha) (*.f64 i (*.f64 i i))) i) (fma.f64 alpha alpha (*.f64 i (-.f64 i alpha)))) |
(/.f64 (*.f64 (*.f64 (+.f64 alpha i) (-.f64 i alpha)) i) (-.f64 i alpha)) |
(/.f64 (*.f64 (*.f64 (+.f64 alpha i) (-.f64 alpha i)) i) (-.f64 alpha i)) |
(*.f64 i (+.f64 alpha i)) |
(*.f64 (+.f64 alpha i) i) |
Compiled 75 960 to 3 810 computations (95% saved)
33 alts after pruning (30 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 387 | 13 | 1 400 |
| Fresh | 9 | 17 | 26 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 399 | 33 | 1 432 |
| Status | Accuracy | Program |
|---|---|---|
| 42.5% | (*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) #s(approx (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) (fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) | |
| 33.9% | (*.f64 (/.f64 (fma.f64 i i (fma.f64 (+.f64 alpha beta) i (*.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) | |
| 22.7% | (*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (*.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) #s(literal -1 binary64))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 #s(literal 1 binary64) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))))) | |
| 26.6% | (*.f64 (/.f64 #s(approx (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (*.f64 beta (+.f64 (+.f64 alpha i) (/.f64 (*.f64 i (+.f64 alpha i)) beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) | |
| 33.9% | (*.f64 #s(approx (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) -1)) (/.f64 (*.f64 i (+.f64 beta i)) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) | |
| 67.5% | (*.f64 #s(approx (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) -1)) #s(literal 1/4 binary64)) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) | |
| 20.0% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ i alpha)) (*.f64 i i)) beta) beta)) | |
| ✓ | 38.3% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (+.f64 beta i))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) |
| 27.1% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)) | |
| 14.4% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i (*.f64 (+.f64 beta i) (+.f64 beta i))) i) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) | |
| 34.0% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (fma.f64 beta (fma.f64 beta #s(literal -1/16 binary64) (*.f64 i #s(literal 1/4 binary64))) (*.f64 (*.f64 i i) #s(literal 1/4 binary64)))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) | |
| 13.0% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (*.f64 (*.f64 i i) (fma.f64 i (-.f64 (*.f64 (/.f64 i (*.f64 beta beta)) #s(literal 5 binary64)) (/.f64 #s(literal 2 binary64) beta)) #s(literal 1 binary64)))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) | |
| 12.1% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (*.f64 (*.f64 i i) (fma.f64 #s(literal -2 binary64) (/.f64 i beta) #s(literal 1 binary64)))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) | |
| 17.3% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (*.f64 i i)) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) | |
| 13.8% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 i i)) (*.f64 beta beta))) | |
| 21.7% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 beta (*.f64 i (+.f64 alpha i))) beta))) | |
| 15.0% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) (*.f64 beta beta)) i)) | |
| 27.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))) | |
| 41.8% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i (+.f64 beta i)) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 beta i)) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))))) | |
| 46.0% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i i) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (+.f64 beta i) (/.f64 (+.f64 beta i) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))))) | |
| 20.0% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(approx (* i (+ i alpha)) (*.f64 i i)) beta) (/.f64 #s(literal 1 binary64) beta))) | |
| 14.6% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 beta beta)) (*.f64 i (+.f64 i alpha)))) | |
| 16.9% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (*.f64 i (*.f64 i (+.f64 beta i))) (*.f64 (+.f64 beta i) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))))))) | |
| 10.6% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (+ (* (+ (* 2 i) beta) (+ (* 2 i) beta)) -1)) (/.f64 (fma.f64 i i (neg.f64 (/.f64 (*.f64 (*.f64 i (*.f64 i i)) #s(literal 6 binary64)) beta))) (*.f64 beta beta)))) | |
| 34.4% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (+ (* (+ (* 2 i) beta) (+ (* 2 i) beta)) -1)) (/.f64 (*.f64 (*.f64 i i) #s(literal 1/4 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))))) | |
| 67.7% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (+ (* (+ (* 2 i) beta) (+ (* 2 i) beta)) -1)) (+.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 beta beta) (*.f64 i i)) #s(literal 1/16 binary64)) (*.f64 #s(literal -1/256 binary64) (/.f64 (fma.f64 #s(literal 4 binary64) (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 (*.f64 beta beta) #s(literal 20 binary64))) (*.f64 i i)))))) | |
| 13.1% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (/.f64 (*.f64 (/.f64 i beta) alpha) beta))) | |
| 13.1% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 (/.f64 alpha beta) (/.f64 i beta)))) | |
| ✓ | 11.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) |
| ✓ | 74.2% | #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
| 73.7% | #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (/.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64))) (pow.f64 (/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) #s(literal -1/256 binary64)) i) #s(literal 3 binary64))) (fma.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (-.f64 (*.f64 (/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) #s(literal -1/256 binary64)) i) (/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) #s(literal -1/256 binary64)) i)) (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) #s(literal -1/256 binary64)) i)))))) | |
| 81.5% | #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 #s(approx (+ 1/16 (/ (* 1/16 (* 2 (+ alpha beta))) i)) (fma.f64 #s(literal 1/8 binary64) (/.f64 beta i) #s(literal 1/16 binary64))) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) | |
| 79.2% | #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 #s(approx (+ 1/16 (/ (* 1/16 (* 2 (+ alpha beta))) i)) (*.f64 (neg.f64 beta) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 alpha i) #s(literal 1/16 binary64)) beta)) (/.f64 #s(literal 1/8 binary64) i)))) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
Compiled 3 746 to 797 computations (78.7% saved)
| Inputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 i i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) (*.f64 beta beta)) i)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 (/.f64 alpha beta) (/.f64 i beta)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (/.f64 (*.f64 (/.f64 i beta) alpha) beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) beta) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ i alpha)) (*.f64 i i)) beta) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 beta beta)) (*.f64 i (+.f64 i alpha)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))) (/.f64 (*.f64 (*.f64 i i) #s(literal 1/4 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (+ (* (+ (* 2 i) beta) (+ (* 2 i) beta)) -1)) (/.f64 (*.f64 (*.f64 i i) #s(literal 1/4 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(approx (* i (+ i alpha)) (*.f64 i i)) beta) (/.f64 #s(literal 1 binary64) beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (*.f64 i i)) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta))) |
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#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 #s(approx (+ 1/16 (/ (* 1/16 (* 2 (+ alpha beta))) i)) (*.f64 (neg.f64 beta) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 alpha i) #s(literal 1/16 binary64)) beta)) (/.f64 #s(literal 1/8 binary64) i)))) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i))) |
(*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) #s(approx (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) (fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) |
(*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) |
(/.f64 (*.f64 (/.f64 i (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(*.f64 (/.f64 #s(approx (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (*.f64 beta (+.f64 (+.f64 alpha i) (/.f64 (*.f64 i (+.f64 alpha i)) beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) |
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (-.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta))) i) (neg.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64))))) (fma.f64 #s(literal -1/256 binary64) (/.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64))) i) (/.f64 (*.f64 (*.f64 #s(literal -2 binary64) (+.f64 alpha beta)) (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64)))) i))) i))) |
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (*.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) #s(literal -1 binary64))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 #s(literal 1 binary64) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))))) |
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (/.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i i) #s(literal 4 binary64))) (+.f64 alpha beta)) (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64)))) (*.f64 (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64)))) (*.f64 (-.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 (*.f64 i i) #s(literal 4 binary64))) (*.f64 i #s(literal 2 binary64))))) (*.f64 (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64)))) (+.f64 alpha (-.f64 beta (*.f64 i #s(literal 2 binary64))))))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (*.f64 (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64)) (/.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 i (+.f64 i (+.f64 alpha beta))))) #s(literal -1 binary64)) (pow.f64 (*.f64 (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (/.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64)) (*.f64 i (+.f64 i (+.f64 alpha beta)))) #s(literal -1 binary64)) (pow.f64 (*.f64 (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) #s(literal -1 binary64))) |
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (/.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64))) (pow.f64 (/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) #s(literal -1/256 binary64)) i) #s(literal 3 binary64))) (fma.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (-.f64 (*.f64 (/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) #s(literal -1/256 binary64)) i) (/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) #s(literal -1/256 binary64)) i)) (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 1/16 binary64)) (/.f64 (*.f64 (fma.f64 (+.f64 alpha beta) #s(literal 8 binary64) (fma.f64 (+.f64 alpha (+.f64 beta #s(literal -1 binary64))) #s(literal 8 binary64) (fma.f64 (+.f64 alpha beta) #s(literal 16 binary64) #s(literal 8 binary64)))) #s(literal -1/256 binary64)) i)))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (-.f64 #s(literal 1/16 binary64) (/.f64 (neg.f64 (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) #s(literal -1/8 binary64) (/.f64 (-.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 alpha (*.f64 beta (+.f64 alpha beta)))) i) (+.f64 (fma.f64 #s(literal 1/16 binary64) (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta))) (*.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64))))) (*.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/256 binary64)))) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 #s(literal 1/16 binary64) (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta))) (*.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64))))) (*.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/256 binary64)))) i) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (+.f64 alpha beta) #s(literal -1/8 binary64)))) i) (/.f64 (*.f64 #s(literal -1/256 binary64) (*.f64 #s(literal -4 binary64) (*.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) i)))) i)))) i))) |
| Outputs |
|---|
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) |
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 #s(approx (+ 1/16 (/ (* 1/16 (* 2 (+ alpha beta))) i)) (fma.f64 #s(literal 1/8 binary64) (/.f64 beta i) #s(literal 1/16 binary64))) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
4 calls:
| 31.0ms | alpha |
| 28.0ms | i |
| 24.0ms | beta |
| 23.0ms | (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 84.9% | 2 | alpha |
| 88.5% | 2 | beta |
| 88.6% | 2 | i |
| 87.4% | 2 | (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
Compiled 68 to 26 computations (61.8% saved)
| Inputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 i i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) (*.f64 beta beta)) i)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 (/.f64 alpha beta) (/.f64 i beta)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (/.f64 (*.f64 (/.f64 i beta) alpha) beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) beta) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ i alpha)) (*.f64 i i)) beta) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 beta beta)) (*.f64 i (+.f64 i alpha)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))) (/.f64 (*.f64 (*.f64 i i) #s(literal 1/4 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (+ (* (+ (* 2 i) beta) (+ (* 2 i) beta)) -1)) (/.f64 (*.f64 (*.f64 i i) #s(literal 1/4 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(approx (* i (+ i alpha)) (*.f64 i i)) beta) (/.f64 #s(literal 1 binary64) beta))) |
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#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta))) |
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(*.f64 (/.f64 (fma.f64 i i (fma.f64 i (+.f64 alpha beta) (*.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) |
(*.f64 (/.f64 (fma.f64 (+.f64 alpha beta) i (fma.f64 i i (*.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) |
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 #s(approx (+ 1/16 (/ (* 1/16 (* 2 (+ alpha beta))) i)) (*.f64 (neg.f64 beta) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 alpha i) #s(literal 1/16 binary64)) beta)) (/.f64 #s(literal 1/8 binary64) i)))) (/.f64 (*.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 4 binary64) (+.f64 (+.f64 alpha beta) #s(literal -1 binary64)) (*.f64 #s(literal 8 binary64) (+.f64 alpha beta))) (+.f64 #s(literal 8 binary64) (*.f64 (+.f64 alpha beta) #s(literal 8 binary64))))) i))) |
(*.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) #s(approx (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) (fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) |
(*.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) |
(/.f64 (*.f64 (/.f64 i (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 (*.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(*.f64 (/.f64 #s(approx (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (*.f64 beta (+.f64 (+.f64 alpha i) (/.f64 (*.f64 i (+.f64 alpha i)) beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) |
| Outputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))) (+.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 beta beta) (*.f64 i i)) #s(literal 1/16 binary64)) (*.f64 #s(literal -1/256 binary64) (/.f64 (fma.f64 (*.f64 beta beta) #s(literal 20 binary64) (*.f64 #s(literal 4 binary64) (fma.f64 beta beta #s(literal -1 binary64)))) (*.f64 i i)))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))) |
2 calls:
| 20.0ms | beta |
| 20.0ms | i |
| Accuracy | Segments | Branch |
|---|---|---|
| 88.5% | 2 | beta |
| 86.6% | 2 | i |
Compiled 8 to 6 computations (25% saved)
| Inputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 i i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) (*.f64 beta beta)) i)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 (/.f64 alpha beta) (/.f64 i beta)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (/.f64 (*.f64 (/.f64 i beta) alpha) beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) beta) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ i alpha)) (*.f64 i i)) beta) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 beta beta)) (*.f64 i (+.f64 i alpha)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))) (/.f64 (*.f64 (*.f64 i i) #s(literal 1/4 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (+ (* (+ (* 2 i) beta) (+ (* 2 i) beta)) -1)) (/.f64 (*.f64 (*.f64 i i) #s(literal 1/4 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(approx (* i (+ i alpha)) (*.f64 i i)) beta) (/.f64 #s(literal 1 binary64) beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (*.f64 i i)) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(literal 1 binary64) (*.f64 beta (/.f64 beta (*.f64 i (+.f64 i alpha)))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 beta (*.f64 i (+.f64 alpha i))) beta))) |
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 #s(approx (+ 1/16 (/ (* 1/16 (* 2 (+ alpha beta))) i)) (fma.f64 #s(literal 1/8 binary64) (/.f64 beta i) #s(literal 1/16 binary64))) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (*.f64 (+.f64 alpha i) (*.f64 i (/.f64 #s(literal 1 binary64) beta))) (/.f64 #s(literal 1 binary64) beta))) |
(*.f64 #s(approx (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) -1)) #s(literal 1/4 binary64)) #s(approx (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i i))))) |
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 #s(literal 2 binary64) (+.f64 alpha beta))) i)) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 beta (*.f64 i (+.f64 alpha i)))) (/.f64 #s(literal 1 binary64) beta))) |
(/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 i (+.f64 alpha i))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))) (/.f64 (fma.f64 i i (neg.f64 (/.f64 (*.f64 (*.f64 i (*.f64 i i)) #s(literal 6 binary64)) beta))) (*.f64 beta beta)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (+ (* (+ (* 2 i) beta) (+ (* 2 i) beta)) -1)) (/.f64 (fma.f64 i i (neg.f64 (/.f64 (*.f64 (*.f64 i (*.f64 i i)) #s(literal 6 binary64)) beta))) (*.f64 beta beta)))) |
(*.f64 #s(approx (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) -1)) #s(literal 1/4 binary64)) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))) |
(/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) #s(literal 1/4 binary64))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
(/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (*.f64 (*.f64 i i) #s(approx (+ 1/4 (/ (* 1/4 (- (* 2 (+ alpha beta)) (+ alpha beta))) i)) #s(literal 1/4 binary64)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (*.f64 (*.f64 i i) (fma.f64 #s(literal -2 binary64) (/.f64 i beta) #s(literal 1 binary64)))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* (/ (* i i) (* (+ (* 2 i) beta) (+ (* 2 i) beta))) (* (+ beta i) (+ beta i))) (fma.f64 beta (fma.f64 beta #s(literal -1/16 binary64) (*.f64 i #s(literal 1/4 binary64))) (*.f64 (*.f64 i i) #s(literal 1/4 binary64)))) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) #s(approx (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1)) #s(literal 1/4 binary64))) |
#s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 #s(approx (+ 1/16 (/ (* 1/16 (* 2 (+ alpha beta))) i)) (*.f64 (neg.f64 beta) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 alpha i) #s(literal 1/16 binary64)) beta)) (/.f64 #s(literal 1/8 binary64) i)))) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i))) |
(/.f64 #s(approx (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (fma.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i (*.f64 i (*.f64 i #s(literal 1/4 binary64))))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 (*.f64 i (*.f64 (+.f64 beta i) (+.f64 beta i))) i) (*.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) |
| Outputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))) |
1 calls:
| 13.0ms | beta |
| Accuracy | Segments | Branch |
|---|---|---|
| 88.3% | 2 | beta |
Compiled 4 to 3 computations (25% saved)
| Inputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 i i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) (*.f64 beta beta)) i)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 (/.f64 alpha beta) (/.f64 i beta)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (/.f64 (*.f64 (/.f64 i beta) alpha) beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) beta) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ i alpha)) (*.f64 i i)) beta) beta)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 beta beta)) (*.f64 i (+.f64 i alpha)))) |
| Outputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ i alpha)) (*.f64 i i)) beta) beta)) |
4 calls:
| 5.0ms | alpha |
| 4.0ms | i |
| 4.0ms | beta |
| 3.0ms | (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 76.0% | 2 | alpha |
| 74.2% | 1 | i |
| 76.7% | 2 | (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
| 81.5% | 2 | beta |
Compiled 68 to 26 computations (61.8% saved)
| Inputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 i i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) (*.f64 beta beta)) i)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 (/.f64 alpha beta) (/.f64 i beta)))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (/.f64 (*.f64 (/.f64 i beta) alpha) beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) beta) beta)) |
| Outputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 (/.f64 alpha beta) (/.f64 i beta)))) |
1 calls:
| 3.0ms | beta |
| Accuracy | Segments | Branch |
|---|---|---|
| 78.8% | 2 | beta |
Compiled 4 to 3 computations (25% saved)
| Inputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 alpha i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 #s(approx (* i (+ alpha i)) (*.f64 i i)) (*.f64 beta beta))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) (*.f64 beta beta)) i)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (*.f64 i (+.f64 alpha i)) (*.f64 beta beta))) |
| Outputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta))))) |
1 calls:
| 2.0ms | beta |
| Accuracy | Segments | Branch |
|---|---|---|
| 78.4% | 2 | beta |
Compiled 4 to 3 computations (25% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
| Outputs |
|---|
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
3 calls:
| 2.0ms | (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
| 1.0ms | alpha |
| 1.0ms | beta |
| Accuracy | Segments | Branch |
|---|---|---|
| 74.2% | 1 | alpha |
| 74.2% | 1 | (/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) |
| 74.2% | 1 | beta |
Compiled 64 to 23 computations (64.1% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 8.0ms | 5.181251726718055e+114 | 9.000207166917823e+114 |
| 5.0ms | 64× | 0 | valid |
Compiled 351 to 147 computations (58.1% saved)
ival-mult: 2.0ms (55.6% of total)ival-div: 1.0ms (27.8% of total)ival-add: 1.0ms (27.8% of total)ival-sub: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 13.0ms | 1.8503474614676987e+143 | 1.6660352022615553e+144 |
| 8.0ms | 96× | 0 | valid |
Compiled 347 to 185 computations (46.7% saved)
ival-add: 2.0ms (36.5% of total)ival-mult: 2.0ms (36.5% of total)ival-div: 1.0ms (18.2% of total)ival-sub: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.8503474614676987e+143 | 1.6660352022615553e+144 |
Compiled 179 to 101 computations (43.6% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 4.0ms | 1.8503474614676987e+143 | 1.6660352022615553e+144 |
Compiled 173 to 95 computations (45.1% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 15.0ms | 5.553650880869515e+224 | 1.0159225974030053e+229 |
| 11.0ms | 128× | 0 | valid |
Compiled 211 to 119 computations (43.6% saved)
ival-mult: 3.0ms (40.2% of total)ival-add: 2.0ms (26.8% of total)ival-sub: 1.0ms (13.4% of total)ival-div: 1.0ms (13.4% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 13.0ms | 1.226177325849214e+238 | 1.5101160554375114e+240 |
| 9.0ms | 112× | 0 | valid |
Compiled 192 to 107 computations (44.3% saved)
ival-mult: 3.0ms (45.8% of total)ival-add: 2.0ms (30.5% of total)ival-sub: 1.0ms (15.3% of total)ival-div: 1.0ms (15.3% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 24× | *-commutative_binary64 |
| 20× | +-commutative_binary64 |
| 8× | sub-neg_binary64 |
| 6× | neg-sub0_binary64 |
| 6× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 131 | 910 |
| 1 | 151 | 910 |
| 2 | 158 | 910 |
| 3 | 164 | 910 |
| 4 | 169 | 910 |
| 5 | 171 | 910 |
| 1× | saturated |
| Inputs |
|---|
(if (<=.f64 i #s(literal 8200000000000000127587212261628112798999251454752703753632118759532837005550996766772880197303389070944891503116288 binary64)) (*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 #s(approx (+ 1/16 (/ (* 1/16 (* 2 (+ alpha beta))) i)) (fma.f64 #s(literal 1/8 binary64) (/.f64 beta i) #s(literal 1/16 binary64))) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)))) |
(if (<=.f64 beta #s(literal 1600000000000000037992691773841768571853852684525891499957543981872379887267232916109084205145733270606953550614144185721269461071824130517499904 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))) (+.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 beta beta) (*.f64 i i)) #s(literal 1/16 binary64)) (*.f64 #s(literal -1/256 binary64) (/.f64 (fma.f64 (*.f64 beta beta) #s(literal 20 binary64) (*.f64 #s(literal 4 binary64) (fma.f64 beta beta #s(literal -1 binary64)))) (*.f64 i i)))))) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta)))) |
(if (<=.f64 beta #s(literal 1600000000000000037992691773841768571853852684525891499957543981872379887267232916109084205145733270606953550614144185721269461071824130517499904 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta)))) |
(if (<=.f64 beta #s(literal 1600000000000000037992691773841768571853852684525891499957543981872379887267232916109084205145733270606953550614144185721269461071824130517499904 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ i alpha)) (*.f64 i i)) beta) beta))) |
(if (<=.f64 beta #s(literal 1700000000000000092065200863084769624201218833164254789294426062868025033664971570281351971840990186809201452297131512524415733641240578593739405832787796249213022746436256058565123540862523099958848147208924671696521721282560 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 (/.f64 alpha beta) (/.f64 i beta))))) |
(if (<=.f64 beta #s(literal 12999999999999999764881677158280098463536362704700692086119981795839630882823981950009929220280988412606792099920826715697335695242318872410678609193614294218199508492816167658183557882560795652782783140981135393982194100683740919642456064 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta)))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
| Outputs |
|---|
(if (<=.f64 i #s(literal 8200000000000000127587212261628112798999251454752703753632118759532837005550996766772880197303389070944891503116288 binary64)) (*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))) #s(approx (* (/ (/ (* i (+ i (+ alpha beta))) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) 1)) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i 2) (+ alpha beta))) (+ (+ (* i 2) (+ alpha beta)) -1))) (-.f64 #s(approx (+ 1/16 (/ (* 1/16 (* 2 (+ alpha beta))) i)) (fma.f64 #s(literal 1/8 binary64) (/.f64 beta i) #s(literal 1/16 binary64))) (/.f64 #s(approx (* 1/256 (+ (* 2 (+ (* 4 (+ (+ alpha beta) -1)) (* 8 (+ alpha beta)))) (+ 8 (* (+ alpha beta) 8)))) (*.f64 beta #s(literal 1/8 binary64))) i)))) |
(if (<=.f64 beta #s(literal 1600000000000000037992691773841768571853852684525891499957543981872379887267232916109084205145733270606953550614144185721269461071824130517499904 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))) (+.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 beta beta) (*.f64 i i)) #s(literal 1/16 binary64)) (*.f64 #s(literal -1/256 binary64) (/.f64 (fma.f64 (*.f64 beta beta) #s(literal 20 binary64) (*.f64 #s(literal 4 binary64) (fma.f64 beta beta #s(literal -1 binary64)))) (*.f64 i i)))))) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta)))) |
(if (<=.f64 beta #s(literal 1600000000000000037992691773841768571853852684525891499957543981872379887267232916109084205145733270606953550614144185721269461071824130517499904 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta)))) |
(if (<=.f64 beta #s(literal 1600000000000000037992691773841768571853852684525891499957543981872379887267232916109084205145733270606953550614144185721269461071824130517499904 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) (/.f64 (/.f64 #s(approx (* i (+ i alpha)) (*.f64 i i)) beta) beta))) |
(if (<=.f64 beta #s(literal 1700000000000000092065200863084769624201218833164254789294426062868025033664971570281351971840990186809201452297131512524415733641240578593739405832787796249213022746436256058565123540862523099958848147208924671696521721282560 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 (/.f64 alpha beta) (/.f64 i beta))))) |
(if (<=.f64 beta #s(literal 1700000000000000092065200863084769624201218833164254789294426062868025033664971570281351971840990186809201452297131512524415733641240578593739405832787796249213022746436256058565123540862523099958848147208924671696521721282560 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 (/.f64 i beta) (/.f64 alpha beta))))) |
(if (<=.f64 beta #s(literal 12999999999999999764881677158280098463536362704700692086119981795839630882823981950009929220280988412606792099920826715697335695242318872410678609193614294218199508492816167658183557882560795652782783140981135393982194100683740919642456064 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) #s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(approx (/ (* i (+ alpha i)) (* beta beta)) (*.f64 alpha (/.f64 i (*.f64 beta beta)))))) |
#s(approx (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)) #s(literal 1/16 binary64)) |
| 9 164× | lower-fma.f64 |
| 9 164× | lower-fma.f32 |
| 7 852× | lower-*.f64 |
| 7 852× | lower-*.f32 |
| 6 934× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 57 | 592 |
| 0 | 93 | 490 |
| 1 | 495 | 490 |
| 2 | 4647 | 490 |
| 0 | 8414 | 486 |
| 0 | 3151 | 56825 |
| 0 | 8303 | 54455 |
| 0 | 17 | 157 |
| 0 | 29 | 127 |
| 1 | 146 | 127 |
| 2 | 1503 | 127 |
| 0 | 8201 | 117 |
| 0 | 1089 | 12630 |
| 1 | 3841 | 11840 |
| 0 | 8260 | 10972 |
| 0 | 2108 | 47035 |
| 1 | 7391 | 47003 |
| 0 | 9110 | 42805 |
| 0 | 87 | 700 |
| 0 | 120 | 583 |
| 1 | 666 | 556 |
| 2 | 6404 | 556 |
| 0 | 8506 | 537 |
| 0 | 2268 | 48093 |
| 1 | 7831 | 48075 |
| 0 | 8152 | 43795 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 452 to 209 computations (53.8% saved)
Compiled 614 to 218 computations (64.5% saved)
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