
Time bar (total: 10.2s)
| 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)
| 455.0ms | 8 256× | 0 | valid |
| 161.0ms | 2 620× | 0 | exit |
ival-expm1: 133.0ms (31.9% of total)ival-mult: 97.0ms (23.3% of total)ival-div: 91.0ms (21.9% of total)ival-sqrt: 77.0ms (18.5% of total)ival-true: 8.0ms (1.9% of total)exact: 6.0ms (1.4% 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 |
|---|---|---|---|---|---|
| 164 | 0 | - | 1 | (0.01132248742408843) | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) |
| 164 | 0 | - | 1 | (0.025343369726707348) | (-.f64 (exp.f64 x) #s(literal 1 binary64)) |
| 4 | 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 | (-150.58615529019949) | 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 | 163 | 3 |
-.f64 | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) | cancellation | 163 | 1 |
/.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 | 4 | 0 |
| ↳ | (exp.f64 (*.f64 #s(literal 2 binary64) x)) | overflow | 4 | |
| ↳ | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) | overflow | 4 | |
| ↳ | (exp.f64 x) | overflow | 4 | |
| ↳ | (-.f64 (exp.f64 x) #s(literal 1 binary64)) | overflow | 4 | |
exp.f64 | (exp.f64 (*.f64 #s(literal 2 binary64) x)) | sensitivity | 1 | 2 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 166 | 1 |
| - | 2 | 87 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 166 | 1 | 0 |
| - | 2 | 4 | 83 |
| number | freq |
|---|---|
| 0 | 88 |
| 1 | 5 |
| 2 | 163 |
| 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 (28.1% of total)ival-expm1: 6.0ms (24.1% of total)ival-mult: 4.0ms (16.1% of total)ival-div: 3.0ms (12.1% of total)ival-sqrt: 3.0ms (12.1% of total)exact: 1.0ms (4% 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 |
|---|---|---|
| ▶ | 35.9% | (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% | (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 | 98.7% | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
| ✓ | accuracy | 40.5% | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) |
| ✓ | accuracy | 40.5% | (-.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 (24.5% of total)ival-expm1: 3.0ms (24.5% of total)ival-div: 2.0ms (16.3% of total)ival-mult: 2.0ms (16.3% of total)ival-sqrt: 2.0ms (16.3% 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 (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 |
|---|
#<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 (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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))> |
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))> |
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))> |
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))> |
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))> |
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))> |
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))> |
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))> |
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 | (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
| 0.0ms | x | @ | 0 | (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
| 0.0ms | x | @ | 0 | (- (exp (* 2 x)) 1) |
| 1× | batch-egg-rewrite |
| 4 562× | lower-fma.f64 |
| 4 562× | lower-fma.f32 |
| 3 484× | lower-*.f32 |
| 3 482× | lower-*.f64 |
| 2 734× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 36 |
| 0 | 17 | 36 |
| 1 | 63 | 22 |
| 2 | 429 | 22 |
| 3 | 4997 | 22 |
| 0 | 8103 | 18 |
| 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) |
(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 |
|---|
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) |
(+.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 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (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 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64))))))) (/.f64 #s(literal 1 binary64) (*.f64 (expm1.f64 x) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (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)))))) |
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(*.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)))) |
(*.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (expm1.f64 x))))) |
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) |
| 1× | egg-herbie |
| 15 504× | lower-fma.f64 |
| 15 504× | lower-fma.f32 |
| 4 704× | lower-*.f64 |
| 4 704× | lower-*.f32 |
| 2 492× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 77 | 480 |
| 1 | 252 | 446 |
| 2 | 663 | 446 |
| 3 | 1429 | 440 |
| 4 | 2558 | 360 |
| 5 | 5941 | 325 |
| 0 | 8294 | 270 |
| 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) |
(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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
| 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 x (+.f64 #s(literal 2 binary64) (+.f64 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) |
(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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
Compiled 17 383 to 2 477 computations (85.8% saved)
8 alts after pruning (8 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 762 | 8 | 770 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 763 | 8 | 771 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 65.1% | (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
| 66.0% | (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) | |
| ▶ | 64.7% | (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
| 64.8% | (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))) | |
| ▶ | 66.2% | (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))) |
| 64.4% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) | |
| ▶ | 70.6% | (sqrt.f64 #s(literal 2 binary64)) |
Compiled 142 to 104 computations (26.8% saved)
| 1× | egg-herbie |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #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 | (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))) |
| 1 172× | lower-fma.f32 |
| 1 160× | lower-fma.f64 |
| 478× | lower-*.f64 |
| 478× | lower-*.f32 |
| 228× | associate-*l* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 20 | 92 |
| 0 | 39 | 92 |
| 1 | 76 | 92 |
| 2 | 156 | 92 |
| 3 | 342 | 92 |
| 4 | 629 | 92 |
| 5 | 850 | 92 |
| 6 | 855 | 92 |
| 0 | 855 | 92 |
| 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 (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) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
x |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
#s(literal 1/2 binary64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
x |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
#s(literal 1/2 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 (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) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
x |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
#s(literal 1/2 binary64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
x |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
#s(literal 1/2 binary64) |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.9% | (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 99.9% | (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 99.7% | (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
| ✓ | accuracy | 99.4% | (/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | accuracy | 99.7% | (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 98.4% | (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #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 | 82.2% | (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (exp.f64 x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| ✓ | accuracy | 100.0% | (-.f64 (exp.f64 x) #s(literal -1 binary64)) |
| 49.0ms | 242× | 0 | valid |
| 3.0ms | 9× | 1 | valid |
| 2.0ms | 4× | 2 | valid |
| 1.0ms | 1× | 5 | exit |
Compiled 94 to 28 computations (70.2% saved)
ival-mult: 15.0ms (36.3% of total)ival-add: 7.0ms (16.9% of total)ival-sqrt: 6.0ms (14.5% of total)const: 4.0ms (9.7% of total)ival-div: 3.0ms (7.3% of total)ival-exp: 2.0ms (4.8% of total)adjust: 1.0ms (2.4% of total)exact: 1.0ms (2.4% of total)ival-sub: 1.0ms (2.4% of total)ival-assert: 0.0ms (0% of total)ival-true: 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 (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 (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (/.f64 x (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))> |
#<alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 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 (+ (* 1/2 (/ (* 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) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (* 1/2 (/ x (sqrt 2)))> |
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))> |
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))> |
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))> |
#<alt (* 1/2 (/ x (sqrt 2)))> |
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (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 (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))> |
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt 1/2> |
#<alt (+ 1/2 (* 3/16 x))> |
#<alt (+ 1/2 (* x (+ 3/16 (* 7/192 x))))> |
#<alt (+ 1/2 (* x (+ 3/16 (* 7/192 x))))> |
#<alt (* 7/192 (pow x 2))> |
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))> |
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))> |
#<alt (* 7/192 (pow x 2))> |
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))> |
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))> |
#<alt 3/16> |
#<alt (+ 3/16 (* 7/192 x))> |
#<alt (+ 3/16 (* 7/192 x))> |
#<alt (+ 3/16 (* 7/192 x))> |
#<alt (* 7/192 x)> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* 7/192 x)> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
33 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | 0 | (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) |
| 1.0ms | x | @ | inf | (sqrt (- (exp x) -1)) |
| 1.0ms | x | @ | inf | (sqrt (+ (* x (+ (* x 1/2) 1)) 2)) |
| 0.0ms | x | @ | inf | (+ (* x (/ 1/2 (sqrt 2))) (sqrt 2)) |
| 0.0ms | x | @ | 0 | (+ (* x (/ 1/2 (sqrt 2))) (sqrt 2)) |
| 1× | batch-egg-rewrite |
| 4 414× | lower-fma.f32 |
| 4 402× | lower-fma.f64 |
| 4 324× | lower-/.f32 |
| 4 320× | lower-/.f64 |
| 3 476× | lower-*.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 20 | 73 |
| 0 | 39 | 73 |
| 1 | 181 | 73 |
| 2 | 1417 | 71 |
| 0 | 8290 | 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 (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)) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 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)) (-.f64 #s(literal 1 binary64) (exp.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)) (-.f64 #s(literal 1 binary64) (exp.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)) (-.f64 #s(literal 1 binary64) (exp.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)) (-.f64 #s(literal 1 binary64) (exp.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 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1/4 binary64)) |
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 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)) (-.f64 #s(literal 1 binary64) (exp.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)) (-.f64 #s(literal 1 binary64) (exp.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)) (-.f64 #s(literal 1 binary64) (exp.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 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))) |
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)))) |
(-.f64 (exp.f64 x) #s(literal -1 binary64)) |
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) |
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal 1 binary64)) |
(fma.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))) |
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) |
(/.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))) |
(/.f64 (-.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64))) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(/.f64 (-.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (expm1.f64 x) #s(literal 1 binary64))) (*.f64 (expm1.f64 x) (expm1.f64 x))) |
(/.f64 (neg.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))) |
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (neg.f64 (expm1.f64 x)))) |
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (*.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (fma.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (*.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.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) (exp.f64 (+.f64 x x))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) |
(/.f64 (-.f64 (*.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))) (+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))) (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64)) |
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(*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (*.f64 x (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal 1/4 binary64)) (*.f64 x (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (*.f64 x (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 x (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (neg.f64 (*.f64 x (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))))) |
(*.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (*.f64 x (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal 1/4 binary64)) (*.f64 x (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))))) |
(*.f64 (neg.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64))))) |
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))) |
(+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))) |
(+.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) |
(+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (neg.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) |
(-.f64 (/.f64 #s(literal 9/256 binary64) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) |
(fma.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (neg.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))) (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64))))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64)))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64))))) |
(/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (neg.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) |
(/.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64))) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) #s(literal 9/256 binary64))) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)))) (neg.f64 (neg.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)))) (neg.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (fma.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) (*.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64))))) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) |
(*.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))) |
| 1× | egg-herbie |
| 10 586× | lower-fma.f64 |
| 10 586× | lower-fma.f32 |
| 3 958× | lower-*.f64 |
| 3 958× | lower-*.f32 |
| 2 708× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 196 | 1199 |
| 1 | 652 | 1039 |
| 2 | 2116 | 953 |
| 3 | 6397 | 949 |
| 0 | 8336 | 866 |
| 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 (+ (* 1/2 (/ (* 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) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(* 1/2 (/ x (sqrt 2))) |
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x))) |
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x))) |
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x))) |
(* 1/2 (/ x (sqrt 2))) |
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))))) |
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))))) |
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (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 (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2)))))) |
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3)))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2)))))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2)))))) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
1/2 |
(+ 1/2 (* 3/16 x)) |
(+ 1/2 (* x (+ 3/16 (* 7/192 x)))) |
(+ 1/2 (* x (+ 3/16 (* 7/192 x)))) |
(* 7/192 (pow x 2)) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(* 7/192 (pow x 2)) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
3/16 |
(+ 3/16 (* 7/192 x)) |
(+ 3/16 (* 7/192 x)) |
(+ 3/16 (* 7/192 x)) |
(* 7/192 x) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* 7/192 x) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
| Outputs |
|---|
(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 x #s(literal 3/16 binary64) #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 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 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 #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 x #s(literal 3/16 binary64) #s(literal 1/2 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 x #s(literal -1/4 binary64) #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 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 3/4 binary64) (*.f64 x (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 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 3/4 binary64) (*.f64 x (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))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) 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) (/ 2 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))) |
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 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (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) (* 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))) |
(* 1/2 (/ x (sqrt 2))) |
(/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(* 1/2 (/ x (sqrt 2))) |
(/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (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) |
(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 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) |
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3)))))) |
(*.f64 (*.f64 x x) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2)))))) |
(*.f64 x (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))) x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2)))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) x))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* 3/16 x)) |
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* x (+ 3/16 (* 7/192 x)))) |
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) |
(+ 1/2 (* x (+ 3/16 (* 7/192 x)))) |
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) |
(* 7/192 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 7/192 binary64)) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(*.f64 x (+.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(*.f64 x (+.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x))) |
(* 7/192 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 7/192 binary64)) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(*.f64 x (+.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(*.f64 x (+.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x))) |
3/16 |
#s(literal 3/16 binary64) |
(+ 3/16 (* 7/192 x)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(+ 3/16 (* 7/192 x)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(+ 3/16 (* 7/192 x)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* 7/192 x) |
(*.f64 x #s(literal 7/192 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* 7/192 x) |
(*.f64 x #s(literal 7/192 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
Compiled 16 404 to 1 736 computations (89.4% saved)
18 alts after pruning (14 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 672 | 12 | 684 |
| Fresh | 1 | 2 | 3 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 0 | 0 |
| Total | 674 | 18 | 692 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 65.1% | (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) |
| ✓ | 65.1% | (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
| 64.1% | (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) | |
| 65.0% | (fma.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) | |
| ▶ | 65.1% | (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
| 64.0% | (/.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #s(literal -2 binary64)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) | |
| 2.6% | (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64))) | |
| 65.1% | (+.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) | |
| 33.5% | (*.f64 (*.f64 x x) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)))) | |
| ▶ | 3.1% | (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
| 3.1% | (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) | |
| 64.8% | (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))) | |
| ✓ | 66.2% | (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ▶ | 4.4% | (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)) |
| 64.4% | (sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))) | |
| ✓ | 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| ▶ | 64.4% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ✓ | 70.6% | (sqrt.f64 #s(literal 2 binary64)) |
Compiled 489 to 303 computations (38% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
| ✓ | cost-diff | 0 | (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 320 | (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 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 | (+.f64 #s(literal 2 binary64) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ✓ | cost-diff | 0 | (/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
| ✓ | cost-diff | 0 | (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
| ✓ | cost-diff | 1664 | (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) |
| 1 136× | lower-fma.f32 |
| 1 124× | lower-fma.f64 |
| 478× | lower-*.f32 |
| 468× | lower-*.f64 |
| 338× | associate-*r* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 161 |
| 0 | 48 | 164 |
| 1 | 97 | 164 |
| 2 | 215 | 156 |
| 3 | 510 | 156 |
| 4 | 974 | 156 |
| 5 | 1084 | 156 |
| 0 | 1084 | 154 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
x |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
#s(literal 1/2 binary64) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
(+.f64 #s(literal 2 binary64) x) |
#s(literal 2 binary64) |
x |
(sqrt.f64 (fma.f64 #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 |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
x |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) |
x |
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) |
#s(literal 1 binary64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
| Outputs |
|---|
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x (/.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 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
x |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
#s(literal 1/2 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 #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 |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64)))) |
x |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) |
x |
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
#s(literal 1/2 binary64) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) |
#s(literal 1 binary64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 99.4% | (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
| ✓ | accuracy | 99.9% | (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
| ✓ | accuracy | 99.8% | (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
| ✓ | accuracy | 99.7% | (/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
| ✓ | 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% | (+.f64 #s(literal 2 binary64) x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ✓ | accuracy | 100.0% | (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 99.9% | (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
| ✓ | accuracy | 99.7% | (/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 99.4% | (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
| 42.0ms | 157× | 0 | invalid |
| 23.0ms | 98× | 0 | valid |
| 1.0ms | 1× | 5 | exit |
Compiled 163 to 32 computations (80.4% saved)
ival-mult: 25.0ms (50.8% of total)ival-add: 8.0ms (16.2% of total)ival-div: 7.0ms (14.2% of total)ival-sqrt: 5.0ms (10.2% of total)const: 4.0ms (8.1% of total)exact: 1.0ms (2% of total)adjust: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))> |
#<alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))> |
#<alt (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))> |
#<alt (/.f64 x (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 #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 (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))> |
#<alt (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))> |
#<alt (sqrt.f64 #s(literal 2 binary64))> |
#<alt (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))> |
#<alt (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))> |
#<alt (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))> |
| Outputs |
|---|
#<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 (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))> |
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))> |
#<alt 3/16> |
#<alt (+ 3/16 (* 7/192 x))> |
#<alt (+ 3/16 (* 7/192 x))> |
#<alt (+ 3/16 (* 7/192 x))> |
#<alt (* 7/192 x)> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* 7/192 x)> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<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 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 (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))> |
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))> |
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))> |
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* 3/16 (/ x (sqrt 2)))> |
#<alt (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))> |
#<alt (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))> |
#<alt (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))> |
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))> |
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))> |
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 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 (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))> |
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* 3/16 x)))> |
#<alt (* x (+ 1/2 (* x (+ 3/16 (* 7/192 x)))))> |
#<alt (* x (+ 1/2 (* x (+ 3/16 (* 7/192 x)))))> |
#<alt (* 7/192 (pow x 3))> |
#<alt (* (pow x 3) (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))> |
#<alt (* (pow x 3) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))> |
#<alt (* 7/192 (pow x 3))> |
#<alt (* (pow x 3) (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192)))> |
#<alt 1/2> |
#<alt (+ 1/2 (* 3/16 x))> |
#<alt (+ 1/2 (* x (+ 3/16 (* 7/192 x))))> |
#<alt (+ 1/2 (* x (+ 3/16 (* 7/192 x))))> |
#<alt (* 7/192 (pow x 2))> |
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))> |
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))> |
#<alt (* 7/192 (pow x 2))> |
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))> |
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (* 1/2 (/ x (sqrt 2)))> |
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))> |
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))> |
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))> |
#<alt (* 1/2 (/ x (sqrt 2)))> |
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))> |
45 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | x | @ | -inf | (* x (+ (* x (+ (* x 7/192) 3/16)) 1/2)) |
| 1.0ms | x | @ | -inf | (sqrt (+ 2 x)) |
| 1.0ms | x | @ | inf | (sqrt (+ 2 x)) |
| 0.0ms | x | @ | 0 | (sqrt (+ (* 1/2 (* x x)) x)) |
| 0.0ms | x | @ | 0 | (* x (/ x (sqrt 2))) |
| 1× | batch-egg-rewrite |
| 4 618× | lower-*.f32 |
| 4 608× | lower-*.f64 |
| 4 540× | lower-/.f32 |
| 4 534× | lower-/.f64 |
| 3 250× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 126 |
| 0 | 48 | 129 |
| 1 | 207 | 120 |
| 2 | 1673 | 116 |
| 0 | 8229 | 114 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/.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 #s(literal 1/2 binary64) (*.f64 x x) x)) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) |
(*.f64 x x) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) |
| Outputs |
|---|
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) |
(+.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) |
(+.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(+.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(+.f64 (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))) |
(+.f64 (/.f64 (fma.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (/.f64 (-.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (/.f64 (-.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) |
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x))) #s(literal 1/2 binary64)) (-.f64 (/.f64 (-.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (/.f64 (-.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) |
(-.f64 (/.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 2 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (/.f64 (-.f64 #s(literal 2 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))) |
(-.f64 (/.f64 (*.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))) (/.f64 (*.f64 (*.f64 (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x)) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x x))) #s(literal 1/2 binary64)) (-.f64 (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))) |
(fma.f64 x (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 x (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))) |
(fma.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
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(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (neg.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))) |
(/.f64 (fma.f64 (neg.f64 (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(/.f64 (fma.f64 (neg.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 x #s(literal 1 binary64)) #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 (fma.f64 (*.f64 x #s(literal 1 binary64)) #s(literal -1 binary64) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))) |
(/.f64 (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(/.f64 (fma.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1 binary64) x) #s(literal -1 binary64) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))) |
(/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))) |
(/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))) (neg.f64 (neg.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) (neg.f64 (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))) |
(pow.f64 (/.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))) #s(literal -1 binary64)) |
(*.f64 (fma.f64 (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))) |
(pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) |
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) |
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)) #s(literal 2 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 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))) |
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64))) |
| 1× | egg-herbie |
| 9 936× | lower-fma.f64 |
| 9 936× | lower-fma.f32 |
| 4 018× | lower-*.f64 |
| 4 018× | lower-*.f32 |
| 2 272× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 249 | 1783 |
| 1 | 774 | 1742 |
| 2 | 2305 | 1622 |
| 3 | 5647 | 1602 |
| 0 | 8275 | 1497 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(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 (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2)))))) |
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3)))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2)))))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2)))))) |
3/16 |
(+ 3/16 (* 7/192 x)) |
(+ 3/16 (* 7/192 x)) |
(+ 3/16 (* 7/192 x)) |
(* 7/192 x) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* 7/192 x) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(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 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) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* 3/16 (/ x (sqrt 2))) |
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(* 7/192 (/ (pow x 2) (sqrt 2))) |
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* 7/192 (/ (pow x 2) (sqrt 2))) |
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 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 (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2)))))) |
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3)))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2)))))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2)))))) |
(* 1/2 x) |
(* x (+ 1/2 (* 3/16 x))) |
(* x (+ 1/2 (* x (+ 3/16 (* 7/192 x))))) |
(* x (+ 1/2 (* x (+ 3/16 (* 7/192 x))))) |
(* 7/192 (pow x 3)) |
(* (pow x 3) (+ 7/192 (* 3/16 (/ 1 x)))) |
(* (pow x 3) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(* (pow x 3) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(* 7/192 (pow x 3)) |
(* (pow x 3) (+ 7/192 (* 3/16 (/ 1 x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192))) |
1/2 |
(+ 1/2 (* 3/16 x)) |
(+ 1/2 (* x (+ 3/16 (* 7/192 x)))) |
(+ 1/2 (* x (+ 3/16 (* 7/192 x)))) |
(* 7/192 (pow x 2)) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(* 7/192 (pow x 2)) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(* 1/2 (/ x (sqrt 2))) |
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x))) |
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x))) |
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x))) |
(* 1/2 (/ x (sqrt 2))) |
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))))) |
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))))) |
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))))) |
| Outputs |
|---|
(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 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2)))))) |
(*.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))))) |
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2)))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))) x))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2)))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) x))) |
3/16 |
#s(literal 3/16 binary64) |
(+ 3/16 (* 7/192 x)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(+ 3/16 (* 7/192 x)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(+ 3/16 (* 7/192 x)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* 7/192 x) |
(*.f64 x #s(literal 7/192 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* 7/192 x) |
(*.f64 x #s(literal 7/192 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 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 (+ (* -1/8 (/ 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 x (/.f64 #s(literal 1/16 binary64) (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 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (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))))))) |
(* 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))))) |
(*.f64 x (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x 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)))))) |
(*.f64 x (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (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))))))) |
(* -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 x (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) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x 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 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 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/32 binary64))) (sqrt.f64 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 x x) #s(literal 1/128 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 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))))) |
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) |
(* 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 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))) |
(* -1 (* x (sqrt 1/2))) |
(*.f64 x (neg.f64 (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 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ 1 (sqrt 1/2)))) x))))) |
(-.f64 (+.f64 (/.f64 #s(literal 1/4 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 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/8 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x))))) |
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/16 binary64) (*.f64 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)))) (*.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) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* 3/16 (/ x (sqrt 2))) |
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* 7/192 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 binary64))) |
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* 7/192 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 binary64))) |
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 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 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2)))))) |
(*.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))))) |
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2)))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))) x))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2)))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) x))) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* 3/16 x))) |
(*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (+ 3/16 (* 7/192 x))))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (+ 3/16 (* 7/192 x))))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) |
(* 7/192 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) |
(* (pow x 3) (+ 7/192 (* 3/16 (/ 1 x)))) |
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* (pow x 3) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(*.f64 x (*.f64 x (fma.f64 x (+.f64 #s(literal 7/192 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 3/16 binary64)))) |
(* (pow x 3) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(*.f64 x (*.f64 x (fma.f64 x (+.f64 #s(literal 7/192 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 3/16 binary64)))) |
(* 7/192 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) |
(* (pow x 3) (+ 7/192 (* 3/16 (/ 1 x)))) |
(*.f64 (*.f64 x x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192))) |
(*.f64 (*.f64 x (*.f64 x x)) (-.f64 #s(literal 7/192 binary64) (/.f64 (+.f64 #s(literal -3/16 binary64) (/.f64 #s(literal -1/2 binary64) x)) x))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192))) |
(*.f64 (*.f64 x (*.f64 x x)) (-.f64 #s(literal 7/192 binary64) (/.f64 (+.f64 #s(literal -3/16 binary64) (/.f64 #s(literal -1/2 binary64) x)) x))) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* 3/16 x)) |
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* x (+ 3/16 (* 7/192 x)))) |
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) |
(+ 1/2 (* x (+ 3/16 (* 7/192 x)))) |
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) |
(* 7/192 (pow x 2)) |
(*.f64 #s(literal 7/192 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(*.f64 x (fma.f64 x (+.f64 #s(literal 7/192 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(*.f64 x (fma.f64 x (+.f64 #s(literal 7/192 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 3/16 binary64))) |
(* 7/192 (pow x 2)) |
(*.f64 #s(literal 7/192 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(*.f64 x (fma.f64 x (+.f64 #s(literal 7/192 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x))))) |
(*.f64 x (fma.f64 x (+.f64 #s(literal 7/192 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 3/16 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) (* 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) (* 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))) |
(* 1/2 (/ x (sqrt 2))) |
(/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(* 1/2 (/ x (sqrt 2))) |
(/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
Compiled 57 349 to 3 219 computations (94.4% saved)
27 alts after pruning (20 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 505 | 16 | 1 521 |
| Fresh | 5 | 4 | 9 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 4 | 4 |
| Total | 1 512 | 27 | 1 539 |
| Status | Accuracy | Program |
|---|---|---|
| 64.1% | (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) | |
| ▶ | 65.1% | (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))))) |
| 65.1% | (fma.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) | |
| ✓ | 65.1% | (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
| 1.3% | (fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 x x) #s(literal 1/128 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x)) | |
| ▶ | 65.1% | (fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
| 64.1% | (/.f64 (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64))) | |
| 64.1% | (/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) | |
| 64.1% | (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) | |
| 64.9% | (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (/.f64 (-.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) | |
| 65.1% | (+.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) | |
| 3.1% | (*.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) x) | |
| ▶ | 3.1% | (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
| ✓ | 3.1% | (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
| 2.6% | (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 7/192 binary64)))) | |
| 4.3% | (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))) | |
| ▶ | 4.3% | (*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
| 2.6% | (*.f64 x (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 binary64)))) | |
| 3.1% | (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) | |
| 64.8% | (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))) | |
| ✓ | 66.2% | (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ✓ | 4.4% | (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)) |
| 64.4% | (sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))) | |
| ✓ | 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| ✓ | 64.4% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ▶ | 2.7% | (sqrt.f64 x) |
| ✓ | 70.6% | (sqrt.f64 #s(literal 2 binary64)) |
Compiled 740 to 477 computations (35.5% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
| ✓ | cost-diff | 384 | (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) |
| ✓ | cost-diff | 640 | (fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | cost-diff | 960 | (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
| ✓ | 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 | (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | cost-diff | 128 | (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
| ✓ | cost-diff | 320 | (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 384 | (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))) |
| ✓ | cost-diff | 704 | (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))) |
| 10 398× | lower-fma.f32 |
| 10 388× | lower-fma.f64 |
| 4 392× | lower-*.f32 |
| 4 374× | lower-*.f64 |
| 2 144× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 31 | 249 |
| 0 | 59 | 237 |
| 1 | 110 | 231 |
| 2 | 246 | 227 |
| 3 | 566 | 227 |
| 4 | 1345 | 227 |
| 5 | 1944 | 227 |
| 6 | 2740 | 227 |
| 7 | 4275 | 227 |
| 8 | 6608 | 227 |
| 0 | 8513 | 218 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
x |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))) |
#s(literal 1 binary64) |
(/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))) |
(/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)) |
(*.f64 x x) |
#s(literal 1/8 binary64) |
#s(literal -2 binary64) |
(sqrt.f64 x) |
x |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
x |
(*.f64 x (/.f64 #s(literal 3/16 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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
x |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
x |
(/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) |
(fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
| Outputs |
|---|
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))))) |
(fma.f64 x (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
x |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) |
#s(literal 1 binary64) |
(/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))) |
(/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(-.f64 (*.f64 (*.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 -2 binary64)) |
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 x #s(literal 1/2 binary64)) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)) |
(*.f64 x x) |
#s(literal 1/8 binary64) |
#s(literal -2 binary64) |
(sqrt.f64 x) |
x |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(*.f64 #s(literal 3/16 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) |
x |
(*.f64 x (/.f64 #s(literal 3/16 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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(/.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
x |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
x |
(/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal 1/4 binary64))) |
(fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
#s(literal 7/192 binary64) |
#s(literal 3/16 binary64) |
(sqrt.f64 #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 99.9% | (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
| ✓ | accuracy | 100.0% | (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
| ✓ | accuracy | 99.9% | (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
| ✓ | accuracy | 99.9% | (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
| ✓ | accuracy | 99.7% | (/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | accuracy | 99.9% | (*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
| ✓ | accuracy | 99.6% | (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 99.9% | (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
| ✓ | accuracy | 99.7% | (/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
| ✓ | accuracy | 99.5% | (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))) |
| ✓ | accuracy | 99.4% | (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
| 50.0ms | 157× | 0 | invalid |
| 27.0ms | 80× | 0 | valid |
| 6.0ms | 12× | 1 | valid |
| 4.0ms | 6× | 2 | valid |
| 1.0ms | 1× | 5 | exit |
Compiled 251 to 38 computations (84.9% saved)
ival-mult: 28.0ms (49.5% of total)ival-div: 11.0ms (19.4% of total)ival-add: 6.0ms (10.6% of total)const: 4.0ms (7.1% of total)ival-sqrt: 4.0ms (7.1% of total)adjust: 1.0ms (1.8% of total)exact: 1.0ms (1.8% of total)ival-sub: 1.0ms (1.8% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))))> |
#<alt (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))> |
#<alt (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))> |
#<alt (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))> |
#<alt (sqrt.f64 x)> |
#<alt (*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))> |
#<alt (*.f64 x (/.f64 #s(literal 3/16 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 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))> |
#<alt (/.f64 x (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))> |
#<alt (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))> |
#<alt (fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))> |
#<alt (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))> |
#<alt (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))> |
#<alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))> |
| Outputs |
|---|
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/4 (* x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* 1/4 (* x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* 1/4 (* x (sqrt 2))))> |
#<alt (* 1/4 (* x (sqrt 2)))> |
#<alt (* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))> |
#<alt (* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))> |
#<alt (* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))> |
#<alt (* 1/4 (* x (sqrt 2)))> |
#<alt (* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2)))))> |
#<alt (/ 1 (sqrt 2))> |
#<alt (+ (* -1/4 (/ x (sqrt 2))) (/ 1 (sqrt 2)))> |
#<alt (+ (* x (- (* 1/16 (/ x (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))> |
#<alt (+ (* x (- (* x (+ (* -1/64 (/ x (sqrt 2))) (* 1/16 (/ 1 (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))> |
#<alt (/ 4 (* x (sqrt 2)))> |
#<alt (/ (- (* 4 (/ 1 (sqrt 2))) (* 16 (/ 1 (* x (sqrt 2))))) x)> |
#<alt (/ (- (+ (* 4 (/ 1 (sqrt 2))) (/ 64 (* (pow x 2) (sqrt 2)))) (/ 16 (* x (sqrt 2)))) x)> |
#<alt (/ (- (+ (* 4 (/ 1 (sqrt 2))) (* 64 (/ 1 (* (pow x 2) (sqrt 2))))) (+ (* 256 (/ 1 (* (pow x 3) (sqrt 2)))) (/ 16 (* x (sqrt 2))))) x)> |
#<alt (/ 4 (* x (sqrt 2)))> |
#<alt (* -1 (/ (- (* 16 (/ 1 (* x (sqrt 2)))) (* 4 (/ 1 (sqrt 2)))) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (* 64 (/ 1 (* x (sqrt 2)))) (* 16 (/ 1 (sqrt 2)))) x)) (* 4 (/ 1 (sqrt 2)))) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 256 (/ 1 (* x (sqrt 2)))) (* 64 (/ 1 (sqrt 2)))) x)) (* 16 (/ 1 (sqrt 2)))) x)) (* 4 (/ 1 (sqrt 2)))) x))> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt (* 1/2 x)> |
#<alt -2> |
#<alt (- (* 1/2 x) 2)> |
#<alt (- (* 1/2 x) 2)> |
#<alt (- (* 1/2 x) 2)> |
#<alt (* 1/2 x)> |
#<alt (* x (- 1/2 (* 2 (/ 1 x))))> |
#<alt (* x (- 1/2 (* 2 (/ 1 x))))> |
#<alt (* x (- 1/2 (* 2 (/ 1 x))))> |
#<alt (* 1/2 x)> |
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 1/2)))> |
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 1/2)))> |
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 1/2)))> |
#<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 (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* 3/16 (/ (pow x 2) (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 (sqrt 2)))> |
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))> |
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))> |
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))> |
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))> |
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (/ x (sqrt 2))> |
#<alt (* 3/16 x)> |
#<alt (* x (+ 3/16 (* 7/192 x)))> |
#<alt (* x (+ 3/16 (* 7/192 x)))> |
#<alt (* x (+ 3/16 (* 7/192 x)))> |
#<alt (* 7/192 (pow x 2))> |
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* 7/192 (pow x 2))> |
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* 1/2 (sqrt 2))> |
#<alt (+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))> |
#<alt (+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))> |
#<alt (+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))> |
#<alt (* 7/192 (* (pow x 2) (sqrt 2)))> |
#<alt (* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))> |
#<alt (* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))> |
#<alt (* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))> |
#<alt (* 7/192 (* (pow x 2) (sqrt 2)))> |
#<alt (* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (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 (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))))> |
#<alt (* 7/384 (* (pow x 3) (sqrt 2)))> |
#<alt (* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))> |
#<alt (* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))> |
#<alt (* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3))))))> |
#<alt (* 7/384 (* (pow x 3) (sqrt 2)))> |
#<alt (* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2)))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2)))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2)))))> |
#<alt (* 1/4 (sqrt 2))> |
#<alt (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))> |
#<alt (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))> |
#<alt (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))> |
#<alt (* 7/384 (* (pow x 2) (sqrt 2)))> |
#<alt (* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))> |
#<alt (* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))> |
#<alt (* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))> |
#<alt (* 7/384 (* (pow x 2) (sqrt 2)))> |
#<alt (* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2))))> |
#<alt (/ -2 (sqrt 2))> |
#<alt (- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2))))> |
#<alt (- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2))))> |
#<alt (- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2))))> |
#<alt (* 1/2 (/ x (sqrt 2)))> |
#<alt (* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2))))))> |
#<alt (* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2))))))> |
#<alt (* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2))))))> |
#<alt (* 1/2 (/ x (sqrt 2)))> |
#<alt (* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt (/ (pow x 2) (sqrt 2))> |
#<alt 3/16> |
#<alt (+ 3/16 (* 7/192 x))> |
#<alt (+ 3/16 (* 7/192 x))> |
#<alt (+ 3/16 (* 7/192 x))> |
#<alt (* 7/192 x)> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* 7/192 x)> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))> |
48 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | inf | (/ 1 (/ (/ (- (* (* x 1/2) 1) 2) (sqrt 2)) (+ (* (* x x) 1/8) -2))) |
| 2.0ms | x | @ | 0 | (/ (- (* (* x 1/2) 1) 2) (sqrt 2)) |
| 1.0ms | x | @ | inf | (+ (* x (/ (+ (* (* x (+ (* x 7/192) 3/16)) (sqrt 2)) (* (sqrt 2) 1/2)) 2)) (sqrt 2)) |
| 1.0ms | x | @ | 0 | (/ 1 (/ (/ (- (* (* x 1/2) 1) 2) (sqrt 2)) (+ (* (* x x) 1/8) -2))) |
| 0.0ms | x | @ | -inf | (/ 1 (/ (/ (- (* (* x 1/2) 1) 2) (sqrt 2)) (+ (* (* x x) 1/8) -2))) |
| 1× | batch-egg-rewrite |
| 5 324× | lower-fma.f32 |
| 5 316× | lower-fma.f64 |
| 4 240× | lower-*.f32 |
| 4 222× | lower-*.f64 |
| 4 042× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 30 | 158 |
| 0 | 56 | 148 |
| 1 | 212 | 140 |
| 2 | 1471 | 140 |
| 0 | 8322 | 133 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64)))) |
(/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))) |
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(sqrt.f64 x) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(*.f64 x (/.f64 #s(literal 3/16 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)) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64))))) #s(literal -1 binary64))) |
(+.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) #s(literal -2 binary64)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))) |
(+.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) #s(literal -2 binary64))) |
(+.f64 (*.f64 #s(literal -2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)))) (*.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))))) |
(+.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)))) (*.f64 #s(literal -2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))))) |
(-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) |
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (/.f64 #s(literal -4 binary64) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal -2 binary64))) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)) (/.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64))) (*.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 4 binary64) (*.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))))) |
(fma.f64 #s(literal -2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (*.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))))) |
(fma.f64 (*.f64 x (*.f64 x #s(literal 1/8 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (*.f64 #s(literal -2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))))) |
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) #s(literal -2 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))) |
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (*.f64 x (*.f64 x #s(literal 1/8 binary64))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) #s(literal -2 binary64))) |
(neg.f64 (*.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64)) #s(literal -8 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -4 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64)) #s(literal -8 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -4 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))))) |
(/.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 2 binary64))))) |
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 2 binary64)) (/.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64)) #s(literal -8 binary64)) (*.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))))) |
(/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)))) #s(literal 1 binary64)) |
(/.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -4 binary64)) (*.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64)))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64))) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64)) #s(literal -8 binary64))) (neg.f64 (*.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/4 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -4 binary64))) (neg.f64 (*.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64))))) |
(/.f64 (*.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) |
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal 2 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal 2 binary64))) |
(/.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64)) #s(literal -8 binary64))) (+.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal 4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/4 binary64)))) |
(/.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/64 binary64)) #s(literal -4 binary64))) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))) |
(/.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
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(*.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)) #s(literal -8 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal 4 binary64)) x))) |
(*.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)) #s(literal -8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal 4 binary64)) x)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))) |
(*.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))) #s(literal -1/2 binary64))) |
(exp.f64 (-.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))) |
(neg.f64 (*.f64 (/.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) x)) |
(neg.f64 (*.f64 x (/.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x)) |
(/.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) |
(/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)))) |
(/.f64 (neg.f64 x) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))) |
(/.f64 (*.f64 x (neg.f64 x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 (neg.f64 (*.f64 x (neg.f64 x))) (sqrt.f64 #s(literal 2 binary64))) |
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (*.f64 x (neg.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) |
(*.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))) |
(+.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)) |
(+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (neg.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) |
(-.f64 (/.f64 #s(literal 9/256 binary64) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) |
(fma.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x #s(literal -7/192 binary64) #s(literal 3/16 binary64))) (neg.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 9/256 binary64) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) (*.f64 x #s(literal -7/1024 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))) (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64))))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (+.f64 #s(literal 9/256 binary64) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) (*.f64 x #s(literal -7/1024 binary64))))) |
(/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (+.f64 #s(literal 9/256 binary64) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) (*.f64 x #s(literal -7/1024 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (fma.f64 x #s(literal -7/192 binary64) #s(literal 3/16 binary64))) |
(/.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64))) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) #s(literal 9/256 binary64))) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)))) (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64))))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)))) (neg.f64 (fma.f64 x #s(literal -7/192 binary64) #s(literal 3/16 binary64)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)))) (neg.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (fma.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) (*.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9/256 binary64) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) (*.f64 x #s(literal -7/1024 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x #s(literal -7/192 binary64) #s(literal 3/16 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64))))))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -7/192 binary64) #s(literal 3/16 binary64)))) |
(*.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))) |
| 1× | egg-herbie |
| 18 874× | lower-fma.f64 |
| 18 874× | lower-fma.f32 |
| 5 652× | lower-*.f64 |
| 5 652× | lower-*.f32 |
| 2 040× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 224 | 1686 |
| 1 | 724 | 1639 |
| 2 | 2057 | 1558 |
| 3 | 5340 | 1551 |
| 0 | 8602 | 1444 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt 2) |
(+ (sqrt 2) (* 1/4 (* x (sqrt 2)))) |
(+ (sqrt 2) (* 1/4 (* x (sqrt 2)))) |
(+ (sqrt 2) (* 1/4 (* x (sqrt 2)))) |
(* 1/4 (* x (sqrt 2))) |
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x))) |
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x))) |
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x))) |
(* 1/4 (* x (sqrt 2))) |
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))))) |
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))))) |
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))))) |
(/ 1 (sqrt 2)) |
(+ (* -1/4 (/ x (sqrt 2))) (/ 1 (sqrt 2))) |
(+ (* x (- (* 1/16 (/ x (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2))) |
(+ (* x (- (* x (+ (* -1/64 (/ x (sqrt 2))) (* 1/16 (/ 1 (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2))) |
(/ 4 (* x (sqrt 2))) |
(/ (- (* 4 (/ 1 (sqrt 2))) (* 16 (/ 1 (* x (sqrt 2))))) x) |
(/ (- (+ (* 4 (/ 1 (sqrt 2))) (/ 64 (* (pow x 2) (sqrt 2)))) (/ 16 (* x (sqrt 2)))) x) |
(/ (- (+ (* 4 (/ 1 (sqrt 2))) (* 64 (/ 1 (* (pow x 2) (sqrt 2))))) (+ (* 256 (/ 1 (* (pow x 3) (sqrt 2)))) (/ 16 (* x (sqrt 2))))) x) |
(/ 4 (* x (sqrt 2))) |
(* -1 (/ (- (* 16 (/ 1 (* x (sqrt 2)))) (* 4 (/ 1 (sqrt 2)))) x)) |
(* -1 (/ (- (* -1 (/ (- (* 64 (/ 1 (* x (sqrt 2)))) (* 16 (/ 1 (sqrt 2)))) x)) (* 4 (/ 1 (sqrt 2)))) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 256 (/ 1 (* x (sqrt 2)))) (* 64 (/ 1 (sqrt 2)))) x)) (* 16 (/ 1 (sqrt 2)))) x)) (* 4 (/ 1 (sqrt 2)))) x)) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
-2 |
(- (* 1/2 x) 2) |
(- (* 1/2 x) 2) |
(- (* 1/2 x) 2) |
(* 1/2 x) |
(* x (- 1/2 (* 2 (/ 1 x)))) |
(* x (- 1/2 (* 2 (/ 1 x)))) |
(* x (- 1/2 (* 2 (/ 1 x)))) |
(* 1/2 x) |
(* -1 (* x (- (* 2 (/ 1 x)) 1/2))) |
(* -1 (* x (- (* 2 (/ 1 x)) 1/2))) |
(* -1 (* x (- (* 2 (/ 1 x)) 1/2))) |
(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))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* 3/16 (/ (pow x 2) (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 (sqrt 2))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(/ x (sqrt 2)) |
(* 3/16 x) |
(* x (+ 3/16 (* 7/192 x))) |
(* x (+ 3/16 (* 7/192 x))) |
(* x (+ 3/16 (* 7/192 x))) |
(* 7/192 (pow x 2)) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(* 7/192 (pow x 2)) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(* 1/2 (sqrt 2)) |
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2))) |
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2))))) |
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2))))) |
(* 7/192 (* (pow x 2) (sqrt 2))) |
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x)))) |
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2)))))) |
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2)))))) |
(* 7/192 (* (pow x 2) (sqrt 2))) |
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (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 (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2))))))) |
(* 7/384 (* (pow x 3) (sqrt 2))) |
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x)))) |
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2)))))) |
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3)))))) |
(* 7/384 (* (pow x 3) (sqrt 2))) |
(* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2))))) |
(* 1/4 (sqrt 2)) |
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2))) |
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2))))) |
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2))))) |
(* 7/384 (* (pow x 2) (sqrt 2))) |
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x)))) |
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2)))))) |
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2)))))) |
(* 7/384 (* (pow x 2) (sqrt 2))) |
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2)))) |
(/ -2 (sqrt 2)) |
(- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2)))) |
(- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2)))) |
(- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2)))) |
(* 1/2 (/ x (sqrt 2))) |
(* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2)))))) |
(* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2)))))) |
(* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2)))))) |
(* 1/2 (/ x (sqrt 2))) |
(* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2)))))) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
(/ (pow x 2) (sqrt 2)) |
3/16 |
(+ 3/16 (* 7/192 x)) |
(+ 3/16 (* 7/192 x)) |
(+ 3/16 (* 7/192 x)) |
(* 7/192 x) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* 7/192 x) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
| Outputs |
|---|
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/4 (* x (sqrt 2)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) |
(+ (sqrt 2) (* 1/4 (* x (sqrt 2)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) |
(+ (sqrt 2) (* 1/4 (* x (sqrt 2)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) |
(* 1/4 (* x (sqrt 2))) |
(*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) |
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) |
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) |
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) |
(* 1/4 (* x (sqrt 2))) |
(*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) |
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) |
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) |
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) |
(/ 1 (sqrt 2)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) |
(+ (* -1/4 (/ x (sqrt 2))) (/ 1 (sqrt 2))) |
(fma.f64 x (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* x (- (* 1/16 (/ x (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2))) |
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(+ (* x (- (* x (+ (* -1/64 (/ x (sqrt 2))) (* 1/16 (/ 1 (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2))) |
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal -1/64 binary64) #s(literal 1/16 binary64)) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(/ 4 (* x (sqrt 2))) |
(/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) |
(/ (- (* 4 (/ 1 (sqrt 2))) (* 16 (/ 1 (* x (sqrt 2))))) x) |
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 4 binary64) (/.f64 #s(literal -16 binary64) x))) x) |
(/ (- (+ (* 4 (/ 1 (sqrt 2))) (/ 64 (* (pow x 2) (sqrt 2)))) (/ 16 (* x (sqrt 2)))) x) |
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (+.f64 (/.f64 #s(literal 64 binary64) x) #s(literal -16 binary64)) (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64)))) x) |
(/ (- (+ (* 4 (/ 1 (sqrt 2))) (* 64 (/ 1 (* (pow x 2) (sqrt 2))))) (+ (* 256 (/ 1 (* (pow x 3) (sqrt 2)))) (/ 16 (* x (sqrt 2))))) x) |
(/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (+.f64 (/.f64 #s(literal 64 binary64) x) #s(literal -16 binary64)) (/.f64 #s(literal -256 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (*.f64 x x)))))) x) |
(/ 4 (* x (sqrt 2))) |
(/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) |
(* -1 (/ (- (* 16 (/ 1 (* x (sqrt 2)))) (* 4 (/ 1 (sqrt 2)))) x)) |
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 4 binary64) (/.f64 #s(literal -16 binary64) x))) x) |
(* -1 (/ (- (* -1 (/ (- (* 64 (/ 1 (* x (sqrt 2)))) (* 16 (/ 1 (sqrt 2)))) x)) (* 4 (/ 1 (sqrt 2)))) x)) |
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (+.f64 (/.f64 #s(literal 64 binary64) x) #s(literal -16 binary64)) (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64)))) x) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 256 (/ 1 (* x (sqrt 2)))) (* 64 (/ 1 (sqrt 2)))) x)) (* 16 (/ 1 (sqrt 2)))) x)) (* 4 (/ 1 (sqrt 2)))) x)) |
(/.f64 (+.f64 (/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (+.f64 (/.f64 #s(literal 256 binary64) x) #s(literal -64 binary64))) x) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 4 binary64) (/.f64 #s(literal -16 binary64) x)))) x) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
-2 |
#s(literal -2 binary64) |
(- (* 1/2 x) 2) |
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) |
(- (* 1/2 x) 2) |
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) |
(- (* 1/2 x) 2) |
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* x (- 1/2 (* 2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) |
(* x (- 1/2 (* 2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) |
(* x (- 1/2 (* 2 (/ 1 x)))) |
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
(* -1 (* x (- (* 2 (/ 1 x)) 1/2))) |
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) |
(* -1 (* x (- (* 2 (/ 1 x)) 1/2))) |
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) |
(* -1 (* x (- (* 2 (/ 1 x)) 1/2))) |
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) |
(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) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* 3/16 (/ x (sqrt 2))) |
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 3/16 (/ x (sqrt 2))) |
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 3/16 (/ x (sqrt 2))) |
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 3/16 (/ x (sqrt 2))) |
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 3/16 (/ x (sqrt 2))) |
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 3/16 (/ x (sqrt 2))) |
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 3/16 (/ x (sqrt 2))) |
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 3/16 (/ x (sqrt 2))) |
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 3/16 (/ x (sqrt 2))) |
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 3/16 (/ x (sqrt 2))) |
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 3/16 (/ x (sqrt 2))) |
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 3/16 (/ x (sqrt 2))) |
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 3/16 (/ (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64))))) |
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64))))) |
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(*.f64 x (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 7/192 binary64))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64))))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64))))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64))))) |
(* 7/192 (/ (pow x 3) (sqrt 2))) |
(*.f64 x (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 7/192 binary64))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64))))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64))))) |
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (*.f64 x (*.f64 x #s(literal 3/16 binary64))))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(/ x (sqrt 2)) |
(/.f64 x (sqrt.f64 #s(literal 2 binary64))) |
(* 3/16 x) |
(*.f64 x #s(literal 3/16 binary64)) |
(* x (+ 3/16 (* 7/192 x))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* x (+ 3/16 (* 7/192 x))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* x (+ 3/16 (* 7/192 x))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* 7/192 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 7/192 binary64))) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* 7/192 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 7/192 binary64))) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) |
(* 1/2 (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) |
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) |
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) |
(* 7/192 (* (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/192 binary64)))) |
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2)))))) |
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (*.f64 x (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) x))) |
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2)))))) |
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (*.f64 x (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) x))) |
(* 7/192 (* (pow x 2) (sqrt 2))) |
(*.f64 x (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/192 binary64)))) |
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2)))) |
(fma.f64 x (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/192 binary64))) (*.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) x)) x)) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2)))) |
(fma.f64 x (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/192 binary64))) (*.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) x)) x)) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/4 (* x (sqrt 2)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) |
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 3/32 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))) |
(+ (sqrt 2) (* x (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2))))))) |
(fma.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 7/384 binary64)) (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(* 7/384 (* (pow x 3) (sqrt 2))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 7/384 binary64))) |
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x)))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64))) |
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2)))))) |
(*.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/4 binary64) x)))) |
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3)))))) |
(fma.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/4 binary64) x))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) |
(* 7/384 (* (pow x 3) (sqrt 2))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 7/384 binary64))) |
(* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2))))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2))))) |
(*.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/4 binary64) x)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2))))) |
(*.f64 (*.f64 x (*.f64 x x)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/384 binary64) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/32 binary64) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)) x))) |
(* 1/4 (sqrt 2)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) |
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64))) |
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 7/384 binary64)) (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64)))) |
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2))))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 7/384 binary64)) (fma.f64 x #s(literal 3/32 binary64) #s(literal 1/4 binary64)))) |
(* 7/384 (* (pow x 2) (sqrt 2))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 7/384 binary64))) |
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x)) |
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2)))))) |
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/4 binary64) x))) |
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2)))))) |
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 #s(literal 1/4 binary64) x))) |
(* 7/384 (* (pow x 2) (sqrt 2))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal 7/384 binary64))) |
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x)))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64)) x)) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2)))) |
(fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) #s(literal 7/384 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x))) x)) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2)))) |
(fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) #s(literal 7/384 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 1/4 binary64) x))) x)) |
(/ -2 (sqrt 2)) |
(/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
(- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2)))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2)))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(- (* 1/2 (/ x (sqrt 2))) (* 2 (/ 1 (sqrt 2)))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 1/2 (/ x (sqrt 2))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) |
(* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2)))))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2)))))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* x (- (* 1/2 (/ 1 (sqrt 2))) (* 2 (/ 1 (* x (sqrt 2)))))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* 1/2 (/ x (sqrt 2))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) |
(* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(* -1 (* x (- (* 2 (/ 1 (* x (sqrt 2)))) (* 1/2 (/ 1 (sqrt 2)))))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
(/ (pow x 2) (sqrt 2)) |
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) |
3/16 |
#s(literal 3/16 binary64) |
(+ 3/16 (* 7/192 x)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(+ 3/16 (* 7/192 x)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(+ 3/16 (* 7/192 x)) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* 7/192 x) |
(*.f64 x #s(literal 7/192 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* 7/192 x) |
(*.f64 x #s(literal 7/192 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
(* x (+ 7/192 (* 3/16 (/ 1 x)))) |
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) |
Compiled 40 860 to 3 858 computations (90.6% saved)
22 alts after pruning (16 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 316 | 8 | 1 324 |
| Fresh | 7 | 8 | 15 |
| Picked | 4 | 1 | 5 |
| Done | 2 | 5 | 7 |
| Total | 1 329 | 22 | 1 351 |
| Status | Accuracy | Program |
|---|---|---|
| 64.1% | (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) | |
| 65.1% | (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)))))) | |
| 3.1% | (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 4 binary64) (/.f64 #s(literal -16 binary64) x))) x))) | |
| 65.1% | (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))) | |
| 65.1% | (fma.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) | |
| 1.3% | (fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 x x) #s(literal 1/128 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x)) | |
| 65.1% | (fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (sqrt.f64 #s(literal 2 binary64))) | |
| 64.1% | (/.f64 (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64))) | |
| 64.1% | (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) | |
| 64.9% | (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (/.f64 (-.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) | |
| 3.1% | (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64))) | |
| 64.8% | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) | |
| 2.6% | (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 7/384 binary64))) | |
| 3.1% | (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) | |
| 64.8% | (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))) | |
| ✓ | 66.2% | (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) |
| ✓ | 4.4% | (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)) |
| 64.4% | (sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))) | |
| ✓ | 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| ✓ | 64.4% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ✓ | 2.7% | (sqrt.f64 x) |
| ✓ | 70.6% | (sqrt.f64 #s(literal 2 binary64)) |
Compiled 1 028 to 392 computations (61.9% 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 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))) |
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) |
(sqrt.f64 (fma.f64 x (fma.f64 x #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))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 7/384 binary64))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64))) |
(*.f64 x (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 binary64)))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 7/192 binary64)))) |
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(*.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) x) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(+.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))) |
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64))) |
(fma.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)))))) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (/.f64 (-.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) |
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 4 binary64) (/.f64 #s(literal -16 binary64) x))) x))) |
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 x x) #s(literal 1/128 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x)) |
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #s(literal -2 binary64)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) |
(*.f64 (*.f64 x x) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x 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))) |
| 10.0ms | (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 -44.7b remaining (-237.9%)
Threshold costs -44.7b (-237.9%)
| 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 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))) |
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) |
(sqrt.f64 (fma.f64 x (fma.f64 x #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))) |
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 7/384 binary64))) |
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))) |
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) (fma.f64 x #s(literal 7/384 binary64) #s(literal 3/32 binary64))) |
(*.f64 x (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 binary64)))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 7/192 binary64)))) |
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) |
(*.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) x) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(+.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))) |
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (sqrt.f64 #s(literal 2 binary64))) |
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) |
(/.f64 (fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64))) |
(fma.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) |
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)))))) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (/.f64 (-.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) |
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) |
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 4 binary64) (/.f64 #s(literal -16 binary64) x))) x))) |
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 x x) #s(literal 1/128 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x)) |
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #s(literal -2 binary64)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) |
(*.f64 (*.f64 x x) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)))) |
| Outputs |
|---|
(sqrt.f64 #s(literal 2 binary64)) |
3 calls:
| 13.0ms | (sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) |
| 11.0ms | x |
| 9.0ms | (/.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 |
|---|---|---|
| 70.6% | 1 | x |
| 70.6% | 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)))) |
| 70.6% | 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)) |
| 15 504× | lower-fma.f64 |
| 15 504× | lower-fma.f32 |
| 4 704× | lower-*.f64 |
| 4 704× | lower-*.f32 |
| 4 562× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 36 |
| 0 | 17 | 36 |
| 1 | 63 | 22 |
| 2 | 429 | 22 |
| 3 | 4997 | 22 |
| 0 | 8103 | 18 |
| 0 | 77 | 480 |
| 1 | 252 | 446 |
| 2 | 663 | 446 |
| 3 | 1429 | 440 |
| 4 | 2558 | 360 |
| 5 | 5941 | 325 |
| 0 | 8294 | 270 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 17 to 15 computations (11.8% saved)
Compiled 42 to 34 computations (19% saved)
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