
Time bar (total: 12.9s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 1 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 2 |
| 50% | 50% | 50% | 0.1% | 0% | 0% | 0% | 3 |
| 50% | 50% | 50% | 0.1% | 0% | 0% | 0% | 4 |
| 75% | 74.9% | 25% | 0.1% | 0% | 0% | 0% | 5 |
| 75% | 74.9% | 25% | 0.1% | 0% | 0% | 0% | 6 |
| 87.5% | 87.4% | 12.5% | 0.1% | 0% | 0% | 0% | 7 |
| 87.5% | 87.4% | 12.5% | 0.1% | 0% | 0% | 0% | 8 |
| 93.7% | 92.5% | 6.2% | 0.1% | 0% | 1.2% | 0% | 9 |
| 93.7% | 92.5% | 6.2% | 0.1% | 0% | 1.2% | 0% | 10 |
| 96.8% | 94.9% | 3.1% | 0.1% | 0% | 1.9% | 0% | 11 |
| 96.8% | 94.9% | 3.1% | 0.1% | 0% | 1.9% | 0% | 12 |
Compiled 31 to 21 computations (32.3% saved)
| 1.1s | 2 317× | 1 | valid |
| 880.0ms | 5 938× | 0 | valid |
| 174.0ms | 952× | 0 | exit |
| 4.0ms | 26× | 1 | exit |
| 0.0ms | 1× | 2 | valid |
ival-exp: 655.0ms (36% of total)ival-mult: 343.0ms (18.9% of total)ival-sub: 230.0ms (12.6% of total)ival-div: 202.0ms (11.1% of total)ival-add: 158.0ms (8.7% of total)ival-neg: 117.0ms (6.4% of total)adjust: 96.0ms (5.3% of total)exact: 9.0ms (0.5% of total)ival-true: 6.0ms (0.3% of total)ival-assert: 3.0ms (0.2% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 64 | 3 | (4.481266380875748e-285 -0.004061213956684603) | 0 | - | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| 0 | 0 | - | 0 | - | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 0 | 0 | - | 0 | - | (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))) |
| 0 | 0 | - | 0 | - | (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)))) |
| 0 | 0 | - | 0 | - | (-.f64 #s(literal 1 binary64) eps) |
| 0 | 0 | - | 0 | - | (+.f64 #s(literal 1 binary64) eps) |
| 0 | 0 | - | 0 | - | (*.f64 (-.f64 #s(literal 1 binary64) eps) x) |
| 0 | 0 | - | 0 | - | (/.f64 #s(literal 1 binary64) eps) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)) |
| 0 | 0 | - | 0 | - | (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) |
| 0 | 0 | - | 0 | - | (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) |
| 0 | 0 | - | 0 | - | (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)) |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| 0 | 0 | - | 0 | - | (*.f64 (+.f64 #s(literal 1 binary64) eps) x) |
| 0 | 0 | - | 0 | - | (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x))) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) | cancellation | 67 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 64 | 0 |
| - | 3 | 189 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 64 | 0 | 0 |
| - | 3 | 0 | 189 |
| number | freq |
|---|---|
| 0 | 189 |
| 1 | 67 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 107.0ms | 128× | 1 | valid |
| 49.0ms | 384× | 0 | valid |
Compiled 317 to 61 computations (80.8% saved)
ival-sub: 69.0ms (52.4% of total)ival-exp: 18.0ms (13.7% of total)ival-mult: 16.0ms (12.2% of total)ival-div: 11.0ms (8.4% of total)ival-add: 6.0ms (4.6% of total)adjust: 5.0ms (3.8% of total)ival-neg: 5.0ms (3.8% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| 1× | egg-herbie |
| 11 102× | lower-fma.f64 |
| 11 102× | lower-fma.f32 |
| 2 706× | lower-*.f32 |
| 2 698× | lower-*.f64 |
| 1 598× | lower--.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 53 | 155 |
| 1 | 168 | 138 |
| 2 | 524 | 135 |
| 3 | 1740 | 135 |
| 4 | 4682 | 133 |
| 0 | 19 | 29 |
| 0 | 34 | 29 |
| 1 | 70 | 29 |
| 2 | 169 | 27 |
| 3 | 513 | 27 |
| 4 | 1130 | 27 |
| 5 | 3343 | 25 |
| 6 | 7591 | 25 |
| 0 | 8123 | 23 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| Outputs |
|---|
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
(fma.f64 (exp.f64 (-.f64 (*.f64 eps x) x)) (+.f64 (/.f64 #s(literal 1/2 binary64) eps) #s(literal 1/2 binary64)) (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) eps)))) |
(abs eps)
Compiled 31 to 19 computations (38.7% saved)
Compiled 2 to 2 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 75.8% | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
Compiled 31 to 19 computations (38.7% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 128 | (*.f64 (+.f64 #s(literal 1 binary64) eps) x) | |
| cost-diff | 128 | (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)) | |
| cost-diff | 128 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) | |
| cost-diff | 704 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 11 102× | lower-fma.f64 |
| 11 102× | lower-fma.f32 |
| 2 706× | lower-*.f32 |
| 2 698× | lower-*.f64 |
| 1 598× | lower--.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 19 | 141 |
| 0 | 34 | 141 |
| 1 | 70 | 141 |
| 2 | 169 | 131 |
| 3 | 513 | 131 |
| 4 | 1130 | 131 |
| 5 | 3343 | 129 |
| 6 | 7591 | 129 |
| 0 | 8123 | 123 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
(-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) |
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) eps) |
eps |
(exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x))) |
(neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)) |
(*.f64 (-.f64 #s(literal 1 binary64) eps) x) |
(-.f64 #s(literal 1 binary64) eps) |
x |
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)))) |
(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) |
(exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))) |
(neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)) |
(*.f64 (+.f64 #s(literal 1 binary64) eps) x) |
(+.f64 #s(literal 1 binary64) eps) |
#s(literal 2 binary64) |
| Outputs |
|---|
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
(fma.f64 (exp.f64 (-.f64 (*.f64 eps x) x)) (+.f64 (/.f64 #s(literal 1/2 binary64) eps) #s(literal 1/2 binary64)) (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) eps)))) |
(-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
(fma.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (-.f64 (*.f64 eps x) x)))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (-.f64 (*.f64 eps x) x))) |
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) eps) |
eps |
(exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x))) |
(exp.f64 (-.f64 (*.f64 eps x) x)) |
(neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)) |
(-.f64 (*.f64 eps x) x) |
(*.f64 (-.f64 #s(literal 1 binary64) eps) x) |
(-.f64 x (*.f64 eps x)) |
(-.f64 #s(literal 1 binary64) eps) |
x |
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)))) |
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) |
(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) |
(+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) |
(exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))) |
(exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) |
(neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(*.f64 (+.f64 #s(literal 1 binary64) eps) x) |
(fma.f64 eps x x) |
(+.f64 #s(literal 1 binary64) eps) |
#s(literal 2 binary64) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x))) | |
| accuracy | 0.00390625 | (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))) | |
| accuracy | 0.01171875 | (*.f64 (-.f64 #s(literal 1 binary64) eps) x) | |
| accuracy | 15.499999999997478 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| 32.0ms | 192× | 0 | valid |
| 21.0ms | 64× | 1 | valid |
Compiled 143 to 21 computations (85.3% saved)
ival-mult: 16.0ms (39.3% of total)ival-exp: 8.0ms (19.6% of total)ival-sub: 4.0ms (9.8% of total)ival-div: 4.0ms (9.8% of total)ival-add: 3.0ms (7.4% of total)adjust: 2.0ms (4.9% of total)ival-neg: 2.0ms (4.9% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))> |
#<alt (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)))))> |
#<alt (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x))> |
#<alt (*.f64 (+.f64 #s(literal 1 binary64) eps) x)> |
#<alt (*.f64 (-.f64 #s(literal 1 binary64) eps) x)> |
#<alt (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)))> |
#<alt (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))> |
| Outputs |
|---|
#<alt (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))> |
#<alt (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))> |
#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))> |
#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))> |
#<alt (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))> |
#<alt (+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))))> |
#<alt (+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
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#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))> |
#<alt (- (+ (exp (neg x)) (+ (* x (exp (neg x))) (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))> |
#<alt (- (+ (exp (neg x)) (+ (* x (exp (neg x))) (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (+ (* 1/2 (* (pow x 2) (exp (neg x)))) (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))> |
#<alt (- (+ (exp (neg x)) (+ (* x (exp (neg x))) (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (+ (* 1/2 (* (pow x 2) (exp (neg x)))) (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (+ (* 1/24 (* (pow x 4) (exp (neg x)))) (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x))))))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))> |
#<alt (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))> |
#<alt (- (+ (exp (neg (* x (- 1 eps)))) (/ (exp (neg (* x (- 1 eps)))) eps)) (+ (* -1 (exp (neg (* x (+ 1 eps))))) (/ (exp (neg (* x (+ 1 eps)))) eps)))> |
#<alt (- (+ (exp (neg (* x (- 1 eps)))) (/ (exp (neg (* x (- 1 eps)))) eps)) (+ (* -1 (exp (neg (* x (+ 1 eps))))) (/ (exp (neg (* x (+ 1 eps)))) eps)))> |
#<alt (- (+ (exp (neg (* x (- 1 eps)))) (/ (exp (neg (* x (- 1 eps)))) eps)) (+ (* -1 (exp (neg (* x (+ 1 eps))))) (/ (exp (neg (* x (+ 1 eps)))) eps)))> |
#<alt (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))> |
#<alt (- (+ (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))> |
#<alt (- (+ (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))> |
#<alt (- (+ (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))> |
#<alt 2> |
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#<alt (+ 2 (* x (- (+ (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))) (* (+ 1 (/ 1 eps)) (- eps 1))) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))> |
#<alt (+ 2 (* x (- (+ (* x (- (+ (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))) (* (+ 1 (/ 1 eps)) (- eps 1))) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))> |
#<alt (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))> |
#<alt (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))> |
#<alt (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))> |
#<alt (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))> |
#<alt (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))> |
#<alt (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))> |
#<alt (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))> |
#<alt (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))> |
#<alt (* -1 x)> |
#<alt (- (* eps x) x)> |
#<alt (- (* eps x) x)> |
#<alt (- (* eps x) x)> |
#<alt (* eps x)> |
#<alt (* eps (- (* -1 (/ x eps)) (* -1 x)))> |
#<alt (* eps (- (* -1 (/ x eps)) (* -1 x)))> |
#<alt (* eps (- (* -1 (/ x eps)) (* -1 x)))> |
#<alt (* eps x)> |
#<alt (* -1 (* eps (- (/ x eps) x)))> |
#<alt (* -1 (* eps (- (/ x eps) x)))> |
#<alt (* -1 (* eps (- (/ x eps) x)))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* -1 (* x (- 1 eps)))> |
#<alt (* -1 (* x (- 1 eps)))> |
#<alt (* -1 (* x (- 1 eps)))> |
#<alt (* -1 (* x (- 1 eps)))> |
#<alt x> |
#<alt (+ x (* eps x))> |
#<alt (+ x (* eps x))> |
#<alt (+ x (* eps x))> |
#<alt (* eps x)> |
#<alt (* eps (+ x (/ x eps)))> |
#<alt (* eps (+ x (/ x eps)))> |
#<alt (* eps (+ x (/ x eps)))> |
#<alt (* eps x)> |
#<alt (* -1 (* eps (+ (* -1 x) (* -1 (/ x eps)))))> |
#<alt (* -1 (* eps (+ (* -1 x) (* -1 (/ x eps)))))> |
#<alt (* -1 (* eps (+ (* -1 x) (* -1 (/ x eps)))))> |
#<alt (* x (+ 1 eps))> |
#<alt (* x (+ 1 eps))> |
#<alt (* x (+ 1 eps))> |
#<alt (* x (+ 1 eps))> |
#<alt (* x (+ 1 eps))> |
#<alt (* x (+ 1 eps))> |
#<alt (* x (+ 1 eps))> |
#<alt (* x (+ 1 eps))> |
#<alt (* x (+ 1 eps))> |
#<alt (* x (+ 1 eps))> |
#<alt (* x (+ 1 eps))> |
#<alt (* x (+ 1 eps))> |
#<alt x> |
#<alt (+ x (* -1 (* eps x)))> |
#<alt (+ x (* -1 (* eps x)))> |
#<alt (+ x (* -1 (* eps x)))> |
#<alt (* -1 (* eps x))> |
#<alt (* eps (+ (* -1 x) (/ x eps)))> |
#<alt (* eps (+ (* -1 x) (/ x eps)))> |
#<alt (* eps (+ (* -1 x) (/ x eps)))> |
#<alt (* -1 (* eps x))> |
#<alt (* -1 (* eps (+ x (* -1 (/ x eps)))))> |
#<alt (* -1 (* eps (+ x (* -1 (/ x eps)))))> |
#<alt (* -1 (* eps (+ x (* -1 (/ x eps)))))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (exp (neg x))> |
#<alt (+ (exp (neg x)) (* -1 (* eps (* x (exp (neg x))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* 1/2 (* eps (* (pow x 2) (exp (neg x))))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* eps (+ (* -1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (- 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (- 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (- 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (- 1 (* -1 eps)))))> |
#<alt 1> |
#<alt (+ 1 (* -1 (* x (+ 1 eps))))> |
#<alt (+ 1 (* x (+ (* -1 (+ 1 eps)) (* 1/2 (* x (pow (+ 1 eps) 2))))))> |
#<alt (+ 1 (* x (+ (* -1 (+ 1 eps)) (* x (+ (* -1/6 (* x (pow (+ 1 eps) 3))) (* 1/2 (pow (+ 1 eps) 2)))))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg x))> |
#<alt (+ (exp (neg x)) (* eps (* x (exp (neg x)))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* x (exp (neg x))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* eps (+ (* 1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))) (* x (exp (neg x))))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (+ 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (+ 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (+ 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (+ 1 (* -1 eps)))))> |
#<alt 1> |
#<alt (+ 1 (* x (- eps 1)))> |
#<alt (+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1)))> |
#<alt (+ 1 (* x (- (+ eps (* x (+ (* 1/6 (* x (pow (- eps 1) 3))) (* 1/2 (pow (- eps 1) 2))))) 1)))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
42 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | x | @ | -inf | (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) |
| 3.0ms | eps | @ | 0 | (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) |
| 2.0ms | eps | @ | -inf | (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) |
| 1.0ms | x | @ | inf | (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) |
| 1.0ms | x | @ | 0 | (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) |
| 1× | egg-herbie |
| 13 416× | lower-fma.f64 |
| 13 416× | lower-fma.f32 |
| 4 390× | lower-*.f64 |
| 4 390× | lower-*.f32 |
| 3 664× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 287 | 2962 |
| 1 | 920 | 2564 |
| 2 | 3114 | 2316 |
| 0 | 8328 | 2191 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) |
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))))))) |
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
1 |
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))) |
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))) |
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))) |
(- (+ (exp (neg x)) (+ (* x (exp (neg x))) (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))) |
(- (+ (exp (neg x)) (+ (* x (exp (neg x))) (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (+ (* 1/2 (* (pow x 2) (exp (neg x)))) (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))) |
(- (+ (exp (neg x)) (+ (* x (exp (neg x))) (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (+ (* 1/2 (* (pow x 2) (exp (neg x)))) (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (+ (* 1/24 (* (pow x 4) (exp (neg x)))) (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x))))))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))) |
(- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))) |
(- (+ (exp (neg (* x (- 1 eps)))) (/ (exp (neg (* x (- 1 eps)))) eps)) (+ (* -1 (exp (neg (* x (+ 1 eps))))) (/ (exp (neg (* x (+ 1 eps)))) eps))) |
(- (+ (exp (neg (* x (- 1 eps)))) (/ (exp (neg (* x (- 1 eps)))) eps)) (+ (* -1 (exp (neg (* x (+ 1 eps))))) (/ (exp (neg (* x (+ 1 eps)))) eps))) |
(- (+ (exp (neg (* x (- 1 eps)))) (/ (exp (neg (* x (- 1 eps)))) eps)) (+ (* -1 (exp (neg (* x (+ 1 eps))))) (/ (exp (neg (* x (+ 1 eps)))) eps))) |
(- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) |
(- (+ (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) |
(- (+ (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) |
(- (+ (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) |
2 |
(+ 2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))) |
(+ 2 (* x (- (+ (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))) (* (+ 1 (/ 1 eps)) (- eps 1))) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))) |
(+ 2 (* x (- (+ (* x (- (+ (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))) (* (+ 1 (/ 1 eps)) (- eps 1))) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))) |
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))) |
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))) |
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))) |
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))) |
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))) |
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))) |
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))) |
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))) |
(* -1 x) |
(- (* eps x) x) |
(- (* eps x) x) |
(- (* eps x) x) |
(* eps x) |
(* eps (- (* -1 (/ x eps)) (* -1 x))) |
(* eps (- (* -1 (/ x eps)) (* -1 x))) |
(* eps (- (* -1 (/ x eps)) (* -1 x))) |
(* eps x) |
(* -1 (* eps (- (/ x eps) x))) |
(* -1 (* eps (- (/ x eps) x))) |
(* -1 (* eps (- (/ x eps) x))) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* -1 (* x (- 1 eps))) |
(* -1 (* x (- 1 eps))) |
(* -1 (* x (- 1 eps))) |
(* -1 (* x (- 1 eps))) |
x |
(+ x (* eps x)) |
(+ x (* eps x)) |
(+ x (* eps x)) |
(* eps x) |
(* eps (+ x (/ x eps))) |
(* eps (+ x (/ x eps))) |
(* eps (+ x (/ x eps))) |
(* eps x) |
(* -1 (* eps (+ (* -1 x) (* -1 (/ x eps))))) |
(* -1 (* eps (+ (* -1 x) (* -1 (/ x eps))))) |
(* -1 (* eps (+ (* -1 x) (* -1 (/ x eps))))) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
x |
(+ x (* -1 (* eps x))) |
(+ x (* -1 (* eps x))) |
(+ x (* -1 (* eps x))) |
(* -1 (* eps x)) |
(* eps (+ (* -1 x) (/ x eps))) |
(* eps (+ (* -1 x) (/ x eps))) |
(* eps (+ (* -1 x) (/ x eps))) |
(* -1 (* eps x)) |
(* -1 (* eps (+ x (* -1 (/ x eps))))) |
(* -1 (* eps (+ x (* -1 (/ x eps))))) |
(* -1 (* eps (+ x (* -1 (/ x eps))))) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(exp (neg x)) |
(+ (exp (neg x)) (* -1 (* eps (* x (exp (neg x)))))) |
(+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* 1/2 (* eps (* (pow x 2) (exp (neg x)))))))) |
(+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* eps (+ (* -1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x))))))))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (- 1 (* -1 eps))))) |
(exp (neg (* x (- 1 (* -1 eps))))) |
(exp (neg (* x (- 1 (* -1 eps))))) |
(exp (neg (* x (- 1 (* -1 eps))))) |
1 |
(+ 1 (* -1 (* x (+ 1 eps)))) |
(+ 1 (* x (+ (* -1 (+ 1 eps)) (* 1/2 (* x (pow (+ 1 eps) 2)))))) |
(+ 1 (* x (+ (* -1 (+ 1 eps)) (* x (+ (* -1/6 (* x (pow (+ 1 eps) 3))) (* 1/2 (pow (+ 1 eps) 2))))))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg x)) |
(+ (exp (neg x)) (* eps (* x (exp (neg x))))) |
(+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* x (exp (neg x)))))) |
(+ (exp (neg x)) (* eps (+ (* eps (+ (* 1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))) (* x (exp (neg x)))))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
1 |
(+ 1 (* x (- eps 1))) |
(+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1))) |
(+ 1 (* x (- (+ eps (* x (+ (* 1/6 (* x (pow (- eps 1) 3))) (* 1/2 (pow (- eps 1) 2))))) 1))) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
| Outputs |
|---|
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x))) |
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x #s(literal -1/6 binary64) #s(literal -1/2 binary64))))) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 eps eps) (fma.f64 (exp.f64 (neg.f64 x)) (-.f64 (*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x #s(literal -1/6 binary64) #s(literal -1/2 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (fma.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64))))))) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)) (*.f64 (*.f64 eps eps) (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (fma.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64)) (*.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/720 binary64) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64))))) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (fma.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64)))))) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x #s(literal -1/6 binary64) #s(literal -1/2 binary64))))))))) |
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))) |
(fma.f64 (+.f64 (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)) (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps))) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))))))) |
(fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/6 binary64) (fma.f64 (+.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))) (*.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)))))) (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))))) (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps))))) #s(literal 1 binary64)) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
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(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
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(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg (* x (+ 1 eps)))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg (* x (- 1 (* -1 eps))))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg (* x (- 1 (* -1 eps))))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg (* x (- 1 (* -1 eps))))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg (* x (- 1 (* -1 eps))))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1 (* x (+ 1 eps)))) |
(-.f64 #s(literal 1 binary64) (fma.f64 x eps x)) |
(+ 1 (* x (+ (* -1 (+ 1 eps)) (* 1/2 (* x (pow (+ 1 eps) 2)))))) |
(fma.f64 x (*.f64 (+.f64 eps #s(literal 1 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 eps #s(literal 1 binary64)) #s(literal -1 binary64))) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1 (+ 1 eps)) (* x (+ (* -1/6 (* x (pow (+ 1 eps) 3))) (* 1/2 (pow (+ 1 eps) 2))))))) |
(fma.f64 x (-.f64 (fma.f64 x (*.f64 (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (fma.f64 (*.f64 x #s(literal -1/6 binary64)) (+.f64 eps #s(literal 1 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64)) eps) #s(literal 1 binary64)) |
(exp (neg (+ x (* eps x)))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg (+ x (* eps x)))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg (+ x (* eps x)))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg (+ x (* eps x)))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg (* x (+ 1 eps)))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg (* x (+ 1 eps)))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg (* x (+ 1 eps)))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg (* x (+ 1 eps)))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg x)) |
(exp.f64 (neg.f64 x)) |
(+ (exp (neg x)) (* eps (* x (exp (neg x))))) |
(*.f64 (fma.f64 x eps #s(literal 1 binary64)) (exp.f64 (neg.f64 x))) |
(+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* x (exp (neg x)))))) |
(fma.f64 eps (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)) (exp.f64 (neg.f64 x))) |
(+ (exp (neg x)) (* eps (+ (* eps (+ (* 1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))) (* x (exp (neg x)))))) |
(fma.f64 eps (*.f64 eps (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x))))))) (*.f64 (fma.f64 x eps #s(literal 1 binary64)) (exp.f64 (neg.f64 x)))) |
(exp (neg (* x (- 1 eps)))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (neg (* x (- 1 eps)))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (neg (* x (- 1 eps)))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (neg (* x (- 1 eps)))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* x (- eps 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) |
(+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1))) |
(fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)) |
(+ 1 (* x (- (+ eps (* x (+ (* 1/6 (* x (pow (- eps 1) 3))) (* 1/2 (pow (- eps 1) 2))))) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (fma.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64))) eps)) #s(literal 1 binary64)) |
(exp (- (* eps x) x)) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (- (* eps x) x)) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (- (* eps x) x)) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (- (* eps x) x)) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (neg (* x (- 1 eps)))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (neg (* x (- 1 eps)))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (neg (* x (- 1 eps)))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp (neg (* x (- 1 eps)))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
| 4 830× | lower-fma.f64 |
| 4 830× | lower-fma.f32 |
| 3 930× | lower-/.f32 |
| 3 926× | lower-/.f64 |
| 3 926× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 19 | 86 |
| 0 | 34 | 86 |
| 1 | 131 | 82 |
| 2 | 932 | 79 |
| 0 | 8931 | 73 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
(-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
(neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)) |
(*.f64 (+.f64 #s(literal 1 binary64) eps) x) |
(*.f64 (-.f64 #s(literal 1 binary64) eps) x) |
(exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))) |
(exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x))) |
| Outputs |
|---|
(+.f64 (*.f64 (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal 1/2 binary64))) (*.f64 (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal 1/2 binary64))) (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))) #s(literal 1/2 binary64)))) |
(+.f64 (*.f64 (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))) #s(literal 1/2 binary64)) (*.f64 (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal 1/2 binary64)))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))))))) |
(+.f64 (*.f64 (*.f64 (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (*.f64 (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))))))) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))))) #s(literal -1/2 binary64))) |
(-.f64 (*.f64 (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal 1/2 binary64))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) #s(literal 1/2 binary64)))) |
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)))) (exp.f64 (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) #s(literal 3 binary64)))) (fma.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))) (exp.f64 (fma.f64 x (+.f64 eps #s(literal -1 binary64)) (*.f64 x (+.f64 eps #s(literal -1 binary64)))))))) #s(literal 2 binary64)) (/.f64 (/.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)))) (exp.f64 (*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))) (exp.f64 (fma.f64 x (+.f64 eps #s(literal -1 binary64)) (*.f64 x (+.f64 eps #s(literal -1 binary64)))))))) #s(literal 2 binary64))) |
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))) (exp.f64 (fma.f64 x (+.f64 eps #s(literal -1 binary64)) (*.f64 x (+.f64 eps #s(literal -1 binary64)))))) (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))))) #s(literal 2 binary64)) (/.f64 (/.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))) (exp.f64 (fma.f64 x (-.f64 #s(literal -1 binary64) eps) (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))))) #s(literal 2 binary64))) |
(-.f64 (/.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)))) (exp.f64 (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) #s(literal 3 binary64)))) (*.f64 #s(literal 2 binary64) (fma.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))) (exp.f64 (fma.f64 x (+.f64 eps #s(literal -1 binary64)) (*.f64 x (+.f64 eps #s(literal -1 binary64))))))))) (/.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)))) (exp.f64 (*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))) (*.f64 #s(literal 2 binary64) (fma.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))) (exp.f64 (fma.f64 x (+.f64 eps #s(literal -1 binary64)) (*.f64 x (+.f64 eps #s(literal -1 binary64)))))))))) |
(-.f64 (/.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))) (exp.f64 (fma.f64 x (+.f64 eps #s(literal -1 binary64)) (*.f64 x (+.f64 eps #s(literal -1 binary64)))))) (*.f64 #s(literal 2 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))))) (/.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))) (exp.f64 (fma.f64 x (-.f64 #s(literal -1 binary64) eps) (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) (*.f64 #s(literal 2 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))))))) |
(-.f64 (/.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) #s(literal 4 binary64))) |
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(exp.f64 (*.f64 (log.f64 (exp.f64 (+.f64 eps #s(literal -1 binary64)))) x)) |
(neg.f64 (/.f64 #s(literal -1 binary64) (exp.f64 (fma.f64 x (neg.f64 eps) x)))) |
(/.f64 #s(literal 1 binary64) (exp.f64 (fma.f64 x (neg.f64 eps) x))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (exp.f64 (fma.f64 x (neg.f64 eps) x))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (fma.f64 x (neg.f64 eps) x)))) |
(pow.f64 (exp.f64 (fma.f64 x (neg.f64 eps) x)) #s(literal -1 binary64)) |
(pow.f64 (exp.f64 #s(literal -1 binary64)) (fma.f64 x (neg.f64 eps) x)) |
(pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) eps)) (neg.f64 x)) |
(pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) eps)) (*.f64 x #s(literal -1 binary64))) |
(pow.f64 (exp.f64 (+.f64 eps #s(literal -1 binary64))) x) |
(pow.f64 (exp.f64 x) (+.f64 eps #s(literal -1 binary64))) |
(pow.f64 (exp.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))) |
(pow.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) x) |
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) x) (-.f64 #s(literal 1 binary64) eps)) |
(pow.f64 (exp.f64 (neg.f64 x)) (-.f64 #s(literal 1 binary64) eps)) |
(*.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))))) |
(*.f64 (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (exp.f64 (fma.f64 x (neg.f64 eps) x))))) |
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) x) (pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (*.f64 x eps)))) |
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) x) (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 (neg.f64 eps) x))) |
(*.f64 (pow.f64 (exp.f64 (fma.f64 x (neg.f64 eps) x)) #s(literal -1/2 binary64)) (pow.f64 (exp.f64 (fma.f64 x (neg.f64 eps) x)) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 x (neg.f64 eps) x) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 x (neg.f64 eps) x) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) eps)) (/.f64 (neg.f64 x) #s(literal 2 binary64))) (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) eps)) (/.f64 (neg.f64 x) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (exp.f64 (+.f64 eps #s(literal -1 binary64))) (/.f64 x #s(literal 2 binary64))) (pow.f64 (exp.f64 (+.f64 eps #s(literal -1 binary64))) (/.f64 x #s(literal 2 binary64)))) |
Compiled 31 250 to 2 467 computations (92.1% saved)
9 alts after pruning (9 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 621 | 9 | 630 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 622 | 9 | 631 |
| Status | Accuracy | Program |
|---|---|---|
| 38.2% | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))))) #s(literal 2 binary64)) | |
| ▶ | 38.1% | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
| ▶ | 55.3% | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 39.9% | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) | |
| 75.8% | (exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))))))) #s(literal -1 binary64))) | |
| ▶ | 73.0% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64))) |
| ▶ | 99.5% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
| 57.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) | |
| ▶ | 42.5% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
Compiled 496 to 264 computations (46.8% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 64 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) | |
| cost-diff | 128 | (*.f64 (+.f64 #s(literal 1 binary64) eps) x) | |
| cost-diff | 128 | (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) | |
| cost-diff | 128 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) | |
| cost-diff | 64 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) | |
| cost-diff | 128 | (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)) | |
| cost-diff | 128 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) | |
| cost-diff | 320 | (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64))) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) x) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64))) | |
| cost-diff | 768 | (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))) | |
| cost-diff | 0 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) | |
| cost-diff | 0 | (exp.f64 (-.f64 (*.f64 x eps) x)) | |
| cost-diff | 0 | (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x))))) | |
| cost-diff | 0 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
| 11 464× | lower-fma.f32 |
| 11 452× | lower-fma.f64 |
| 3 564× | lower--.f32 |
| 3 552× | lower--.f64 |
| 3 500× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 70 | 844 |
| 0 | 122 | 839 |
| 1 | 256 | 829 |
| 2 | 782 | 813 |
| 3 | 3770 | 798 |
| 0 | 8197 | 779 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
#s(literal 1/2 binary64) |
(+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(-.f64 (*.f64 x eps) x) |
(*.f64 x eps) |
x |
eps |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(neg.f64 (fma.f64 x eps x)) |
(fma.f64 x eps x) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) |
(+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) |
(/.f64 (+.f64 eps #s(literal 1 binary64)) eps) |
(+.f64 eps #s(literal 1 binary64)) |
eps |
#s(literal 1 binary64) |
(-.f64 #s(literal -1 binary64) eps) |
#s(literal -1 binary64) |
(fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) |
(fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) |
(*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))) |
(+.f64 #s(literal -1 binary64) eps) |
(+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)) |
(/.f64 (+.f64 #s(literal -1 binary64) eps) eps) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
(-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) |
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) eps) |
eps |
(exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x))) |
(neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)) |
(*.f64 (-.f64 #s(literal 1 binary64) eps) x) |
(-.f64 #s(literal 1 binary64) eps) |
x |
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64))) |
(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) |
#s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)) |
#s(literal 2 binary64) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
(-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) |
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) eps) |
eps |
#s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)) |
x |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
(+.f64 #s(literal -1 binary64) eps) |
#s(literal -1 binary64) |
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)))) |
(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) |
(exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))) |
(neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)) |
(*.f64 (+.f64 #s(literal 1 binary64) eps) x) |
(+.f64 #s(literal 1 binary64) eps) |
#s(literal 2 binary64) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 eps x) x)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 eps x) x)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
#s(literal 1/2 binary64) |
(+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))) |
(+.f64 (exp.f64 (-.f64 (*.f64 eps x) x)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
(exp.f64 (-.f64 (*.f64 eps x) x)) |
(-.f64 (*.f64 x eps) x) |
(-.f64 (*.f64 eps x) x) |
(*.f64 x eps) |
(*.f64 eps x) |
x |
eps |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) |
(neg.f64 (fma.f64 x eps x)) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(fma.f64 x eps x) |
(fma.f64 eps x x) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (+.f64 (+.f64 eps #s(literal -1 binary64)) (+.f64 (/.f64 (+.f64 eps #s(literal -1 binary64)) eps) (fma.f64 (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (neg.f64 eps) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 eps #s(literal -1 binary64)) eps))) (*.f64 x (fma.f64 eps #s(literal 1/2 binary64) #s(literal -1/2 binary64))))))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (+.f64 (+.f64 eps #s(literal -1 binary64)) (+.f64 (/.f64 (+.f64 eps #s(literal -1 binary64)) eps) (fma.f64 (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (neg.f64 eps) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 eps #s(literal -1 binary64)) eps))) (*.f64 x (fma.f64 eps #s(literal 1/2 binary64) #s(literal -1/2 binary64))))))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
x |
(+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) |
(+.f64 (+.f64 eps #s(literal -1 binary64)) (+.f64 (/.f64 (+.f64 eps #s(literal -1 binary64)) eps) (fma.f64 (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (neg.f64 eps) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 eps #s(literal -1 binary64)) eps))) (*.f64 x (fma.f64 eps #s(literal 1/2 binary64) #s(literal -1/2 binary64))))))) |
(+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) |
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) |
(/.f64 (+.f64 eps #s(literal 1 binary64)) eps) |
(/.f64 (+.f64 #s(literal 1 binary64) eps) eps) |
(+.f64 eps #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) eps) |
eps |
#s(literal 1 binary64) |
(-.f64 #s(literal -1 binary64) eps) |
#s(literal -1 binary64) |
(fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps))) (*.f64 (fma.f64 x (fma.f64 eps #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (+.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 eps #s(literal -1 binary64)) eps))))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 eps #s(literal -1 binary64)) (+.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 eps #s(literal -1 binary64)) eps)))))) |
(fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) |
(fma.f64 (-.f64 #s(literal -1 binary64) eps) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 eps #s(literal -1 binary64)) (+.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 eps #s(literal -1 binary64)) eps))))) |
(*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))) |
(*.f64 (+.f64 eps #s(literal -1 binary64)) (+.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 eps #s(literal -1 binary64)) eps)))) |
(+.f64 #s(literal -1 binary64) eps) |
(+.f64 eps #s(literal -1 binary64)) |
(+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)) |
(+.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 eps #s(literal -1 binary64)) eps))) |
(/.f64 (+.f64 #s(literal -1 binary64) eps) eps) |
(/.f64 (+.f64 eps #s(literal -1 binary64)) eps) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
(fma.f64 (-.f64 (/.f64 #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)) eps) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (-.f64 (*.f64 eps x) x))))) |
(-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) |
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (-.f64 (*.f64 eps x) x)) (-.f64 #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)) (/.f64 #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)) eps))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (-.f64 (*.f64 eps x) x))) |
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) eps) |
eps |
(exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x))) |
(exp.f64 (-.f64 (*.f64 eps x) x)) |
(neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)) |
(-.f64 (*.f64 eps x) x) |
(*.f64 (-.f64 #s(literal 1 binary64) eps) x) |
(-.f64 x (*.f64 eps x)) |
(-.f64 #s(literal 1 binary64) eps) |
x |
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64))) |
(-.f64 (/.f64 #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)) eps) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64))) |
(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) |
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps)) |
#s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)) |
#s(literal 2 binary64) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 (+.f64 eps #s(literal -1 binary64)) (fma.f64 x (*.f64 x (fma.f64 eps #s(literal 1/2 binary64) #s(literal -1/2 binary64))) x) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (*.f64 (*.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) #s(literal -1/2 binary64))) |
(-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 (+.f64 eps #s(literal -1 binary64)) (fma.f64 x (*.f64 x (fma.f64 eps #s(literal 1/2 binary64) #s(literal -1/2 binary64))) x) #s(literal 1 binary64))) (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 (+.f64 eps #s(literal -1 binary64)) (fma.f64 x (*.f64 x (fma.f64 eps #s(literal 1/2 binary64) #s(literal -1/2 binary64))) x) #s(literal 1 binary64)))) |
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) eps) |
eps |
#s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64))) |
#s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 (+.f64 eps #s(literal -1 binary64)) (fma.f64 x (*.f64 x (fma.f64 eps #s(literal 1/2 binary64) #s(literal -1/2 binary64))) x) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)) |
(fma.f64 (+.f64 eps #s(literal -1 binary64)) (fma.f64 x (*.f64 x (fma.f64 eps #s(literal 1/2 binary64) #s(literal -1/2 binary64))) x) #s(literal 1 binary64)) |
x |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) |
(*.f64 (+.f64 eps #s(literal -1 binary64)) (fma.f64 x (fma.f64 eps #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) |
(fma.f64 x (fma.f64 eps #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(+.f64 #s(literal -1 binary64) eps) |
(+.f64 eps #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)))) |
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) |
(-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) |
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps)) |
(exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))) |
(exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) |
(neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(*.f64 (+.f64 #s(literal 1 binary64) eps) x) |
(fma.f64 eps x x) |
(+.f64 #s(literal 1 binary64) eps) |
#s(literal 2 binary64) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.03515625 | (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) | |
| accuracy | 2.8257072919335933 | (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)) | |
| accuracy | 15.499999999997478 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) | |
| accuracy | 28.10727135129044 | #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64))) | |
| accuracy | 0.00390625 | (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x))) | |
| accuracy | 0.01171875 | (*.f64 (-.f64 #s(literal 1 binary64) eps) x) | |
| accuracy | 15.499999999997478 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) | |
| accuracy | 36.99143274735364 | #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)) | |
| accuracy | 5.030817201037822 | (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))) | |
| accuracy | 18.605111781140387 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64))) | |
| accuracy | 24.88696073502889 | (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) | |
| accuracy | 29.088808368419762 | (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) | |
| accuracy | 36.793839520773204 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) | |
| accuracy | 0.00390625 | (exp.f64 (-.f64 (*.f64 x eps) x)) | |
| accuracy | 0.00390625 | (exp.f64 (neg.f64 (fma.f64 x eps x))) | |
| accuracy | 0.015625 | (-.f64 (*.f64 x eps) x) | |
| accuracy | 0.3024004356261579 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
| 85.0ms | 108× | 1 | valid |
| 71.0ms | 116× | 0 | valid |
| 47.0ms | 32× | 2 | valid |
Compiled 719 to 53 computations (92.6% saved)
ival-mult: 69.0ms (45.7% of total)ival-add: 24.0ms (15.9% of total)adjust: 22.0ms (14.6% of total)ival-exp: 13.0ms (8.6% of total)ival-div: 11.0ms (7.3% of total)ival-sub: 8.0ms (5.3% of total)ival-neg: 4.0ms (2.7% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x))))))> |
#<alt (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))> |
#<alt (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x))))> |
#<alt (exp.f64 (-.f64 (*.f64 x eps) x))> |
#<alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64))> |
#<alt (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))> |
#<alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64)))> |
#<alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64))> |
#<alt (*.f64 #s(literal 1/2 binary64) x)> |
#<alt (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))> |
#<alt (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64))))> |
#<alt (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x))> |
#<alt (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64))> |
#<alt (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x)))))> |
#<alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64))> |
#<alt (*.f64 (+.f64 #s(literal 1 binary64) eps) x)> |
#<alt (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))> |
#<alt (-.f64 (*.f64 x eps) x)> |
#<alt (exp.f64 (neg.f64 (fma.f64 x eps x)))> |
#<alt (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))> |
#<alt (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))> |
#<alt #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64))> |
#<alt (*.f64 (-.f64 #s(literal 1 binary64) eps) x)> |
#<alt (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))> |
#<alt #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))> |
#<alt (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64))> |
#<alt (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps))> |
| Outputs |
|---|
#<alt (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))> |
#<alt (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))> |
#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))> |
#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))> |
#<alt (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))> |
#<alt (+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))))> |
#<alt (+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (* x (- (+ eps (* -1 (+ 1 eps))) 1))))> |
#<alt (+ 1 (* x (+ (* 1/2 (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2))))) (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1)))))> |
#<alt (+ 1 (* x (+ (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1)) (* x (+ (* 1/2 (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))) (* 1/2 (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2)))))))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))))> |
#<alt (* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))))> |
#<alt (* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))))> |
#<alt (* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))))> |
#<alt (exp (neg x))> |
#<alt (+ (exp (neg x)) (* 1/2 (* eps (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x)))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* 1/2 (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x))))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* 1/2 (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x))))) (* eps (+ (* 1/2 (* eps (+ (* -1/6 (* (pow x 3) (exp (neg x)))) (* 1/6 (* (pow x 3) (exp (neg x))))))) (* 1/2 (* (pow x 2) (exp (neg x)))))))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
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#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))> |
#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))> |
#<alt (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))> |
#<alt (+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))))> |
#<alt (+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* -1 (* x (+ 1 (* -1 eps))))> |
#<alt (* -1 (* x (+ 1 (* -1 eps))))> |
#<alt (* -1 (* x (+ 1 (* -1 eps))))> |
#<alt (* -1 (* x (+ 1 (* -1 eps))))> |
#<alt (* -1 x)> |
#<alt (- (* eps x) x)> |
#<alt (- (* eps x) x)> |
#<alt (- (* eps x) x)> |
#<alt (* eps x)> |
#<alt (* eps (+ x (* -1 (/ x eps))))> |
#<alt (* eps (+ x (* -1 (/ x eps))))> |
#<alt (* eps (+ x (* -1 (/ x eps))))> |
#<alt (* eps x)> |
#<alt (* -1 (* eps (+ (* -1 x) (/ x eps))))> |
#<alt (* -1 (* eps (+ (* -1 x) (/ x eps))))> |
#<alt (* -1 (* eps (+ (* -1 x) (/ x eps))))> |
#<alt 1> |
#<alt (+ 1 (* -1 (* x (+ 1 eps))))> |
#<alt (+ 1 (* x (+ (* -1 (+ 1 eps)) (* 1/2 (* x (pow (+ 1 eps) 2))))))> |
#<alt (+ 1 (* x (+ (* -1 (+ 1 eps)) (* x (+ (* -1/6 (* x (pow (+ 1 eps) 3))) (* 1/2 (pow (+ 1 eps) 2)))))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (neg x))> |
#<alt (+ (exp (neg x)) (* -1 (* eps (* x (exp (neg x))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* 1/2 (* eps (* (pow x 2) (exp (neg x))))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* eps (+ (* -1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (* -1 x)> |
#<alt (+ (* -1 x) (* (pow eps 2) x))> |
#<alt (+ (* -1 x) (* (pow eps 2) x))> |
#<alt (+ (* -1 x) (* (pow eps 2) x))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt -2> |
#<alt (- (* 2 (pow eps 2)) 2)> |
#<alt (- (* 2 (pow eps 2)) 2)> |
#<alt (- (* 2 (pow eps 2)) 2)> |
#<alt (* 2 (pow eps 2))> |
#<alt (* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2)))))> |
#<alt (* 2 (pow eps 2))> |
#<alt (* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2)))))> |
#<alt (exp (neg x))> |
#<alt (+ (exp (neg x)) (* -1 (* eps (* x (exp (neg x))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* 1/2 (* eps (* (pow x 2) (exp (neg x))))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* eps (+ (* -1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (- 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (- 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (- 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (- 1 (* -1 eps)))))> |
#<alt 1> |
#<alt (+ 1 (* -1 (* x (+ 1 eps))))> |
#<alt (+ 1 (* x (+ (* -1 (+ 1 eps)) (* 1/2 (* x (pow (+ 1 eps) 2))))))> |
#<alt (+ 1 (* x (+ (* -1 (+ 1 eps)) (* x (+ (* -1/6 (* x (pow (+ 1 eps) 3))) (* 1/2 (pow (+ 1 eps) 2)))))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt (exp (neg (* x (+ 1 eps))))> |
#<alt x> |
#<alt (+ x (* -1 (* eps x)))> |
#<alt (+ x (* -1 (* eps x)))> |
#<alt (+ x (* -1 (* eps x)))> |
#<alt (* -1 (* eps x))> |
#<alt (* eps (+ (* -1 x) (/ x eps)))> |
#<alt (* eps (+ (* -1 x) (/ x eps)))> |
#<alt (* eps (+ (* -1 x) (/ x eps)))> |
#<alt (* -1 (* eps x))> |
#<alt (* -1 (* eps (+ x (* -1 (/ x eps)))))> |
#<alt (* -1 (* eps (+ x (* -1 (/ x eps)))))> |
#<alt (* -1 (* eps (+ x (* -1 (/ x eps)))))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (* x (- 1 eps))> |
#<alt (exp (neg x))> |
#<alt (+ (exp (neg x)) (* eps (* x (exp (neg x)))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* x (exp (neg x))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* eps (+ (* 1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))) (* x (exp (neg x))))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (+ 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (+ 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (+ 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (+ 1 (* -1 eps)))))> |
#<alt 1> |
#<alt (+ 1 (* x (- eps 1)))> |
#<alt (+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1)))> |
#<alt (+ 1 (* x (- (+ eps (* x (+ (* 1/6 (* x (pow (- eps 1) 3))) (* 1/2 (pow (- eps 1) 2))))) 1)))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg x))> |
#<alt (+ (exp (neg x)) (* eps (* x (exp (neg x)))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* x (exp (neg x))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* eps (+ (* 1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))) (* x (exp (neg x))))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (+ 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (+ 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (+ 1 (* -1 eps)))))> |
#<alt (exp (neg (* x (+ 1 (* -1 eps)))))> |
#<alt 1> |
#<alt (+ 1 (* x (- eps 1)))> |
#<alt (+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1)))> |
#<alt (+ 1 (* x (- (+ eps (* x (+ (* 1/6 (* x (pow (- eps 1) 3))) (* 1/2 (pow (- eps 1) 2))))) 1)))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt (exp (neg (* x (- 1 eps))))> |
#<alt 1> |
#<alt (+ 1 (* x (- eps 1)))> |
#<alt (+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1)))> |
#<alt (+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1)))> |
#<alt (* 1/2 (* (pow x 2) (pow (- eps 1) 2)))> |
#<alt (* (pow x 2) (- (+ (* 1/2 (pow (- eps 1) 2)) (/ eps x)) (/ 1 x)))> |
#<alt (* (pow x 2) (- (+ (* 1/2 (pow (- eps 1) 2)) (+ (/ 1 (pow x 2)) (/ eps x))) (/ 1 x)))> |
#<alt (* (pow x 2) (- (+ (* 1/2 (pow (- eps 1) 2)) (+ (/ 1 (pow x 2)) (/ eps x))) (/ 1 x)))> |
#<alt (* 1/2 (* (pow x 2) (pow (- eps 1) 2)))> |
#<alt (* (pow x 2) (- (+ (* 1/2 (pow (- eps 1) 2)) (/ eps x)) (/ 1 x)))> |
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (- eps 1)) (/ 1 x)) x)) (* 1/2 (pow (- eps 1) 2))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (- eps 1)) (/ 1 x)) x)) (* 1/2 (pow (- eps 1) 2))))> |
#<alt (+ 1 (* -1 (* x (+ 1 (* -1/2 x)))))> |
#<alt (+ 1 (+ (* -1 (* x (+ 1 (* -1/2 x)))) (* eps (* x (+ 1 (* -1 x))))))> |
#<alt (+ 1 (+ (* -1 (* x (+ 1 (* -1/2 x)))) (* eps (+ (* 1/2 (* eps (pow x 2))) (* x (+ 1 (* -1 x)))))))> |
#<alt (+ 1 (+ (* -1 (* x (+ 1 (* -1/2 x)))) (* eps (+ (* 1/2 (* eps (pow x 2))) (* x (+ 1 (* -1 x)))))))> |
#<alt (* 1/2 (* (pow eps 2) (pow x 2)))> |
#<alt (* (pow eps 2) (+ (* 1/2 (pow x 2)) (/ (* x (+ 1 (* -1 x))) eps)))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (* x (+ 1 (* -1/2 x))) (pow eps 2))) (+ (* 1/2 (pow x 2)) (+ (/ 1 (pow eps 2)) (/ (* x (+ 1 (* -1 x))) eps)))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (* x (+ 1 (* -1/2 x))) (pow eps 2))) (+ (* 1/2 (pow x 2)) (+ (/ 1 (pow eps 2)) (/ (* x (+ 1 (* -1 x))) eps)))))> |
#<alt (* 1/2 (* (pow eps 2) (pow x 2)))> |
#<alt (* (pow eps 2) (+ (* 1/2 (pow x 2)) (/ (* x (+ 1 (* -1 x))) eps)))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (* x (+ 1 (* -1 x)))) (* -1 (/ (+ 1 (* -1 (* x (+ 1 (* -1/2 x))))) eps))) eps)) (* 1/2 (pow x 2))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (* x (+ 1 (* -1 x)))) (* -1 (/ (+ 1 (* -1 (* x (+ 1 (* -1/2 x))))) eps))) eps)) (* 1/2 (pow x 2))))> |
#<alt (- eps 1)> |
#<alt (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1)> |
#<alt (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1)> |
#<alt (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1)> |
#<alt (* 1/2 (* x (pow (- eps 1) 2)))> |
#<alt (* x (- (+ (* 1/2 (pow (- eps 1) 2)) (/ eps x)) (/ 1 x)))> |
#<alt (* x (- (+ (* 1/2 (pow (- eps 1) 2)) (/ eps x)) (/ 1 x)))> |
#<alt (* x (- (+ (* 1/2 (pow (- eps 1) 2)) (/ eps x)) (/ 1 x)))> |
#<alt (* 1/2 (* x (pow (- eps 1) 2)))> |
#<alt (* -1 (* x (+ (* -1 (/ (- eps 1) x)) (* -1/2 (pow (- eps 1) 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- eps 1) x)) (* -1/2 (pow (- eps 1) 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- eps 1) x)) (* -1/2 (pow (- eps 1) 2)))))> |
#<alt (* -1 (+ 1 (* -1/2 x)))> |
#<alt (+ (* -1 (+ 1 (* -1/2 x))) (* eps (+ 1 (* -1 x))))> |
#<alt (+ (* -1 (+ 1 (* -1/2 x))) (* eps (+ 1 (+ (* -1 x) (* 1/2 (* eps x))))))> |
#<alt (+ (* -1 (+ 1 (* -1/2 x))) (* eps (+ 1 (+ (* -1 x) (* 1/2 (* eps x))))))> |
#<alt (* 1/2 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1 (/ x eps)) (+ (* 1/2 x) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ x eps)) (+ (* -1 (/ (+ 1 (* -1/2 x)) (pow eps 2))) (+ (* 1/2 x) (/ 1 eps)))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ x eps)) (+ (* -1 (/ (+ 1 (* -1/2 x)) (pow eps 2))) (+ (* 1/2 x) (/ 1 eps)))))> |
#<alt (* 1/2 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1 (/ x eps)) (+ (* 1/2 x) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* -1 x))) (+ (* -1/2 (/ x eps)) (/ 1 eps))) eps)) (* 1/2 x)))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* -1 x))) (+ (* -1/2 (/ x eps)) (/ 1 eps))) eps)) (* 1/2 x)))> |
156 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 10.0ms | eps | @ | inf | (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) |
| 5.0ms | x | @ | inf | (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) |
| 3.0ms | x | @ | 0 | (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) |
| 1.0ms | eps | @ | 0 | (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) |
| 1.0ms | x | @ | 0 | (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x)))) |
| 1× | egg-herbie |
| 13 204× | lower-fma.f64 |
| 13 204× | lower-fma.f32 |
| 6 178× | lower-*.f64 |
| 6 178× | lower-*.f32 |
| 4 086× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 592 | 12240 |
| 1 | 1987 | 11256 |
| 2 | 6826 | 11225 |
| 0 | 8121 | 10709 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
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1 |
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(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
1 |
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(* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))) |
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(+ (exp (neg x)) (* eps (+ (* 1/2 (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x))))) (* eps (+ (* 1/2 (* eps (+ (* -1/6 (* (pow x 3) (exp (neg x)))) (* 1/6 (* (pow x 3) (exp (neg x))))))) (* 1/2 (* (pow x 2) (exp (neg x))))))))) |
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(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
2 |
(+ 2 (* x (- (+ eps (* -1 (+ 1 eps))) 1))) |
(+ 2 (* x (- (+ eps (+ (* -1 (+ 1 eps)) (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2)))))) 1))) |
(+ 2 (* x (- (+ eps (+ (* -1 (+ 1 eps)) (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (+ (* 1/2 (pow (- eps 1) 2)) (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))))))) 1))) |
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(+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))) |
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(* 2 (exp (neg x))) |
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(+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (+ (* eps (* (pow x 2) (exp (neg x)))) (* x (exp (neg x))))))) |
(+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (+ (* eps (+ (* eps (+ (* -1/6 (* (pow x 3) (exp (neg x)))) (* 1/6 (* (pow x 3) (exp (neg x)))))) (* (pow x 2) (exp (neg x))))) (* x (exp (neg x))))))) |
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1 |
(+ 1 (* x (- eps 1))) |
(+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1))) |
(+ 1 (* x (- (+ eps (* x (+ (* 1/6 (* x (pow (- eps 1) 3))) (* 1/2 (pow (- eps 1) 2))))) 1))) |
(exp (- (* eps x) x)) |
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(exp (- (* eps x) x)) |
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(exp (+ (* -1 x) (* eps x))) |
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(exp (+ (* -1 x) (* eps x))) |
(exp (neg x)) |
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1 |
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(/ -1 eps) |
(/ (- (* -1 (* eps x)) 1) eps) |
(/ (- (* eps (+ eps (* -1 x))) 1) eps) |
(/ (- (* eps (+ (* -1 x) (* eps (+ 1 (* eps x))))) 1) eps) |
(* (pow eps 2) x) |
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2 |
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1 |
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2 |
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(+ 2 (* x (- (+ (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))) (* (+ 1 (/ 1 eps)) (- eps 1))) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))) |
(+ 2 (* x (- (+ (* x (- (+ (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))) (* (+ 1 (/ 1 eps)) (- eps 1))) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))) |
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))) |
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))) |
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))) |
(- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))) |
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))) |
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))) |
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))) |
(- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))) |
1 |
(+ 1 (* 1/2 (* x (- eps 1)))) |
(+ 1 (* 1/2 (* x (- eps 1)))) |
(+ 1 (* 1/2 (* x (- eps 1)))) |
(* 1/2 (* x (- eps 1))) |
(* x (+ (* 1/2 (- eps 1)) (/ 1 x))) |
(* x (+ (* 1/2 (- eps 1)) (/ 1 x))) |
(* x (+ (* 1/2 (- eps 1)) (/ 1 x))) |
(* 1/2 (* x (- eps 1))) |
(* -1 (* x (- (* -1/2 (- eps 1)) (/ 1 x)))) |
(* -1 (* x (- (* -1/2 (- eps 1)) (/ 1 x)))) |
(* -1 (* x (- (* -1/2 (- eps 1)) (/ 1 x)))) |
(+ 1 (* -1/2 x)) |
(+ 1 (+ (* -1/2 x) (* 1/2 (* eps x)))) |
(+ 1 (+ (* -1/2 x) (* 1/2 (* eps x)))) |
(+ 1 (+ (* -1/2 x) (* 1/2 (* eps x)))) |
(* 1/2 (* eps x)) |
(* eps (+ (* -1/2 (/ x eps)) (+ (* 1/2 x) (/ 1 eps)))) |
(* eps (+ (* -1/2 (/ x eps)) (+ (* 1/2 x) (/ 1 eps)))) |
(* eps (+ (* -1/2 (/ x eps)) (+ (* 1/2 x) (/ 1 eps)))) |
(* 1/2 (* eps x)) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 x)) eps)) (* -1/2 x)))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 x)) eps)) (* -1/2 x)))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 x)) eps)) (* -1/2 x)))) |
x |
(+ x (* eps x)) |
(+ x (* eps x)) |
(+ x (* eps x)) |
(* eps x) |
(* eps (+ x (/ x eps))) |
(* eps (+ x (/ x eps))) |
(* eps (+ x (/ x eps))) |
(* eps x) |
(* -1 (* eps (+ (* -1 x) (* -1 (/ x eps))))) |
(* -1 (* eps (+ (* -1 x) (* -1 (/ x eps))))) |
(* -1 (* eps (+ (* -1 x) (* -1 (/ x eps))))) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* x (+ 1 eps)) |
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) |
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))))))) |
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
1 |
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))) |
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))) |
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* -1 (* x (+ 1 (* -1 eps)))) |
(* -1 (* x (+ 1 (* -1 eps)))) |
(* -1 (* x (+ 1 (* -1 eps)))) |
(* -1 (* x (+ 1 (* -1 eps)))) |
(* -1 x) |
(- (* eps x) x) |
(- (* eps x) x) |
(- (* eps x) x) |
(* eps x) |
(* eps (+ x (* -1 (/ x eps)))) |
(* eps (+ x (* -1 (/ x eps)))) |
(* eps (+ x (* -1 (/ x eps)))) |
(* eps x) |
(* -1 (* eps (+ (* -1 x) (/ x eps)))) |
(* -1 (* eps (+ (* -1 x) (/ x eps)))) |
(* -1 (* eps (+ (* -1 x) (/ x eps)))) |
1 |
(+ 1 (* -1 (* x (+ 1 eps)))) |
(+ 1 (* x (+ (* -1 (+ 1 eps)) (* 1/2 (* x (pow (+ 1 eps) 2)))))) |
(+ 1 (* x (+ (* -1 (+ 1 eps)) (* x (+ (* -1/6 (* x (pow (+ 1 eps) 3))) (* 1/2 (pow (+ 1 eps) 2))))))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (- (* -1 x) (* eps x))) |
(exp (- (* -1 x) (* eps x))) |
(exp (- (* -1 x) (* eps x))) |
(exp (- (* -1 x) (* eps x))) |
(exp (neg x)) |
(+ (exp (neg x)) (* -1 (* eps (* x (exp (neg x)))))) |
(+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* 1/2 (* eps (* (pow x 2) (exp (neg x)))))))) |
(+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* eps (+ (* -1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x))))))))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(* -1 x) |
(+ (* -1 x) (* (pow eps 2) x)) |
(+ (* -1 x) (* (pow eps 2) x)) |
(+ (* -1 x) (* (pow eps 2) x)) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
-2 |
(- (* 2 (pow eps 2)) 2) |
(- (* 2 (pow eps 2)) 2) |
(- (* 2 (pow eps 2)) 2) |
(* 2 (pow eps 2)) |
(* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2))))) |
(* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2))))) |
(* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2))))) |
(* 2 (pow eps 2)) |
(* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2))))) |
(* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2))))) |
(* (pow eps 2) (- 2 (* 2 (/ 1 (pow eps 2))))) |
(exp (neg x)) |
(+ (exp (neg x)) (* -1 (* eps (* x (exp (neg x)))))) |
(+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* 1/2 (* eps (* (pow x 2) (exp (neg x)))))))) |
(+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* eps (+ (* -1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x))))))))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (- 1 (* -1 eps))))) |
(exp (neg (* x (- 1 (* -1 eps))))) |
(exp (neg (* x (- 1 (* -1 eps))))) |
(exp (neg (* x (- 1 (* -1 eps))))) |
1 |
(+ 1 (* -1 (* x (+ 1 eps)))) |
(+ 1 (* x (+ (* -1 (+ 1 eps)) (* 1/2 (* x (pow (+ 1 eps) 2)))))) |
(+ 1 (* x (+ (* -1 (+ 1 eps)) (* x (+ (* -1/6 (* x (pow (+ 1 eps) 3))) (* 1/2 (pow (+ 1 eps) 2))))))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (+ 1 eps)))) |
(exp (neg (* x (+ 1 eps)))) |
x |
(+ x (* -1 (* eps x))) |
(+ x (* -1 (* eps x))) |
(+ x (* -1 (* eps x))) |
(* -1 (* eps x)) |
(* eps (+ (* -1 x) (/ x eps))) |
(* eps (+ (* -1 x) (/ x eps))) |
(* eps (+ (* -1 x) (/ x eps))) |
(* -1 (* eps x)) |
(* -1 (* eps (+ x (* -1 (/ x eps))))) |
(* -1 (* eps (+ x (* -1 (/ x eps))))) |
(* -1 (* eps (+ x (* -1 (/ x eps))))) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(* x (- 1 eps)) |
(exp (neg x)) |
(+ (exp (neg x)) (* eps (* x (exp (neg x))))) |
(+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* x (exp (neg x)))))) |
(+ (exp (neg x)) (* eps (+ (* eps (+ (* 1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))) (* x (exp (neg x)))))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
1 |
(+ 1 (* x (- eps 1))) |
(+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1))) |
(+ 1 (* x (- (+ eps (* x (+ (* 1/6 (* x (pow (- eps 1) 3))) (* 1/2 (pow (- eps 1) 2))))) 1))) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg x)) |
(+ (exp (neg x)) (* eps (* x (exp (neg x))))) |
(+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* x (exp (neg x)))))) |
(+ (exp (neg x)) (* eps (+ (* eps (+ (* 1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))) (* x (exp (neg x)))))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
1 |
(+ 1 (* x (- eps 1))) |
(+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1))) |
(+ 1 (* x (- (+ eps (* x (+ (* 1/6 (* x (pow (- eps 1) 3))) (* 1/2 (pow (- eps 1) 2))))) 1))) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
(exp (neg (* x (- 1 eps)))) |
1 |
(+ 1 (* x (- eps 1))) |
(+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1))) |
(+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1))) |
(* 1/2 (* (pow x 2) (pow (- eps 1) 2))) |
(* (pow x 2) (- (+ (* 1/2 (pow (- eps 1) 2)) (/ eps x)) (/ 1 x))) |
(* (pow x 2) (- (+ (* 1/2 (pow (- eps 1) 2)) (+ (/ 1 (pow x 2)) (/ eps x))) (/ 1 x))) |
(* (pow x 2) (- (+ (* 1/2 (pow (- eps 1) 2)) (+ (/ 1 (pow x 2)) (/ eps x))) (/ 1 x))) |
(* 1/2 (* (pow x 2) (pow (- eps 1) 2))) |
(* (pow x 2) (- (+ (* 1/2 (pow (- eps 1) 2)) (/ eps x)) (/ 1 x))) |
(* (pow x 2) (+ (* -1 (/ (- (* -1 (- eps 1)) (/ 1 x)) x)) (* 1/2 (pow (- eps 1) 2)))) |
(* (pow x 2) (+ (* -1 (/ (- (* -1 (- eps 1)) (/ 1 x)) x)) (* 1/2 (pow (- eps 1) 2)))) |
(+ 1 (* -1 (* x (+ 1 (* -1/2 x))))) |
(+ 1 (+ (* -1 (* x (+ 1 (* -1/2 x)))) (* eps (* x (+ 1 (* -1 x)))))) |
(+ 1 (+ (* -1 (* x (+ 1 (* -1/2 x)))) (* eps (+ (* 1/2 (* eps (pow x 2))) (* x (+ 1 (* -1 x))))))) |
(+ 1 (+ (* -1 (* x (+ 1 (* -1/2 x)))) (* eps (+ (* 1/2 (* eps (pow x 2))) (* x (+ 1 (* -1 x))))))) |
(* 1/2 (* (pow eps 2) (pow x 2))) |
(* (pow eps 2) (+ (* 1/2 (pow x 2)) (/ (* x (+ 1 (* -1 x))) eps))) |
(* (pow eps 2) (+ (* -1 (/ (* x (+ 1 (* -1/2 x))) (pow eps 2))) (+ (* 1/2 (pow x 2)) (+ (/ 1 (pow eps 2)) (/ (* x (+ 1 (* -1 x))) eps))))) |
(* (pow eps 2) (+ (* -1 (/ (* x (+ 1 (* -1/2 x))) (pow eps 2))) (+ (* 1/2 (pow x 2)) (+ (/ 1 (pow eps 2)) (/ (* x (+ 1 (* -1 x))) eps))))) |
(* 1/2 (* (pow eps 2) (pow x 2))) |
(* (pow eps 2) (+ (* 1/2 (pow x 2)) (/ (* x (+ 1 (* -1 x))) eps))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (* x (+ 1 (* -1 x)))) (* -1 (/ (+ 1 (* -1 (* x (+ 1 (* -1/2 x))))) eps))) eps)) (* 1/2 (pow x 2)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (* x (+ 1 (* -1 x)))) (* -1 (/ (+ 1 (* -1 (* x (+ 1 (* -1/2 x))))) eps))) eps)) (* 1/2 (pow x 2)))) |
(- eps 1) |
(- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1) |
(- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1) |
(- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1) |
(* 1/2 (* x (pow (- eps 1) 2))) |
(* x (- (+ (* 1/2 (pow (- eps 1) 2)) (/ eps x)) (/ 1 x))) |
(* x (- (+ (* 1/2 (pow (- eps 1) 2)) (/ eps x)) (/ 1 x))) |
(* x (- (+ (* 1/2 (pow (- eps 1) 2)) (/ eps x)) (/ 1 x))) |
(* 1/2 (* x (pow (- eps 1) 2))) |
(* -1 (* x (+ (* -1 (/ (- eps 1) x)) (* -1/2 (pow (- eps 1) 2))))) |
(* -1 (* x (+ (* -1 (/ (- eps 1) x)) (* -1/2 (pow (- eps 1) 2))))) |
(* -1 (* x (+ (* -1 (/ (- eps 1) x)) (* -1/2 (pow (- eps 1) 2))))) |
(* -1 (+ 1 (* -1/2 x))) |
(+ (* -1 (+ 1 (* -1/2 x))) (* eps (+ 1 (* -1 x)))) |
(+ (* -1 (+ 1 (* -1/2 x))) (* eps (+ 1 (+ (* -1 x) (* 1/2 (* eps x)))))) |
(+ (* -1 (+ 1 (* -1/2 x))) (* eps (+ 1 (+ (* -1 x) (* 1/2 (* eps x)))))) |
(* 1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1 (/ x eps)) (+ (* 1/2 x) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1 (/ x eps)) (+ (* -1 (/ (+ 1 (* -1/2 x)) (pow eps 2))) (+ (* 1/2 x) (/ 1 eps))))) |
(* (pow eps 2) (+ (* -1 (/ x eps)) (+ (* -1 (/ (+ 1 (* -1/2 x)) (pow eps 2))) (+ (* 1/2 x) (/ 1 eps))))) |
(* 1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1 (/ x eps)) (+ (* 1/2 x) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* -1 x))) (+ (* -1/2 (/ x eps)) (/ 1 eps))) eps)) (* 1/2 x))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* -1 x))) (+ (* -1/2 (/ x eps)) (/ 1 eps))) eps)) (* 1/2 x))) |
| Outputs |
|---|
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 x (exp.f64 (neg.f64 x))))) |
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 eps eps) (-.f64 (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 #s(literal 1/2 binary64) x)))) (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64))))) (fma.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 x (exp.f64 (neg.f64 x)))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) (-.f64 (fma.f64 (*.f64 eps eps) (-.f64 (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))))) (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64))))) (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 #s(literal 1/2 binary64) x))))) (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64))))) (*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 x (exp.f64 (neg.f64 x)))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))))))) |
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) (fma.f64 (*.f64 eps eps) (fma.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64)) (*.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/720 binary64) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64)))))) (-.f64 (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))))) (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64)))))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 #s(literal 1/2 binary64) x)))) (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64))))))) (*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 x (exp.f64 (neg.f64 x)))))) |
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) eps))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) eps))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) eps))) |
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) eps))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) eps))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) eps))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal -1 binary64) eps)))) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))) |
(fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal -1 binary64) eps) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps))) (*.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps))))) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps)))))) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))))))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal -1 binary64) eps))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 x (*.f64 #s(literal 1/6 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps))) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps))) (*.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps))))))))) #s(literal 1 binary64)) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps))) (*.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps))) (*.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps))) (*.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps))) (*.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps))) (*.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps))) (*.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps))) (*.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps))) (*.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (* x (- (+ eps (* -1 (+ 1 eps))) 1)))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* 1/2 (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2))))) (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1))))) |
(fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1)) (* x (+ (* 1/2 (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))) (* 1/2 (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2))))))))) |
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) #s(literal 1/6 binary64))))) (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps))))) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))) #s(literal 1 binary64)) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(exp (neg x)) |
(exp.f64 (neg.f64 x)) |
(+ (exp (neg x)) (* 1/2 (* eps (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x))))))) |
(fma.f64 eps #s(literal 0 binary64) (exp.f64 (neg.f64 x))) |
(+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* 1/2 (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x)))))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 (exp.f64 (neg.f64 x)) (*.f64 eps (*.f64 x x)) #s(literal 0 binary64)) (exp.f64 (neg.f64 x))) |
(+ (exp (neg x)) (* eps (+ (* 1/2 (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x))))) (* eps (+ (* 1/2 (* eps (+ (* -1/6 (* (pow x 3) (exp (neg x)))) (* 1/6 (* (pow x 3) (exp (neg x))))))) (* 1/2 (* (pow x 2) (exp (neg x))))))))) |
(fma.f64 eps (fma.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 (exp.f64 (neg.f64 x)) (*.f64 x x) (*.f64 eps #s(literal 0 binary64))) #s(literal 0 binary64)) (exp.f64 (neg.f64 x))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
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1 |
#s(literal 1 binary64) |
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-2 |
#s(literal -2 binary64) |
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(*.f64 (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -2 binary64) (*.f64 eps eps))) eps) eps) |
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(*.f64 (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -2 binary64) (*.f64 eps eps))) eps) eps) |
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(*.f64 (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -2 binary64) (*.f64 eps eps))) eps) eps) |
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(*.f64 (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -2 binary64) (*.f64 eps eps))) eps) eps) |
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(exp.f64 (neg.f64 x)) |
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(fma.f64 (*.f64 x (neg.f64 eps)) (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x))) |
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(exp (neg (* x (- 1 (* -1 eps))))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp (neg (* x (- 1 (* -1 eps))))) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
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1 |
#s(literal 1 binary64) |
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x |
(+ x (* -1 (* eps x))) |
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(exp.f64 (fma.f64 x eps (neg.f64 x))) |
1 |
#s(literal 1 binary64) |
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(exp (- (* eps x) x)) |
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(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
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(exp.f64 (fma.f64 x eps (neg.f64 x))) |
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(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (neg (* x (- 1 eps)))) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (neg x)) |
(exp.f64 (neg.f64 x)) |
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(*.f64 (fma.f64 x eps #s(literal 1 binary64)) (exp.f64 (neg.f64 x))) |
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(exp.f64 (fma.f64 x eps (neg.f64 x))) |
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(exp.f64 (fma.f64 x eps (neg.f64 x))) |
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(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (neg (* x (- 1 eps)))) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (neg (* x (+ 1 (* -1 eps))))) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
1 |
#s(literal 1 binary64) |
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(+ 1 (* x (- (+ eps (* x (+ (* 1/6 (* x (pow (- eps 1) 3))) (* 1/2 (pow (- eps 1) 2))))) 1))) |
(fma.f64 x (+.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)))) #s(literal -1 binary64))) #s(literal 1 binary64)) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
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(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (neg (* x (- 1 eps)))) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
1 |
#s(literal 1 binary64) |
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(+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1))) |
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(* 1/2 (* (pow x 2) (pow (- eps 1) 2))) |
(*.f64 (*.f64 x x) (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)))) |
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(* (pow x 2) (- (+ (* 1/2 (pow (- eps 1) 2)) (+ (/ 1 (pow x 2)) (/ eps x))) (/ 1 x))) |
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(* 1/2 (* (pow x 2) (pow (- eps 1) 2))) |
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(* (pow x 2) (+ (* -1 (/ (- (* -1 (- eps 1)) (/ 1 x)) x)) (* 1/2 (pow (- eps 1) 2)))) |
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(+ 1 (* -1 (* x (+ 1 (* -1/2 x))))) |
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(+ 1 (+ (* -1 (* x (+ 1 (* -1/2 x)))) (* eps (+ (* 1/2 (* eps (pow x 2))) (* x (+ 1 (* -1 x))))))) |
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(* 1/2 (* (pow eps 2) (pow x 2))) |
(*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))) |
(* (pow eps 2) (+ (* 1/2 (pow x 2)) (/ (* x (+ 1 (* -1 x))) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (/.f64 (-.f64 x (*.f64 x x)) eps))) |
(* (pow eps 2) (+ (* -1 (/ (* x (+ 1 (* -1/2 x))) (pow eps 2))) (+ (* 1/2 (pow x 2)) (+ (/ 1 (pow eps 2)) (/ (* x (+ 1 (* -1 x))) eps))))) |
(*.f64 (*.f64 eps eps) (fma.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (*.f64 eps eps)) (fma.f64 x (/.f64 (-.f64 #s(literal 1 binary64) x) eps) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))) |
(* (pow eps 2) (+ (* -1 (/ (* x (+ 1 (* -1/2 x))) (pow eps 2))) (+ (* 1/2 (pow x 2)) (+ (/ 1 (pow eps 2)) (/ (* x (+ 1 (* -1 x))) eps))))) |
(*.f64 (*.f64 eps eps) (fma.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (*.f64 eps eps)) (fma.f64 x (/.f64 (-.f64 #s(literal 1 binary64) x) eps) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))) |
(* 1/2 (* (pow eps 2) (pow x 2))) |
(*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))) |
(* (pow eps 2) (+ (* 1/2 (pow x 2)) (/ (* x (+ 1 (* -1 x))) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (/.f64 (-.f64 x (*.f64 x x)) eps))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (* x (+ 1 (* -1 x)))) (* -1 (/ (+ 1 (* -1 (* x (+ 1 (* -1/2 x))))) eps))) eps)) (* 1/2 (pow x 2)))) |
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x (*.f64 #s(literal 1/2 binary64) x)) (/.f64 (-.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) (/.f64 (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal 1 binary64)) eps)) eps))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (* x (+ 1 (* -1 x)))) (* -1 (/ (+ 1 (* -1 (* x (+ 1 (* -1/2 x))))) eps))) eps)) (* 1/2 (pow x 2)))) |
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x (*.f64 #s(literal 1/2 binary64) x)) (/.f64 (-.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) (/.f64 (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal 1 binary64)) eps)) eps))) |
(- eps 1) |
(+.f64 #s(literal -1 binary64) eps) |
(- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1) |
(fma.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64))) (+.f64 #s(literal -1 binary64) eps)) |
(- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1) |
(fma.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64))) (+.f64 #s(literal -1 binary64) eps)) |
(- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1) |
(fma.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64))) (+.f64 #s(literal -1 binary64) eps)) |
(* 1/2 (* x (pow (- eps 1) 2))) |
(*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)))) |
(* x (- (+ (* 1/2 (pow (- eps 1) 2)) (/ eps x)) (/ 1 x))) |
(*.f64 x (fma.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) eps) x))) |
(* x (- (+ (* 1/2 (pow (- eps 1) 2)) (/ eps x)) (/ 1 x))) |
(*.f64 x (fma.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) eps) x))) |
(* x (- (+ (* 1/2 (pow (- eps 1) 2)) (/ eps x)) (/ 1 x))) |
(*.f64 x (fma.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal -1 binary64) eps) x))) |
(* 1/2 (* x (pow (- eps 1) 2))) |
(*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)))) |
(* -1 (* x (+ (* -1 (/ (- eps 1) x)) (* -1/2 (pow (- eps 1) 2))))) |
(*.f64 (neg.f64 x) (fma.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 eps #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) eps) x))) |
(* -1 (* x (+ (* -1 (/ (- eps 1) x)) (* -1/2 (pow (- eps 1) 2))))) |
(*.f64 (neg.f64 x) (fma.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 eps #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) eps) x))) |
(* -1 (* x (+ (* -1 (/ (- eps 1) x)) (* -1/2 (pow (- eps 1) 2))))) |
(*.f64 (neg.f64 x) (fma.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 eps #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) eps) x))) |
(* -1 (+ 1 (* -1/2 x))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) |
(+ (* -1 (+ 1 (* -1/2 x))) (* eps (+ 1 (* -1 x)))) |
(fma.f64 eps (-.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) |
(+ (* -1 (+ 1 (* -1/2 x))) (* eps (+ 1 (+ (* -1 x) (* 1/2 (* eps x)))))) |
(fma.f64 eps (fma.f64 x (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) |
(+ (* -1 (+ 1 (* -1/2 x))) (* eps (+ 1 (+ (* -1 x) (* 1/2 (* eps x)))))) |
(fma.f64 eps (fma.f64 x (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) |
(* 1/2 (* (pow eps 2) x)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 eps eps))) |
(* (pow eps 2) (+ (* -1 (/ x eps)) (+ (* 1/2 x) (/ 1 eps)))) |
(*.f64 eps (*.f64 eps (fma.f64 #s(literal 1/2 binary64) x (/.f64 (-.f64 #s(literal 1 binary64) x) eps)))) |
(* (pow eps 2) (+ (* -1 (/ x eps)) (+ (* -1 (/ (+ 1 (* -1/2 x)) (pow eps 2))) (+ (* 1/2 x) (/ 1 eps))))) |
(*.f64 (*.f64 eps eps) (+.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (-.f64 #s(literal 1 binary64) x) eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (*.f64 eps eps)))) |
(* (pow eps 2) (+ (* -1 (/ x eps)) (+ (* -1 (/ (+ 1 (* -1/2 x)) (pow eps 2))) (+ (* 1/2 x) (/ 1 eps))))) |
(*.f64 (*.f64 eps eps) (+.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (-.f64 #s(literal 1 binary64) x) eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (*.f64 eps eps)))) |
(* 1/2 (* (pow eps 2) x)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 eps eps))) |
(* (pow eps 2) (+ (* -1 (/ x eps)) (+ (* 1/2 x) (/ 1 eps)))) |
(*.f64 eps (*.f64 eps (fma.f64 #s(literal 1/2 binary64) x (/.f64 (-.f64 #s(literal 1 binary64) x) eps)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* -1 x))) (+ (* -1/2 (/ x eps)) (/ 1 eps))) eps)) (* 1/2 x))) |
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 (+.f64 (+.f64 (fma.f64 x (/.f64 #s(literal -1/2 binary64) eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) x) eps))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* -1 x))) (+ (* -1/2 (/ x eps)) (/ 1 eps))) eps)) (* 1/2 x))) |
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 (+.f64 (+.f64 (fma.f64 x (/.f64 #s(literal -1/2 binary64) eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) x) eps))) |
| 5 152× | lower-fma.f32 |
| 5 140× | lower-fma.f64 |
| 4 944× | lower-*.f32 |
| 4 920× | lower-*.f64 |
| 2 188× | lower-pow.f64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 70 | 629 |
| 0 | 122 | 630 |
| 1 | 496 | 604 |
| 2 | 4980 | 604 |
| 0 | 8176 | 604 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))) |
(exp.f64 (-.f64 (*.f64 x eps) x)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
(fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64))) |
(-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) |
(neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
(-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) |
(*.f64 (+.f64 #s(literal 1 binary64) eps) x) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
(-.f64 (*.f64 x eps) x) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) |
(fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) |
#s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)) |
(*.f64 (-.f64 #s(literal 1 binary64) eps) x) |
(exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x))) |
#s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))))) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))))) |
(fma.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
(fma.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))))) |
(fma.f64 (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
(fma.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))))) |
(/.f64 (fma.f64 (exp.f64 (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) #s(literal 3 binary64))) #s(literal 1/8 binary64) (*.f64 (exp.f64 (*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))) #s(literal 1/8 binary64))) (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))))) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))))) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))))) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) #s(literal 3 binary64))) (exp.f64 (*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (+.f64 (exp.f64 (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) #s(literal 2 binary64))) (-.f64 (exp.f64 (*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))) (exp.f64 (fma.f64 x (+.f64 eps #s(literal -1 binary64)) (*.f64 x (-.f64 #s(literal -1 binary64) eps))))))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (exp.f64 (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) #s(literal 2 binary64))) (exp.f64 (*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))))) (-.f64 (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
(/.f64 (*.f64 (+.f64 (exp.f64 (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) #s(literal 3 binary64))) (exp.f64 (*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (+.f64 (exp.f64 (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) #s(literal 2 binary64))) (-.f64 (exp.f64 (*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))) (exp.f64 (fma.f64 x (+.f64 eps #s(literal -1 binary64)) (*.f64 x (-.f64 #s(literal -1 binary64) eps))))))) |
(/.f64 (*.f64 (-.f64 (exp.f64 (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) #s(literal 2 binary64))) (exp.f64 (*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (-.f64 (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
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(*.f64 x (-.f64 #s(literal 1 binary64) eps)) |
(*.f64 (-.f64 #s(literal 1 binary64) eps) x) |
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(exp.f64 (*.f64 (log.f64 (exp.f64 (-.f64 #s(literal 1 binary64) eps))) (neg.f64 x))) |
(exp.f64 (*.f64 (log.f64 (exp.f64 (+.f64 eps #s(literal -1 binary64)))) x)) |
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(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps eps)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) (*.f64 x (+.f64 eps #s(literal -1 binary64)))) #s(literal -1 binary64))) (*.f64 (-.f64 #s(literal -1 binary64) eps) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal -1 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps #s(literal -1 binary64)) (*.f64 (+.f64 eps #s(literal -1 binary64)) (+.f64 eps #s(literal -1 binary64)))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (fma.f64 eps (*.f64 eps eps) #s(literal -1 binary64))) (*.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) (*.f64 x (+.f64 eps #s(literal -1 binary64)))) #s(literal 1 binary64)) (*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))))) (fma.f64 eps (+.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps #s(literal -1 binary64)) (*.f64 (+.f64 eps #s(literal -1 binary64)) (+.f64 eps #s(literal -1 binary64)))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) (*.f64 x (+.f64 eps #s(literal -1 binary64)))) #s(literal 1 binary64)) (*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))))) (-.f64 #s(literal -1 binary64) eps))) |
(/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) (*.f64 x (+.f64 eps #s(literal -1 binary64)))) #s(literal -1 binary64)) (fma.f64 eps (*.f64 eps eps) #s(literal -1 binary64))) (*.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal -1 binary64)) (fma.f64 eps (+.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))) |
(/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) (*.f64 x (+.f64 eps #s(literal -1 binary64)))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) eps))) |
(/.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))) (neg.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64)))) (neg.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 eps (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 eps (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64)))) (*.f64 eps (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))))) (fma.f64 (neg.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))) (neg.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))) (-.f64 (*.f64 (*.f64 eps (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 eps (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64)))) (*.f64 (neg.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 eps (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))))))) |
(/.f64 (-.f64 (*.f64 (neg.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))) (neg.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64)))) (*.f64 (*.f64 eps (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 eps (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))))) (-.f64 (neg.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 eps (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))))) |
(/.f64 (*.f64 (+.f64 eps #s(literal -1 binary64)) (fma.f64 (*.f64 (+.f64 eps #s(literal -1 binary64)) (*.f64 (+.f64 eps #s(literal -1 binary64)) (+.f64 eps #s(literal -1 binary64)))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (-.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) (*.f64 x (+.f64 eps #s(literal -1 binary64)))) #s(literal 1 binary64)) (*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64)))))) |
(/.f64 (*.f64 (+.f64 eps #s(literal -1 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) (*.f64 x (+.f64 eps #s(literal -1 binary64)))) #s(literal -1 binary64))) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal -1 binary64))) |
(/.f64 (*.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64)) (fma.f64 eps (*.f64 eps eps) #s(literal -1 binary64))) (fma.f64 eps (+.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))) |
(/.f64 (*.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 eps eps))) (-.f64 #s(literal -1 binary64) eps)) |
(/.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) #s(literal -1 binary64)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))) (fma.f64 eps (+.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) eps)) |
(/.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps #s(literal -1 binary64)) (*.f64 (+.f64 eps #s(literal -1 binary64)) (+.f64 eps #s(literal -1 binary64)))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (+.f64 eps #s(literal -1 binary64))) (-.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) (*.f64 x (+.f64 eps #s(literal -1 binary64)))) #s(literal 1 binary64)) (*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64)))))) |
(/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))) (*.f64 x (+.f64 eps #s(literal -1 binary64)))) #s(literal -1 binary64)) (+.f64 eps #s(literal -1 binary64))) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal -1 binary64))) |
(*.f64 (+.f64 eps #s(literal -1 binary64)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64))) |
(*.f64 (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64)) (+.f64 eps #s(literal -1 binary64))) |
Compiled 59 271 to 3 449 computations (94.2% saved)
18 alts after pruning (17 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 283 | 15 | 1 298 |
| Fresh | 2 | 2 | 4 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 0 | 0 |
| Total | 1 289 | 18 | 1 307 |
| Status | Accuracy | Program |
|---|---|---|
| 29.0% | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (+.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)))) #s(literal -1 binary64))) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) | |
| 32.2% | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) | |
| 75.8% | (exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))))))) #s(literal -1 binary64))) | |
| ▶ | 74.0% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
| 60.5% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (*.f64 eps (*.f64 eps (+.f64 x (/.f64 #s(literal 1 binary64) eps)))))) #s(literal 1 binary64))) | |
| 72.9% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 x (*.f64 eps eps))) #s(literal 1 binary64))) | |
| ▶ | 61.1% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))) |
| 61.9% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) #s(approx (exp (neg (+ (* x eps) x))) #s(literal 1 binary64))))) | |
| ▶ | 83.9% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
| ▶ | 63.8% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
| 57.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) | |
| 37.3% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) #s(approx (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x)))) (fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps))) (*.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) #s(literal 1/6 binary64)))))) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)))) #s(literal 2 binary64))))) | |
| ▶ | 41.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
| 33.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))))) | |
| 72.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) | |
| 42.1% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) | |
| 71.2% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (exp.f64 (neg.f64 x)))) | |
| ✓ | 42.5% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
Compiled 798 to 437 computations (45.2% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) | |
| cost-diff | 0 | (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x))))) | |
| cost-diff | 0 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) x) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) | |
| cost-diff | 128 | (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) | |
| cost-diff | 0 | #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) x) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))) | |
| cost-diff | 0 | (*.f64 x #s(literal -1/2 binary64)) | |
| cost-diff | 0 | (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) | |
| cost-diff | 0 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) | |
| cost-diff | 0 | (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) | |
| cost-diff | 0 | (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) | |
| cost-diff | 0 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
| 14 766× | lower-fma.f32 |
| 14 754× | lower-fma.f64 |
| 5 234× | lower-*.f32 |
| 5 218× | lower-*.f64 |
| 3 398× | lower--.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 80 | 1031 |
| 0 | 115 | 1031 |
| 1 | 257 | 1026 |
| 2 | 754 | 1016 |
| 3 | 3554 | 971 |
| 0 | 8790 | 930 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
#s(literal 1/2 binary64) |
(+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) |
(exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) |
#s(approx (- (* x eps) x) (*.f64 x eps)) |
(*.f64 x eps) |
x |
eps |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(neg.f64 (fma.f64 x eps x)) |
(fma.f64 x eps x) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
x |
(*.f64 x #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
#s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) |
(*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps))))) |
eps |
(*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))) |
(-.f64 x (/.f64 x (*.f64 eps eps))) |
(/.f64 x (*.f64 eps eps)) |
(*.f64 eps eps) |
#s(literal 1 binary64) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) |
(+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) |
(/.f64 (+.f64 eps #s(literal 1 binary64)) eps) |
(+.f64 eps #s(literal 1 binary64)) |
eps |
#s(literal 1 binary64) |
(-.f64 #s(literal -1 binary64) eps) |
#s(literal -1 binary64) |
#s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps)) |
(/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps) |
(fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) |
(-.f64 (fma.f64 x (*.f64 eps eps) eps) x) |
(fma.f64 x (*.f64 eps eps) eps) |
(*.f64 eps eps) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
#s(literal 1/2 binary64) |
(+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))) |
#s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(neg.f64 (fma.f64 x eps x)) |
(fma.f64 x eps x) |
x |
eps |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))))) |
#s(literal 1/2 binary64) |
(+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) |
(+.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) |
(exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) |
(exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) |
#s(approx (- (* x eps) x) (*.f64 x eps)) |
#s(approx (- (* x eps) x) (*.f64 eps x)) |
(*.f64 x eps) |
(*.f64 eps x) |
x |
eps |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) |
(neg.f64 (fma.f64 x eps x)) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(fma.f64 x eps x) |
(fma.f64 eps x x) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
x |
(*.f64 x #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 (*.f64 eps eps) (-.f64 x (/.f64 x (*.f64 eps eps))))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 (*.f64 eps eps) (-.f64 x (/.f64 x (*.f64 eps eps))))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
x |
#s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) |
#s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 (*.f64 eps eps) (-.f64 x (/.f64 x (*.f64 eps eps))))) |
(*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps))))) |
(*.f64 (*.f64 eps eps) (-.f64 x (/.f64 x (*.f64 eps eps)))) |
eps |
(*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))) |
(-.f64 x (/.f64 x (*.f64 eps eps))) |
(/.f64 x (*.f64 eps eps)) |
(*.f64 eps eps) |
#s(literal 1 binary64) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (+.f64 #s(literal -1 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (+.f64 #s(literal -1 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
x |
(+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) |
(+.f64 (+.f64 #s(literal -1 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) #s(literal -1 binary64)) eps))) |
(+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) |
(+.f64 #s(literal -1 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) eps)) |
(/.f64 (+.f64 eps #s(literal 1 binary64)) eps) |
(/.f64 (+.f64 #s(literal 1 binary64) eps) eps) |
(+.f64 eps #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) eps) |
eps |
#s(literal 1 binary64) |
(-.f64 #s(literal -1 binary64) eps) |
#s(literal -1 binary64) |
#s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps)) |
#s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) #s(literal -1 binary64)) eps)) |
(/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps) |
(/.f64 (fma.f64 eps (fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) #s(literal -1 binary64)) eps) |
(fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) |
(fma.f64 eps (fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) #s(literal -1 binary64)) |
(-.f64 (fma.f64 x (*.f64 eps eps) eps) x) |
(fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) |
(fma.f64 x (*.f64 eps eps) eps) |
(fma.f64 eps (*.f64 eps x) eps) |
(*.f64 eps eps) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)))) |
#s(literal 1/2 binary64) |
(+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))) |
(+.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64))) |
#s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) |
(neg.f64 (fma.f64 x eps x)) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(fma.f64 x eps x) |
(fma.f64 eps x x) |
x |
eps |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (neg.f64 (fma.f64 x eps x)) | |
| accuracy | 0.00390625 | (exp.f64 (neg.f64 (fma.f64 x eps x))) | |
| accuracy | 0.3024004356261579 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) | |
| accuracy | 36.98496295625584 | #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) | |
| accuracy | 5.929828876118877 | (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps) | |
| accuracy | 6.408237388687392 | (fma.f64 x (*.f64 eps eps) eps) | |
| accuracy | 18.605111781140387 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) | |
| accuracy | 29.088808368419762 | (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) | |
| accuracy | 4.771994259738847 | (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps))))) | |
| accuracy | 7.368506796672326 | (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))) | |
| accuracy | 8.712131779807335 | (/.f64 x (*.f64 eps eps)) | |
| accuracy | 18.605111781140387 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))) | |
| accuracy | 0 | (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) | |
| accuracy | 0 | (*.f64 x #s(literal -1/2 binary64)) | |
| accuracy | 18.605111781140387 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) | |
| accuracy | 27.210811177054754 | #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) | |
| accuracy | 0.00390625 | (exp.f64 (neg.f64 (fma.f64 x eps x))) | |
| accuracy | 0.00390625 | (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) | |
| accuracy | 0.3024004356261579 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) | |
| accuracy | 27.625978359598232 | #s(approx (- (* x eps) x) (*.f64 x eps)) |
| 136.0ms | 108× | 1 | valid |
| 47.0ms | 116× | 0 | valid |
| 37.0ms | 32× | 2 | valid |
Compiled 714 to 63 computations (91.2% saved)
ival-mult: 61.0ms (33.9% of total)ival-div: 39.0ms (21.7% of total)ival-add: 26.0ms (14.5% of total)adjust: 22.0ms (12.2% of total)ival-exp: 13.0ms (7.2% of total)ival-sub: 12.0ms (6.7% of total)ival-neg: 5.0ms (2.8% of total)exact: 1.0ms (0.6% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x))))))> |
#<alt (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x)))))> |
#<alt (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x))))> |
#<alt (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps)))> |
#<alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))> |
#<alt #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))> |
#<alt (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))> |
#<alt (*.f64 x #s(literal -1/2 binary64))> |
#<alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64)))> |
#<alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))> |
#<alt (*.f64 #s(literal 1/2 binary64) x)> |
#<alt #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps))))))> |
#<alt (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)> |
#<alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)))> |
#<alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))> |
#<alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x))))))> |
#<alt (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))> |
#<alt (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x))))> |
#<alt #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64))> |
#<alt #s(approx (- (* x eps) x) (*.f64 x eps))> |
#<alt (exp.f64 (neg.f64 (fma.f64 x eps x)))> |
#<alt (/.f64 x (*.f64 eps eps))> |
#<alt (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps))))> |
#<alt (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))> |
#<alt (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps)))> |
#<alt (fma.f64 x (*.f64 eps eps) eps)> |
#<alt (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps)> |
#<alt (neg.f64 (fma.f64 x eps x))> |
| Outputs |
|---|
#<alt (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))> |
#<alt (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))> |
#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))> |
#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))> |
#<alt (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))> |
#<alt (+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))))> |
#<alt (+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (* x (- (+ eps (* -1 (+ 1 eps))) 1))))> |
#<alt (+ 1 (* x (+ (* 1/2 (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2))))) (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1)))))> |
#<alt (+ 1 (* x (+ (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1)) (* x (+ (* 1/2 (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))) (* 1/2 (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2)))))))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))))> |
#<alt (* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))))> |
#<alt (* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))))> |
#<alt (* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))))> |
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#<alt 2> |
#<alt (+ 2 (* x (- (+ eps (* -1 (+ 1 eps))) 1)))> |
#<alt (+ 2 (* x (- (+ eps (+ (* -1 (+ 1 eps)) (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2)))))) 1)))> |
#<alt (+ 2 (* x (- (+ eps (+ (* -1 (+ 1 eps)) (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (+ (* 1/2 (pow (- eps 1) 2)) (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))))))) 1)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))> |
#<alt (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))> |
#<alt (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))> |
#<alt (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))> |
#<alt (* 2 (exp (neg x)))> |
#<alt (+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x))))))> |
#<alt (+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (+ (* eps (* (pow x 2) (exp (neg x)))) (* x (exp (neg x)))))))> |
#<alt (+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (+ (* eps (+ (* eps (+ (* -1/6 (* (pow x 3) (exp (neg x)))) (* 1/6 (* (pow x 3) (exp (neg x)))))) (* (pow x 2) (exp (neg x))))) (* x (exp (neg x)))))))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt 1> |
#<alt (+ 1 (* x (- eps 1)))> |
#<alt (+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1)))> |
#<alt (+ 1 (* x (- (+ eps (* x (+ (* 1/6 (* x (pow (- eps 1) 3))) (* 1/2 (pow (- eps 1) 2))))) 1)))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (+ (* -1 x) (* eps x)))> |
#<alt (exp (+ (* -1 x) (* eps x)))> |
#<alt (exp (+ (* -1 x) (* eps x)))> |
#<alt (exp (+ (* -1 x) (* eps x)))> |
#<alt (exp (neg x))> |
#<alt (+ (exp (neg x)) (* eps (* x (exp (neg x)))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* x (exp (neg x))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* eps (+ (* 1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))) (* x (exp (neg x))))))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* -1 (* x (+ 1 (* -1 eps))))> |
#<alt (* -1 (* x (+ 1 (* -1 eps))))> |
#<alt (* -1 (* x (+ 1 (* -1 eps))))> |
#<alt (* -1 (* x (+ 1 (* -1 eps))))> |
#<alt (* -1 x)> |
#<alt (- (* eps x) x)> |
#<alt (- (* eps x) x)> |
#<alt (- (* eps x) x)> |
#<alt (* eps x)> |
#<alt (* eps (+ x (* -1 (/ x eps))))> |
#<alt (* eps (+ x (* -1 (/ x eps))))> |
#<alt (* eps (+ x (* -1 (/ x eps))))> |
#<alt (* eps x)> |
#<alt (* -1 (* eps (+ (* -1 x) (/ x eps))))> |
#<alt (* -1 (* eps (+ (* -1 x) (/ x eps))))> |
#<alt (* -1 (* eps (+ (* -1 x) (/ x eps))))> |
#<alt 1> |
#<alt (+ 1 (* -1 (* x (+ 1 eps))))> |
#<alt (+ 1 (* x (+ (* -1 (+ 1 eps)) (* 1/2 (* x (pow (+ 1 eps) 2))))))> |
#<alt (+ 1 (* x (+ (* -1 (+ 1 eps)) (* x (+ (* -1/6 (* x (pow (+ 1 eps) 3))) (* 1/2 (pow (+ 1 eps) 2)))))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (neg x))> |
#<alt (+ (exp (neg x)) (* -1 (* eps (* x (exp (neg x))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* 1/2 (* eps (* (pow x 2) (exp (neg x))))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* eps (+ (* -1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (/ x (pow eps 2))> |
#<alt (* -1 (/ x eps))> |
#<alt (/ (+ (* -1 x) (* (pow eps 2) x)) eps)> |
#<alt (/ (+ (* -1 x) (* (pow eps 2) x)) eps)> |
#<alt (/ (+ (* -1 x) (* (pow eps 2) x)) eps)> |
#<alt (* eps x)> |
#<alt (* eps (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* eps (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* eps (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* eps x)> |
#<alt (* -1 (* eps (+ (* -1 x) (/ x (pow eps 2)))))> |
#<alt (* -1 (* eps (+ (* -1 x) (/ x (pow eps 2)))))> |
#<alt (* -1 (* eps (+ (* -1 x) (/ x (pow eps 2)))))> |
#<alt (* eps (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* eps (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* eps (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* eps (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* eps (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* eps (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* eps (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* eps (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* -1 (* eps (* x (- (/ 1 (pow eps 2)) 1))))> |
#<alt (* -1 (* eps (* x (- (/ 1 (pow eps 2)) 1))))> |
#<alt (* -1 (* eps (* x (- (/ 1 (pow eps 2)) 1))))> |
#<alt (* -1 (* eps (* x (- (/ 1 (pow eps 2)) 1))))> |
#<alt (* -1 x)> |
#<alt (+ (* -1 x) (* (pow eps 2) x))> |
#<alt (+ (* -1 x) (* (pow eps 2) x))> |
#<alt (+ (* -1 x) (* (pow eps 2) x))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2)))))> |
#<alt (* -1 (* (pow eps 2) (* x (- (/ 1 (pow eps 2)) 1))))> |
#<alt (* -1 (* (pow eps 2) (* x (- (/ 1 (pow eps 2)) 1))))> |
#<alt (* -1 (* (pow eps 2) (* x (- (/ 1 (pow eps 2)) 1))))> |
#<alt (* -1 (* (pow eps 2) (* x (- (/ 1 (pow eps 2)) 1))))> |
#<alt (* -1 x)> |
#<alt (+ (* -1 x) (* (pow eps 2) x))> |
#<alt (+ (* -1 x) (* (pow eps 2) x))> |
#<alt (+ (* -1 x) (* (pow eps 2) x))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt eps> |
#<alt (+ eps (* (pow eps 2) x))> |
#<alt (+ eps (* (pow eps 2) x))> |
#<alt (+ eps (* (pow eps 2) x))> |
#<alt (* (pow eps 2) x)> |
#<alt (* x (+ (/ eps x) (pow eps 2)))> |
#<alt (* x (+ (/ eps x) (pow eps 2)))> |
#<alt (* x (+ (/ eps x) (pow eps 2)))> |
#<alt (* (pow eps 2) x)> |
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2)))))> |
#<alt eps> |
#<alt (* eps (+ 1 (* eps x)))> |
#<alt (* eps (+ 1 (* eps x)))> |
#<alt (* eps (+ 1 (* eps x)))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (/ -1 eps)> |
#<alt (/ (- (* -1 (* eps x)) 1) eps)> |
#<alt (/ (- (* eps (+ eps (* -1 x))) 1) eps)> |
#<alt (/ (- (* eps (+ (* -1 x) (* eps (+ 1 (* eps x))))) 1) eps)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ x (+ (* -1 (/ x (pow eps 2))) (/ 1 eps))))> |
#<alt (* (pow eps 2) (- (+ x (+ (* -1 (/ x (pow eps 2))) (/ 1 eps))) (/ 1 (pow eps 3))))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ (- (/ x eps) 1) eps))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ (- (* -1 (/ (- (* -1 x) (/ 1 eps)) eps)) 1) eps))))> |
#<alt (/ (- (pow eps 2) 1) eps)> |
#<alt (- (+ eps (* x (- (pow eps 2) 1))) (/ 1 eps))> |
#<alt (- (+ eps (* x (- (pow eps 2) 1))) (/ 1 eps))> |
#<alt (- (+ eps (* x (- (pow eps 2) 1))) (/ 1 eps))> |
#<alt (* x (- (pow eps 2) 1))> |
#<alt (* x (- (+ (/ eps x) (pow eps 2)) (+ 1 (/ 1 (* eps x)))))> |
#<alt (* x (- (+ (/ eps x) (pow eps 2)) (+ 1 (/ 1 (* eps x)))))> |
#<alt (* x (- (+ (/ eps x) (pow eps 2)) (+ 1 (/ 1 (* eps x)))))> |
#<alt (* -1 (* x (+ 1 (* -1 (pow eps 2)))))> |
#<alt (* -1 (* x (+ 1 (+ (* -1 (/ (- eps (/ 1 eps)) x)) (* -1 (pow eps 2))))))> |
#<alt (* -1 (* x (+ 1 (+ (* -1 (/ (- eps (/ 1 eps)) x)) (* -1 (pow eps 2))))))> |
#<alt (* -1 (* x (+ 1 (+ (* -1 (/ (- eps (/ 1 eps)) x)) (* -1 (pow eps 2))))))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (- 1 (* -1 eps))))> |
#<alt (* -1 (* x (- 1 (* -1 eps))))> |
#<alt (* -1 (* x (- 1 (* -1 eps))))> |
#<alt (* -1 (* x (- 1 (* -1 eps))))> |
#<alt (* -1 x)> |
#<alt (- (* -1 (* eps x)) x)> |
#<alt (- (* -1 (* eps x)) x)> |
#<alt (- (* -1 (* eps x)) x)> |
#<alt (* -1 (* eps x))> |
#<alt (* eps (- (* -1 (/ x eps)) x))> |
#<alt (* eps (- (* -1 (/ x eps)) x))> |
#<alt (* eps (- (* -1 (/ x eps)) x))> |
#<alt (* -1 (* eps x))> |
#<alt (* -1 (* eps (- (/ x eps) (* -1 x))))> |
#<alt (* -1 (* eps (- (/ x eps) (* -1 x))))> |
#<alt (* -1 (* eps (- (/ x eps) (* -1 x))))> |
159 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 5.0ms | x | @ | 0 | (/ x (* eps eps)) |
| 0.0ms | x | @ | -inf | (/ (+ (* eps (- (+ (* x (* eps eps)) eps) x)) -1) eps) |
| 0.0ms | x | @ | inf | (/ x (* eps eps)) |
| 0.0ms | x | @ | -inf | (/ x (* eps eps)) |
| 0.0ms | x | @ | 0 | (/ (+ (* eps (- (+ (* x (* eps eps)) eps) x)) -1) eps) |
| 1× | egg-herbie |
| 10 278× | lower-fma.f64 |
| 10 278× | lower-fma.f32 |
| 6 398× | lower-*.f64 |
| 6 398× | lower-*.f32 |
| 2 242× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 438 | 11214 |
| 1 | 1460 | 10416 |
| 2 | 4991 | 10150 |
| 0 | 8313 | 9642 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) |
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))))))) |
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
1 |
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))) |
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))) |
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1 |
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2 |
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1 |
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1 |
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1 |
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1 |
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(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* -1/2 x) |
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1 |
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1 |
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(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(* 1/4 (* (pow x 2) (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(+ 1 (* -1/2 (pow x 2))) |
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(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* 1/2 (* (pow eps 2) (pow x 2))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* -1 x) |
(+ (* -1 x) (* (pow eps 2) x)) |
(+ (* -1 x) (* (pow eps 2) x)) |
(+ (* -1 x) (* (pow eps 2) x)) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
eps |
(+ eps (* x (- (pow eps 2) 1))) |
(+ eps (* x (- (pow eps 2) 1))) |
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(* x (- (pow eps 2) 1)) |
(* x (- (+ (/ eps x) (pow eps 2)) 1)) |
(* x (- (+ (/ eps x) (pow eps 2)) 1)) |
(* x (- (+ (/ eps x) (pow eps 2)) 1)) |
(* -1 (* x (+ 1 (* -1 (pow eps 2))))) |
(* -1 (* x (+ 1 (+ (* -1 (/ eps x)) (* -1 (pow eps 2)))))) |
(* -1 (* x (+ 1 (+ (* -1 (/ eps x)) (* -1 (pow eps 2)))))) |
(* -1 (* x (+ 1 (+ (* -1 (/ eps x)) (* -1 (pow eps 2)))))) |
(* -1 x) |
(- eps x) |
(- (* eps (+ 1 (* eps x))) x) |
(- (* eps (+ 1 (* eps x))) x) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) (+ x (+ (* -1 (/ x (pow eps 2))) (/ 1 eps)))) |
(* (pow eps 2) (+ x (+ (* -1 (/ x (pow eps 2))) (/ 1 eps)))) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (/ 1 eps))) |
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(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
1 |
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))) |
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))) |
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
1 |
(+ 1 (* 1/4 (* (pow x 2) (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))) |
(+ 1 (* 1/4 (* (pow x 2) (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))) |
(+ 1 (* 1/4 (* (pow x 2) (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))) |
(* 1/4 (* (pow x 2) (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(* 1/4 (* (pow x 2) (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (* (pow eps 2) (pow x 2))))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (* (pow eps 2) (pow x 2))))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (* (pow eps 2) (pow x 2))))) |
(* 1/2 (* (pow eps 2) (pow x 2))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* 1/2 (* (pow eps 2) (pow x 2))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) |
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))))))) |
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
1 |
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))) |
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))) |
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
1 |
(+ 1 (* 1/2 (* x (- (+ eps (* -1 (+ 1 eps))) 1)))) |
(+ 1 (* x (+ (* 1/2 (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2))))) (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1))))) |
(+ 1 (* x (+ (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1)) (* x (+ (* 1/2 (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))) (* 1/2 (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2))))))))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))) |
(* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))) |
(* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))) |
(* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))) |
(exp (neg x)) |
(+ (exp (neg x)) (* 1/2 (* eps (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x))))))) |
(+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* 1/2 (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x)))))))) |
(+ (exp (neg x)) (* eps (+ (* 1/2 (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x))))) (* eps (+ (* 1/2 (* eps (+ (* -1/6 (* (pow x 3) (exp (neg x)))) (* 1/6 (* (pow x 3) (exp (neg x))))))) (* 1/2 (* (pow x 2) (exp (neg x))))))))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
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(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
2 |
(+ 2 (* x (- (+ eps (* -1 (+ 1 eps))) 1))) |
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(+ 2 (* x (- (+ eps (+ (* -1 (+ 1 eps)) (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (+ (* 1/2 (pow (- eps 1) 2)) (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))))))) 1))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))) |
(+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))) |
(+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))) |
(+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))) |
(* 2 (exp (neg x))) |
(+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x)))))) |
(+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (+ (* eps (* (pow x 2) (exp (neg x)))) (* x (exp (neg x))))))) |
(+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (+ (* eps (+ (* eps (+ (* -1/6 (* (pow x 3) (exp (neg x)))) (* 1/6 (* (pow x 3) (exp (neg x)))))) (* (pow x 2) (exp (neg x))))) (* x (exp (neg x))))))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
1 |
(+ 1 (* x (- eps 1))) |
(+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1))) |
(+ 1 (* x (- (+ eps (* x (+ (* 1/6 (* x (pow (- eps 1) 3))) (* 1/2 (pow (- eps 1) 2))))) 1))) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (+ (* -1 x) (* eps x))) |
(exp (+ (* -1 x) (* eps x))) |
(exp (+ (* -1 x) (* eps x))) |
(exp (+ (* -1 x) (* eps x))) |
(exp (neg x)) |
(+ (exp (neg x)) (* eps (* x (exp (neg x))))) |
(+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* x (exp (neg x)))))) |
(+ (exp (neg x)) (* eps (+ (* eps (+ (* 1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))) (* x (exp (neg x)))))) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* x (- eps 1)) |
(* -1 (* x (+ 1 (* -1 eps)))) |
(* -1 (* x (+ 1 (* -1 eps)))) |
(* -1 (* x (+ 1 (* -1 eps)))) |
(* -1 (* x (+ 1 (* -1 eps)))) |
(* -1 x) |
(- (* eps x) x) |
(- (* eps x) x) |
(- (* eps x) x) |
(* eps x) |
(* eps (+ x (* -1 (/ x eps)))) |
(* eps (+ x (* -1 (/ x eps)))) |
(* eps (+ x (* -1 (/ x eps)))) |
(* eps x) |
(* -1 (* eps (+ (* -1 x) (/ x eps)))) |
(* -1 (* eps (+ (* -1 x) (/ x eps)))) |
(* -1 (* eps (+ (* -1 x) (/ x eps)))) |
1 |
(+ 1 (* -1 (* x (+ 1 eps)))) |
(+ 1 (* x (+ (* -1 (+ 1 eps)) (* 1/2 (* x (pow (+ 1 eps) 2)))))) |
(+ 1 (* x (+ (* -1 (+ 1 eps)) (* x (+ (* -1/6 (* x (pow (+ 1 eps) 3))) (* 1/2 (pow (+ 1 eps) 2))))))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (- (* -1 x) (* eps x))) |
(exp (- (* -1 x) (* eps x))) |
(exp (- (* -1 x) (* eps x))) |
(exp (- (* -1 x) (* eps x))) |
(exp (neg x)) |
(+ (exp (neg x)) (* -1 (* eps (* x (exp (neg x)))))) |
(+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* 1/2 (* eps (* (pow x 2) (exp (neg x)))))))) |
(+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* eps (+ (* -1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x))))))))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(/ x (pow eps 2)) |
(* -1 (/ x eps)) |
(/ (+ (* -1 x) (* (pow eps 2) x)) eps) |
(/ (+ (* -1 x) (* (pow eps 2) x)) eps) |
(/ (+ (* -1 x) (* (pow eps 2) x)) eps) |
(* eps x) |
(* eps (+ x (* -1 (/ x (pow eps 2))))) |
(* eps (+ x (* -1 (/ x (pow eps 2))))) |
(* eps (+ x (* -1 (/ x (pow eps 2))))) |
(* eps x) |
(* -1 (* eps (+ (* -1 x) (/ x (pow eps 2))))) |
(* -1 (* eps (+ (* -1 x) (/ x (pow eps 2))))) |
(* -1 (* eps (+ (* -1 x) (/ x (pow eps 2))))) |
(* eps (* x (- 1 (/ 1 (pow eps 2))))) |
(* eps (* x (- 1 (/ 1 (pow eps 2))))) |
(* eps (* x (- 1 (/ 1 (pow eps 2))))) |
(* eps (* x (- 1 (/ 1 (pow eps 2))))) |
(* eps (* x (- 1 (/ 1 (pow eps 2))))) |
(* eps (* x (- 1 (/ 1 (pow eps 2))))) |
(* eps (* x (- 1 (/ 1 (pow eps 2))))) |
(* eps (* x (- 1 (/ 1 (pow eps 2))))) |
(* -1 (* eps (* x (- (/ 1 (pow eps 2)) 1)))) |
(* -1 (* eps (* x (- (/ 1 (pow eps 2)) 1)))) |
(* -1 (* eps (* x (- (/ 1 (pow eps 2)) 1)))) |
(* -1 (* eps (* x (- (/ 1 (pow eps 2)) 1)))) |
(* -1 x) |
(+ (* -1 x) (* (pow eps 2) x)) |
(+ (* -1 x) (* (pow eps 2) x)) |
(+ (* -1 x) (* (pow eps 2) x)) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2))))) |
(* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2))))) |
(* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2))))) |
(* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2))))) |
(* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2))))) |
(* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2))))) |
(* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2))))) |
(* (pow eps 2) (* x (- 1 (/ 1 (pow eps 2))))) |
(* -1 (* (pow eps 2) (* x (- (/ 1 (pow eps 2)) 1)))) |
(* -1 (* (pow eps 2) (* x (- (/ 1 (pow eps 2)) 1)))) |
(* -1 (* (pow eps 2) (* x (- (/ 1 (pow eps 2)) 1)))) |
(* -1 (* (pow eps 2) (* x (- (/ 1 (pow eps 2)) 1)))) |
(* -1 x) |
(+ (* -1 x) (* (pow eps 2) x)) |
(+ (* -1 x) (* (pow eps 2) x)) |
(+ (* -1 x) (* (pow eps 2) x)) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
eps |
(+ eps (* (pow eps 2) x)) |
(+ eps (* (pow eps 2) x)) |
(+ eps (* (pow eps 2) x)) |
(* (pow eps 2) x) |
(* x (+ (/ eps x) (pow eps 2))) |
(* x (+ (/ eps x) (pow eps 2))) |
(* x (+ (/ eps x) (pow eps 2))) |
(* (pow eps 2) x) |
(* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))) |
(* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))) |
(* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))) |
eps |
(* eps (+ 1 (* eps x))) |
(* eps (+ 1 (* eps x))) |
(* eps (+ 1 (* eps x))) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(/ -1 eps) |
(/ (- (* -1 (* eps x)) 1) eps) |
(/ (- (* eps (+ eps (* -1 x))) 1) eps) |
(/ (- (* eps (+ (* -1 x) (* eps (+ 1 (* eps x))))) 1) eps) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) (+ x (+ (* -1 (/ x (pow eps 2))) (/ 1 eps)))) |
(* (pow eps 2) (- (+ x (+ (* -1 (/ x (pow eps 2))) (/ 1 eps))) (/ 1 (pow eps 3)))) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) (+ x (* -1 (/ (- (/ x eps) 1) eps)))) |
(* (pow eps 2) (+ x (* -1 (/ (- (* -1 (/ (- (* -1 x) (/ 1 eps)) eps)) 1) eps)))) |
(/ (- (pow eps 2) 1) eps) |
(- (+ eps (* x (- (pow eps 2) 1))) (/ 1 eps)) |
(- (+ eps (* x (- (pow eps 2) 1))) (/ 1 eps)) |
(- (+ eps (* x (- (pow eps 2) 1))) (/ 1 eps)) |
(* x (- (pow eps 2) 1)) |
(* x (- (+ (/ eps x) (pow eps 2)) (+ 1 (/ 1 (* eps x))))) |
(* x (- (+ (/ eps x) (pow eps 2)) (+ 1 (/ 1 (* eps x))))) |
(* x (- (+ (/ eps x) (pow eps 2)) (+ 1 (/ 1 (* eps x))))) |
(* -1 (* x (+ 1 (* -1 (pow eps 2))))) |
(* -1 (* x (+ 1 (+ (* -1 (/ (- eps (/ 1 eps)) x)) (* -1 (pow eps 2)))))) |
(* -1 (* x (+ 1 (+ (* -1 (/ (- eps (/ 1 eps)) x)) (* -1 (pow eps 2)))))) |
(* -1 (* x (+ 1 (+ (* -1 (/ (- eps (/ 1 eps)) x)) (* -1 (pow eps 2)))))) |
(* -1 (* x (+ 1 eps))) |
(* -1 (* x (+ 1 eps))) |
(* -1 (* x (+ 1 eps))) |
(* -1 (* x (+ 1 eps))) |
(* -1 (* x (+ 1 eps))) |
(* -1 (* x (+ 1 eps))) |
(* -1 (* x (+ 1 eps))) |
(* -1 (* x (+ 1 eps))) |
(* -1 (* x (- 1 (* -1 eps)))) |
(* -1 (* x (- 1 (* -1 eps)))) |
(* -1 (* x (- 1 (* -1 eps)))) |
(* -1 (* x (- 1 (* -1 eps)))) |
(* -1 x) |
(- (* -1 (* eps x)) x) |
(- (* -1 (* eps x)) x) |
(- (* -1 (* eps x)) x) |
(* -1 (* eps x)) |
(* eps (- (* -1 (/ x eps)) x)) |
(* eps (- (* -1 (/ x eps)) x)) |
(* eps (- (* -1 (/ x eps)) x)) |
(* -1 (* eps x)) |
(* -1 (* eps (- (/ x eps) (* -1 x)))) |
(* -1 (* eps (- (/ x eps) (* -1 x)))) |
(* -1 (* eps (- (/ x eps) (* -1 x)))) |
| Outputs |
|---|
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 x (exp.f64 (neg.f64 x)) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))) |
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 eps eps) (fma.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 #s(literal 1/2 binary64) x))) (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 #s(literal 1/2 binary64) x))))) (fma.f64 x (exp.f64 (neg.f64 x)) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) (fma.f64 (*.f64 eps eps) (fma.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)))))) (fma.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 #s(literal 1/2 binary64) x))) (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 #s(literal 1/2 binary64) x)))))) (*.f64 #s(literal 1/2 binary64) (fma.f64 x (exp.f64 (neg.f64 x)) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))))))) |
(fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 #s(literal 1/2 binary64) x))) (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 #s(literal 1/2 binary64) x))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) (fma.f64 (*.f64 eps eps) (fma.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64)) (*.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64)) (*.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 6 binary64)))))) (fma.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 (exp.f64 (neg.f64 x)) (fma.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))))))))) (*.f64 #s(literal 1/2 binary64) (fma.f64 x (exp.f64 (neg.f64 x)) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))) |
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) eps)))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) eps)))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) eps)))) |
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) eps)))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) eps)))) |
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1 |
#s(literal 1 binary64) |
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1 |
#s(literal 1 binary64) |
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(exp (neg x)) |
(exp.f64 (neg.f64 x)) |
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2 |
#s(literal 2 binary64) |
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(* 2 (exp (neg x))) |
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1 |
#s(literal 1 binary64) |
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(exp (- (* eps x) x)) |
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1 |
#s(literal 1 binary64) |
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1 |
#s(literal 1 binary64) |
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1 |
#s(literal 1 binary64) |
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(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 eps #s(literal 1 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
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(exp.f64 (neg.f64 x)) |
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2 |
#s(literal 2 binary64) |
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(fma.f64 x (+.f64 #s(literal -1 binary64) (-.f64 eps (+.f64 eps #s(literal 1 binary64)))) #s(literal 2 binary64)) |
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(* 2 (exp (neg x))) |
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(fma.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64) #s(literal 0 binary64)) |
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1 |
#s(literal 1 binary64) |
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1 |
#s(literal 1 binary64) |
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eps |
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(- (+ eps (* x (- (pow eps 2) 1))) (/ 1 eps)) |
(fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps))) |
(- (+ eps (* x (- (pow eps 2) 1))) (/ 1 eps)) |
(fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps))) |
(* x (- (pow eps 2) 1)) |
(*.f64 x (fma.f64 eps eps #s(literal -1 binary64))) |
(* x (- (+ (/ eps x) (pow eps 2)) (+ 1 (/ 1 (* eps x))))) |
(*.f64 x (+.f64 (/.f64 eps x) (fma.f64 eps eps (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x eps)))))) |
(* x (- (+ (/ eps x) (pow eps 2)) (+ 1 (/ 1 (* eps x))))) |
(*.f64 x (+.f64 (/.f64 eps x) (fma.f64 eps eps (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x eps)))))) |
(* x (- (+ (/ eps x) (pow eps 2)) (+ 1 (/ 1 (* eps x))))) |
(*.f64 x (+.f64 (/.f64 eps x) (fma.f64 eps eps (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x eps)))))) |
(* -1 (* x (+ 1 (* -1 (pow eps 2))))) |
(*.f64 x (fma.f64 eps eps #s(literal -1 binary64))) |
(* -1 (* x (+ 1 (+ (* -1 (/ (- eps (/ 1 eps)) x)) (* -1 (pow eps 2)))))) |
(fma.f64 x (fma.f64 eps eps (/.f64 (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) x)) (neg.f64 x)) |
(* -1 (* x (+ 1 (+ (* -1 (/ (- eps (/ 1 eps)) x)) (* -1 (pow eps 2)))))) |
(fma.f64 x (fma.f64 eps eps (/.f64 (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) x)) (neg.f64 x)) |
(* -1 (* x (+ 1 (+ (* -1 (/ (- eps (/ 1 eps)) x)) (* -1 (pow eps 2)))))) |
(fma.f64 x (fma.f64 eps eps (/.f64 (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) x)) (neg.f64 x)) |
(* -1 (* x (+ 1 eps))) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(* -1 (* x (+ 1 eps))) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(* -1 (* x (+ 1 eps))) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(* -1 (* x (+ 1 eps))) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(* -1 (* x (+ 1 eps))) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(* -1 (* x (+ 1 eps))) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(* -1 (* x (+ 1 eps))) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(* -1 (* x (+ 1 eps))) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(* -1 (* x (- 1 (* -1 eps)))) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(* -1 (* x (- 1 (* -1 eps)))) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(* -1 (* x (- 1 (* -1 eps)))) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(* -1 (* x (- 1 (* -1 eps)))) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(* -1 x) |
(neg.f64 x) |
(- (* -1 (* eps x)) x) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(- (* -1 (* eps x)) x) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(- (* -1 (* eps x)) x) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(* -1 (* eps x)) |
(*.f64 x (neg.f64 eps)) |
(* eps (- (* -1 (/ x eps)) x)) |
(*.f64 eps (-.f64 (/.f64 (neg.f64 x) eps) x)) |
(* eps (- (* -1 (/ x eps)) x)) |
(*.f64 eps (-.f64 (/.f64 (neg.f64 x) eps) x)) |
(* eps (- (* -1 (/ x eps)) x)) |
(*.f64 eps (-.f64 (/.f64 (neg.f64 x) eps) x)) |
(* -1 (* eps x)) |
(*.f64 x (neg.f64 eps)) |
(* -1 (* eps (- (/ x eps) (* -1 x)))) |
(*.f64 eps (-.f64 (/.f64 (neg.f64 x) eps) x)) |
(* -1 (* eps (- (/ x eps) (* -1 x)))) |
(*.f64 eps (-.f64 (/.f64 (neg.f64 x) eps) x)) |
(* -1 (* eps (- (/ x eps) (* -1 x)))) |
(*.f64 eps (-.f64 (/.f64 (neg.f64 x) eps) x)) |
| 5 700× | lower-fma.f32 |
| 5 688× | lower-fma.f64 |
| 5 100× | lower-*.f32 |
| 5 084× | lower-*.f64 |
| 2 410× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 80 | 888 |
| 0 | 115 | 888 |
| 1 | 546 | 873 |
| 2 | 5516 | 873 |
| 0 | 8360 | 855 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) |
(exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 x #s(literal -1/2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) |
(-.f64 (fma.f64 x (*.f64 eps eps) eps) x) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))) |
#s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) |
#s(approx (- (* x eps) x) (*.f64 x eps)) |
(exp.f64 (neg.f64 (fma.f64 x eps x))) |
(/.f64 x (*.f64 eps eps)) |
(*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))) |
(*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps))))) |
(+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) |
(fma.f64 x (*.f64 eps eps) eps) |
(/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps) |
(neg.f64 (fma.f64 x eps x)) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))))) |
(fma.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
(fma.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))))) |
(fma.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
(fma.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))))) |
(/.f64 (fma.f64 (exp.f64 (*.f64 #s(approx (- (* x eps) x) (*.f64 eps x)) #s(literal 3 binary64))) #s(literal 1/8 binary64) (*.f64 (exp.f64 (*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))) #s(literal 1/8 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))))) (-.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) (*.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (*.f64 #s(approx (- (* x eps) x) (*.f64 eps x)) #s(literal 3 binary64))) (exp.f64 (*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (+.f64 (exp.f64 (+.f64 #s(approx (- (* x eps) x) (*.f64 eps x)) #s(approx (- (* x eps) x) (*.f64 eps x)))) (-.f64 (exp.f64 (fma.f64 x (-.f64 #s(literal -1 binary64) eps) (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) (exp.f64 (+.f64 #s(approx (- (* x eps) x) (*.f64 eps x)) (*.f64 x (-.f64 #s(literal -1 binary64) eps))))))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (exp.f64 (+.f64 #s(approx (- (* x eps) x) (*.f64 eps x)) #s(approx (- (* x eps) x) (*.f64 eps x)))) (exp.f64 (fma.f64 x (-.f64 #s(literal -1 binary64) eps) (*.f64 x (-.f64 #s(literal -1 binary64) eps)))))) (-.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
(/.f64 (*.f64 (+.f64 (exp.f64 (*.f64 #s(approx (- (* x eps) x) (*.f64 eps x)) #s(literal 3 binary64))) (exp.f64 (*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (+.f64 (exp.f64 (+.f64 #s(approx (- (* x eps) x) (*.f64 eps x)) #s(approx (- (* x eps) x) (*.f64 eps x)))) (-.f64 (exp.f64 (fma.f64 x (-.f64 #s(literal -1 binary64) eps) (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) (exp.f64 (+.f64 #s(approx (- (* x eps) x) (*.f64 eps x)) (*.f64 x (-.f64 #s(literal -1 binary64) eps))))))) |
(/.f64 (*.f64 (-.f64 (exp.f64 (+.f64 #s(approx (- (* x eps) x) (*.f64 eps x)) #s(approx (- (* x eps) x) (*.f64 eps x)))) (exp.f64 (fma.f64 x (-.f64 #s(literal -1 binary64) eps) (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) #s(literal 1/2 binary64)) (-.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) |
(*.f64 (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) #s(literal 1/2 binary64)) |
(+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) |
(+.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) |
(-.f64 (/.f64 (exp.f64 (+.f64 #s(approx (- (* x eps) x) (*.f64 eps x)) #s(approx (- (* x eps) x) (*.f64 eps x)))) (-.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))))) (/.f64 (exp.f64 (fma.f64 x (-.f64 #s(literal -1 binary64) eps) (*.f64 x (-.f64 #s(literal -1 binary64) eps)))) (-.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps)))))) |
(fma.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) |
(fma.f64 (exp.f64 (*.f64 eps (neg.f64 x))) (exp.f64 (neg.f64 x)) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) (pow.f64 (exp.f64 (*.f64 eps x)) #s(literal -1 binary64)) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) |
(fma.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) x) (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 eps x)) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) |
(fma.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 #s(literal 1 binary64) x)) (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 eps x)) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) |
(fma.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 x #s(literal 1 binary64))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 eps x)) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) |
(fma.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 eps x)) (pow.f64 (exp.f64 #s(literal -1 binary64)) x) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) |
(fma.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 eps x)) (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 #s(literal 1 binary64) x)) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) |
(fma.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 eps x)) (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 x #s(literal 1 binary64))) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) |
(fma.f64 (pow.f64 (exp.f64 (*.f64 eps x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) |
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(-.f64 #s(literal 0 binary64) (fma.f64 eps x x)) |
(-.f64 (neg.f64 x) (*.f64 eps x)) |
(-.f64 (*.f64 eps (neg.f64 x)) x) |
(fma.f64 eps (neg.f64 x) (neg.f64 x)) |
(fma.f64 x #s(literal -1 binary64) (*.f64 (*.f64 eps x) #s(literal -1 binary64))) |
(fma.f64 x (neg.f64 eps) (neg.f64 x)) |
(fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 x #s(literal -1 binary64))) |
(fma.f64 #s(literal -1 binary64) x (*.f64 eps (neg.f64 x))) |
(fma.f64 #s(literal -1 binary64) (*.f64 eps x) (neg.f64 x)) |
(fma.f64 (neg.f64 x) eps (neg.f64 x)) |
(fma.f64 (neg.f64 eps) x (neg.f64 x)) |
(neg.f64 (fma.f64 eps x x)) |
(/.f64 (fma.f64 (*.f64 eps x) (*.f64 eps (*.f64 eps (*.f64 x x))) (*.f64 x (*.f64 x x))) (neg.f64 (fma.f64 eps (*.f64 eps (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 eps x)))))) |
(/.f64 (*.f64 (fma.f64 eps x x) (-.f64 (*.f64 eps x) x)) (neg.f64 (-.f64 (*.f64 eps x) x))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 eps x) (*.f64 eps (*.f64 eps (*.f64 x x))) (*.f64 x (*.f64 x x)))) (fma.f64 eps (*.f64 eps (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 eps x))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 eps x x) (-.f64 (*.f64 eps x) x))) (-.f64 (*.f64 eps x) x)) |
(/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 (*.f64 eps x) (*.f64 eps (*.f64 eps (*.f64 x x)))) (*.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 (*.f64 eps (neg.f64 x)) (*.f64 eps (neg.f64 x)) (-.f64 (*.f64 (neg.f64 x) (neg.f64 x)) (*.f64 (*.f64 eps (neg.f64 x)) (neg.f64 x))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 eps x x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 eps x x) (fma.f64 eps x x) (*.f64 #s(literal 0 binary64) (fma.f64 eps x x))))) |
(/.f64 (-.f64 (*.f64 (*.f64 eps (neg.f64 x)) (*.f64 eps (neg.f64 x))) (*.f64 (neg.f64 x) (neg.f64 x))) (-.f64 (*.f64 eps (neg.f64 x)) (neg.f64 x))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (fma.f64 eps x x) (fma.f64 eps x x))) (+.f64 #s(literal 0 binary64) (fma.f64 eps x x))) |
(/.f64 (*.f64 #s(literal -1 binary64) (fma.f64 (*.f64 eps x) (*.f64 eps (*.f64 eps (*.f64 x x))) (*.f64 x (*.f64 x x)))) (fma.f64 eps (*.f64 eps (*.f64 x x)) (*.f64 x (-.f64 x (*.f64 eps x))))) |
(/.f64 (*.f64 #s(literal -1 binary64) (*.f64 (fma.f64 eps x x) (-.f64 (*.f64 eps x) x))) (-.f64 (*.f64 eps x) x)) |
(/.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) #s(literal 1 binary64)) (neg.f64 x)) (fma.f64 eps eps (-.f64 #s(literal 1 binary64) eps))) |
(/.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) #s(literal 1 binary64)) (neg.f64 x)) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps eps)) (neg.f64 x)) (-.f64 #s(literal 1 binary64) eps)) |
(/.f64 (*.f64 (fma.f64 eps eps #s(literal -1 binary64)) (neg.f64 x)) (+.f64 eps #s(literal -1 binary64))) |
(*.f64 x (-.f64 #s(literal -1 binary64) eps)) |
(*.f64 (fma.f64 eps x x) #s(literal -1 binary64)) |
(*.f64 #s(literal -1 binary64) (fma.f64 eps x x)) |
(*.f64 (+.f64 #s(literal 1 binary64) eps) (neg.f64 x)) |
(*.f64 (-.f64 #s(literal -1 binary64) eps) x) |
(*.f64 (neg.f64 x) (+.f64 #s(literal 1 binary64) eps)) |
Compiled 32 780 to 2 099 computations (93.6% saved)
21 alts after pruning (19 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 174 | 12 | 1 186 |
| Fresh | 5 | 7 | 12 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 183 | 21 | 1 204 |
| Status | Accuracy | Program |
|---|---|---|
| 29.0% | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (+.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)))) #s(literal -1 binary64))) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) | |
| 32.2% | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) | |
| 75.8% | (exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))))))) #s(literal -1 binary64))) | |
| 44.3% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) | |
| ▶ | 44.9% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
| ▶ | 74.0% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
| 60.5% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (*.f64 eps (*.f64 eps (+.f64 x (/.f64 #s(literal 1 binary64) eps)))))) #s(literal 1 binary64))) | |
| 75.3% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 x eps)))) #s(literal 1 binary64))) | |
| ▶ | 84.1% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
| 62.0% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) #s(approx (exp (neg (+ (* x eps) x))) #s(literal 1 binary64))))) | |
| 64.0% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) | |
| 56.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) (*.f64 (fma.f64 x eps x) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) | |
| ▶ | 48.9% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
| 57.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) | |
| ✓ | 41.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
| ▶ | 41.4% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
| 33.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))))) | |
| 46.4% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) | |
| 72.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 eps #s(literal 1 binary64))) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) | |
| 71.2% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (exp.f64 (neg.f64 x)))) | |
| ✓ | 42.5% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
Compiled 952 to 499 computations (47.6% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) | |
| cost-diff | 128 | (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) | |
| cost-diff | 2560 | (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) | |
| cost-diff | 0 | (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) x) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) | |
| cost-diff | 0 | (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) | |
| cost-diff | 0 | (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) | |
| cost-diff | 0 | #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))) | |
| cost-diff | 0 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) | |
| cost-diff | 0 | #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) | |
| cost-diff | 0 | (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))))) | |
| cost-diff | 0 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) | |
| cost-diff | 0 | (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) | |
| cost-diff | 0 | (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps)))))) | |
| cost-diff | 0 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
| 10 992× | lower-fma.f32 |
| 10 972× | lower-fma.f64 |
| 3 966× | lower-+.f32 |
| 3 954× | lower-+.f64 |
| 3 690× | lower--.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 101 | 1423 |
| 0 | 149 | 1407 |
| 1 | 316 | 1392 |
| 2 | 883 | 1282 |
| 3 | 4032 | 1234 |
| 0 | 8162 | 1183 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps)))))) |
#s(literal 1/2 binary64) |
(+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))) |
(exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) |
#s(approx (- (* x eps) x) (*.f64 x eps)) |
(*.f64 x eps) |
x |
eps |
(exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps)))) |
#s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))) |
(*.f64 x (neg.f64 eps)) |
(neg.f64 eps) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))))) |
#s(literal 1/2 binary64) |
(+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))) |
#s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
#s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))) |
(-.f64 #s(literal 1 binary64) (fma.f64 x eps x)) |
(fma.f64 x eps x) |
x |
eps |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) |
(*.f64 (*.f64 x x) (*.f64 x x)) |
(*.f64 x x) |
x |
#s(literal 1/4 binary64) |
#s(literal -1 binary64) |
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) |
(*.f64 x #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) |
(+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) |
(/.f64 (+.f64 eps #s(literal 1 binary64)) eps) |
(+.f64 eps #s(literal 1 binary64)) |
eps |
#s(literal 1 binary64) |
(-.f64 #s(literal -1 binary64) eps) |
#s(literal -1 binary64) |
#s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps)) |
(/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps) |
(fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) |
#s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) |
(*.f64 x (*.f64 eps eps)) |
(*.f64 eps eps) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) |
(+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) |
(/.f64 (+.f64 eps #s(literal 1 binary64)) eps) |
(+.f64 eps #s(literal 1 binary64)) |
eps |
#s(literal 1 binary64) |
(-.f64 #s(literal -1 binary64) eps) |
#s(literal -1 binary64) |
#s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps)) |
(/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps) |
(fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) |
(/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) |
(*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) |
(fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) |
(fma.f64 eps x #s(literal 1 binary64)) |
(-.f64 (fma.f64 x (*.f64 eps eps) eps) x) |
(fma.f64 x (*.f64 eps eps) eps) |
(*.f64 eps eps) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 eps (neg.f64 x))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 eps (neg.f64 x)))))) |
#s(literal 1/2 binary64) |
(+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))) |
(+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 eps (neg.f64 x))))) |
(exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) |
(exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) |
#s(approx (- (* x eps) x) (*.f64 x eps)) |
#s(approx (- (* x eps) x) (*.f64 eps x)) |
(*.f64 x eps) |
(*.f64 eps x) |
x |
eps |
(exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps)))) |
(exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 eps (neg.f64 x)))) |
#s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))) |
#s(approx (neg (+ (* x eps) x)) (*.f64 eps (neg.f64 x))) |
(*.f64 x (neg.f64 eps)) |
(*.f64 eps (neg.f64 x)) |
(neg.f64 eps) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 eps x x)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 eps x x))))) |
#s(literal 1/2 binary64) |
(+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))) |
(+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 eps x x)))) |
#s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
#s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))) |
#s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 eps x x))) |
(-.f64 #s(literal 1 binary64) (fma.f64 x eps x)) |
(-.f64 #s(literal 1 binary64) (fma.f64 eps x x)) |
(fma.f64 x eps x) |
(fma.f64 eps x x) |
x |
eps |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))) |
#s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) |
(fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) |
(*.f64 (*.f64 x x) (*.f64 x x)) |
(*.f64 x x) |
x |
#s(literal 1/4 binary64) |
#s(literal -1 binary64) |
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) |
(*.f64 x #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (+.f64 (+.f64 #s(literal -1 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 eps (*.f64 eps x))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (+.f64 (+.f64 #s(literal -1 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 eps (*.f64 eps x))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
x |
(+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) |
(+.f64 (+.f64 #s(literal -1 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 eps (*.f64 eps x))) #s(literal -1 binary64)) eps))) |
(+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) |
(+.f64 #s(literal -1 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) eps)) |
(/.f64 (+.f64 eps #s(literal 1 binary64)) eps) |
(/.f64 (+.f64 #s(literal 1 binary64) eps) eps) |
(+.f64 eps #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) eps) |
eps |
#s(literal 1 binary64) |
(-.f64 #s(literal -1 binary64) eps) |
#s(literal -1 binary64) |
#s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps)) |
#s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 eps (*.f64 eps x))) #s(literal -1 binary64)) eps)) |
(/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps) |
(/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 eps (*.f64 eps x))) #s(literal -1 binary64)) eps) |
(fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) |
(fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 eps (*.f64 eps x))) #s(literal -1 binary64)) |
#s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) |
#s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 eps (*.f64 eps x))) |
(*.f64 x (*.f64 eps eps)) |
(*.f64 eps (*.f64 eps x)) |
(*.f64 eps eps) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal -1 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)) |
(fma.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal -1 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
x |
(+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) |
(+.f64 (+.f64 #s(literal -1 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) #s(literal -1 binary64)) eps))) |
(+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) |
(+.f64 #s(literal -1 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) eps)) |
(/.f64 (+.f64 eps #s(literal 1 binary64)) eps) |
(/.f64 (+.f64 #s(literal 1 binary64) eps) eps) |
(+.f64 eps #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) eps) |
eps |
#s(literal 1 binary64) |
(-.f64 #s(literal -1 binary64) eps) |
#s(literal -1 binary64) |
#s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps)) |
#s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) #s(literal -1 binary64)) eps)) |
(/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps) |
(/.f64 (fma.f64 eps (fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) #s(literal -1 binary64)) eps) |
(fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) |
(fma.f64 eps (fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) #s(literal -1 binary64)) |
(/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) |
(fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) |
(*.f64 (fma.f64 eps (fma.f64 eps x #s(literal 1 binary64)) x) (fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps)) |
(fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) |
(fma.f64 eps (fma.f64 eps x #s(literal 1 binary64)) x) |
(fma.f64 eps x #s(literal 1 binary64)) |
(-.f64 (fma.f64 x (*.f64 eps eps) eps) x) |
(fma.f64 x (fma.f64 eps eps #s(literal -1 binary64)) eps) |
(fma.f64 x (*.f64 eps eps) eps) |
(fma.f64 eps (*.f64 eps x) eps) |
(*.f64 eps eps) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 6.408237388687392 | (fma.f64 x (*.f64 eps eps) eps) | |
| accuracy | 18.605111781140387 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) | |
| accuracy | 29.088808368419762 | (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) | |
| accuracy | 35.843594455379794 | (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) | |
| accuracy | 7.574018915799161 | (*.f64 x (*.f64 eps eps)) | |
| accuracy | 18.605111781140387 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) | |
| accuracy | 29.088808368419762 | (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) | |
| accuracy | 35.932132474785774 | #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) | |
| accuracy | 0.09765625 | (*.f64 (*.f64 x x) (*.f64 x x)) | |
| accuracy | 18.605111781140387 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) | |
| accuracy | 22.775273883715997 | (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) | |
| accuracy | 27.210811177054754 | #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))) | |
| accuracy | 0 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))))) | |
| accuracy | 0.3024004356261579 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) | |
| accuracy | 32.26754376365461 | #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))) | |
| accuracy | 36.98496295625584 | #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) | |
| accuracy | 0.00390625 | (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps)))) | |
| accuracy | 0.3024004356261579 | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) | |
| accuracy | 26.910902042065562 | #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))) | |
| accuracy | 27.625978359598232 | #s(approx (- (* x eps) x) (*.f64 x eps)) |
| 152.0ms | 108× | 1 | valid |
| 63.0ms | 32× | 2 | valid |
| 50.0ms | 116× | 0 | valid |
Compiled 931 to 77 computations (91.7% saved)
ival-mult: 102.0ms (47.8% of total)ival-div: 29.0ms (13.6% of total)ival-add: 27.0ms (12.7% of total)adjust: 26.0ms (12.2% of total)ival-exp: 13.0ms (6.1% of total)ival-sub: 10.0ms (4.7% of total)ival-neg: 4.0ms (1.9% of total)exact: 1.0ms (0.5% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps)))))))> |
#<alt (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))> |
#<alt (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps)))))> |
#<alt (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps)))> |
#<alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))))))> |
#<alt (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))> |
#<alt (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))))> |
#<alt #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64))> |
#<alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))> |
#<alt #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))> |
#<alt (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))> |
#<alt (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64))> |
#<alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)))> |
#<alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))> |
#<alt (*.f64 #s(literal 1/2 binary64) x)> |
#<alt (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps)))> |
#<alt (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x))> |
#<alt (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)> |
#<alt #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)))> |
#<alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))> |
#<alt #s(approx (- (* x eps) x) (*.f64 x eps))> |
#<alt #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps)))> |
#<alt (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))> |
#<alt #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))> |
#<alt (*.f64 (*.f64 x x) (*.f64 x x))> |
#<alt #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps)))> |
#<alt (*.f64 x (*.f64 eps eps))> |
#<alt (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps)))> |
#<alt (fma.f64 x (*.f64 eps eps) eps)> |
| Outputs |
|---|
#<alt (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))> |
#<alt (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))> |
#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))> |
#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))> |
#<alt (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))> |
#<alt (+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))))> |
#<alt (+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (* x (- (+ eps (* -1 (+ 1 eps))) 1))))> |
#<alt (+ 1 (* x (+ (* 1/2 (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2))))) (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1)))))> |
#<alt (+ 1 (* x (+ (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1)) (* x (+ (* 1/2 (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))) (* 1/2 (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2)))))))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))))> |
#<alt (* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))))> |
#<alt (* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))))> |
#<alt (* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))))> |
#<alt (exp (neg x))> |
#<alt (+ (exp (neg x)) (* 1/2 (* eps (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x)))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* 1/2 (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x))))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* 1/2 (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x))))) (* eps (+ (* 1/2 (* eps (+ (* -1/6 (* (pow x 3) (exp (neg x)))) (* 1/6 (* (pow x 3) (exp (neg x))))))) (* 1/2 (* (pow x 2) (exp (neg x)))))))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt (* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))))> |
#<alt 2> |
#<alt (+ 2 (* x (- (+ eps (* -1 (+ 1 eps))) 1)))> |
#<alt (+ 2 (* x (- (+ eps (+ (* -1 (+ 1 eps)) (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2)))))) 1)))> |
#<alt (+ 2 (* x (- (+ eps (+ (* -1 (+ 1 eps)) (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (+ (* 1/2 (pow (- eps 1) 2)) (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))))))) 1)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))> |
#<alt (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))> |
#<alt (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))> |
#<alt (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))> |
#<alt (* 2 (exp (neg x)))> |
#<alt (+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x))))))> |
#<alt (+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (+ (* eps (* (pow x 2) (exp (neg x)))) (* x (exp (neg x)))))))> |
#<alt (+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (+ (* eps (+ (* eps (+ (* -1/6 (* (pow x 3) (exp (neg x)))) (* 1/6 (* (pow x 3) (exp (neg x)))))) (* (pow x 2) (exp (neg x))))) (* x (exp (neg x)))))))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))> |
#<alt 1> |
#<alt (+ 1 (* x (- eps 1)))> |
#<alt (+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1)))> |
#<alt (+ 1 (* x (- (+ eps (* x (+ (* 1/6 (* x (pow (- eps 1) 3))) (* 1/2 (pow (- eps 1) 2))))) 1)))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (+ (* -1 x) (* eps x)))> |
#<alt (exp (+ (* -1 x) (* eps x)))> |
#<alt (exp (+ (* -1 x) (* eps x)))> |
#<alt (exp (+ (* -1 x) (* eps x)))> |
#<alt (exp (neg x))> |
#<alt (+ (exp (neg x)) (* eps (* x (exp (neg x)))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* x (exp (neg x))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* eps (+ (* 1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))) (* x (exp (neg x))))))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (exp (- (* eps x) x))> |
#<alt (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))> |
#<alt (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))> |
#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))> |
#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))> |
#<alt (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps)))))))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
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#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt 1> |
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#<alt (+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
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#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt 1> |
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#<alt (* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2))))> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
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#<alt (* 1/2 (* (pow eps 2) (pow x 2)))> |
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#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* -1 x)> |
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#<alt (+ (* -1 x) (* (pow eps 2) x))> |
#<alt (* (pow eps 2) x)> |
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#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
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#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
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#<alt (* -1 x)> |
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#<alt (- (* eps (+ 1 (* eps x))) x)> |
#<alt (- (* eps (+ 1 (* eps x))) x)> |
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#<alt (* (pow eps 2) x)> |
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#<alt eps> |
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#<alt eps> |
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#<alt (* -1 (* x (+ 1 (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))))> |
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#<alt (* -1 (* x (+ 1 (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))))> |
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#<alt (- (* eps (+ 1 (* eps x))) x)> |
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#<alt (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))> |
#<alt (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))))> |
#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))))))> |
#<alt (+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x))))))))))))> |
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#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps)))> |
#<alt (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))> |
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#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt (+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))))> |
#<alt 1> |
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#<alt (+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1))))))))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
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#<alt (* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt (* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1))))> |
#<alt 1> |
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#<alt (* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2))))> |
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#<alt (* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2))))> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
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#<alt (* 1/2 (* (pow eps 2) (pow x 2)))> |
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#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2)))))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
#<alt (* x (- eps 1))> |
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#<alt (* x (- eps 1))> |
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#<alt (* -1 (* x (+ 1 (* -1 eps))))> |
#<alt (* -1 (* x (+ 1 (* -1 eps))))> |
#<alt (* -1 x)> |
#<alt (- (* eps x) x)> |
#<alt (- (* eps x) x)> |
#<alt (- (* eps x) x)> |
#<alt (* eps x)> |
#<alt (* eps (+ x (* -1 (/ x eps))))> |
#<alt (* eps (+ x (* -1 (/ x eps))))> |
#<alt (* eps (+ x (* -1 (/ x eps))))> |
#<alt (* eps x)> |
#<alt (* -1 (* eps (+ (* -1 x) (/ x eps))))> |
#<alt (* -1 (* eps (+ (* -1 x) (/ x eps))))> |
#<alt (* -1 (* eps (+ (* -1 x) (/ x eps))))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (+ 1 eps)))> |
#<alt (* -1 (* x (- 1 (* -1 eps))))> |
#<alt (* -1 (* x (- 1 (* -1 eps))))> |
#<alt (* -1 (* x (- 1 (* -1 eps))))> |
#<alt (* -1 (* x (- 1 (* -1 eps))))> |
#<alt (* -1 x)> |
#<alt (- (* -1 (* eps x)) x)> |
#<alt (- (* -1 (* eps x)) x)> |
#<alt (- (* -1 (* eps x)) x)> |
#<alt (* -1 (* eps x))> |
#<alt (* eps (- (* -1 (/ x eps)) x))> |
#<alt (* eps (- (* -1 (/ x eps)) x))> |
#<alt (* eps (- (* -1 (/ x eps)) x))> |
#<alt (* -1 (* eps x))> |
#<alt (* -1 (* eps (- (/ x eps) (* -1 x))))> |
#<alt (* -1 (* eps (- (/ x eps) (* -1 x))))> |
#<alt (* -1 (* eps (- (/ x eps) (* -1 x))))> |
#<alt 1> |
#<alt (+ 1 (* -1 (* x (+ 1 eps))))> |
#<alt (+ 1 (* x (+ (* -1 (+ 1 eps)) (* 1/2 (* x (pow (+ 1 eps) 2))))))> |
#<alt (+ 1 (* x (+ (* -1 (+ 1 eps)) (* x (+ (* -1/6 (* x (pow (+ 1 eps) 3))) (* 1/2 (pow (+ 1 eps) 2)))))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (neg x))> |
#<alt (+ (exp (neg x)) (* -1 (* eps (* x (exp (neg x))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* 1/2 (* eps (* (pow x 2) (exp (neg x))))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* eps (+ (* -1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt 1> |
#<alt (+ 1 (* -1 (* x (+ 1 eps))))> |
#<alt (+ 1 (* x (+ (* -1 (+ 1 eps)) (* 1/2 (* x (pow (+ 1 eps) 2))))))> |
#<alt (+ 1 (* x (+ (* -1 (+ 1 eps)) (* x (+ (* -1/6 (* x (pow (+ 1 eps) 3))) (* 1/2 (pow (+ 1 eps) 2)))))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (- (* -1 x) (* eps x)))> |
#<alt (exp (neg x))> |
#<alt (+ (exp (neg x)) (* -1 (* eps (* x (exp (neg x))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* 1/2 (* eps (* (pow x 2) (exp (neg x))))))))> |
#<alt (+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* eps (+ (* -1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (exp (neg (+ x (* eps x))))> |
#<alt (pow x 4)> |
#<alt (pow x 4)> |
#<alt (pow x 4)> |
#<alt (pow x 4)> |
#<alt (pow x 4)> |
#<alt (pow x 4)> |
#<alt (pow x 4)> |
#<alt (pow x 4)> |
#<alt (pow x 4)> |
#<alt (pow x 4)> |
#<alt (pow x 4)> |
#<alt (pow x 4)> |
#<alt eps> |
#<alt (+ eps (* x (- (pow eps 2) 1)))> |
#<alt (+ eps (* x (- (pow eps 2) 1)))> |
#<alt (+ eps (* x (- (pow eps 2) 1)))> |
#<alt (* x (- (pow eps 2) 1))> |
#<alt (* x (- (+ (/ eps x) (pow eps 2)) 1))> |
#<alt (* x (- (+ (/ eps x) (pow eps 2)) 1))> |
#<alt (* x (- (+ (/ eps x) (pow eps 2)) 1))> |
#<alt (* -1 (* x (+ 1 (* -1 (pow eps 2)))))> |
#<alt (* -1 (* x (+ 1 (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))))> |
#<alt (* -1 (* x (+ 1 (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))))> |
#<alt (* -1 (* x (+ 1 (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))))> |
#<alt (* -1 x)> |
#<alt (- eps x)> |
#<alt (- (* eps (+ 1 (* eps x))) x)> |
#<alt (- (* eps (+ 1 (* eps x))) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ x (+ (* -1 (/ x (pow eps 2))) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ x (+ (* -1 (/ x (pow eps 2))) (/ 1 eps))))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ (- (/ x eps) 1) eps))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ (- (/ x eps) 1) eps))))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* -1 x)> |
#<alt (+ (* -1 x) (* (pow eps 2) x))> |
#<alt (+ (* -1 x) (* (pow eps 2) x))> |
#<alt (+ (* -1 x) (* (pow eps 2) x))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ x (* -1 (/ x (pow eps 2)))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt (* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))))> |
#<alt eps> |
#<alt (+ eps (* (pow eps 2) x))> |
#<alt (+ eps (* (pow eps 2) x))> |
#<alt (+ eps (* (pow eps 2) x))> |
#<alt (* (pow eps 2) x)> |
#<alt (* x (+ (/ eps x) (pow eps 2)))> |
#<alt (* x (+ (/ eps x) (pow eps 2)))> |
#<alt (* x (+ (/ eps x) (pow eps 2)))> |
#<alt (* (pow eps 2) x)> |
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2)))))> |
#<alt eps> |
#<alt (* eps (+ 1 (* eps x)))> |
#<alt (* eps (+ 1 (* eps x)))> |
#<alt (* eps (+ 1 (* eps x)))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ x (/ 1 eps)))> |
162 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | inf | (/ (+ (* (* (* x x) (* x x)) 1/4) -1) (+ (* x (* x -1/2)) -1)) |
| 0.0ms | x | @ | 0 | (/ (+ (* (* (* x x) (* x x)) 1/4) -1) (+ (* x (* x -1/2)) -1)) |
| 0.0ms | x | @ | inf | (* x (* eps eps)) |
| 0.0ms | x | @ | inf | (+ (* (* (* x x) (* x x)) 1/4) -1) |
| 0.0ms | x | @ | -inf | (* x (* eps eps)) |
| 1× | egg-herbie |
| 10 072× | lower-fma.f64 |
| 10 072× | lower-fma.f32 |
| 6 084× | lower-*.f64 |
| 6 084× | lower-*.f32 |
| 2 400× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 392 | 11205 |
| 1 | 1305 | 10427 |
| 2 | 4434 | 9802 |
| 0 | 8160 | 9265 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) |
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))))))) |
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
1 |
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))) |
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))) |
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
1 |
(+ 1 (* 1/2 (* x (- (+ eps (* -1 (+ 1 eps))) 1)))) |
(+ 1 (* x (+ (* 1/2 (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2))))) (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1))))) |
(+ 1 (* x (+ (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1)) (* x (+ (* 1/2 (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))) (* 1/2 (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2))))))))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))) |
(* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))) |
(* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))) |
(* 1/2 (+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x))))) |
(exp (neg x)) |
(+ (exp (neg x)) (* 1/2 (* eps (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x))))))) |
(+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* 1/2 (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x)))))))) |
(+ (exp (neg x)) (* eps (+ (* 1/2 (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x))))) (* eps (+ (* 1/2 (* eps (+ (* -1/6 (* (pow x 3) (exp (neg x)))) (* 1/6 (* (pow x 3) (exp (neg x))))))) (* 1/2 (* (pow x 2) (exp (neg x))))))))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
2 |
(+ 2 (* x (- (+ eps (* -1 (+ 1 eps))) 1))) |
(+ 2 (* x (- (+ eps (+ (* -1 (+ 1 eps)) (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2)))))) 1))) |
(+ 2 (* x (- (+ eps (+ (* -1 (+ 1 eps)) (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (+ (* 1/2 (pow (- eps 1) 2)) (* x (+ (* -1/6 (pow (+ 1 eps) 3)) (* 1/6 (pow (- eps 1) 3))))))))) 1))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))) |
(+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))) |
(+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))) |
(+ (exp (+ (* -1 x) (* eps x))) (exp (- (* -1 x) (* eps x)))) |
(* 2 (exp (neg x))) |
(+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (* x (exp (neg x)))))) |
(+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (+ (* eps (* (pow x 2) (exp (neg x)))) (* x (exp (neg x))))))) |
(+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (+ (* eps (+ (* eps (+ (* -1/6 (* (pow x 3) (exp (neg x)))) (* 1/6 (* (pow x 3) (exp (neg x)))))) (* (pow x 2) (exp (neg x))))) (* x (exp (neg x))))))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
(+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x))) |
1 |
(+ 1 (* x (- eps 1))) |
(+ 1 (* x (- (+ eps (* 1/2 (* x (pow (- eps 1) 2)))) 1))) |
(+ 1 (* x (- (+ eps (* x (+ (* 1/6 (* x (pow (- eps 1) 3))) (* 1/2 (pow (- eps 1) 2))))) 1))) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (+ (* -1 x) (* eps x))) |
(exp (+ (* -1 x) (* eps x))) |
(exp (+ (* -1 x) (* eps x))) |
(exp (+ (* -1 x) (* eps x))) |
(exp (neg x)) |
(+ (exp (neg x)) (* eps (* x (exp (neg x))))) |
(+ (exp (neg x)) (* eps (+ (* 1/2 (* eps (* (pow x 2) (exp (neg x))))) (* x (exp (neg x)))))) |
(+ (exp (neg x)) (* eps (+ (* eps (+ (* 1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x)))))) (* x (exp (neg x)))))) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) |
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1 |
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1 |
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2 |
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(* 2 (exp (neg x))) |
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(+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (+ (* eps (* (pow x 2) (exp (neg x)))) (* x (exp (neg x))))))) |
(+ (* 2 (exp (neg x))) (* eps (+ (* -1 (* x (exp (neg x)))) (+ (* eps (+ (* eps (+ (* -1/6 (* (pow x 3) (exp (neg x)))) (* 1/6 (* (pow x 3) (exp (neg x)))))) (* (pow x 2) (exp (neg x))))) (* x (exp (neg x))))))) |
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1 |
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(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (+ (* -1 x) (* eps x))) |
(exp (+ (* -1 x) (* eps x))) |
(exp (+ (* -1 x) (* eps x))) |
(exp (+ (* -1 x) (* eps x))) |
(exp (neg x)) |
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(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(exp (- (* eps x) x)) |
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) |
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(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))) |
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1 |
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1 |
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(* 1/4 (* (pow x 2) (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(* 1/4 (* (pow x 2) (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(* (pow x 2) (+ (* 1/4 (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps))))) (/ 1 (pow x 2)))) |
(+ 1 (* -1/2 (pow x 2))) |
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(+ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (* (pow eps 2) (pow x 2))))) |
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(* 1/2 (* (pow eps 2) (pow x 2))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* 1/2 (* (pow eps 2) (pow x 2))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/2 (pow x 2)) (/ 1 (pow eps 2))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* -1/2 (pow x 2))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
-1 |
(- (* 1/4 (pow x 4)) 1) |
(- (* 1/4 (pow x 4)) 1) |
(- (* 1/4 (pow x 4)) 1) |
(* 1/4 (pow x 4)) |
(* (pow x 4) (- 1/4 (/ 1 (pow x 4)))) |
(* (pow x 4) (- 1/4 (/ 1 (pow x 4)))) |
(* (pow x 4) (- 1/4 (/ 1 (pow x 4)))) |
(* 1/4 (pow x 4)) |
(* (pow x 4) (- 1/4 (/ 1 (pow x 4)))) |
(* (pow x 4) (- 1/4 (/ 1 (pow x 4)))) |
(* (pow x 4) (- 1/4 (/ 1 (pow x 4)))) |
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) |
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(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) |
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1 |
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1 |
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1 |
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1 |
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(exp (- (* -1 x) (* eps x))) |
(exp (- (* -1 x) (* eps x))) |
(exp (- (* -1 x) (* eps x))) |
(exp (neg x)) |
(+ (exp (neg x)) (* -1 (* eps (* x (exp (neg x)))))) |
(+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* 1/2 (* eps (* (pow x 2) (exp (neg x)))))))) |
(+ (exp (neg x)) (* eps (+ (* -1 (* x (exp (neg x)))) (* eps (+ (* -1/6 (* eps (* (pow x 3) (exp (neg x))))) (* 1/2 (* (pow x 2) (exp (neg x))))))))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(exp (neg (+ x (* eps x)))) |
(pow x 4) |
(pow x 4) |
(pow x 4) |
(pow x 4) |
(pow x 4) |
(pow x 4) |
(pow x 4) |
(pow x 4) |
(pow x 4) |
(pow x 4) |
(pow x 4) |
(pow x 4) |
eps |
(+ eps (* x (- (pow eps 2) 1))) |
(+ eps (* x (- (pow eps 2) 1))) |
(+ eps (* x (- (pow eps 2) 1))) |
(* x (- (pow eps 2) 1)) |
(* x (- (+ (/ eps x) (pow eps 2)) 1)) |
(* x (- (+ (/ eps x) (pow eps 2)) 1)) |
(* x (- (+ (/ eps x) (pow eps 2)) 1)) |
(* -1 (* x (+ 1 (* -1 (pow eps 2))))) |
(* -1 (* x (+ 1 (+ (* -1 (/ eps x)) (* -1 (pow eps 2)))))) |
(* -1 (* x (+ 1 (+ (* -1 (/ eps x)) (* -1 (pow eps 2)))))) |
(* -1 (* x (+ 1 (+ (* -1 (/ eps x)) (* -1 (pow eps 2)))))) |
(* -1 x) |
(- eps x) |
(- (* eps (+ 1 (* eps x))) x) |
(- (* eps (+ 1 (* eps x))) x) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) (+ x (+ (* -1 (/ x (pow eps 2))) (/ 1 eps)))) |
(* (pow eps 2) (+ x (+ (* -1 (/ x (pow eps 2))) (/ 1 eps)))) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) (+ x (* -1 (/ (- (/ x eps) 1) eps)))) |
(* (pow eps 2) (+ x (* -1 (/ (- (/ x eps) 1) eps)))) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* -1 x) |
(+ (* -1 x) (* (pow eps 2) x)) |
(+ (* -1 x) (* (pow eps 2) x)) |
(+ (* -1 x) (* (pow eps 2) x)) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
eps |
(+ eps (* (pow eps 2) x)) |
(+ eps (* (pow eps 2) x)) |
(+ eps (* (pow eps 2) x)) |
(* (pow eps 2) x) |
(* x (+ (/ eps x) (pow eps 2))) |
(* x (+ (/ eps x) (pow eps 2))) |
(* x (+ (/ eps x) (pow eps 2))) |
(* (pow eps 2) x) |
(* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))) |
(* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))) |
(* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))) |
eps |
(* eps (+ 1 (* eps x))) |
(* eps (+ 1 (* eps x))) |
(* eps (+ 1 (* eps x))) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) x) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(* (pow eps 2) (+ x (/ 1 eps))) |
| Outputs |
|---|
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))) |
(+ (* 1/2 (* (pow eps 2) (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))) (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x)))))))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x #s(literal -1/6 binary64) #s(literal -1/2 binary64))))) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x)))))))))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (*.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (fma.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64))))) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x #s(literal -1/6 binary64) #s(literal -1/2 binary64)))))) (*.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))))) |
(+ (* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (- (+ (* 1/6 (* (pow x 3) (exp (neg x)))) (* 1/2 (* (pow x 2) (exp (neg x))))) (+ (* -1/2 (* (pow x 2) (exp (neg x)))) (* -1/6 (* (pow x 3) (exp (neg x))))))) (* (pow eps 2) (+ (* 1/2 (* (pow eps 2) (- (+ (* 1/5040 (* (pow x 7) (exp (neg x)))) (* 1/720 (* (pow x 6) (exp (neg x))))) (+ (* -1/720 (* (pow x 6) (exp (neg x)))) (* -1/5040 (* (pow x 7) (exp (neg x)))))))) (* 1/2 (- (+ (* 1/120 (* (pow x 5) (exp (neg x)))) (* 1/24 (* (pow x 4) (exp (neg x))))) (+ (* -1/24 (* (pow x 4) (exp (neg x)))) (* -1/120 (* (pow x 5) (exp (neg x)))))))))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))) (*.f64 (*.f64 eps eps) (*.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (exp.f64 (neg.f64 x)) (-.f64 (fma.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 5 binary64)) (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (fma.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64)) (*.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/720 binary64) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64))))))) (*.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x #s(literal -1/6 binary64) #s(literal -1/2 binary64))))))))) |
(* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) eps)))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) eps)))) |
(+ (* 1/2 (- (exp (neg (* x (- 1 eps)))) (* -1 (exp (neg (* x (+ 1 eps))))))) (* 1/2 (/ (- (exp (neg (* x (- 1 eps)))) (exp (neg (* x (+ 1 eps))))) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) eps)))) |
(* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps)))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x))))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) eps)))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) eps)))) |
(+ (* -1/2 (/ (- (* -1 (exp (neg (* x (+ 1 (* -1 eps)))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))) eps)) (* 1/2 (- (exp (neg (* x (+ 1 (* -1 eps))))) (* -1 (exp (neg (* x (- 1 (* -1 eps))))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (/.f64 (-.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (exp.f64 (neg.f64 (fma.f64 x eps x)))) eps)))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (* x (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))))) |
(fma.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal -1 binary64) eps))) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* 1/2 (* x (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))) (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1)))))))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal -1 binary64) eps))) (*.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)))))))) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* 1/2 (- (* (+ 1 (/ 1 eps)) (- eps 1)) (* -1 (* (+ 1 eps) (- (/ 1 eps) 1))))) (* x (+ (* 1/2 (* x (- (* 1/6 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 3))) (* -1/6 (* (pow (+ 1 eps) 3) (- (/ 1 eps) 1)))))) (* 1/2 (- (* 1/2 (* (+ 1 (/ 1 eps)) (pow (- eps 1) 2))) (* 1/2 (* (pow (+ 1 eps) 2) (- (/ 1 eps) 1)))))))))) |
(fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 x (*.f64 #s(literal 1/6 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps)))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))))) (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))))) x (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal -1 binary64) eps))))) #s(literal 1 binary64)) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(* 1/2 (- (* (exp (- (* eps x) x)) (+ 1 (/ 1 eps))) (* (exp (neg (+ x (* eps x)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
(* 1/2 (- (* (exp (neg (* x (- 1 eps)))) (+ 1 (/ 1 eps))) (* (exp (neg (* x (+ 1 eps)))) (- (/ 1 eps) 1)))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (exp.f64 (fma.f64 x eps (neg.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (exp.f64 (neg.f64 (fma.f64 x eps x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (* x (- (+ eps (* -1 (+ 1 eps))) 1)))) |
(-.f64 #s(literal 1 binary64) x) |
(+ 1 (* x (+ (* 1/2 (* x (+ (* 1/2 (pow (+ 1 eps) 2)) (* 1/2 (pow (- eps 1) 2))))) (* 1/2 (- (+ eps (* -1 (+ 1 eps))) 1))))) |
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(* 1/2 (+ (exp (neg (+ x (* eps x)))) (exp (- (* eps x) x)))) |
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(exp (neg x)) |
(exp.f64 (neg.f64 x)) |
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2 |
#s(literal 2 binary64) |
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(fma.f64 x #s(literal -2 binary64) #s(literal 2 binary64)) |
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(* 2 (exp (neg x))) |
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(fma.f64 eps (*.f64 (exp.f64 (neg.f64 x)) (*.f64 eps (*.f64 x x))) (*.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64))) |
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1 |
#s(literal 1 binary64) |
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(fma.f64 x (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) |
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(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (+ (* -1 x) (* eps x))) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (+ (* -1 x) (* eps x))) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (+ (* -1 x) (* eps x))) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (+ (* -1 x) (* eps x))) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (neg x)) |
(exp.f64 (neg.f64 x)) |
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(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(exp (- (* eps x) x)) |
(exp.f64 (fma.f64 x eps (neg.f64 x))) |
(* 1/2 (- (+ (exp (neg x)) (* x (exp (neg x)))) (+ (* -1 (exp (neg x))) (* -1 (* x (exp (neg x))))))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))) |
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2 |
#s(literal 2 binary64) |
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#s(literal 1 binary64) |
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(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* -1 x) |
(neg.f64 x) |
(+ (* -1 x) (* (pow eps 2) x)) |
(*.f64 x (fma.f64 eps eps #s(literal -1 binary64))) |
(+ (* -1 x) (* (pow eps 2) x)) |
(*.f64 x (fma.f64 eps eps #s(literal -1 binary64))) |
(+ (* -1 x) (* (pow eps 2) x)) |
(*.f64 x (fma.f64 eps eps #s(literal -1 binary64))) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(fma.f64 x (*.f64 eps eps) (/.f64 (*.f64 x (neg.f64 eps)) eps)) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(fma.f64 x (*.f64 eps eps) (/.f64 (*.f64 x (neg.f64 eps)) eps)) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(fma.f64 x (*.f64 eps eps) (/.f64 (*.f64 x (neg.f64 eps)) eps)) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(fma.f64 x (*.f64 eps eps) (/.f64 (*.f64 x (neg.f64 eps)) eps)) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(fma.f64 x (*.f64 eps eps) (/.f64 (*.f64 x (neg.f64 eps)) eps)) |
(* (pow eps 2) (+ x (* -1 (/ x (pow eps 2))))) |
(fma.f64 x (*.f64 eps eps) (/.f64 (*.f64 x (neg.f64 eps)) eps)) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(*.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(*.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(*.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(*.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(*.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(*.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(*.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(*.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(*.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(*.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(*.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (* x (+ (* -1 (* (+ 1 eps) (- (/ 1 eps) eps))) (* (- eps 1) (- eps (/ 1 eps)))))) |
(*.f64 (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 eps (/.f64 #s(literal -1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) x)) |
eps |
(+ eps (* (pow eps 2) x)) |
(fma.f64 x (*.f64 eps eps) eps) |
(+ eps (* (pow eps 2) x)) |
(fma.f64 x (*.f64 eps eps) eps) |
(+ eps (* (pow eps 2) x)) |
(fma.f64 x (*.f64 eps eps) eps) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* x (+ (/ eps x) (pow eps 2))) |
(*.f64 x (fma.f64 eps eps (/.f64 eps x))) |
(* x (+ (/ eps x) (pow eps 2))) |
(*.f64 x (fma.f64 eps eps (/.f64 eps x))) |
(* x (+ (/ eps x) (pow eps 2))) |
(*.f64 x (fma.f64 eps eps (/.f64 eps x))) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))) |
(*.f64 x (fma.f64 eps eps (/.f64 eps x))) |
(* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))) |
(*.f64 x (fma.f64 eps eps (/.f64 eps x))) |
(* -1 (* x (+ (* -1 (/ eps x)) (* -1 (pow eps 2))))) |
(*.f64 x (fma.f64 eps eps (/.f64 eps x))) |
eps |
(* eps (+ 1 (* eps x))) |
(fma.f64 x (*.f64 eps eps) eps) |
(* eps (+ 1 (* eps x))) |
(fma.f64 x (*.f64 eps eps) eps) |
(* eps (+ 1 (* eps x))) |
(fma.f64 x (*.f64 eps eps) eps) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(fma.f64 x (*.f64 eps eps) eps) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(fma.f64 x (*.f64 eps eps) eps) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(fma.f64 x (*.f64 eps eps) eps) |
(* (pow eps 2) x) |
(*.f64 x (*.f64 eps eps)) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(fma.f64 x (*.f64 eps eps) eps) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(fma.f64 x (*.f64 eps eps) eps) |
(* (pow eps 2) (+ x (/ 1 eps))) |
(fma.f64 x (*.f64 eps eps) eps) |
| 4 354× | lower-fma.f32 |
| 4 334× | lower-fma.f64 |
| 4 312× | lower-*.f32 |
| 4 290× | lower-*.f64 |
| 2 802× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 101 | 1071 |
| 0 | 149 | 1045 |
| 1 | 678 | 954 |
| 2 | 6634 | 954 |
| 0 | 8303 | 933 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps)))))) |
(+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))) |
(exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))))) |
(+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))) |
#s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
(+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) |
(/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) |
(-.f64 (fma.f64 x (*.f64 eps eps) eps) x) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)) |
#s(approx (- (* x eps) x) (*.f64 x eps)) |
#s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))) |
(exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps)))) |
#s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))) |
(*.f64 (*.f64 x x) (*.f64 x x)) |
#s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) |
(*.f64 x (*.f64 eps eps)) |
(+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) |
(fma.f64 x (*.f64 eps eps) eps) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 eps (neg.f64 x))))))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x)))) (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 eps (neg.f64 x)))))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 eps (neg.f64 x))))) (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))))) |
(fma.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 eps (neg.f64 x)))))) |
(fma.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 eps (neg.f64 x)))) (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))))) |
(fma.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 eps (neg.f64 x)))))) |
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(pow.f64 (/.f64 (fma.f64 #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps)) (-.f64 #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps)) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps))) (*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)))) (fma.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps))) (*.f64 #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps)) (*.f64 #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps)))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps))) (*.f64 (+.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps))) (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps))))) #s(literal -1 binary64)) |
(*.f64 (fma.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) (*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps))) (*.f64 #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps)) (*.f64 #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps))))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps)) (-.f64 #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps)) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps))) (*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)))))) |
(*.f64 (*.f64 (+.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps))) (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps)))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 eps (*.f64 eps x) eps) x) #s(literal -1 binary64)) eps))))) |
(+.f64 eps (*.f64 x (*.f64 eps eps))) |
(+.f64 (*.f64 x (*.f64 eps eps)) eps) |
(-.f64 (/.f64 (*.f64 (*.f64 eps x) (*.f64 eps (*.f64 x (*.f64 eps eps)))) (-.f64 (*.f64 x (*.f64 eps eps)) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x (*.f64 eps eps)) eps))) |
(fma.f64 #s(literal 1 binary64) eps (*.f64 x (*.f64 eps eps))) |
(fma.f64 eps #s(literal 1 binary64) (*.f64 x (*.f64 eps eps))) |
(fma.f64 eps (*.f64 eps x) eps) |
(fma.f64 x (*.f64 eps eps) eps) |
(fma.f64 (*.f64 eps x) eps eps) |
(fma.f64 (*.f64 eps eps) x eps) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (-.f64 eps (*.f64 x (*.f64 eps eps))) (*.f64 (*.f64 eps x) (*.f64 eps (*.f64 x (*.f64 eps eps))))) (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps x) (*.f64 x (*.f64 x (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x (*.f64 eps eps)) eps) (*.f64 (fma.f64 eps (*.f64 eps x) eps) (-.f64 (*.f64 x (*.f64 eps eps)) eps)))) |
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps x) (*.f64 x (*.f64 x (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps)))) (fma.f64 eps (-.f64 eps (*.f64 x (*.f64 eps eps))) (*.f64 (*.f64 eps x) (*.f64 eps (*.f64 x (*.f64 eps eps)))))) |
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps x) (*.f64 x (*.f64 x (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps)))) (fma.f64 eps eps (-.f64 (*.f64 (*.f64 eps x) (*.f64 eps (*.f64 x (*.f64 eps eps)))) (*.f64 eps (*.f64 x (*.f64 eps eps)))))) |
(/.f64 (*.f64 (fma.f64 eps (*.f64 eps x) eps) (-.f64 (*.f64 x (*.f64 eps eps)) eps)) (-.f64 (*.f64 x (*.f64 eps eps)) eps)) |
(/.f64 (neg.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps x) (*.f64 x (*.f64 x (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (fma.f64 eps (-.f64 eps (*.f64 x (*.f64 eps eps))) (*.f64 (*.f64 eps x) (*.f64 eps (*.f64 x (*.f64 eps eps))))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 eps (*.f64 eps x) eps) (-.f64 (*.f64 x (*.f64 eps eps)) eps))) (neg.f64 (-.f64 (*.f64 x (*.f64 eps eps)) eps))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps x) (*.f64 eps (*.f64 x (*.f64 eps eps))))) (-.f64 eps (*.f64 x (*.f64 eps eps)))) |
(/.f64 (*.f64 eps (fma.f64 (*.f64 eps x) (*.f64 x (*.f64 x (*.f64 eps eps))) #s(literal 1 binary64))) (fma.f64 eps (*.f64 eps (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 eps x)))) |
(/.f64 (*.f64 eps (fma.f64 eps (*.f64 eps (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 eps x #s(literal -1 binary64))) |
(/.f64 (*.f64 (fma.f64 (*.f64 eps x) (*.f64 x (*.f64 x (*.f64 eps eps))) #s(literal 1 binary64)) eps) (fma.f64 eps (*.f64 eps (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 eps x)))) |
(/.f64 (*.f64 (fma.f64 eps (*.f64 eps (*.f64 x x)) #s(literal -1 binary64)) eps) (fma.f64 eps x #s(literal -1 binary64))) |
(pow.f64 (/.f64 (fma.f64 eps (-.f64 eps (*.f64 x (*.f64 eps eps))) (*.f64 (*.f64 eps x) (*.f64 eps (*.f64 x (*.f64 eps eps))))) (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps x) (*.f64 x (*.f64 x (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (*.f64 x (*.f64 eps eps)) eps) (*.f64 (fma.f64 eps (*.f64 eps x) eps) (-.f64 (*.f64 x (*.f64 eps eps)) eps))) #s(literal -1 binary64)) |
(*.f64 eps (fma.f64 eps x #s(literal 1 binary64))) |
(*.f64 (fma.f64 eps x #s(literal 1 binary64)) eps) |
(*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps x) (*.f64 x (*.f64 x (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps (*.f64 x (*.f64 eps eps))) (*.f64 (*.f64 eps x) (*.f64 eps (*.f64 x (*.f64 eps eps))))))) |
(*.f64 (*.f64 (fma.f64 eps (*.f64 eps x) eps) (-.f64 (*.f64 x (*.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 eps eps)) eps))) |
Compiled 37 877 to 2 123 computations (94.4% saved)
23 alts after pruning (18 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 083 | 6 | 1 089 |
| Fresh | 2 | 12 | 14 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 2 | 2 |
| Total | 1 087 | 23 | 1 110 |
| Status | Accuracy | Program |
|---|---|---|
| 29.0% | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (+.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)))) #s(literal -1 binary64))) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) | |
| 32.2% | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) | |
| 75.8% | (exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))))))) #s(literal -1 binary64))) | |
| 44.3% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) | |
| ✓ | 74.0% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
| 60.5% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (*.f64 eps (*.f64 eps (+.f64 x (/.f64 #s(literal 1 binary64) eps)))))) #s(literal 1 binary64))) | |
| 75.3% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 x eps)))) #s(literal 1 binary64))) | |
| ✓ | 84.1% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
| 62.0% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) #s(approx (exp (neg (+ (* x eps) x))) #s(literal 1 binary64))))) | |
| 47.0% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (fma.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64))) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64))) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) | |
| 64.0% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) | |
| 56.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) (*.f64 (fma.f64 x eps x) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) | |
| 56.7% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (fma.f64 (*.f64 x #s(literal -1/6 binary64)) (+.f64 eps #s(literal 1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) | |
| ✓ | 48.9% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
| 57.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) | |
| ✓ | 41.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
| 50.5% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) | |
| 33.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))))) | |
| 46.4% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) | |
| 72.6% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) #s(literal -1 binary64)) #s(literal 1 binary64)))) | |
| 42.1% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (-.f64 #s(literal 1 binary64) x))) | |
| 71.2% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (exp.f64 (neg.f64 x)))) | |
| ✓ | 42.5% | #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
Compiled 1 504 to 481 computations (68% saved)
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (-.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 x eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 x (*.f64 eps eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) #s(literal -1 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 eps #s(literal 1 binary64))) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (fma.f64 (*.f64 x #s(literal -1/6 binary64)) (+.f64 eps #s(literal 1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (*.f64 eps (*.f64 eps (+.f64 x (/.f64 #s(literal 1 binary64) eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (fma.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64))) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64))) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) (*.f64 (fma.f64 x eps x) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (exp.f64 (neg.f64 x)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) #s(approx (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x)))) (fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps))) (*.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) #s(literal 1/6 binary64)))))) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)))) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (+.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)))) #s(literal -1 binary64))) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) #s(approx (exp (neg (+ (* x eps) x))) #s(literal 1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) #s(approx (exp (neg (+ (* x eps) x))) #s(literal 1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64)))))))) #s(literal -1 binary64))) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
4 calls:
| 32.0ms | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| 13.0ms | x |
| 12.0ms | eps |
| 10.0ms | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
| 99.5% | 1 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 99.5% | 1 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
Compiled 66 to 40 computations (39.4% saved)
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (-.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 x eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 x (*.f64 eps eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) #s(literal -1 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 eps #s(literal 1 binary64))) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (fma.f64 (*.f64 x #s(literal -1/6 binary64)) (+.f64 eps #s(literal 1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (*.f64 eps (*.f64 eps (+.f64 x (/.f64 #s(literal 1 binary64) eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (fma.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64))) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64))) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) (*.f64 (fma.f64 x eps x) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (exp.f64 (neg.f64 x)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) #s(approx (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x)))) (fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps))) (*.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) #s(literal 1/6 binary64)))))) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)))) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (+.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)))) #s(literal -1 binary64))) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) #s(approx (exp (neg (+ (* x eps) x))) #s(literal 1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) #s(approx (exp (neg (+ (* x eps) x))) #s(literal 1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
4 calls:
| 14.0ms | x |
| 13.0ms | eps |
| 11.0ms | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| 11.0ms | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 90.2% | 2 | x |
| 100.0% | 2 | eps |
| 100.0% | 2 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 100.0% | 2 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
Compiled 66 to 40 computations (39.4% saved)
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (-.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 x eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 x (*.f64 eps eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) #s(literal -1 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 eps #s(literal 1 binary64))) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (fma.f64 (*.f64 x #s(literal -1/6 binary64)) (+.f64 eps #s(literal 1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (*.f64 eps (*.f64 eps (+.f64 x (/.f64 #s(literal 1 binary64) eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (fma.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64))) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64))) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) (*.f64 (fma.f64 x eps x) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (exp.f64 (neg.f64 x)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) #s(approx (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x)))) (fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps))) (*.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) #s(literal 1/6 binary64)))))) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)))) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (+.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)))) #s(literal -1 binary64))) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) #s(approx (exp (neg (+ (* x eps) x))) #s(literal 1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) #s(approx (exp (neg (+ (* x eps) x))) #s(literal 1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
3 calls:
| 15.0ms | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 12.0ms | eps |
| 8.0ms | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 95.2% | 2 | eps |
| 95.2% | 2 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 95.2% | 2 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
Compiled 63 to 38 computations (39.7% saved)
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (-.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 x eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 x (*.f64 eps eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) #s(literal -1 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 eps #s(literal 1 binary64))) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (fma.f64 (*.f64 x #s(literal -1/6 binary64)) (+.f64 eps #s(literal 1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (*.f64 eps (*.f64 eps (+.f64 x (/.f64 #s(literal 1 binary64) eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (fma.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64))) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64))) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) (*.f64 (fma.f64 x eps x) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (exp.f64 (neg.f64 x)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) #s(approx (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x)))) (fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps))) (*.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) #s(literal 1/6 binary64)))))) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)))) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (+.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)))) #s(literal -1 binary64))) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) #s(approx (exp (neg (+ (* x eps) x))) #s(literal 1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) #s(approx (exp (neg (+ (* x eps) x))) #s(literal 1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (fma.f64 x (*.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal -1 binary64) eps) (*.f64 (+.f64 #s(literal -1 binary64) eps) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps))))) (+.f64 (+.f64 #s(literal -1 binary64) eps) (/.f64 (+.f64 #s(literal -1 binary64) eps) eps)))) #s(literal 1 binary64))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x))))) #s(literal 2 binary64)) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
3 calls:
| 11.0ms | eps |
| 10.0ms | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| 8.0ms | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 93.0% | 3 | eps |
| 94.8% | 2 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 94.8% | 2 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
Compiled 63 to 38 computations (39.7% saved)
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (-.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 x eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 x (*.f64 eps eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) #s(literal -1 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 eps #s(literal 1 binary64))) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (fma.f64 (*.f64 x #s(literal -1/6 binary64)) (+.f64 eps #s(literal 1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (*.f64 eps (*.f64 eps (+.f64 x (/.f64 #s(literal 1 binary64) eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (fma.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64))) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64))) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) (*.f64 (fma.f64 x eps x) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (exp.f64 (neg.f64 x)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (/.f64 (*.f64 (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x) (-.f64 (fma.f64 x (*.f64 eps eps) eps) x)) (fma.f64 (fma.f64 eps x #s(literal 1 binary64)) eps x)) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) #s(approx (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x)))) (fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps))) (*.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (*.f64 (+.f64 #s(literal -1 binary64) eps) #s(literal 1/6 binary64)))))) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)))) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (+.f64 eps (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) eps) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (*.f64 (+.f64 #s(literal -1 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps #s(literal -1/2 binary64)))) #s(literal -1 binary64))) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) #s(approx (exp (neg (+ (* x eps) x))) #s(literal 1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps))))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) #s(approx (exp (neg (+ (* x eps) x))) #s(literal 1 binary64))))) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (exp.f64 (neg.f64 x)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
2 calls:
| 11.0ms | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| 7.0ms | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 94.3% | 2 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 94.3% | 2 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
Compiled 60 to 36 computations (40% saved)
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (-.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 x eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 x (*.f64 eps eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) #s(literal -1 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 eps #s(literal 1 binary64))) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (fma.f64 (*.f64 x #s(literal -1/6 binary64)) (+.f64 eps #s(literal 1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (*.f64 eps (*.f64 eps (+.f64 x (/.f64 #s(literal 1 binary64) eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)) (fma.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64))) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64))) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) (*.f64 (fma.f64 x eps x) (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)))))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 (-.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps (-.f64 (fma.f64 x (*.f64 eps eps) eps) x) #s(literal -1 binary64)) eps)))) #s(literal 1 binary64))) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64))) |
4 calls:
| 7.0ms | eps |
| 7.0ms | x |
| 7.0ms | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 6.0ms | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 85.4% | 3 | x |
| 83.7% | 2 | eps |
| 87.3% | 2 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 87.3% | 2 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
Compiled 66 to 40 computations (39.4% saved)
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (-.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 x eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 x (*.f64 eps eps))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) #s(literal -1 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps (*.f64 eps (-.f64 x (/.f64 x (*.f64 eps eps)))))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 1 binary64) eps)))) (fma.f64 #s(literal 1/2 binary64) (-.f64 eps (+.f64 eps #s(literal 1 binary64))) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) #s(literal 1 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) #s(approx (exp (neg (* (+ 1 eps) x))) #s(literal 1 binary64)))) #s(literal 2 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (fma.f64 x (fma.f64 x (*.f64 (*.f64 (+.f64 eps #s(literal 1 binary64)) (+.f64 eps #s(literal 1 binary64))) (fma.f64 (*.f64 x #s(literal -1/6 binary64)) (+.f64 eps #s(literal 1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (*.f64 eps (*.f64 eps (+.f64 x (/.f64 #s(literal 1 binary64) eps)))))) #s(literal 1 binary64))) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) |
2 calls:
| 4.0ms | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| 4.0ms | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 86.2% | 2 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 86.2% | 2 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
Compiled 60 to 36 computations (40% saved)
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (-.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 x eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 x (*.f64 eps eps))) #s(literal 1 binary64))) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 x eps)))) #s(literal 1 binary64))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) |
4 calls:
| 12.0ms | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| 3.0ms | eps |
| 3.0ms | x |
| 3.0ms | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 75.3% | 1 | eps |
| 83.3% | 2 | x |
| 77.9% | 2 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 77.9% | 2 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
Compiled 66 to 40 computations (39.4% saved)
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (-.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x)))))) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps)))))) |
3 calls:
| 7.0ms | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| 3.0ms | x |
| 2.0ms | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 77.9% | 2 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 77.9% | 2 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| 75.1% | 3 | x |
Compiled 63 to 38 computations (39.7% saved)
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (-.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (-.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
4 calls:
| 3.0ms | x |
| 2.0ms | eps |
| 2.0ms | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| 2.0ms | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 48.9% | 1 | x |
| 48.9% | 1 | eps |
| 48.9% | 1 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 48.9% | 1 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
Compiled 66 to 40 computations (39.4% saved)
Total -0.8b remaining (-2.2%)
Threshold costs -0.8b (-2.2%)
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (-.f64 #s(literal 1 binary64) x))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
4 calls:
| 2.0ms | eps |
| 2.0ms | x |
| 2.0ms | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 2.0ms | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 42.5% | 1 | (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64)) |
| 42.5% | 1 | (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) |
| 42.5% | 1 | x |
| 42.5% | 1 | eps |
Compiled 66 to 40 computations (39.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0 | 2.0 |
Compiled 34 to 24 computations (29.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 0.0 | 2.0 |
Compiled 34 to 24 computations (29.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 12.401496509149604 | +inf |
Compiled 34 to 24 computations (29.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 12.401496509149604 | +inf |
Compiled 34 to 24 computations (29.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 12.401496509149604 | +inf |
Compiled 34 to 24 computations (29.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 12.401496509149604 | +inf |
Compiled 34 to 24 computations (29.4% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 35.0ms | 0.001994585943309913 | 1479.3998019707817 |
| 15.0ms | 42× | 1 | valid |
| 10.0ms | 99× | 0 | valid |
| 1.0ms | 3× | 2 | valid |
Compiled 304 to 177 computations (41.8% saved)
ival-exp: 8.0ms (36.5% of total)ival-mult: 4.0ms (18.3% of total)ival-div: 3.0ms (13.7% of total)ival-sub: 2.0ms (9.1% of total)ival-add: 2.0ms (9.1% of total)adjust: 2.0ms (9.1% of total)ival-neg: 2.0ms (9.1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 12.401496509149604 | +inf |
Compiled 34 to 24 computations (29.4% saved)
| 1× | egg-herbie |
| 262× | distribute-lft-neg-in_binary64 |
| 158× | neg-mul-1_binary64 |
| 140× | neg-sub0_binary64 |
| 104× | *-commutative_binary64 |
| 100× | +-commutative_binary64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 158 | 1579 |
| 1 | 219 | 1579 |
| 2 | 269 | 1564 |
| 3 | 328 | 1564 |
| 4 | 379 | 1564 |
| 5 | 461 | 1564 |
| 6 | 545 | 1564 |
| 7 | 649 | 1564 |
| 8 | 759 | 1564 |
| 9 | 835 | 1564 |
| 10 | 884 | 1564 |
| 11 | 911 | 1564 |
| 12 | 922 | 1564 |
| 13 | 926 | 1564 |
| 1× | saturated |
| Inputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
(if (<=.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 0 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps)))))))) |
(if (<=.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 0 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))) |
(if (<=.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 20 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)))) |
(if (<=.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 20 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (* 1/2 (+ (exp (- (* x eps) x)) (exp (neg (+ (* x eps) x))))) (exp.f64 (neg.f64 x)))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)))) |
(if (<=.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 20 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)))) |
(if (<=.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 20 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps))))))) |
(if (<=.f64 x #s(literal 280 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 x eps)))) #s(literal 1 binary64))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps))))))) |
(if (<=.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 20 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps))))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
| Outputs |
|---|
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 x eps) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 (-.f64 (*.f64 eps x) x)) (exp.f64 (neg.f64 (fma.f64 x eps x)))))) |
(if (<=.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 0 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 x eps))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 x (neg.f64 eps)))))))) |
(if (<=.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))))) (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)))) #s(literal 0 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 x (+.f64 x #s(literal 2 binary64)))))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 (exp.f64 #s(approx (- (* x eps) x) (*.f64 eps x))) (exp.f64 #s(approx (neg (+ (* x eps) x)) (*.f64 eps (neg.f64 x)))))))) |
(if (<=.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 0 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1 binary64) eps) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 2 binary64))) |
(if (<=.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))))) (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)))) #s(literal 0 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 x (+.f64 x #s(literal 2 binary64)))))) (/.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(approx (exp (neg (* (- 1 eps) x))) (fma.f64 x (*.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (+.f64 eps #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 eps #s(literal -1 binary64))) #s(literal 1 binary64)))) (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)))) #s(literal 2 binary64))) |
(if (<=.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 20 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (+.f64 x #s(literal 2 binary64)) x)))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (+.f64 (/.f64 (+.f64 eps #s(literal 1 binary64)) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)))) |
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(if (<=.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))))) (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)))) #s(literal 20 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (+.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) eps) eps) (-.f64 #s(literal -1 binary64) eps)) #s(approx (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))) (/.f64 (fma.f64 eps #s(approx (- (+ (* x (* eps eps)) eps) x) (*.f64 x (*.f64 eps eps))) #s(literal -1 binary64)) eps))) #s(literal 1 binary64)))) |
(if (<=.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 20 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps))))))) |
(if (<=.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))))) (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)))) #s(literal 20 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (/.f64 #s(approx (+ (* (* (* x x) (* x x)) 1/4) -1) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps))))))) |
(if (<=.f64 x #s(literal 280 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 x eps)))) #s(literal 1 binary64))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps))))))) |
(if (<=.f64 x #s(literal 280 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(approx (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps)))) (*.f64 eps #s(approx (* eps (- x (/ x (* eps eps)))) (*.f64 eps x)))) #s(literal 1 binary64))) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps))))))) |
(if (<=.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) eps) x)))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (exp.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) eps) x))))) #s(literal 20 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps))))))) |
(if (<=.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (exp.f64 (*.f64 x (+.f64 eps #s(literal -1 binary64))))) (*.f64 (exp.f64 (*.f64 x (-.f64 #s(literal -1 binary64) eps))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps)))) #s(literal 20 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) #s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(approx (+ (* (* 1/2 x) (+ (+ (/ (+ eps 1) eps) (- -1 eps)) (+ (* x (* 1/2 (+ (* (+ (/ (+ eps 1) eps) (- -1 eps)) (- -1 eps)) (* (+ -1 eps) (+ (+ -1 eps) (/ (+ -1 eps) eps)))))) (+ (+ -1 eps) (/ (+ -1 eps) eps))))) 1) (*.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x (*.f64 eps eps))))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(approx (exp (- (* x eps) x)) #s(literal 1 binary64)) #s(approx (exp (neg (+ (* x eps) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x eps x)))))) |
#s(approx (/ (- (* (+ 1 (/ 1 eps)) (exp (neg (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (neg (* (+ 1 eps) x))))) 2) #s(literal 1 binary64)) |
| 13 416× | lower-fma.f64 |
| 13 416× | lower-fma.f32 |
| 13 204× | lower-fma.f64 |
| 13 204× | lower-fma.f32 |
| 10 278× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 438 | 11214 |
| 1 | 1460 | 10416 |
| 2 | 4991 | 10150 |
| 0 | 8313 | 9642 |
| 0 | 80 | 888 |
| 0 | 115 | 888 |
| 1 | 546 | 873 |
| 2 | 5516 | 873 |
| 0 | 8360 | 855 |
| 0 | 392 | 11205 |
| 1 | 1305 | 10427 |
| 2 | 4434 | 9802 |
| 0 | 8160 | 9265 |
| 0 | 592 | 12240 |
| 1 | 1987 | 11256 |
| 2 | 6826 | 11225 |
| 0 | 8121 | 10709 |
| 0 | 287 | 2962 |
| 1 | 920 | 2564 |
| 2 | 3114 | 2316 |
| 0 | 8328 | 2191 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node 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 |
Compiled 636 to 196 computations (69.2% saved)
(abs eps)
Compiled 1 250 to 332 computations (73.4% saved)
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