
Time bar (total: 7.2s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 0 |
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 1 |
| 50% | 50% | 50% | 0% | 0% | 0% | 0% | 2 |
| 75% | 75% | 25% | 0% | 0% | 0% | 0% | 3 |
| 87.5% | 87.5% | 12.5% | 0% | 0% | 0% | 0% | 4 |
| 93.8% | 93.7% | 6.2% | 0% | 0% | 0% | 0% | 5 |
| 96.9% | 96.8% | 3.1% | 0% | 0% | 0% | 0% | 6 |
| 98.4% | 98.4% | 1.6% | 0% | 0% | 0% | 0% | 7 |
| 99.2% | 99.2% | 0.8% | 0% | 0% | 0% | 0% | 8 |
| 99.6% | 99.6% | 0.4% | 0% | 0% | 0% | 0% | 9 |
| 99.8% | 99.8% | 0.2% | 0% | 0% | 0% | 0% | 10 |
| 99.9% | 99.9% | 0.1% | 0% | 0% | 0% | 0% | 11 |
| 100% | 99.9% | 0% | 0% | 0% | 0% | 0% | 12 |
Compiled 14 to 9 computations (35.7% saved)
| 472.0ms | 8 256× | 0 | valid |
| 139.0ms | 2 551× | 0 | exit |
ival-expm1: 128.0ms (32.8% of total)ival-mult: 97.0ms (24.8% of total)ival-div: 78.0ms (20% of total)ival-sqrt: 71.0ms (18.2% of total)ival-true: 8.0ms (2% of total)exact: 6.0ms (1.5% of total)ival-assert: 4.0ms (1% of total)| 1× | egg-herbie |
| 15 394× | lower-fma.f64 |
| 15 394× | lower-fma.f32 |
| 2 850× | lower--.f32 |
| 2 846× | lower--.f64 |
| 2 458× | lower-*.f32 |
Useful iterations: 5 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 12 | 29 |
| 1 | 32 | 27 |
| 2 | 55 | 27 |
| 3 | 89 | 27 |
| 4 | 143 | 13 |
| 5 | 250 | 13 |
| 6 | 513 | 13 |
| 7 | 2039 | 13 |
| 8 | 7136 | 13 |
| 0 | 10 | 12 |
| 0 | 17 | 12 |
| 1 | 29 | 12 |
| 2 | 35 | 12 |
| 3 | 47 | 12 |
| 4 | 73 | 7 |
| 5 | 126 | 5 |
| 6 | 203 | 5 |
| 7 | 606 | 5 |
| 8 | 2926 | 5 |
| 9 | 6783 | 5 |
| 0 | 8197 | 5 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) |
| Outputs |
|---|
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 175 | 0 | - | 0 | - | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) |
| 175 | 0 | - | 0 | - | (-.f64 (exp.f64 x) #s(literal 1 binary64)) |
| 2 | 0 | - | 0 | - | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
| 0 | 1 | (124.83777898865645) | 0 | - | (exp.f64 (*.f64 #s(literal 2 binary64) x)) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (*.f64 #s(literal 2 binary64) x) |
| 0 | 0 | - | 0 | - | (sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| 0 | 0 | - | 0 | - | (exp.f64 x) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (exp.f64 x) #s(literal 1 binary64)) | cancellation | 175 | 1 |
-.f64 | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) | cancellation | 175 | 0 |
/.f64 | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) | o/o | 2 | 0 |
| ↳ | (exp.f64 (*.f64 #s(literal 2 binary64) x)) | overflow | 2 | |
| ↳ | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) | overflow | 2 | |
| ↳ | (exp.f64 x) | overflow | 2 | |
| ↳ | (-.f64 (exp.f64 x) #s(literal 1 binary64)) | overflow | 2 | |
exp.f64 | (exp.f64 (*.f64 #s(literal 2 binary64) x)) | sensitivity | 1 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 177 | 0 |
| - | 1 | 78 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 177 | 0 | 0 |
| - | 1 | 1 | 77 |
| number | freq |
|---|---|
| 0 | 78 |
| 1 | 3 |
| 2 | 175 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 39.0ms | 512× | 0 | valid |
Compiled 120 to 44 computations (63.3% saved)
ival-exp: 7.0ms (28.4% of total)ival-expm1: 6.0ms (24.4% of total)ival-mult: 4.0ms (16.2% of total)ival-div: 3.0ms (12.2% of total)ival-sqrt: 3.0ms (12.2% of total)exact: 1.0ms (4.1% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)Compiled 1 to 1 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 31.7% | (sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) |
Compiled 13 to 10 computations (23.1% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 128 | (*.f64 #s(literal 2 binary64) x) |
| ✓ | cost-diff | 192 | (-.f64 (exp.f64 x) #s(literal 1 binary64)) |
| ✓ | cost-diff | 192 | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 7104 | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
| 15 394× | lower-fma.f64 |
| 15 394× | lower-fma.f32 |
| 2 850× | lower--.f32 |
| 2 846× | lower--.f64 |
| 2 458× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 45 |
| 0 | 17 | 45 |
| 1 | 29 | 45 |
| 2 | 35 | 45 |
| 3 | 47 | 45 |
| 4 | 73 | 35 |
| 5 | 126 | 31 |
| 6 | 203 | 31 |
| 7 | 606 | 31 |
| 8 | 2926 | 31 |
| 9 | 6783 | 31 |
| 0 | 8197 | 27 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) |
(exp.f64 (*.f64 #s(literal 2 binary64) x)) |
(*.f64 #s(literal 2 binary64) x) |
#s(literal 2 binary64) |
x |
#s(literal 1 binary64) |
(-.f64 (exp.f64 x) #s(literal 1 binary64)) |
(exp.f64 x) |
| Outputs |
|---|
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) |
(expm1.f64 (+.f64 x x)) |
(exp.f64 (*.f64 #s(literal 2 binary64) x)) |
(exp.f64 (+.f64 x x)) |
(*.f64 #s(literal 2 binary64) x) |
(+.f64 x x) |
#s(literal 2 binary64) |
x |
#s(literal 1 binary64) |
(-.f64 (exp.f64 x) #s(literal 1 binary64)) |
(expm1.f64 x) |
(exp.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (exp.f64 x) |
| ✓ | accuracy | 99.4% | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
| ✓ | accuracy | 36.1% | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) |
| ✓ | accuracy | 36.1% | (-.f64 (exp.f64 x) #s(literal 1 binary64)) |
| 19.0ms | 256× | 0 | valid |
Compiled 47 to 12 computations (74.5% saved)
ival-exp: 3.0ms (24.6% of total)ival-expm1: 3.0ms (24.6% of total)ival-div: 2.0ms (16.4% of total)ival-mult: 2.0ms (16.4% of total)ival-sqrt: 2.0ms (16.4% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))> |
#<alt (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))> |
#<alt (-.f64 (exp.f64 x) #s(literal 1 binary64))> |
#<alt (*.f64 #s(literal 2 binary64) x)> |
#<alt (exp.f64 x)> |
| Outputs |
|---|
#<alt 2> |
#<alt (+ 2 x)> |
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))> |
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))> |
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))> |
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))> |
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))> |
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))> |
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))> |
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))> |
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))> |
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))> |
#<alt (* 2 x)> |
#<alt (* x (+ 2 (* 2 x)))> |
#<alt (* x (+ 2 (* x (+ 2 (* 4/3 x)))))> |
#<alt (* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))> |
#<alt (- (exp (* 2 x)) 1)> |
#<alt (- (exp (* 2 x)) 1)> |
#<alt (- (exp (* 2 x)) 1)> |
#<alt (- (exp (* 2 x)) 1)> |
#<alt (- (exp (* 2 x)) 1)> |
#<alt (- (exp (* 2 x)) 1)> |
#<alt (- (exp (* 2 x)) 1)> |
#<alt (- (exp (* 2 x)) 1)> |
#<alt x> |
#<alt (* x (+ 1 (* 1/2 x)))> |
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))> |
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))> |
#<alt (- (exp x) 1)> |
#<alt (- (exp x) 1)> |
#<alt (- (exp x) 1)> |
#<alt (- (exp x) 1)> |
#<alt (- (exp x) 1)> |
#<alt (- (exp x) 1)> |
#<alt (- (exp x) 1)> |
#<alt (- (exp x) 1)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt 1> |
#<alt (+ 1 x)> |
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))> |
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
15 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | inf | (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
| 1.0ms | x | @ | -inf | (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
| 0.0ms | x | @ | 0 | (- (exp (* 2 x)) 1) |
| 0.0ms | x | @ | 0 | (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
| 0.0ms | x | @ | -inf | (* 2 x) |
| 1× | batch-egg-rewrite |
| 5 402× | lower-fma.f64 |
| 5 402× | lower-fma.f32 |
| 4 492× | lower-*.f32 |
| 4 490× | lower-*.f64 |
| 2 532× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 26 |
| 0 | 15 | 26 |
| 1 | 56 | 19 |
| 2 | 378 | 19 |
| 3 | 4533 | 19 |
| 0 | 8161 | 15 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) |
(-.f64 (exp.f64 x) #s(literal 1 binary64)) |
(*.f64 #s(literal 2 binary64) x) |
(exp.f64 x) |
| Outputs |
|---|
(exp.f64 (log1p.f64 (exp.f64 x))) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(+.f64 (exp.f64 x) #s(literal 1 binary64)) |
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal -1 binary64) (expm1.f64 x))) |
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64))) |
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1 binary64))) |
(+.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x))) |
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x))) |
(+.f64 (*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (exp.f64 (+.f64 x x))) (*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(+.f64 (*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (exp.f64 (+.f64 x x)))) |
(+.f64 (*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (exp.f64 x))) |
(+.f64 (*.f64 (exp.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))))) |
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (*.f64 (exp.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))))) |
(+.f64 (*.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (*.f64 (exp.f64 x) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))))) |
(-.f64 (exp.f64 x) #s(literal -1 binary64)) |
(-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x)))) |
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) |
(-.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) |
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 x))) |
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 x))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (expm1.f64 x))) (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x)))) |
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))))) (/.f64 #s(literal 1 binary64) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))))) |
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))))) |
(-.f64 (/.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (/.f64 (expm1.f64 x) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))) |
(-.f64 (/.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal -3 binary64)) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))))) |
(-.f64 (/.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))))) |
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal -1 binary64) (expm1.f64 x))) |
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64))) |
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1 binary64))) |
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))))) |
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal -1 binary64) (expm1.f64 x))) |
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(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 (+.f64 x x)))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 (+.f64 x x)))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (neg.f64 (expm1.f64 (+.f64 x x)))) (/.f64 (expm1.f64 x) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))) |
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (/.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 6 binary64)))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))))) |
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 4 binary64)))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))) |
(*.f64 (*.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x)))) |
(*.f64 (*.f64 (expm1.f64 (+.f64 x x)) (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x #s(literal 6 binary64))))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) |
(*.f64 (*.f64 (expm1.f64 (+.f64 x x)) (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x #s(literal 4 binary64))))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) |
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (expm1.f64 x))) |
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x) (neg.f64 (expm1.f64 x)))) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) |
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))) |
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (-.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))) |
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))) |
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (expm1.f64 x))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) |
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 3 binary64)))) (fma.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (+.f64 x x))) (exp.f64 (*.f64 x #s(literal 4 binary64))))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (-.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (+.f64 x x)) (exp.f64 x))) |
(log.f64 (exp.f64 (+.f64 x x))) |
(+.f64 x x) |
(+.f64 (+.f64 x x) #s(literal 0 binary64)) |
(+.f64 #s(literal 0 binary64) (+.f64 x x)) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))) (log.f64 (*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))) |
(+.f64 (log.f64 (*.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))))) (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
(fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) |
(fma.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
(fma.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)) (log.f64 (*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))) |
(fma.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 0 binary64)) |
(fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64) (log.f64 (*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 4 binary64) #s(literal 0 binary64)) |
(fma.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64) #s(literal 0 binary64)) |
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64) #s(literal 0 binary64)) |
(/.f64 (fma.f64 (*.f64 x x) x (*.f64 (*.f64 x x) x)) (fma.f64 x x (-.f64 (*.f64 x x) (*.f64 x x)))) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 x x)) (-.f64 x x)) |
(*.f64 #s(literal 2 binary64) x) |
(*.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
(*.f64 x #s(literal 2 binary64)) |
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 4 binary64)) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) |
(*.f64 (fma.f64 x #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) |
(exp.f64 x) |
(exp.f64 (*.f64 x #s(literal 1 binary64))) |
(pow.f64 (exp.f64 x) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (exp.f64 x)) |
(*.f64 (exp.f64 x) #s(literal 1 binary64)) |
| 1× | egg-herbie |
| 18 226× | lower-fma.f64 |
| 18 226× | lower-fma.f32 |
| 2 938× | lower-+.f64 |
| 2 938× | lower-+.f32 |
| 2 780× | lower--.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 49 | 342 |
| 1 | 155 | 342 |
| 2 | 335 | 342 |
| 3 | 752 | 342 |
| 4 | 1201 | 302 |
| 5 | 1536 | 286 |
| 6 | 2025 | 286 |
| 7 | 2949 | 286 |
| 8 | 4633 | 286 |
| 0 | 8302 | 232 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
2 |
(+ 2 x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(* 2 x) |
(* x (+ 2 (* 2 x))) |
(* x (+ 2 (* x (+ 2 (* 4/3 x))))) |
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x))))))) |
(- (exp (* 2 x)) 1) |
(- (exp (* 2 x)) 1) |
(- (exp (* 2 x)) 1) |
(- (exp (* 2 x)) 1) |
(- (exp (* 2 x)) 1) |
(- (exp (* 2 x)) 1) |
(- (exp (* 2 x)) 1) |
(- (exp (* 2 x)) 1) |
x |
(* x (+ 1 (* 1/2 x))) |
(* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) |
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))) |
(- (exp x) 1) |
(- (exp x) 1) |
(- (exp x) 1) |
(- (exp x) 1) |
(- (exp x) 1) |
(- (exp x) 1) |
(- (exp x) 1) |
(- (exp x) 1) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
1 |
(+ 1 x) |
(+ 1 (* x (+ 1 (* 1/2 x)))) |
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
| Outputs |
|---|
2 |
#s(literal 2 binary64) |
(+ 2 x) |
(+.f64 #s(literal 2 binary64) x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(* 2 x) |
(+.f64 x x) |
(* x (+ 2 (* 2 x))) |
(*.f64 #s(literal 2 binary64) (fma.f64 x x x)) |
(* x (+ 2 (* x (+ 2 (* 4/3 x))))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 4/3 binary64) #s(literal 2 binary64)) #s(literal 2 binary64))) |
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x))))))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 2/3 binary64) #s(literal 4/3 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (+.f64 x x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (+.f64 x x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (+.f64 x x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (+.f64 x x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (+.f64 x x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (+.f64 x x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (+.f64 x x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (+.f64 x x)) |
x |
(* x (+ 1 (* 1/2 x))) |
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) |
(* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) |
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x) |
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))) |
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x) |
(- (exp x) 1) |
(expm1.f64 x) |
(- (exp x) 1) |
(expm1.f64 x) |
(- (exp x) 1) |
(expm1.f64 x) |
(- (exp x) 1) |
(expm1.f64 x) |
(- (exp x) 1) |
(expm1.f64 x) |
(- (exp x) 1) |
(expm1.f64 x) |
(- (exp x) 1) |
(expm1.f64 x) |
(- (exp x) 1) |
(expm1.f64 x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
(* 2 x) |
(+.f64 x x) |
1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 (* x (+ 1 (* 1/2 x)))) |
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
Compiled 16 824 to 2 356 computations (86% saved)
5 alts after pruning (5 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 710 | 5 | 715 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 711 | 5 | 716 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 68.7% | (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ▶ | 70.2% | (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ▶ | 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| ▶ | 68.6% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ▶ | 74.4% | (sqrt.f64 #s(literal 2 binary64)) |
Compiled 70 to 56 computations (20% saved)
| 1× | egg-herbie |
Found 13 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 2 binary64) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (exp.f64 x) |
| ✓ | cost-diff | 0 | (-.f64 (exp.f64 x) #s(literal -1 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| 400× | lower-fma.f32 |
| 390× | lower-fma.f64 |
| 134× | lower-*.f64 |
| 134× | lower-*.f32 |
| 132× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 19 | 85 |
| 0 | 37 | 85 |
| 1 | 67 | 85 |
| 2 | 113 | 85 |
| 3 | 202 | 85 |
| 4 | 249 | 85 |
| 5 | 255 | 85 |
| 0 | 255 | 85 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
(-.f64 (exp.f64 x) #s(literal -1 binary64)) |
(exp.f64 x) |
x |
#s(literal -1 binary64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
(+.f64 #s(literal 2 binary64) x) |
#s(literal 2 binary64) |
x |
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) |
x |
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) |
#s(literal 1/2 binary64) |
#s(literal 1 binary64) |
#s(literal 2 binary64) |
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
x |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
#s(literal 1/6 binary64) |
#s(literal 1/2 binary64) |
#s(literal 1 binary64) |
#s(literal 2 binary64) |
| Outputs |
|---|
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))) |
(-.f64 (exp.f64 x) #s(literal -1 binary64)) |
(+.f64 (exp.f64 x) #s(literal 1 binary64)) |
(exp.f64 x) |
x |
#s(literal -1 binary64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
(sqrt.f64 (+.f64 x #s(literal 2 binary64))) |
(+.f64 #s(literal 2 binary64) x) |
(+.f64 x #s(literal 2 binary64)) |
#s(literal 2 binary64) |
x |
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) |
x |
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) |
#s(literal 1/2 binary64) |
#s(literal 1 binary64) |
#s(literal 2 binary64) |
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
x |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
#s(literal 1/6 binary64) |
#s(literal 1/2 binary64) |
#s(literal 1 binary64) |
#s(literal 2 binary64) |
Found 13 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 2 binary64) x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| ✓ | accuracy | 100.0% | (exp.f64 x) |
| ✓ | accuracy | 100.0% | (-.f64 (exp.f64 x) #s(literal -1 binary64)) |
| 31.0ms | 179× | 0 | valid |
| 16.0ms | 77× | 0 | invalid |
Compiled 101 to 26 computations (74.3% saved)
ival-add: 10.0ms (30% of total)ival-mult: 8.0ms (24% of total)ival-sqrt: 8.0ms (24% of total)const: 4.0ms (12% of total)ival-exp: 2.0ms (6% of total)ival-sub: 1.0ms (3% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))> |
#<alt (-.f64 (exp.f64 x) #s(literal -1 binary64))> |
#<alt (exp.f64 x)> |
#<alt (sqrt.f64 #s(literal 2 binary64))> |
#<alt (sqrt.f64 (+.f64 #s(literal 2 binary64) x))> |
#<alt (+.f64 #s(literal 2 binary64) x)> |
#<alt (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))> |
#<alt (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))> |
#<alt (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))> |
#<alt (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))> |
#<alt (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))> |
#<alt (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))> |
#<alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))> |
| Outputs |
|---|
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (sqrt (+ 1 (exp x)))> |
#<alt (sqrt (+ 1 (exp x)))> |
#<alt (sqrt (+ 1 (exp x)))> |
#<alt (sqrt (+ 1 (exp x)))> |
#<alt (sqrt (+ 1 (exp x)))> |
#<alt (sqrt (+ 1 (exp x)))> |
#<alt (sqrt (+ 1 (exp x)))> |
#<alt (sqrt (+ 1 (exp x)))> |
#<alt 2> |
#<alt (+ 2 x)> |
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))> |
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt 1> |
#<alt (+ 1 x)> |
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))> |
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt 2> |
#<alt (+ 2 x)> |
#<alt (+ 2 x)> |
#<alt (+ 2 x)> |
#<alt x> |
#<alt (* x (+ 1 (* 2 (/ 1 x))))> |
#<alt (* x (+ 1 (* 2 (/ 1 x))))> |
#<alt (* x (+ 1 (* 2 (/ 1 x))))> |
#<alt x> |
#<alt (* x (+ 1 (* 2 (/ 1 x))))> |
#<alt (* x (+ 1 (* 2 (/ 1 x))))> |
#<alt (* x (+ 1 (* 2 (/ 1 x))))> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))> |
#<alt (* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))> |
#<alt (* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))> |
#<alt (* -1 (* x (sqrt 1/2)))> |
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))> |
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))> |
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))> |
#<alt 2> |
#<alt (+ 2 x)> |
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))> |
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))> |
#<alt (* 1/2 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))> |
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))> |
#<alt (* 1/2 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))> |
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))> |
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))> |
#<alt 2> |
#<alt (+ 2 x)> |
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))> |
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt 1/2> |
#<alt (+ 1/2 (* 1/6 x))> |
#<alt (+ 1/2 (* 1/6 x))> |
#<alt (+ 1/2 (* 1/6 x))> |
#<alt (* 1/6 x)> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* 1/6 x)> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
36 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | -inf | (sqrt (+ 2 x)) |
| 2.0ms | x | @ | inf | (sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)) |
| 1.0ms | x | @ | -inf | (sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)) |
| 1.0ms | x | @ | 0 | (sqrt (+ 2 x)) |
| 1.0ms | x | @ | inf | (sqrt (+ (* x (+ (* x 1/2) 1)) 2)) |
| 1× | batch-egg-rewrite |
| 4 428× | lower-fma.f32 |
| 4 418× | lower-fma.f64 |
| 4 328× | lower-*.f64 |
| 4 328× | lower-*.f32 |
| 4 210× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 19 | 71 |
| 0 | 37 | 71 |
| 1 | 155 | 71 |
| 2 | 1136 | 71 |
| 0 | 8248 | 71 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
(-.f64 (exp.f64 x) #s(literal -1 binary64)) |
(exp.f64 x) |
(sqrt.f64 #s(literal 2 binary64)) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
(+.f64 #s(literal 2 binary64) x) |
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) |
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
| Outputs |
|---|
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64))) |
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x))))) |
(/.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))) |
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x))) |
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))) |
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x)))) |
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))) |
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x)))) |
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1/4 binary64)) |
(*.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))) |
(*.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))) |
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)))) |
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 x)))) |
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64))) |
(+.f64 (exp.f64 x) #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (exp.f64 x))) |
(+.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (exp.f64 x)))) |
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (exp.f64 x)) #s(literal -1 binary64))) |
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(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/36 binary64) (*.f64 x x))))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64))))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64))))) |
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))) |
(/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/36 binary64) (*.f64 x x))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) #s(literal 1/10077696 binary64) #s(literal 1/512 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/46656 binary64) (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/1728 binary64)))) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/46656 binary64) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal -1/8 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1/46656 binary64) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1296 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) #s(literal 1/144 binary64)))) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1296 binary64) #s(literal -1/16 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64))))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64)))) |
(/.f64 (neg.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/36 binary64) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64))))))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/36 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
| 1× | egg-herbie |
| 11 602× | lower-fma.f64 |
| 11 602× | lower-fma.f32 |
| 5 042× | lower-*.f64 |
| 5 042× | lower-*.f32 |
| 3 340× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 277 | 1514 |
| 1 | 881 | 1294 |
| 2 | 2969 | 1264 |
| 0 | 8377 | 1149 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(sqrt (+ 1 (exp x))) |
(sqrt (+ 1 (exp x))) |
(sqrt (+ 1 (exp x))) |
(sqrt (+ 1 (exp x))) |
(sqrt (+ 1 (exp x))) |
(sqrt (+ 1 (exp x))) |
(sqrt (+ 1 (exp x))) |
(sqrt (+ 1 (exp x))) |
2 |
(+ 2 x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
1 |
(+ 1 x) |
(+ 1 (* x (+ 1 (* 1/2 x)))) |
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3))))) |
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
2 |
(+ 2 x) |
(+ 2 x) |
(+ 2 x) |
x |
(* x (+ 1 (* 2 (/ 1 x)))) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(* x (+ 1 (* 2 (/ 1 x)))) |
x |
(* x (+ 1 (* 2 (/ 1 x)))) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* x (sqrt 1/2)) |
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))) |
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))) |
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))) |
(* -1 (* x (sqrt 1/2))) |
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))) |
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x))))) |
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x))))) |
2 |
(+ 2 x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* 1/2 x)) |
(+ 1 (* 1/2 x)) |
(* 1/2 x) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* 1/2 x) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
2 |
(+ 2 x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3))))))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
1/2 |
(+ 1/2 (* 1/6 x)) |
(+ 1/2 (* 1/6 x)) |
(+ 1/2 (* 1/6 x)) |
(* 1/6 x) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* 1/6 x) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
| Outputs |
|---|
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt (+ 1 (exp x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (+ 1 (exp x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (+ 1 (exp x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (+ 1 (exp x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (+ 1 (exp x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (+ 1 (exp x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (+ 1 (exp x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (+ 1 (exp x))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
2 |
#s(literal 2 binary64) |
(+ 2 x) |
(+.f64 #s(literal 2 binary64) x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(+ 1 (exp x)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(+ 1 (exp x)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(+ 1 (exp x)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(+ 1 (exp x)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(+ 1 (exp x)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(+ 1 (exp x)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(+ 1 (exp x)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(+ 1 (exp x)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 (* x (+ 1 (* 1/2 x)))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
(exp x) |
(exp.f64 x) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 x (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/16 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3))))) |
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5))))))) |
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7)))))))) |
(*.f64 x (+.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(neg.f64 (*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(neg.f64 (*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) |
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x)) |
2 |
#s(literal 2 binary64) |
(+ 2 x) |
(+.f64 #s(literal 2 binary64) x) |
(+ 2 x) |
(+.f64 #s(literal 2 binary64) x) |
(+ 2 x) |
(+.f64 #s(literal 2 binary64) x) |
x |
(* x (+ 1 (* 2 (/ 1 x)))) |
(+.f64 #s(literal 2 binary64) x) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(+.f64 #s(literal 2 binary64) x) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(+.f64 #s(literal 2 binary64) x) |
x |
(* x (+ 1 (* 2 (/ 1 x)))) |
(+.f64 #s(literal 2 binary64) x) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(+.f64 #s(literal 2 binary64) x) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(+.f64 #s(literal 2 binary64) x) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 x (*.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))) |
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))) |
(fma.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/4 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))) |
(+.f64 (fma.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/4 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -3/4 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) |
(* -1 (* x (sqrt 1/2))) |
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))) |
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x))))) |
(-.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x))))) |
(-.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 3/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) |
2 |
#s(literal 2 binary64) |
(+ 2 x) |
(+.f64 #s(literal 2 binary64) x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) |
(* 1/2 (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) |
(* 1/2 (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(+ 1 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(+ 1 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(* x (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(* x (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(* x (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(* x (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(*.f64 (*.f64 x x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(*.f64 (*.f64 x x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x #s(literal 1/6 binary64)) #s(literal -1/16 binary64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))) |
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(*.f64 (*.f64 x x) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (fma.f64 (/.f64 x #s(literal 1/6 binary64)) #s(literal -1/16 binary64) #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))) x) (*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))))) |
2 |
#s(literal 2 binary64) |
(+ 2 x) |
(+.f64 #s(literal 2 binary64) x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(* 1/6 (pow x 3)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3))))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(* 1/6 (pow x 3)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) |
(*.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (neg.f64 (*.f64 x (*.f64 x x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6))) |
(neg.f64 (*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -2 binary64) (*.f64 x x))) x))))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* 1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/6 binary64))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* 1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/6 binary64))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* 1/6 x)) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/6 x)) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/6 x)) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
Compiled 13 939 to 1 906 computations (86.3% saved)
15 alts after pruning (10 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 574 | 10 | 584 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 5 | 5 |
| Done | 0 | 0 | 0 |
| Total | 574 | 15 | 589 |
| Status | Accuracy | Program |
|---|---|---|
| 68.9% | (fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) | |
| ▶ | 69.9% | (fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
| ▶ | 67.7% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))) |
| 3.0% | (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) | |
| 68.7% | (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))) | |
| ✓ | 68.7% | (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ✓ | 70.2% | (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| 2.5% | (sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)) | |
| ▶ | 4.1% | (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)) |
| ✓ | 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| ✓ | 68.6% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ▶ | 3.4% | (sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) |
| 2.3% | (sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))) | |
| ▶ | 2.5% | (sqrt.f64 x) |
| ✓ | 74.4% | (sqrt.f64 #s(literal 2 binary64)) |
Compiled 273 to 184 computations (32.6% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))) |
| ✓ | cost-diff | 0 | (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 0 | (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | cost-diff | 1344 | (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
| 588× | lower-fma.f32 |
| 576× | lower-fma.f64 |
| 286× | lower-*.f32 |
| 280× | lower-*.f64 |
| 164× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 155 |
| 0 | 47 | 155 |
| 1 | 83 | 155 |
| 2 | 151 | 155 |
| 3 | 294 | 154 |
| 4 | 383 | 154 |
| 5 | 437 | 151 |
| 6 | 490 | 151 |
| 7 | 490 | 151 |
| 0 | 490 | 149 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
x |
(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) |
#s(literal 3/16 binary64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
#s(literal 1/2 binary64) |
(sqrt.f64 x) |
x |
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
#s(literal 1/2 binary64) |
(*.f64 x x) |
x |
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) |
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) |
x |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
#s(literal 1/6 binary64) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))) |
#s(literal 1 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
x |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
#s(literal 1/6 binary64) |
#s(literal 1/2 binary64) |
#s(literal 2 binary64) |
| Outputs |
|---|
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
x |
(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) |
#s(literal 3/16 binary64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
#s(literal 1/2 binary64) |
(sqrt.f64 x) |
x |
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)) |
(sqrt.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) |
#s(literal 1/2 binary64) |
(*.f64 x x) |
x |
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) |
(sqrt.f64 (*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) |
(*.f64 x (*.f64 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))) |
x |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
#s(literal 1/6 binary64) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))) |
#s(literal 1 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
x |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
#s(literal 1/6 binary64) |
#s(literal 1/2 binary64) |
#s(literal 2 binary64) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ✓ | accuracy | 99.4% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))) |
| ✓ | accuracy | 100.0% | (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 83.6% | (sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) |
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)) |
| ✓ | accuracy | 100.0% | (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
| ✓ | accuracy | 100.0% | (fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 99.4% | (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
| 59.0ms | 96× | 0 | valid |
| 33.0ms | 160× | 0 | invalid |
Compiled 181 to 31 computations (82.9% saved)
ival-div: 29.0ms (47.8% of total)ival-mult: 12.0ms (19.8% of total)ival-sqrt: 8.0ms (13.2% of total)ival-add: 7.0ms (11.5% of total)const: 4.0ms (6.6% of total)exact: 1.0ms (1.6% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))> |
#<alt (fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (sqrt.f64 #s(literal 2 binary64))> |
#<alt (sqrt.f64 x)> |
#<alt (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))> |
#<alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)> |
#<alt (*.f64 x x)> |
#<alt (sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))> |
#<alt (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))> |
#<alt (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))> |
#<alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))> |
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))))> |
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))> |
#<alt (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))> |
#<alt (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))> |
#<alt (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))> |
| Outputs |
|---|
#<alt (/ 1/2 (sqrt 2))> |
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))> |
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))> |
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))> |
#<alt (* 3/16 (/ x (sqrt 2)))> |
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))> |
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))> |
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))> |
#<alt (* 3/16 (/ x (sqrt 2)))> |
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))> |
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))> |
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))> |
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))> |
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (sqrt x)> |
#<alt (+ (sqrt x) (* 1/4 (sqrt (pow x 3))))> |
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))> |
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))> |
#<alt (* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))> |
#<alt (* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))> |
#<alt (* -1 (* x (sqrt 1/2)))> |
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))> |
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))> |
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/8 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/2 x)))> |
#<alt (* x (+ 1 (* 1/2 x)))> |
#<alt (* x (+ 1 (* 1/2 x)))> |
#<alt (* 1/2 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))> |
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))> |
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))> |
#<alt (* 1/2 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))> |
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))> |
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))> |
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))> |
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))> |
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))> |
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))> |
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))> |
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))> |
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))> |
#<alt (* 1/2 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))> |
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))> |
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* 1/6 x)))> |
#<alt (* x (+ 1/2 (* 1/6 x)))> |
#<alt (* x (+ 1/2 (* 1/6 x)))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt 1/2> |
#<alt (+ 1/2 (* 1/6 x))> |
#<alt (+ 1/2 (* 1/6 x))> |
#<alt (+ 1/2 (* 1/6 x))> |
#<alt (* 1/6 x)> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* 1/6 x)> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))> |
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))> |
#<alt (sqrt 1/2)> |
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))> |
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))> |
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))> |
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt 6))> |
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))) x)> |
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6)))) x)> |
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 18 (* 81 (/ x (pow (sqrt 6) 2)))) (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))))) x)> |
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -6) (sqrt -1))))> |
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1)))) x))> |
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))> |
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* -1 (/ (+ (* -9 (* (sqrt x) (/ (sqrt -1) (sqrt -6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 18 (* -81 (/ x (pow (sqrt -6) 2))))) (sqrt -6))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))> |
#<alt 1/2> |
#<alt (+ 1/2 (* -1/4 x))> |
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))> |
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))> |
#<alt (/ 6 (pow x 3))> |
#<alt (/ (- 6 (* 18 (/ 1 x))) (pow x 3))> |
#<alt (/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))> |
#<alt (/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))> |
#<alt (/ 6 (pow x 3))> |
#<alt (* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))> |
#<alt (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))> |
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))> |
#<alt 2> |
#<alt (+ 2 x)> |
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))> |
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
45 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 7.0ms | x | @ | -inf | (* x (+ (* x 1/6) 1/2)) |
| 2.0ms | x | @ | 0 | (sqrt (/ 1 (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))) |
| 1.0ms | x | @ | -inf | (sqrt (/ 1 (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))) |
| 1.0ms | x | @ | -inf | (sqrt (* x (* x (+ (* x 1/6) 1/2)))) |
| 1.0ms | x | @ | 0 | (+ (* x (/ 3/16 (sqrt 2))) (/ 1/2 (sqrt 2))) |
| 1× | batch-egg-rewrite |
| 5 676× | lower-fma.f32 |
| 5 664× | lower-fma.f64 |
| 3 868× | lower-/.f32 |
| 3 860× | lower-/.f64 |
| 3 708× | lower-*.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 136 |
| 0 | 47 | 136 |
| 1 | 198 | 131 |
| 2 | 1460 | 126 |
| 0 | 8257 | 126 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
(sqrt.f64 x) |
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(*.f64 x x) |
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) |
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
| Outputs |
|---|
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)))) |
(+.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 9/512 binary64)) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) |
(-.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 9/512 binary64)) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/8 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) |
(-.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 9/512 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))) |
(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 #s(literal 3/16 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)))) |
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)))) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)))) |
(fma.f64 (*.f64 (*.f64 x x) #s(literal 9/512 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x #s(literal 16/3 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (*.f64 x #s(literal 3/16 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (neg.f64 (*.f64 x #s(literal 3/16 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (*.f64 x #s(literal -3/16 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (*.f64 #s(literal -3/16 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/2 binary64)) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)))) |
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(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (*.f64 (/.f64 (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (-.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) (*.f64 x #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (+.f64 (/.f64 (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))) |
(*.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))) |
(*.f64 (neg.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))) |
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))) |
| 1× | egg-herbie |
| 12 860× | lower-fma.f64 |
| 12 860× | lower-fma.f32 |
| 5 710× | lower-*.f64 |
| 5 710× | lower-*.f32 |
| 4 296× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 433 | 2238 |
| 1 | 1331 | 2124 |
| 2 | 4089 | 2062 |
| 0 | 8314 | 1913 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ 1/2 (sqrt 2)) |
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))) |
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))) |
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))) |
(* 3/16 (/ x (sqrt 2))) |
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(* 3/16 (/ x (sqrt 2))) |
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2))))) |
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2))))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2))))) |
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2))))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt x) |
(+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x)))))))) |
(* x (sqrt 1/2)) |
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))) |
(* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3))))) |
(* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) |
(* -1 (* x (sqrt 1/2))) |
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))) |
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ 1 (sqrt 1/2)))) x))))) |
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/8 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x))))) |
x |
(* x (+ 1 (* 1/2 x))) |
(* x (+ 1 (* 1/2 x))) |
(* x (+ 1 (* 1/2 x))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* x (sqrt 1/2)) |
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))) |
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))) |
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (* 1/6 x))) |
(* (pow x 2) (+ 1/2 (* 1/6 x))) |
(* (pow x 2) (+ 1/2 (* 1/6 x))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/6 x))) |
(* x (+ 1/2 (* 1/6 x))) |
(* x (+ 1/2 (* 1/6 x))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
1/2 |
(+ 1/2 (* 1/6 x)) |
(+ 1/2 (* 1/6 x)) |
(+ 1/2 (* 1/6 x)) |
(* 1/6 x) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* 1/6 x) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2)))) |
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2)))))) |
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2)))))) |
(* (sqrt (/ 1 (pow x 3))) (sqrt 6)) |
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))) x) |
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6)))) x) |
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 18 (* 81 (/ x (pow (sqrt 6) 2)))) (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))))) x) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -6) (sqrt -1)))) |
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1)))) x)) |
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x)) |
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* -1 (/ (+ (* -9 (* (sqrt x) (/ (sqrt -1) (sqrt -6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 18 (* -81 (/ x (pow (sqrt -6) 2))))) (sqrt -6))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x)) |
1/2 |
(+ 1/2 (* -1/4 x)) |
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4))) |
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4))) |
(/ 6 (pow x 3)) |
(/ (- 6 (* 18 (/ 1 x))) (pow x 3)) |
(/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3)) |
(/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3)) |
(/ 6 (pow x 3)) |
(* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3))) |
(* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3))) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3))) |
2 |
(+ 2 x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3))))))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
| Outputs |
|---|
(/ 1/2 (sqrt 2)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) |
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) |
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) |
(* 3/16 (/ x (sqrt 2))) |
(/.f64 (*.f64 #s(literal 3/16 binary64) x) (sqrt.f64 #s(literal 2 binary64))) |
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) |
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) |
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) |
(* 3/16 (/ x (sqrt 2))) |
(/.f64 (*.f64 #s(literal 3/16 binary64) x) (sqrt.f64 #s(literal 2 binary64))) |
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) |
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) |
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(/.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) |
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) |
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2))))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)))) |
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2))))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(/.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) |
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) |
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2))))) |
(*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x))) |
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2))))) |
(*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x))) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) |
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 x)) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))))) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/32 binary64) #s(literal 1 binary64)) (sqrt.f64 x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x)))))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x)) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))) |
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3))))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))) |
(* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) |
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x x)))) (fma.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) |
(* -1 (* x (sqrt 1/2))) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (neg.f64 x)) |
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))) |
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ 1 (sqrt 1/2)))) x))))) |
(neg.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x x)))))))) |
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/8 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x))))) |
(-.f64 (fma.f64 x (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/16 binary64) (*.f64 x (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))))) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) |
x |
(* x (+ 1 (* 1/2 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(* x (+ 1 (* 1/2 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(* x (+ 1 (* 1/2 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(* 1/2 (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(* 1/2 (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))) |
(*.f64 x (fma.f64 x (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))) |
(*.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal -1/144 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/3456 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/144 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(*.f64 (*.f64 x x) (fma.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/128 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal 1/6 binary64)) #s(literal 5 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)) (*.f64 (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))) |
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal 3/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal 3/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) #s(literal 1/4 binary64)) (*.f64 (/.f64 (*.f64 #s(literal 1/128 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))) |
(* 1/2 (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (* 1/6 x))) |
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (+ 1/2 (* 1/6 x))) |
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (+ 1/2 (* 1/6 x))) |
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* 1/6 (pow x 3)) |
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* 1/6 (pow x 3)) |
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* 1/6 x))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* 1/6 x))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* 1/6 x))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* 1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/6 binary64))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* 1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/6 binary64))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* 1/6 x)) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/6 x)) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/6 x)) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(*.f64 (*.f64 x x) (fma.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(*.f64 x (*.f64 x (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(*.f64 x (*.f64 x (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 x #s(literal -1/6 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/6 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))) |
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(*.f64 x (*.f64 x (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 x #s(literal -1/6 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64))))) x) (*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))) |
(sqrt 1/2) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2)))) |
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) |
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2)))))) |
(fma.f64 x (fma.f64 x (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2)))))) |
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/512 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(* (sqrt (/ 1 (pow x 3))) (sqrt 6)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 6 binary64))) |
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 6 binary64)) (*.f64 (/.f64 #s(literal -9 binary64) (sqrt.f64 #s(literal 6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) x) |
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6)))) x) |
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -9 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 9 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 6 binary64)))) x) |
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 18 (* 81 (/ x (pow (sqrt 6) 2)))) (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 6 binary64)) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 9 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -9 binary64))) (*.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal 81 binary64) (/.f64 x #s(literal 6 binary64)) #s(literal 18 binary64))) (sqrt.f64 #s(literal 6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) x) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -6) (sqrt -1)))) |
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -6 binary64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) |
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1)))) x)) |
(/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -6 binary64))) (*.f64 #s(literal -9 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 #s(literal -6 binary64))))) (neg.f64 x)) |
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x)) |
(/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 9 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -9 binary64))) (*.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x)) |
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* -1 (/ (+ (* -9 (* (sqrt x) (/ (sqrt -1) (sqrt -6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 18 (* -81 (/ x (pow (sqrt -6) 2))))) (sqrt -6))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x)) |
(/.f64 (-.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -6 binary64))) (*.f64 #s(literal -9 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 #s(literal -6 binary64))))) (/.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -81 binary64) (/.f64 x #s(literal -6 binary64)) #s(literal 18 binary64))) (sqrt.f64 #s(literal -6 binary64))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (*.f64 (*.f64 (sqrt.f64 x) #s(literal -9 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 x (*.f64 x x)))) (neg.f64 x)) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/4 x)) |
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4))) |
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) |
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4))) |
(fma.f64 x (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/96 binary64) #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) |
(/ 6 (pow x 3)) |
(/.f64 #s(literal 6 binary64) (*.f64 x (*.f64 x x))) |
(/ (- 6 (* 18 (/ 1 x))) (pow x 3)) |
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (*.f64 x (*.f64 x x))) |
(/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3)) |
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) x) #s(literal -18 binary64)) x)) (*.f64 x (*.f64 x x))) |
(/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3)) |
(/.f64 (+.f64 (+.f64 #s(literal 6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) x) #s(literal -18 binary64)) x)) (/.f64 #s(literal -18 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x))) |
(/ 6 (pow x 3)) |
(/.f64 #s(literal 6 binary64) (*.f64 x (*.f64 x x))) |
(* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3))) |
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (*.f64 x (*.f64 x x))) |
(* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3))) |
(/.f64 (+.f64 #s(literal -6 binary64) (/.f64 (+.f64 #s(literal 18 binary64) (/.f64 #s(literal -18 binary64) x)) x)) (neg.f64 (*.f64 x (*.f64 x x)))) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3))) |
(/.f64 (-.f64 #s(literal -6 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 18 binary64) (/.f64 #s(literal -18 binary64) x)) x) #s(literal -18 binary64)) x)) (neg.f64 (*.f64 x (*.f64 x x)))) |
2 |
#s(literal 2 binary64) |
(+ 2 x) |
(+.f64 #s(literal 2 binary64) x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(* 1/6 (pow x 3)) |
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3))))))) |
(*.f64 x (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64))))) |
(* 1/6 (pow x 3)) |
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) |
(*.f64 (*.f64 x (*.f64 x x)) (neg.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6))) |
(*.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -2 binary64) (*.f64 x x))) x)) (neg.f64 (*.f64 x (*.f64 x x)))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* 1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/6 binary64))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* 1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/6 binary64))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
Compiled 23 475 to 3 115 computations (86.7% saved)
21 alts after pruning (15 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 925 | 12 | 937 |
| Fresh | 2 | 3 | 5 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 5 | 5 |
| Total | 931 | 21 | 952 |
| Status | Accuracy | Program |
|---|---|---|
| 69.9% | (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) | |
| ▶ | 69.9% | (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64))) |
| 1.3% | (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x)) | |
| 68.9% | (fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) | |
| 68.8% | (fma.f64 x (/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) | |
| 69.9% | (fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) | |
| 4.2% | (/.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) | |
| ▶ | 67.7% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) |
| ▶ | 69.6% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) |
| ▶ | 73.3% | (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
| 69.9% | (+.f64 (*.f64 x (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) | |
| 4.0% | (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) | |
| 2.7% | (*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x) | |
| ▶ | 3.0% | (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
| ✓ | 68.7% | (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ✓ | 70.2% | (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| 2.5% | (sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)) | |
| ✓ | 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| ✓ | 68.6% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ✓ | 2.5% | (sqrt.f64 x) |
| ✓ | 74.4% | (sqrt.f64 #s(literal 2 binary64)) |
Compiled 448 to 300 computations (33% saved)
| 1× | egg-herbie |
Found 15 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | cost-diff | 320 | (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 640 | (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | cost-diff | 960 | (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) |
| ✓ | cost-diff | 0 | (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) |
| ✓ | cost-diff | 0 | (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
| 652× | lower-fma.f32 |
| 642× | lower-fma.f64 |
| 574× | lower-*.f32 |
| 564× | lower-*.f64 |
| 362× | associate-*r* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 134 |
| 0 | 46 | 134 |
| 1 | 73 | 128 |
| 2 | 118 | 128 |
| 3 | 215 | 124 |
| 4 | 402 | 124 |
| 5 | 513 | 124 |
| 6 | 527 | 124 |
| 7 | 541 | 124 |
| 8 | 541 | 124 |
| 9 | 654 | 124 |
| 10 | 654 | 124 |
| 11 | 683 | 124 |
| 12 | 683 | 124 |
| 13 | 685 | 124 |
| 0 | 685 | 120 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
#s(literal 1 binary64) |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
x |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) |
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) |
x |
#s(literal -1/4 binary64) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) |
x |
(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) |
(*.f64 x x) |
#s(literal 1/48 binary64) |
#s(literal -1/4 binary64) |
#s(literal 1/2 binary64) |
(fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) |
#s(literal 1/2 binary64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64))) |
(*.f64 x #s(literal 3/16 binary64)) |
x |
#s(literal 3/16 binary64) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
#s(literal 1 binary64) |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) |
x |
(sqrt.f64 #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) |
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) |
x |
#s(literal -1/4 binary64) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) |
(sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) |
x |
(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) |
(fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) |
(*.f64 x x) |
#s(literal 1/48 binary64) |
#s(literal -1/4 binary64) |
#s(literal 1/2 binary64) |
(fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64))) |
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) |
#s(literal 1/2 binary64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) |
(*.f64 x #s(literal 3/16 binary64)) |
x |
#s(literal 3/16 binary64) |
Found 15 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal 3/16 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) |
| ✓ | accuracy | 99.4% | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64))) |
| ✓ | accuracy | 100.0% | (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 99.0% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 100.0% | (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 99.0% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 #s(literal 1/2 binary64)) |
| ✓ | accuracy | 99.5% | (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 #s(literal 1/2 binary64)) |
| ✓ | accuracy | 98.9% | (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
| 38.0ms | 176× | 0 | valid |
| 16.0ms | 80× | 0 | invalid |
Compiled 150 to 31 computations (79.3% saved)
ival-mult: 17.0ms (43.6% of total)ival-sqrt: 7.0ms (18% of total)ival-add: 6.0ms (15.4% of total)ival-div: 5.0ms (12.8% of total)const: 4.0ms (10.3% of total)exact: 1.0ms (2.6% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))> |
#<alt (sqrt.f64 #s(literal 1/2 binary64))> |
#<alt (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))> |
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))> |
#<alt (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))> |
#<alt (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))> |
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))> |
#<alt (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))> |
#<alt (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))> |
#<alt (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64))> |
#<alt (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64))))> |
#<alt (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))> |
#<alt (sqrt.f64 #s(literal 2 binary64))> |
#<alt (*.f64 x x)> |
#<alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))> |
#<alt (*.f64 x #s(literal 3/16 binary64))> |
| Outputs |
|---|
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* (sqrt (/ 1 x)) (sqrt -4))> |
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))> |
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))> |
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))> |
#<alt (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))> |
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))> |
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))> |
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))> |
#<alt (sqrt 1/2)> |
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))> |
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))> |
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))> |
#<alt (* (sqrt x) (sqrt -1/4))> |
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))> |
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))> |
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))> |
#<alt (* -1/2 (* (sqrt x) (sqrt -1)))> |
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))> |
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))> |
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))> |
#<alt 1/2> |
#<alt (+ 1/2 (* -1/4 x))> |
#<alt (+ 1/2 (* -1/4 x))> |
#<alt (+ 1/2 (* -1/4 x))> |
#<alt (* -1/4 x)> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))> |
#<alt (* -1/4 x)> |
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt 48))> |
#<alt (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))) x)> |
#<alt (/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48)))) x)> |
#<alt (/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (+ (* 3456 (* (sqrt (/ 1 (pow x 9))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))))) x)> |
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -48) (sqrt -1))))> |
#<alt (* -1 (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -48)))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))> |
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 576 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))> |
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* -1 (/ (+ (* -576 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 3456 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) x))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))> |
#<alt (sqrt 1/2)> |
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))> |
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))> |
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/48))> |
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48))))> |
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48)))))> |
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 9))) (/ 1 (pow (sqrt 1/48) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48))))))> |
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/48)))> |
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/48)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -1/48)))) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (sqrt -1/48) 3)))) (* 1/4 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) x)) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))> |
#<alt 1/2> |
#<alt (+ 1/2 (* -1/4 x))> |
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))> |
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))> |
#<alt (* 1/48 (pow x 3))> |
#<alt (* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* 1/48 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))> |
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))> |
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))> |
#<alt -1/4> |
#<alt (- (* 1/48 (pow x 2)) 1/4)> |
#<alt (- (* 1/48 (pow x 2)) 1/4)> |
#<alt (- (* 1/48 (pow x 2)) 1/4)> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* 1/2 (sqrt 2))> |
#<alt (+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))> |
#<alt (+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))> |
#<alt (+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))> |
#<alt (* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))> |
#<alt (* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))> |
#<alt (* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))> |
#<alt (* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/4 (* x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))> |
#<alt (+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))> |
#<alt (* 3/32 (* (pow x 2) (sqrt 2)))> |
#<alt (* (pow x 2) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))> |
#<alt (* (pow x 2) (+ (* 3/32 (sqrt 2)) (+ (* 1/4 (/ (sqrt 2) x)) (/ (sqrt 2) (pow x 2)))))> |
#<alt (* (pow x 2) (+ (* 3/32 (sqrt 2)) (+ (* 1/4 (/ (sqrt 2) x)) (/ (sqrt 2) (pow x 2)))))> |
#<alt (* 3/32 (* (pow x 2) (sqrt 2)))> |
#<alt (* (pow x 2) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))))> |
#<alt (* 1/4 (sqrt 2))> |
#<alt (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))> |
#<alt (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))> |
#<alt (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))> |
#<alt (* 3/32 (* x (sqrt 2)))> |
#<alt (* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))> |
#<alt (* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))> |
#<alt (* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))))> |
#<alt (* 3/32 (* x (sqrt 2)))> |
#<alt (* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2)))))> |
#<alt (* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2)))))> |
#<alt (* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2)))))> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* 3/16 (* x (sqrt 2)))> |
#<alt (* 3/16 x)> |
#<alt (* 3/16 x)> |
#<alt (* 3/16 x)> |
#<alt (* 3/16 x)> |
#<alt (* 3/16 x)> |
#<alt (* 3/16 x)> |
#<alt (* 3/16 x)> |
#<alt (* 3/16 x)> |
#<alt (* 3/16 x)> |
#<alt (* 3/16 x)> |
#<alt (* 3/16 x)> |
#<alt (* 3/16 x)> |
42 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | inf | (sqrt (+ (* x (+ (* (* x x) 1/48) -1/4)) 1/2)) |
| 1.0ms | x | @ | -inf | (sqrt (+ (* x (+ (* (* x x) 1/48) -1/4)) 1/2)) |
| 1.0ms | x | @ | inf | (sqrt (+ (* x -1/4) 1/2)) |
| 1.0ms | x | @ | -inf | (/ 1 (sqrt (+ (* x (+ (* (* x x) 1/48) -1/4)) 1/2))) |
| 1.0ms | x | @ | inf | (/ 1 (sqrt (+ (* x -1/4) 1/2))) |
| 1× | batch-egg-rewrite |
| 8 050× | lower-fma.f32 |
| 8 040× | lower-fma.f64 |
| 5 606× | lower-*.f32 |
| 5 596× | lower-*.f64 |
| 3 276× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 115 |
| 0 | 46 | 115 |
| 1 | 161 | 106 |
| 2 | 1059 | 106 |
| 0 | 8385 | 103 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) |
(sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) |
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) |
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) |
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) |
(fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) |
(sqrt.f64 #s(literal 2 binary64)) |
(*.f64 x x) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64))) |
(*.f64 x #s(literal 3/16 binary64)) |
| Outputs |
|---|
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) |
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) |
(pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64)) |
(pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64))) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64)))) |
(exp.f64 (neg.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64)))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(neg.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(/.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64)) |
(pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64)) |
(pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64)) |
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) |
(/.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) |
(*.f64 (*.f64 x (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) #s(literal -1/2 binary64))) |
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))) |
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))) |
(pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) |
(pow.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))) |
(*.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (fma.f64 #s(literal -1/64 binary64) (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/8 binary64)))) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (fma.f64 x (*.f64 #s(literal 1/16 binary64) x) #s(literal -1/4 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64))) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64))) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))) |
(exp.f64 (neg.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))) |
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(/.f64 (neg.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 x x) #s(literal 9/256 binary64)))))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -3/16 binary64)))))) |
(/.f64 (neg.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal 9/256 binary64)) (fma.f64 x #s(literal -3/16 binary64) #s(literal 1/2 binary64))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 x x) #s(literal 9/256 binary64)))) #s(literal 1/2 binary64))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -3/16 binary64)))))) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 #s(literal 1/8 binary64) (-.f64 (*.f64 (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))))) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1/8 binary64) (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) (-.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))))) |
(/.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))) (-.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))) |
(/.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (-.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1/8 binary64)) (-.f64 (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (-.f64 (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 3/16 binary64)))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal 9/256 binary64)) (fma.f64 x #s(literal -3/16 binary64) #s(literal 1/2 binary64))))) |
(*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 x x) #s(literal 9/256 binary64))))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -3/16 binary64)))))) |
(*.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal 9/256 binary64)) (fma.f64 x #s(literal -3/16 binary64) #s(literal 1/2 binary64))))) |
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 x x) #s(literal 9/256 binary64)))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -3/16 binary64)))))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 x x) #s(literal 9/256 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -3/16 binary64))))) |
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 x x) #s(literal 9/256 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -3/16 binary64))))) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))) |
(sqrt.f64 #s(literal 2 binary64)) |
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) |
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) |
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) |
(pow.f64 x #s(literal 2 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64)) |
(*.f64 x x) |
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x))) |
(*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64))) |
(*.f64 #s(literal 3/16 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) |
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)) x) |
(*.f64 (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) |
(*.f64 (*.f64 (*.f64 x #s(literal 3/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) |
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 3/16 binary64))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 3/16 binary64)))) |
(*.f64 x #s(literal 3/16 binary64)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) |
(*.f64 #s(literal 3/16 binary64) x) |
(*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(*.f64 (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 x (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 3/16 binary64)) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 3/16 binary64))) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x) (*.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) x) |
(*.f64 (*.f64 (*.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) |
| 1× | egg-herbie |
| 10 996× | lower-fma.f64 |
| 10 996× | lower-fma.f32 |
| 6 268× | lower-*.f64 |
| 6 268× | lower-*.f32 |
| 3 494× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 380 | 2194 |
| 1 | 1078 | 1989 |
| 2 | 3345 | 1914 |
| 3 | 6961 | 1914 |
| 0 | 8042 | 1825 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* (sqrt (/ 1 x)) (sqrt -4)) |
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))) |
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))) |
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))) |
(* 2 (* (sqrt (/ 1 x)) (sqrt -1))) |
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))) |
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))) |
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2)))) |
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2)))))) |
(+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2)))))) |
(* (sqrt x) (sqrt -1/4)) |
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))) |
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))) |
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))) |
(* -1/2 (* (sqrt x) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))) |
1/2 |
(+ 1/2 (* -1/4 x)) |
(+ 1/2 (* -1/4 x)) |
(+ 1/2 (* -1/4 x)) |
(* -1/4 x) |
(* x (- (* 1/2 (/ 1 x)) 1/4)) |
(* x (- (* 1/2 (/ 1 x)) 1/4)) |
(* x (- (* 1/2 (/ 1 x)) 1/4)) |
(* -1/4 x) |
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x))))) |
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x))))) |
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x))))) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* (sqrt (/ 1 (pow x 3))) (sqrt 48)) |
(/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))) x) |
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48)))) x) |
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (+ (* 3456 (* (sqrt (/ 1 (pow x 9))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))))) x) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -48) (sqrt -1)))) |
(* -1 (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -48)))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x)) |
(* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 576 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x)) |
(* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* -1 (/ (+ (* -576 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 3456 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) x))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x)) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2)))) |
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2)))))) |
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2)))))) |
(* (sqrt (pow x 3)) (sqrt 1/48)) |
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48)))) |
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48))))) |
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 9))) (/ 1 (pow (sqrt 1/48) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48)))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/48))) |
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/48)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -1/48)))) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (sqrt -1/48) 3)))) (* 1/4 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) x)) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48))))) |
1/2 |
(+ 1/2 (* -1/4 x)) |
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4))) |
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4))) |
(* 1/48 (pow x 3)) |
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) |
(* 1/48 (pow x 3)) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48))) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3)))))) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3)))))) |
-1/4 |
(- (* 1/48 (pow x 2)) 1/4) |
(- (* 1/48 (pow x 2)) 1/4) |
(- (* 1/48 (pow x 2)) 1/4) |
(* 1/48 (pow x 2)) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* 1/48 (pow x 2)) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* 1/2 (sqrt 2)) |
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2))) |
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2))) |
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2))) |
(* 3/16 (* x (sqrt 2))) |
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x)))) |
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x)))) |
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x)))) |
(* 3/16 (* x (sqrt 2))) |
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))))) |
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))))) |
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))))) |
(sqrt 2) |
(+ (sqrt 2) (* 1/4 (* x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2))))) |
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2))))) |
(* 3/32 (* (pow x 2) (sqrt 2))) |
(* (pow x 2) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x)))) |
(* (pow x 2) (+ (* 3/32 (sqrt 2)) (+ (* 1/4 (/ (sqrt 2) x)) (/ (sqrt 2) (pow x 2))))) |
(* (pow x 2) (+ (* 3/32 (sqrt 2)) (+ (* 1/4 (/ (sqrt 2) x)) (/ (sqrt 2) (pow x 2))))) |
(* 3/32 (* (pow x 2) (sqrt 2))) |
(* (pow x 2) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2)))) |
(* 1/4 (sqrt 2)) |
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2))) |
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2))) |
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2))) |
(* 3/32 (* x (sqrt 2))) |
(* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x)))) |
(* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x)))) |
(* x (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x)))) |
(* 3/32 (* x (sqrt 2))) |
(* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))))) |
(* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))))) |
(* -1 (* x (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* 3/16 (* x (sqrt 2))) |
(* 3/16 (* x (sqrt 2))) |
(* 3/16 (* x (sqrt 2))) |
(* 3/16 (* x (sqrt 2))) |
(* 3/16 (* x (sqrt 2))) |
(* 3/16 (* x (sqrt 2))) |
(* 3/16 (* x (sqrt 2))) |
(* 3/16 (* x (sqrt 2))) |
(* 3/16 (* x (sqrt 2))) |
(* 3/16 (* x (sqrt 2))) |
(* 3/16 (* x (sqrt 2))) |
(* 3/16 (* x (sqrt 2))) |
(* 3/16 x) |
(* 3/16 x) |
(* 3/16 x) |
(* 3/16 x) |
(* 3/16 x) |
(* 3/16 x) |
(* 3/16 x) |
(* 3/16 x) |
(* 3/16 x) |
(* 3/16 x) |
(* 3/16 x) |
(* 3/16 x) |
| Outputs |
|---|
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 5/64 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ 1 x)) (sqrt -4)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) |
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -4 binary64) (sqrt.f64 #s(literal -4 binary64))))) |
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -4 binary64))) (fma.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64)))) |
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -4 binary64))) (fma.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 x #s(literal -4 binary64) #s(literal 32 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -4 binary64)))))) |
(* 2 (* (sqrt (/ 1 x)) (sqrt -1))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))) |
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -2 binary64)))) |
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -2 binary64))))) |
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))) |
(-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -2 binary64)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 x #s(literal -4 binary64) #s(literal 32 binary64)) (*.f64 #s(literal 4 binary64) (sqrt.f64 x)))) (*.f64 x (*.f64 x x)))) |
(sqrt 1/2) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2)))) |
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) |
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2)))))) |
(fma.f64 x (fma.f64 x (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2)))))) |
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal -1/1024 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) |
(* (sqrt x) (sqrt -1/4)) |
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1/4 binary64))) |
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1/4 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64))))) |
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))) |
(*.f64 x (fma.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1/4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1/4 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64)))))) |
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))) |
(*.f64 x (fma.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1/4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1/4 binary64)) #s(literal 5 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1/4 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64))))))) |
(* -1/2 (* (sqrt x) (sqrt -1))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))) |
(*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))) |
(*.f64 x (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64)))))) |
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))) |
(*.f64 x (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))))) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/4 x)) |
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* -1/4 x)) |
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* -1/4 x)) |
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) |
(* -1/4 x) |
(*.f64 x #s(literal -1/4 binary64)) |
(* x (- (* 1/2 (/ 1 x)) 1/4)) |
(*.f64 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/2 binary64) x))) |
(* x (- (* 1/2 (/ 1 x)) 1/4)) |
(*.f64 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/2 binary64) x))) |
(* x (- (* 1/2 (/ 1 x)) 1/4)) |
(*.f64 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/2 binary64) x))) |
(* -1/4 x) |
(*.f64 x #s(literal -1/4 binary64)) |
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x))))) |
(*.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (neg.f64 x)) |
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x))))) |
(*.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (neg.f64 x)) |
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x))))) |
(*.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (neg.f64 x)) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(* (sqrt (/ 1 (pow x 3))) (sqrt 48)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 48 binary64))) |
(/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 288 binary64) (sqrt.f64 #s(literal 48 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 48 binary64)))) x) |
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48)))) x) |
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 48 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 288 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal -576 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 48 binary64)))) x) |
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (+ (* 3456 (* (sqrt (/ 1 (pow x 9))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))))) x) |
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 48 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal -576 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 288 binary64) (*.f64 #s(literal 3456 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 9 binary64))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 48 binary64)))) x) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -48) (sqrt -1)))) |
(neg.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -48 binary64)))) |
(* -1 (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -48)))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 288 binary64)) (sqrt.f64 #s(literal -48 binary64))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -48 binary64)))) (neg.f64 x)) |
(* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 576 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x)) |
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(sqrt 1/2) |
(sqrt.f64 #s(literal 1/2 binary64)) |
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2)))) |
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) |
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2)))))) |
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(* (sqrt (pow x 3)) (sqrt 1/48)) |
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(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 9))) (/ 1 (pow (sqrt 1/48) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48)))))) |
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(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/48))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/48 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x))))) |
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/48)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48))))) |
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(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (sqrt -1/48) 3)))) (* 1/4 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) x)) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48))))) |
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1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/4 x)) |
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4))) |
(fma.f64 x (fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) |
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4))) |
(fma.f64 x (fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) |
(* 1/48 (pow x 3)) |
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/48 binary64)) |
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) |
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(* 1/48 (pow x 3)) |
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-1/4 |
#s(literal -1/4 binary64) |
(- (* 1/48 (pow x 2)) 1/4) |
(fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64)) |
(- (* 1/48 (pow x 2)) 1/4) |
(fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64)) |
(- (* 1/48 (pow x 2)) 1/4) |
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(* 1/48 (pow x 2)) |
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(*.f64 (*.f64 x x) (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) |
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(*.f64 (*.f64 x x) (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) |
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(*.f64 (*.f64 x x) (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) |
(* 1/48 (pow x 2)) |
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(* 1/2 (sqrt 2)) |
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(* 3/16 (* x (sqrt 2))) |
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(sqrt 2) |
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(* 3/32 (* (pow x 2) (sqrt 2))) |
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(* 1/4 (sqrt 2)) |
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(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64))) |
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(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64))) |
(* 3/32 (* x (sqrt 2))) |
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(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x)))) |
(* 3/32 (* x (sqrt 2))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/32 binary64))) |
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(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x)))) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* 3/16 (* x (sqrt 2))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) |
(* 3/16 (* x (sqrt 2))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) |
(* 3/16 (* x (sqrt 2))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) |
(* 3/16 (* x (sqrt 2))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) |
(* 3/16 (* x (sqrt 2))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) |
(* 3/16 (* x (sqrt 2))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) |
(* 3/16 (* x (sqrt 2))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) |
(* 3/16 (* x (sqrt 2))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) |
(* 3/16 (* x (sqrt 2))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) |
(* 3/16 (* x (sqrt 2))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) |
(* 3/16 (* x (sqrt 2))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) |
(* 3/16 (* x (sqrt 2))) |
(*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) |
(* 3/16 x) |
(*.f64 x #s(literal 3/16 binary64)) |
(* 3/16 x) |
(*.f64 x #s(literal 3/16 binary64)) |
(* 3/16 x) |
(*.f64 x #s(literal 3/16 binary64)) |
(* 3/16 x) |
(*.f64 x #s(literal 3/16 binary64)) |
(* 3/16 x) |
(*.f64 x #s(literal 3/16 binary64)) |
(* 3/16 x) |
(*.f64 x #s(literal 3/16 binary64)) |
(* 3/16 x) |
(*.f64 x #s(literal 3/16 binary64)) |
(* 3/16 x) |
(*.f64 x #s(literal 3/16 binary64)) |
(* 3/16 x) |
(*.f64 x #s(literal 3/16 binary64)) |
(* 3/16 x) |
(*.f64 x #s(literal 3/16 binary64)) |
(* 3/16 x) |
(*.f64 x #s(literal 3/16 binary64)) |
(* 3/16 x) |
(*.f64 x #s(literal 3/16 binary64)) |
Compiled 17 127 to 2 308 computations (86.5% saved)
18 alts after pruning (8 fresh and 10 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 723 | 5 | 728 |
| Fresh | 7 | 3 | 10 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 6 | 6 |
| Total | 731 | 18 | 749 |
| Status | Accuracy | Program |
|---|---|---|
| 69.9% | (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) | |
| 1.3% | (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x)) | |
| 68.9% | (fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 5/64 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) | |
| 68.8% | (fma.f64 x (/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) | |
| ✓ | 67.7% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | 69.6% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) |
| ✓ | 73.3% | (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
| 68.9% | (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) | |
| 2.7% | (*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x) | |
| 69.9% | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 3/32 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)))) | |
| 4.2% | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 3/32 binary64))) | |
| ✓ | 3.0% | (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
| ✓ | 68.7% | (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ✓ | 70.2% | (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ✓ | 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| ✓ | 68.6% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ✓ | 2.5% | (sqrt.f64 x) |
| ✓ | 74.4% | (sqrt.f64 #s(literal 2 binary64)) |
Compiled 570 to 261 computations (54.2% saved)
| Inputs |
|---|
(sqrt.f64 #s(literal 2 binary64)) |
(sqrt.f64 x) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)) |
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x) |
(*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 3/32 binary64))) |
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) |
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) |
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(/.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 3/32 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))) |
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) |
(+.f64 (*.f64 x (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 5/64 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x)) |
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) |
| Outputs |
|---|
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
3 calls:
| 15.0ms | x |
| 10.0ms | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
| 7.0ms | (sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | (sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) |
| 100.0% | 1 | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
Compiled 27 to 20 computations (25.9% saved)
Total -47.1b remaining (-287.1%)
Threshold costs -47.1b (-287.1%)
| Inputs |
|---|
(sqrt.f64 #s(literal 2 binary64)) |
(sqrt.f64 x) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)) |
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x) |
(*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) |
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 3/32 binary64))) |
(sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) |
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) |
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(/.f64 (*.f64 #s(literal 3/16 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 3/32 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))) |
(sqrt.f64 (fma.f64 x (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) |
(+.f64 (*.f64 x (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 5/64 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x)) |
| Outputs |
|---|
(sqrt.f64 #s(literal 2 binary64)) |
3 calls:
| 9.0ms | x |
| 7.0ms | (sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) |
| 7.0ms | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 74.4% | 1 | x |
| 74.4% | 1 | (sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) |
| 74.4% | 1 | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
Compiled 27 to 20 computations (25.9% saved)
| 1× | egg-herbie |
| 4× | +-commutative_binary64 |
| 4× | sub-neg_binary64 |
| 2× | neg-sub0_binary64 |
| 2× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 7 | 7 |
| 1 | 9 | 7 |
| 2 | 13 | 7 |
| 3 | 14 | 7 |
| 4 | 15 | 7 |
| 1× | saturated |
| Inputs |
|---|
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
| Outputs |
|---|
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
| 18 226× | lower-fma.f64 |
| 18 226× | lower-fma.f32 |
| 5 402× | lower-fma.f64 |
| 5 402× | lower-fma.f32 |
| 4 492× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 49 | 342 |
| 1 | 155 | 342 |
| 2 | 335 | 342 |
| 3 | 752 | 342 |
| 4 | 1201 | 302 |
| 5 | 1536 | 286 |
| 6 | 2025 | 286 |
| 7 | 2949 | 286 |
| 8 | 4633 | 286 |
| 0 | 8302 | 232 |
| 0 | 9 | 26 |
| 0 | 15 | 26 |
| 1 | 56 | 19 |
| 2 | 378 | 19 |
| 3 | 4533 | 19 |
| 0 | 8161 | 15 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 17 to 15 computations (11.8% saved)
Compiled 42 to 34 computations (19% saved)
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