
Time bar (total: 7.4s)
| 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)
| 452.0ms | 8 256× | 0 | valid |
| 156.0ms | 2 669× | 0 | exit |
ival-expm1: 146.0ms (36.9% of total)ival-sqrt: 83.0ms (21% of total)ival-mult: 78.0ms (19.7% of total)ival-div: 72.0ms (18.2% of total)ival-true: 7.0ms (1.8% of total)exact: 6.0ms (1.5% of total)ival-assert: 4.0ms (1% of total)| 2× | egg-herbie |
| 15 394× | accelerator-lowering-fma.f32 |
| 15 394× | accelerator-lowering-fma.f64 |
| 2 850× | --lowering--.f32 |
| 2 850× | --lowering--.f64 |
| 2 458× | *-lowering-*.f32 |
Useful iterations: 5 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 19 | 41 |
| 1 | 44 | 39 |
| 2 | 70 | 39 |
| 3 | 113 | 39 |
| 4 | 192 | 20 |
| 5 | 340 | 18 |
| 6 | 672 | 18 |
| 7 | 2570 | 18 |
| 0 | 10 | 12 |
| 1 | 22 | 12 |
| 2 | 28 | 12 |
| 3 | 40 | 12 |
| 4 | 66 | 7 |
| 5 | 119 | 5 |
| 6 | 195 | 5 |
| 7 | 593 | 5 |
| 8 | 2904 | 5 |
| 9 | 6743 | 5 |
| 0 | 8156 | 5 |
| 1× | iter limit |
| 1× | node limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
| Outputs |
|---|
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
| Inputs |
|---|
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1))) |
(neg (sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1)))) |
| Outputs |
|---|
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt (+ 1 (exp x))) |
(sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1))) |
(sqrt (+ 1 (exp (neg x)))) |
(neg (sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1)))) |
(neg (sqrt (+ 1 (exp (neg x))))) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 156 | 0 | - | 0 | - | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) |
| 156 | 0 | - | 0 | - | (-.f64 (exp.f64 x) #s(literal 1 binary64)) |
| 1 | 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 | 0 | - | 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 | 156 | 0 |
-.f64 | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) | cancellation | 156 | 0 |
/.f64 | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) | o/o | 1 | 0 |
| ↳ | (exp.f64 (*.f64 #s(literal 2 binary64) x)) | overflow | 1 | |
| ↳ | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) | overflow | 1 | |
| ↳ | (exp.f64 x) | overflow | 1 | |
| ↳ | (-.f64 (exp.f64 x) #s(literal 1 binary64)) | overflow | 1 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 157 | 0 |
| - | 0 | 99 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 157 | 0 | 0 |
| - | 0 | 1 | 98 |
| number | freq |
|---|---|
| 0 | 99 |
| 1 | 1 |
| 2 | 156 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 38.0ms | 512× | 0 | valid |
Compiled 120 to 44 computations (63.3% saved)
ival-exp: 7.0ms (29.5% of total)ival-expm1: 6.0ms (25.3% of total)ival-div: 4.0ms (16.9% of total)ival-mult: 4.0ms (16.9% of total)ival-sqrt: 3.0ms (12.6% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)Compiled 1 to 1 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 40.4% | (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 | 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)))) |
| ✓ | cost-diff | 128 | (-.f64 (exp.f64 x) #s(literal 1 binary64)) |
| ✓ | cost-diff | 128 | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 6528 | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
| 15 394× | accelerator-lowering-fma.f32 |
| 15 394× | accelerator-lowering-fma.f64 |
| 2 850× | --lowering--.f32 |
| 2 850× | --lowering--.f64 |
| 2 458× | *-lowering-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 45 |
| 1 | 22 | 45 |
| 2 | 28 | 45 |
| 3 | 40 | 45 |
| 4 | 66 | 35 |
| 5 | 119 | 31 |
| 6 | 195 | 31 |
| 7 | 593 | 31 |
| 8 | 2904 | 31 |
| 9 | 6743 | 31 |
| 0 | 8156 | 27 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(- (exp (* 2 x)) 1) |
(exp (* 2 x)) |
(* 2 x) |
2 |
x |
1 |
(- (exp x) 1) |
(exp x) |
| Outputs |
|---|
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
(sqrt.f64 (+.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) |
(expm1.f64 (*.f64 #s(literal 2 binary64) x)) |
(exp (* 2 x)) |
(exp.f64 (*.f64 #s(literal 2 binary64) x)) |
(* 2 x) |
(*.f64 #s(literal 2 binary64) x) |
2 |
#s(literal 2 binary64) |
x |
1 |
#s(literal 1 binary64) |
(- (exp x) 1) |
(expm1.f64 x) |
(exp 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 | 99.7% | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
| ✓ | accuracy | 43.8% | (-.f64 (exp.f64 x) #s(literal 1 binary64)) |
| ✓ | accuracy | 43.8% | (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) |
| 22.0ms | 256× | 0 | valid |
Compiled 47 to 12 computations (74.5% saved)
ival-expm1: 6.0ms (39.2% of total)ival-exp: 3.0ms (19.6% of total)ival-div: 2.0ms (13.1% of total)ival-mult: 2.0ms (13.1% of total)ival-sqrt: 2.0ms (13.1% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))> |
#<alt (- (exp (* 2 x)) 1)> |
#<alt (- (exp x) 1)> |
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))> |
| 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 (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)))> |
12 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× | accelerator-lowering-fma.f32 |
| 4 562× | accelerator-lowering-fma.f64 |
| 3 484× | *-lowering-*.f32 |
| 3 484× | *-lowering-*.f64 |
| 2 734× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 33 |
| 1 | 56 | 19 |
| 2 | 421 | 19 |
| 3 | 4985 | 19 |
| 0 | 8093 | 15 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (- (exp (* 2 x)) 1) (- (exp x) 1)) |
(- (exp (* 2 x)) 1) |
(- (exp x) 1) |
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) |
| Outputs |
|---|
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(+.f64 (exp.f64 x) #s(literal 1 binary64)) |
(+.f64 (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)) (/.f64 #s(literal -1 binary64) (expm1.f64 x))) |
(+.f64 (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64))) |
(+.f64 (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) 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 #s(literal 2 binary64) x)) (expm1.f64 x))) |
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64)) (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))) |
(+.f64 (*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (exp.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(+.f64 (*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (exp.f64 (*.f64 #s(literal 2 binary64) x)))) |
(+.f64 (*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) (*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (exp.f64 x))) |
(+.f64 (*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))))) |
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))))) |
(+.f64 (*.f64 (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (*.f64 (exp.f64 x) (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))))) |
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) |
(-.f64 (exp.f64 x) #s(literal -1 binary64)) |
(-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 x)))) |
(-.f64 (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) 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 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 x))) |
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) (expm1.f64 x))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 x)))) |
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))))) (/.f64 #s(literal 1 binary64) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))))) |
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(-.f64 (/.f64 (*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) 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))) (+.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal -3 binary64)) (+.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))))))) |
(-.f64 (/.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))))) |
(fma.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal -1 binary64) (expm1.f64 x))) |
(fma.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64))) |
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(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (expm1.f64 x) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))) |
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (/.f64 (expm1.f64 x) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 6 binary64)))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 4 binary64)))) (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(*.f64 (*.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) |
(*.f64 (*.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x #s(literal 6 binary64))))) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) |
(*.f64 (*.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x #s(literal 4 binary64))))) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (-.f64 (*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)) (expm1.f64 x))) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x)))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (+.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (expm1.f64 x))) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (expm1.f64 x))) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 3 binary64)))) (+.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (*.f64 #s(literal 2 binary64) x)))))) |
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (-.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (exp.f64 x))) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (exp.f64 x)))) |
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64))) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (exp.f64 (log1p.f64 (exp.f64 x)))) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x)))) |
(neg.f64 (/.f64 (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (expm1.f64 x))))) |
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (expm1.f64 x)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (sqrt.f64 (expm1.f64 x))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)))) |
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64)))) (sqrt.f64 (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))))))) |
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64)))) (sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (expm1.f64 x)))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(/.f64 (sqrt.f64 (-.f64 (*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)) (expm1.f64 x))) (pow.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x))))) |
(/.f64 (sqrt.f64 (-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (sqrt.f64 (+.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (expm1.f64 x))))) |
(/.f64 (*.f64 (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal 1 binary64)) (sqrt.f64 (expm1.f64 x))) |
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (expm1.f64 x))) (sqrt.f64 (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))))) |
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (expm1.f64 x))) (sqrt.f64 (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
(pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)) #s(literal -1/4 binary64)) |
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 #s(literal 1 binary64) (exp.f64 (log1p.f64 (exp.f64 x)))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(*.f64 (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)) (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) |
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1/2 binary64))) |
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (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 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) |
| 1× | egg-herbie |
| 15 504× | accelerator-lowering-fma.f32 |
| 15 504× | accelerator-lowering-fma.f64 |
| 4 704× | *-lowering-*.f32 |
| 4 704× | *-lowering-*.f64 |
| 2 492× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 77 | 444 |
| 1 | 252 | 410 |
| 2 | 663 | 410 |
| 3 | 1429 | 404 |
| 4 | 2558 | 324 |
| 5 | 5941 | 289 |
| 0 | 8294 | 234 |
| 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) |
(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)))) |
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 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 #s(literal 2 binary64) x) |
(* x (+ 2 (* 2 x))) |
(*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x))) |
(* x (+ 2 (* x (+ 2 (* 4/3 x))))) |
(*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))))) |
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x))))))) |
(*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))))))) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (*.f64 #s(literal 2 binary64) x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (*.f64 #s(literal 2 binary64) x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (*.f64 #s(literal 2 binary64) x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (*.f64 #s(literal 2 binary64) x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (*.f64 #s(literal 2 binary64) x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (*.f64 #s(literal 2 binary64) x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (*.f64 #s(literal 2 binary64) x)) |
(- (exp (* 2 x)) 1) |
(expm1.f64 (*.f64 #s(literal 2 binary64) x)) |
x |
(* x (+ 1 (* 1/2 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
(* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))) |
(- (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) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 3/16 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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 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 17 113 to 2 377 computations (86.1% saved)
7 alts after pruning (7 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 728 | 7 | 735 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 729 | 7 | 736 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
| 61.1% | (+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) | |
| 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) | |
| ▶ | 60.9% | (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) |
| ▶ | 62.9% | (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))) |
| ▶ | 60.6% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ▶ | 68.1% | (sqrt.f64 #s(literal 2 binary64)) |
Compiled 118 to 92 computations (22% saved)
| 1× | egg-herbie |
Found 15 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
| ✓ | cost-diff | 0 | (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 2 binary64) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (exp.f64 x) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (exp.f64 x)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
| ✓ | cost-diff | 0 | (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
| 400× | accelerator-lowering-fma.f32 |
| 400× | accelerator-lowering-fma.f64 |
| 134× | *-lowering-*.f32 |
| 134× | *-lowering-*.f64 |
| 132× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 140 |
| 1 | 54 | 140 |
| 2 | 98 | 140 |
| 3 | 189 | 140 |
| 4 | 236 | 140 |
| 5 | 244 | 140 |
| 0 | 244 | 122 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(pow (/ 1 (+ 1 (exp x))) -1/2) |
(/ 1 (+ 1 (exp x))) |
1 |
(+ 1 (exp x)) |
(exp x) |
x |
-1/2 |
(sqrt 2) |
2 |
(sqrt (+ 2 x)) |
(+ 2 x) |
2 |
x |
(sqrt (+ 2 (* x (+ 1 (* x 1/2))))) |
(+ 2 (* x (+ 1 (* x 1/2)))) |
2 |
(* x (+ 1 (* x 1/2))) |
x |
(+ 1 (* x 1/2)) |
1 |
(* x 1/2) |
1/2 |
(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))) |
2 |
(* x (+ 1 (* x (+ 1/2 (* x 1/6))))) |
x |
(+ 1 (* x (+ 1/2 (* x 1/6)))) |
1 |
(* x (+ 1/2 (* x 1/6))) |
(+ 1/2 (* x 1/6)) |
1/2 |
(* x 1/6) |
1/6 |
| Outputs |
|---|
(pow (/ 1 (+ 1 (exp x))) -1/2) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
(/ 1 (+ 1 (exp x))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
1 |
#s(literal 1 binary64) |
(+ 1 (exp x)) |
(+.f64 #s(literal 1 binary64) (exp.f64 x)) |
(exp x) |
(exp.f64 x) |
x |
-1/2 |
#s(literal -1/2 binary64) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
2 |
#s(literal 2 binary64) |
(sqrt (+ 2 x)) |
(sqrt.f64 (+.f64 x #s(literal 2 binary64))) |
(+ 2 x) |
(+.f64 x #s(literal 2 binary64)) |
2 |
#s(literal 2 binary64) |
x |
(sqrt (+ 2 (* x (+ 1 (* x 1/2))))) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))) |
(+ 2 (* x (+ 1 (* x 1/2)))) |
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))) |
2 |
#s(literal 2 binary64) |
(* x (+ 1 (* x 1/2))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
x |
(+ 1 (* x 1/2)) |
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) |
1 |
#s(literal 1 binary64) |
(* x 1/2) |
(*.f64 x #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))) |
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) |
2 |
#s(literal 2 binary64) |
(* x (+ 1 (* x (+ 1/2 (* x 1/6))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
x |
(+ 1 (* x (+ 1/2 (* x 1/6)))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
1 |
#s(literal 1 binary64) |
(* x (+ 1/2 (* x 1/6))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(+ 1/2 (* x 1/6)) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(* x 1/6) |
(*.f64 x #s(literal 1/6 binary64)) |
1/6 |
#s(literal 1/6 binary64) |
Found 15 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) |
| ✓ | accuracy | 100.0% | (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
| ✓ | accuracy | 100.0% | (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
| ✓ | accuracy | 99.7% | (*.f64 x #s(literal 1/6 binary64)) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))) |
| ✓ | accuracy | 100.0% | (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 2 binary64) x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
| ✓ | accuracy | 100.0% | (exp.f64 x) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 1 binary64) (exp.f64 x)) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
| 46.0ms | 157× | 0 | valid |
| 20.0ms | 99× | 0 | invalid |
Compiled 142 to 27 computations (81% saved)
ival-mult: 12.0ms (27.9% of total)ival-add: 8.0ms (18.6% of total)ival-sqrt: 6.0ms (14% of total)const: 6.0ms (14% of total)ival-pow: 5.0ms (11.6% of total)ival-div: 2.0ms (4.7% of total)ival-exp: 2.0ms (4.7% of total)exact: 1.0ms (2.3% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (pow (/ 1 (+ 1 (exp x))) -1/2)> |
#<alt (/ 1 (+ 1 (exp x)))> |
#<alt (+ 1 (exp x))> |
#<alt (exp x)> |
#<alt (sqrt 2)> |
#<alt (sqrt (+ 2 x))> |
#<alt (+ 2 x)> |
#<alt (sqrt (+ 2 (* x (+ 1 (* x 1/2)))))> |
#<alt (+ 2 (* x (+ 1 (* x 1/2))))> |
#<alt (* x (+ 1 (* x 1/2)))> |
#<alt (+ 1 (* x 1/2))> |
#<alt (sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))> |
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))> |
#<alt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))> |
#<alt (+ 1 (* x (+ 1/2 (* x 1/6))))> |
#<alt (* x 1/2)> |
#<alt (* x 1/6)> |
#<alt (* x (+ 1/2 (* x 1/6)))> |
| 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 1/2> |
#<alt (+ 1/2 (* -1/4 x))> |
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))> |
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))> |
#<alt (/ 1 (+ 1 (exp x)))> |
#<alt (/ 1 (+ 1 (exp x)))> |
#<alt (/ 1 (+ 1 (exp x)))> |
#<alt (/ 1 (+ 1 (exp x)))> |
#<alt (/ 1 (+ 1 (exp x)))> |
#<alt (/ 1 (+ 1 (exp x)))> |
#<alt (/ 1 (+ 1 (exp x)))> |
#<alt (/ 1 (+ 1 (exp x)))> |
#<alt 2> |
#<alt (+ 2 x)> |
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))> |
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt (+ 1 (exp x))> |
#<alt 1> |
#<alt (+ 1 x)> |
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))> |
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (exp x)> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt 2> |
#<alt (+ 2 x)> |
#<alt (+ 2 x)> |
#<alt (+ 2 x)> |
#<alt x> |
#<alt (* x (+ 1 (* 2 (/ 1 x))))> |
#<alt (* x (+ 1 (* 2 (/ 1 x))))> |
#<alt (* x (+ 1 (* 2 (/ 1 x))))> |
#<alt x> |
#<alt (* x (+ 1 (* 2 (/ 1 x))))> |
#<alt (* x (+ 1 (* 2 (/ 1 x))))> |
#<alt (* x (+ 1 (* 2 (/ 1 x))))> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))> |
#<alt (* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))> |
#<alt (* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))> |
#<alt (* -1 (* x (sqrt 1/2)))> |
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))> |
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))> |
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))> |
#<alt 2> |
#<alt (+ 2 x)> |
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))> |
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))> |
#<alt (* 1/2 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))> |
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))> |
#<alt (* 1/2 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))> |
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))> |
#<alt 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 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (* x (+ 1/2 (/ 1 x)))> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))> |
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))> |
#<alt 2> |
#<alt (+ 2 x)> |
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))> |
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/2 x)))> |
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))> |
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* 1/2 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 (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* 1/6 x)))> |
#<alt (* x (+ 1/2 (* 1/6 x)))> |
#<alt (* x (+ 1/2 (* 1/6 x)))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
51 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | -inf | (sqrt (+ 2 x)) |
| 1.0ms | x | @ | 0 | (+ 2 (* x (+ 1 (* x 1/2)))) |
| 1.0ms | x | @ | -inf | (sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))) |
| 1.0ms | x | @ | -inf | (pow (/ 1 (+ 1 (exp x))) -1/2) |
| 1.0ms | x | @ | inf | (sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))) |
| 1× | batch-egg-rewrite |
| 4 354× | /-lowering-/.f32 |
| 4 354× | /-lowering-/.f64 |
| 4 018× | *-lowering-*.f32 |
| 4 018× | *-lowering-*.f64 |
| 2 880× | accelerator-lowering-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 120 |
| 1 | 154 | 118 |
| 2 | 1281 | 117 |
| 0 | 8129 | 99 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(pow (/ 1 (+ 1 (exp x))) -1/2) |
(/ 1 (+ 1 (exp x))) |
(+ 1 (exp x)) |
(exp x) |
(sqrt 2) |
(sqrt (+ 2 x)) |
(+ 2 x) |
(sqrt (+ 2 (* x (+ 1 (* x 1/2))))) |
(+ 2 (* x (+ 1 (* x 1/2)))) |
(* x (+ 1 (* x 1/2))) |
(+ 1 (* x 1/2)) |
(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))) |
(* x (+ 1 (* x (+ 1/2 (* x 1/6))))) |
(+ 1 (* x (+ 1/2 (* x 1/6)))) |
(* x 1/2) |
(* x 1/6) |
(* x (+ 1/2 (* x 1/6))) |
| Outputs |
|---|
(exp.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))))) |
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64))) #s(literal -1/4 binary64))) |
(exp.f64 (*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1/4 binary64)) #s(literal 2 binary64))) |
(exp.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1/4 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1/4 binary64)))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)) #s(literal -1/4 binary64)) |
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1/4 binary64)) |
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x)))) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64))) |
(*.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 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x)))) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x))) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64))) |
(exp.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x)))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 x)))) |
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (/.f64 (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) |
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (/.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))) |
(neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 x)))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 x))) |
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) |
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) |
(/.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (-.f64 #s(literal -1 binary64) (exp.f64 x))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (exp.f64 x) (expm1.f64 x)) #s(literal 3 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (exp.f64 x) (expm1.f64 x)) #s(literal 2 binary64)) (*.f64 (exp.f64 x) (expm1.f64 x)))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (exp.f64 x) (expm1.f64 x)) #s(literal 2 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (exp.f64 x))))) |
(pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log1p.f64 (exp.f64 x))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 x)))) |
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))) |
(*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) |
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x)))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (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 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (neg.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(exp.f64 (log1p.f64 (exp.f64 x))) |
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 x))) |
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1 binary64))) |
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64)) (/.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))) |
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) |
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (neg.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal 1 binary64)) |
(neg.f64 (-.f64 #s(literal -1 binary64) (exp.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x #s(literal 2 binary64))))) |
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(/.f64 (-.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal -1 binary64)) |
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x)))) |
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) |
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)) |
(/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) |
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(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) |
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (*.f64 x #s(literal 1/6 binary64))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))) (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)) (*.f64 x (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)) (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) x))) |
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal 1/6 binary64))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) (-.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) |
(/.f64 (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 x (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x))) |
(/.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) x) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x))) |
(/.f64 (neg.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))))) (neg.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))) (neg.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))) |
(/.f64 (neg.f64 (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))) |
(/.f64 (neg.f64 (*.f64 x (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)))) |
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)))) |
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (+.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 x #s(literal 1/2 binary64)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (-.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 x #s(literal 1/2 binary64)))) |
(*.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) x) |
(*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64)) |
(*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))))) |
(*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))) |
(*.f64 (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))) |
(*.f64 (*.f64 x (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)))) |
(*.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))) |
(*.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)))) |
| 1× | egg-herbie |
| 11 686× | accelerator-lowering-fma.f32 |
| 11 686× | accelerator-lowering-fma.f64 |
| 5 130× | *-lowering-*.f32 |
| 5 130× | *-lowering-*.f64 |
| 3 484× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 291 | 1962 |
| 1 | 906 | 1710 |
| 2 | 3039 | 1652 |
| 0 | 8459 | 1517 |
| 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))) |
1/2 |
(+ 1/2 (* -1/4 x)) |
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4))) |
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4))) |
(/ 1 (+ 1 (exp x))) |
(/ 1 (+ 1 (exp x))) |
(/ 1 (+ 1 (exp x))) |
(/ 1 (+ 1 (exp x))) |
(/ 1 (+ 1 (exp x))) |
(/ 1 (+ 1 (exp x))) |
(/ 1 (+ 1 (exp x))) |
(/ 1 (+ 1 (exp x))) |
2 |
(+ 2 x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
(+ 1 (exp x)) |
1 |
(+ 1 x) |
(+ 1 (* x (+ 1 (* 1/2 x)))) |
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(exp x) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3))))) |
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
2 |
(+ 2 x) |
(+ 2 x) |
(+ 2 x) |
x |
(* x (+ 1 (* 2 (/ 1 x)))) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(* x (+ 1 (* 2 (/ 1 x)))) |
x |
(* x (+ 1 (* 2 (/ 1 x)))) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* x (sqrt 1/2)) |
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))) |
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))) |
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))) |
(* -1 (* x (sqrt 1/2))) |
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))) |
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x))))) |
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x))))) |
2 |
(+ 2 x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
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))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* 1/2 x)) |
(+ 1 (* 1/2 x)) |
(* 1/2 x) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* 1/2 x) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(* x (+ 1/2 (/ 1 x))) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
2 |
(+ 2 x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3))))))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6))) |
x |
(* x (+ 1 (* 1/2 x))) |
(* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) |
(* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* 1/2 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) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/6 x))) |
(* x (+ 1/2 (* 1/6 x))) |
(* x (+ 1/2 (* 1/6 x))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
| Outputs |
|---|
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (+.f64 (*.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))))) |
(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))) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/4 x)) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) |
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))) |
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/48 binary64) (*.f64 (*.f64 x x) #s(literal -1/480 binary64))))))) |
(/ 1 (+ 1 (exp x))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(/ 1 (+ 1 (exp x))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(/ 1 (+ 1 (exp x))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(/ 1 (+ 1 (exp x))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(/ 1 (+ 1 (exp x))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(/ 1 (+ 1 (exp x))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(/ 1 (+ 1 (exp x))) |
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) |
(/ 1 (+ 1 (exp x))) |
(/.f64 #s(literal 1 binary64) (+.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)))) |
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 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)))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))) |
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 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)))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))) |
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (/.f64 #s(literal -1/16 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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (+.f64 (/.f64 (*.f64 x #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)))))))) |
(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 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) |
(* 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (*.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 #s(literal 0 binary64) (*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))) |
(* -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 (-.f64 #s(literal 0 binary64) (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.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)))))))) |
2 |
#s(literal 2 binary64) |
(+ 2 x) |
(+.f64 #s(literal 2 binary64) x) |
(+ 2 x) |
(+.f64 #s(literal 2 binary64) x) |
(+ 2 x) |
(+.f64 #s(literal 2 binary64) x) |
x |
(* x (+ 1 (* 2 (/ 1 x)))) |
(+.f64 #s(literal 2 binary64) x) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(+.f64 #s(literal 2 binary64) x) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(+.f64 #s(literal 2 binary64) x) |
x |
(* x (+ 1 (* 2 (/ 1 x)))) |
(+.f64 #s(literal 2 binary64) x) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(+.f64 #s(literal 2 binary64) x) |
(* x (+ 1 (* 2 (/ 1 x)))) |
(+.f64 #s(literal 2 binary64) x) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (+.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 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)))))) |
(+.f64 (*.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)))))) |
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x x))))) |
(* 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 (*.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x x)) (/.f64 (/.f64 #s(literal -3/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x x))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) |
(* -1 (* x (sqrt 1/2))) |
(-.f64 #s(literal 0 binary64) (*.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 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 #s(literal 1 binary64) (/.f64 (+.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))))) #s(literal 1 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 x (+.f64 (/.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)))) x) (-.f64 #s(literal 0 binary64) (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)))) |
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))) |
(* 1/2 (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x)))))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x)))))) |
(* 1/2 (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x)))))) |
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x)))))) |
x |
(* x (+ 1 (* 1/2 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) |
(* x (+ 1 (* 1/2 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) |
(* x (+ 1 (* 1/2 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) |
(* 1/2 (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) |
(* 1/2 (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) |
(* (pow x 2) (+ 1/2 (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) |
(+ 1 (* 1/2 x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) |
(+ 1 (* 1/2 x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) |
(* x (+ 1/2 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) |
(* x (+ 1/2 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) |
(* x (+ 1/2 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) |
(* x (+ 1/2 (/ 1 x))) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (+.f64 (*.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(*.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/6 binary64)))) (sqrt.f64 #s(literal 1/6 binary64))))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/6 binary64)))) (sqrt.f64 #s(literal -1/6 binary64))))) x))) |
2 |
#s(literal 2 binary64) |
(+ 2 x) |
(+.f64 #s(literal 2 binary64) x) |
(+ 2 (* x (+ 1 (* 1/2 x)))) |
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3))))))) |
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64))))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) |
(*.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -2 binary64) (*.f64 x x)))) x)))) |
x |
(* x (+ 1 (* 1/2 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) |
(* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
(* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) |
(*.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) |
(*.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* 1/6 x))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* x (+ 1/2 (* 1/6 x))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* x (+ 1/2 (* 1/6 x))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
Compiled 19 847 to 2 534 computations (87.2% saved)
11 alts after pruning (8 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 768 | 7 | 775 |
| Fresh | 1 | 1 | 2 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 0 | 0 |
| Total | 771 | 11 | 782 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
| ▶ | 61.7% | (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))) #s(literal -1/2 binary64)) |
| ▶ | 63.6% | (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) |
| 2.8% | (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) | |
| ▶ | 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| ✓ | 60.6% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| 2.1% | (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) | |
| ▶ | 3.1% | (sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
| 2.0% | (sqrt.f64 (*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))) | |
| ▶ | 2.1% | (sqrt.f64 x) |
| ✓ | 68.1% | (sqrt.f64 #s(literal 2 binary64)) |
Compiled 155 to 120 computations (22.6% saved)
| 1× | egg-herbie |
Found 15 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))) |
| ✓ | cost-diff | 0 | (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x)))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))) |
| ✓ | cost-diff | 0 | (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))) #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
| ✓ | cost-diff | 0 | (*.f64 x #s(literal -1/4 binary64)) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) |
| ✓ | cost-diff | 0 | (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 x) |
| ✓ | 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))) |
| 96× | accelerator-lowering-fma.f32 |
| 96× | accelerator-lowering-fma.f64 |
| 86× | *-lowering-*.f32 |
| 86× | *-lowering-*.f64 |
| 44× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 125 |
| 1 | 52 | 125 |
| 2 | 103 | 125 |
| 3 | 116 | 125 |
| 0 | 116 | 113 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(sqrt (- (exp x) -1)) |
(- (exp x) -1) |
(exp x) |
x |
-1 |
(sqrt x) |
x |
(pow (+ 1/2 (* x -1/4)) -1/2) |
(+ 1/2 (* x -1/4)) |
1/2 |
(* x -1/4) |
x |
-1/4 |
-1/2 |
(sqrt (* x (* x (+ 1/2 (* x 1/6))))) |
(* x (* x (+ 1/2 (* x 1/6)))) |
x |
(* x (+ 1/2 (* x 1/6))) |
(+ 1/2 (* x 1/6)) |
1/2 |
(* x 1/6) |
1/6 |
(pow (+ 1/2 (* x (+ -1/4 (* 1/48 (* x x))))) -1/2) |
(+ 1/2 (* x (+ -1/4 (* 1/48 (* x x))))) |
1/2 |
(* x (+ -1/4 (* 1/48 (* x x)))) |
x |
(+ -1/4 (* 1/48 (* x x))) |
-1/4 |
(* 1/48 (* x x)) |
1/48 |
(* x x) |
-1/2 |
| Outputs |
|---|
(sqrt (- (exp x) -1)) |
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))) |
(- (exp x) -1) |
(+.f64 (exp.f64 x) #s(literal 1 binary64)) |
(exp x) |
(exp.f64 x) |
x |
-1 |
#s(literal -1 binary64) |
(sqrt x) |
(sqrt.f64 x) |
x |
(pow (+ 1/2 (* x -1/4)) -1/2) |
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) |
(+ 1/2 (* x -1/4)) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(* x -1/4) |
(*.f64 x #s(literal -1/4 binary64)) |
x |
-1/4 |
#s(literal -1/4 binary64) |
-1/2 |
#s(literal -1/2 binary64) |
(sqrt (* x (* x (+ 1/2 (* x 1/6))))) |
(sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
(* x (* x (+ 1/2 (* x 1/6)))) |
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
x |
(* x (+ 1/2 (* x 1/6))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(+ 1/2 (* x 1/6)) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(* x 1/6) |
(*.f64 x #s(literal 1/6 binary64)) |
1/6 |
#s(literal 1/6 binary64) |
(pow (+ 1/2 (* x (+ -1/4 (* 1/48 (* x x))))) -1/2) |
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))) #s(literal -1/2 binary64)) |
(+ 1/2 (* x (+ -1/4 (* 1/48 (* x x))))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))) |
1/2 |
#s(literal 1/2 binary64) |
(* x (+ -1/4 (* 1/48 (* x x)))) |
(*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x)))) |
x |
(+ -1/4 (* 1/48 (* x x))) |
(+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))) |
-1/4 |
#s(literal -1/4 binary64) |
(* 1/48 (* x x)) |
(*.f64 #s(literal 1/48 binary64) (*.f64 x x)) |
1/48 |
#s(literal 1/48 binary64) |
(* x x) |
(*.f64 x x) |
-1/2 |
#s(literal -1/2 binary64) |
Found 15 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))) |
| ✓ | accuracy | 100.0% | (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x)))) |
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 99.9% | (*.f64 #s(literal 1/48 binary64) (*.f64 x x)) |
| ✓ | accuracy | 100.0% | (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
| ✓ | accuracy | 100.0% | (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
| ✓ | accuracy | 99.9% | (*.f64 x #s(literal 1/6 binary64)) |
| ✓ | accuracy | 86.9% | (sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
| ✓ | accuracy | 100.0% | (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal -1/4 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 x) |
| ✓ | accuracy | 100.0% | (exp.f64 x) |
| ✓ | accuracy | 100.0% | (-.f64 (exp.f64 x) #s(literal -1 binary64)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| 77.0ms | 179× | 0 | invalid |
| 18.0ms | 77× | 0 | valid |
Compiled 127 to 27 computations (78.7% saved)
ival-sqrt: 28.0ms (34.7% of total)ival-add: 19.0ms (23.6% of total)ival-mult: 10.0ms (12.4% of total)ival-pow: 10.0ms (12.4% of total)const: 6.0ms (7.4% of total)ival-exp: 5.0ms (6.2% of total)ival-sub: 1.0ms (1.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt (sqrt (- (exp x) -1))> |
#<alt (- (exp x) -1)> |
#<alt (exp x)> |
#<alt (sqrt x)> |
#<alt (pow (+ 1/2 (* x -1/4)) -1/2)> |
#<alt (+ 1/2 (* x -1/4))> |
#<alt (* x -1/4)> |
#<alt (sqrt (* x (* x (+ 1/2 (* x 1/6)))))> |
#<alt (* x (* x (+ 1/2 (* x 1/6))))> |
#<alt (* x (+ 1/2 (* x 1/6)))> |
#<alt (+ 1/2 (* x 1/6))> |
#<alt (pow (+ 1/2 (* x (+ -1/4 (* 1/48 (* x x))))) -1/2)> |
#<alt (+ 1/2 (* x (+ -1/4 (* 1/48 (* x x)))))> |
#<alt (* x (+ -1/4 (* 1/48 (* x x))))> |
#<alt (+ -1/4 (* 1/48 (* x x)))> |
#<alt (* x 1/6)> |
#<alt (* 1/48 (* x x))> |
#<alt (* x x)> |
| 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 x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (sqrt x)> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* (sqrt (/ 1 x)) (sqrt -4))> |
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))> |
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))> |
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))> |
#<alt (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))> |
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))> |
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))> |
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))> |
#<alt 1/2> |
#<alt (+ 1/2 (* -1/4 x))> |
#<alt (+ 1/2 (* -1/4 x))> |
#<alt (+ 1/2 (* -1/4 x))> |
#<alt (* -1/4 x)> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))> |
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))> |
#<alt (* -1/4 x)> |
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))> |
#<alt (* -1/4 x)> |
#<alt (* -1/4 x)> |
#<alt (* -1/4 x)> |
#<alt (* -1/4 x)> |
#<alt (* -1/4 x)> |
#<alt (* -1/4 x)> |
#<alt (* -1/4 x)> |
#<alt (* -1/4 x)> |
#<alt (* -1/4 x)> |
#<alt (* -1/4 x)> |
#<alt (* -1/4 x)> |
#<alt (* -1/4 x)> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))> |
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))> |
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))> |
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))> |
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))> |
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))> |
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))> |
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))> |
#<alt (* 1/2 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))> |
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))> |
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* 1/6 x)))> |
#<alt (* x (+ 1/2 (* 1/6 x)))> |
#<alt (* x (+ 1/2 (* 1/6 x)))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt 1/2> |
#<alt (+ 1/2 (* 1/6 x))> |
#<alt (+ 1/2 (* 1/6 x))> |
#<alt (+ 1/2 (* 1/6 x))> |
#<alt (* 1/6 x)> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* 1/6 x)> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (sqrt 2)> |
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))> |
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))> |
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt 48))> |
#<alt (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))) x)> |
#<alt (/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48)))) x)> |
#<alt (/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (+ (* 3456 (* (sqrt (/ 1 (pow x 9))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))))) x)> |
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -48) (sqrt -1))))> |
#<alt (* -1 (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -48)))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))> |
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 576 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))> |
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* -1 (/ (+ (* -576 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 3456 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) x))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))> |
#<alt 1/2> |
#<alt (+ 1/2 (* -1/4 x))> |
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))> |
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))> |
#<alt (* 1/48 (pow x 3))> |
#<alt (* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* 1/48 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))> |
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))> |
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))> |
#<alt (* -1/4 x)> |
#<alt (* x (- (* 1/48 (pow x 2)) 1/4))> |
#<alt (* x (- (* 1/48 (pow x 2)) 1/4))> |
#<alt (* x (- (* 1/48 (pow x 2)) 1/4))> |
#<alt (* 1/48 (pow x 3))> |
#<alt (* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* 1/48 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))> |
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))> |
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))> |
#<alt -1/4> |
#<alt (- (* 1/48 (pow x 2)) 1/4)> |
#<alt (- (* 1/48 (pow x 2)) 1/4)> |
#<alt (- (* 1/48 (pow x 2)) 1/4)> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* 1/48 (pow x 2))> |
#<alt (* 1/48 (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 (pow x 2)> |
54 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | 0 | (+ 1/2 (* x -1/4)) |
| 1.0ms | x | @ | -inf | (sqrt (* x (* x (+ 1/2 (* x 1/6))))) |
| 1.0ms | x | @ | inf | (pow (+ 1/2 (* x -1/4)) -1/2) |
| 1.0ms | x | @ | -inf | (pow (+ 1/2 (* x (+ -1/4 (* 1/48 (* x x))))) -1/2) |
| 1.0ms | x | @ | inf | (pow (+ 1/2 (* x (+ -1/4 (* 1/48 (* x x))))) -1/2) |
| 1× | batch-egg-rewrite |
| 7 076× | accelerator-lowering-fma.f32 |
| 7 076× | accelerator-lowering-fma.f64 |
| 5 590× | *-lowering-*.f32 |
| 5 590× | *-lowering-*.f64 |
| 3 314× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 110 |
| 1 | 131 | 110 |
| 2 | 934 | 108 |
| 0 | 8348 | 96 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt (- (exp x) -1)) |
(- (exp x) -1) |
(exp x) |
(sqrt x) |
(pow (+ 1/2 (* x -1/4)) -1/2) |
(+ 1/2 (* x -1/4)) |
(* x -1/4) |
(sqrt (* x (* x (+ 1/2 (* x 1/6))))) |
(* x (* x (+ 1/2 (* x 1/6)))) |
(* x (+ 1/2 (* x 1/6))) |
(+ 1/2 (* x 1/6)) |
(pow (+ 1/2 (* x (+ -1/4 (* 1/48 (* x x))))) -1/2) |
(+ 1/2 (* x (+ -1/4 (* 1/48 (* x x))))) |
(* x (+ -1/4 (* 1/48 (* x x)))) |
(+ -1/4 (* 1/48 (* x x))) |
(* x 1/6) |
(* 1/48 (* x x)) |
(* x x) |
| 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 #s(literal 2 binary64) 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 (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64)) (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) |
(/.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) |
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.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 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))) |
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (neg.f64 (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64)))) |
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
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(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2304 binary64))))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))))) |
(/.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2304 binary64)))) #s(literal -1/16 binary64))) (neg.f64 (+.f64 (*.f64 #s(literal 1/48 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))) |
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2304 binary64)))) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))) (/.f64 #s(literal 1/16 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64))))) (+.f64 (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2304 binary64)))) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))) (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2304 binary64)))) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64))))) (*.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))) (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2304 binary64)))) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))) (/.f64 #s(literal 1/16 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64))))) (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2304 binary64)))) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))) (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2304 binary64)))) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))))) (+.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))) (/.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2304 binary64)))) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x)))) #s(literal -1 binary64)) |
(*.f64 (+.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/110592 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/2304 binary64)) #s(literal -1/192 binary64)))))) |
(*.f64 (+.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/110592 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2304 binary64)))) (-.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) #s(literal -1/192 binary64)))))) |
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x)))) |
(*.f64 (-.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2304 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64))))) |
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/110592 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/16 binary64) (neg.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/2304 binary64)) #s(literal -1/192 binary64))))))) |
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2304 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))))) |
(*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/2304 binary64)))) #s(literal -1/16 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/48 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))) |
(*.f64 x #s(literal 1/6 binary64)) |
(*.f64 #s(literal 1/6 binary64) x) |
(*.f64 x (*.f64 x #s(literal 1/48 binary64))) |
(*.f64 #s(literal 1/48 binary64) (*.f64 x x)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(*.f64 (*.f64 x #s(literal 1/48 binary64)) x) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) |
(pow.f64 x #s(literal 2 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64)) |
(*.f64 x x) |
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x))) |
| 1× | egg-herbie |
| 11 208× | accelerator-lowering-fma.f32 |
| 11 208× | accelerator-lowering-fma.f64 |
| 5 902× | *-lowering-*.f32 |
| 5 902× | *-lowering-*.f64 |
| 3 502× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 304 | 2027 |
| 1 | 840 | 1856 |
| 2 | 2484 | 1836 |
| 3 | 5087 | 1827 |
| 0 | 8124 | 1706 |
| 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 x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* (sqrt (/ 1 x)) (sqrt -4)) |
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))) |
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))) |
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))) |
(* 2 (* (sqrt (/ 1 x)) (sqrt -1))) |
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))) |
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))) |
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))) |
1/2 |
(+ 1/2 (* -1/4 x)) |
(+ 1/2 (* -1/4 x)) |
(+ 1/2 (* -1/4 x)) |
(* -1/4 x) |
(* x (- (* 1/2 (/ 1 x)) 1/4)) |
(* x (- (* 1/2 (/ 1 x)) 1/4)) |
(* x (- (* 1/2 (/ 1 x)) 1/4)) |
(* -1/4 x) |
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x))))) |
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x))))) |
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x))))) |
(* -1/4 x) |
(* -1/4 x) |
(* -1/4 x) |
(* -1/4 x) |
(* -1/4 x) |
(* -1/4 x) |
(* -1/4 x) |
(* -1/4 x) |
(* -1/4 x) |
(* -1/4 x) |
(* -1/4 x) |
(* -1/4 x) |
(* x (sqrt 1/2)) |
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))) |
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))) |
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))) |
(* 1/2 (pow x 2)) |
(* (pow x 2) (+ 1/2 (* 1/6 x))) |
(* (pow x 2) (+ 1/2 (* 1/6 x))) |
(* (pow x 2) (+ 1/2 (* 1/6 x))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/6 x))) |
(* x (+ 1/2 (* 1/6 x))) |
(* x (+ 1/2 (* 1/6 x))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
1/2 |
(+ 1/2 (* 1/6 x)) |
(+ 1/2 (* 1/6 x)) |
(+ 1/2 (* 1/6 x)) |
(* 1/6 x) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* 1/6 x) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(sqrt 2) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(* (sqrt (/ 1 (pow x 3))) (sqrt 48)) |
(/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))) x) |
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48)))) x) |
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (+ (* 3456 (* (sqrt (/ 1 (pow x 9))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))))) x) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -48) (sqrt -1)))) |
(* -1 (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -48)))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x)) |
(* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 576 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x)) |
(* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* -1 (/ (+ (* -576 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 3456 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) x))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x)) |
1/2 |
(+ 1/2 (* -1/4 x)) |
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4))) |
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4))) |
(* 1/48 (pow x 3)) |
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) |
(* 1/48 (pow x 3)) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48))) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3)))))) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3)))))) |
(* -1/4 x) |
(* x (- (* 1/48 (pow x 2)) 1/4)) |
(* x (- (* 1/48 (pow x 2)) 1/4)) |
(* x (- (* 1/48 (pow x 2)) 1/4)) |
(* 1/48 (pow x 3)) |
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* 1/48 (pow x 3)) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48))) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48))) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48))) |
-1/4 |
(- (* 1/48 (pow x 2)) 1/4) |
(- (* 1/48 (pow x 2)) 1/4) |
(- (* 1/48 (pow x 2)) 1/4) |
(* 1/48 (pow x 2)) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* 1/48 (pow x 2)) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/48 (pow x 2)) |
(* 1/48 (pow x 2)) |
(* 1/48 (pow x 2)) |
(* 1/48 (pow x 2)) |
(* 1/48 (pow x 2)) |
(* 1/48 (pow x 2)) |
(* 1/48 (pow x 2)) |
(* 1/48 (pow x 2)) |
(* 1/48 (pow x 2)) |
(* 1/48 (pow x 2)) |
(* 1/48 (pow x 2)) |
(* 1/48 (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) |
(pow x 2) |
| Outputs |
|---|
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 3/16 binary64) x) (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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal 7/192 binary64) x) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 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)))) |
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))) |
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 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)))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))) |
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 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 x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 3/16 binary64) x) (sqrt.f64 #s(literal 2 binary64)))))) |
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 5/64 binary64) x) (sqrt.f64 #s(literal 2 binary64)))))))) |
(* (sqrt (/ 1 x)) (sqrt -4)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) |
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))) |
(+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -4 binary64) (sqrt.f64 #s(literal -4 binary64))))) |
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))) |
(+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (/.f64 (+.f64 (*.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (sqrt.f64 #s(literal -4 binary64)))) |
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))) |
(+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (/.f64 (+.f64 (*.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (sqrt.f64 #s(literal -4 binary64)))) (*.f64 (/.f64 (+.f64 #s(literal -16 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal -4 binary64)))) (sqrt.f64 #s(literal -4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))) |
(* 2 (* (sqrt (/ 1 x)) (sqrt -1))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))) |
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -2 binary64))))) |
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))) |
(-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 32 binary64) (*.f64 x #s(literal -4 binary64)))) (*.f64 (sqrt.f64 x) #s(literal 4 binary64)))) (*.f64 x (*.f64 x x)))) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/4 x)) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64))) |
(+ 1/2 (* -1/4 x)) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64))) |
(+ 1/2 (* -1/4 x)) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64))) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* x (- (* 1/2 (/ 1 x)) 1/4)) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64))) |
(* x (- (* 1/2 (/ 1 x)) 1/4)) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64))) |
(* x (- (* 1/2 (/ 1 x)) 1/4)) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64))) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x))))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64))) |
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x))))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64))) |
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x))))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64))) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))) |
(*.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 x #s(literal 1/12 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) |
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))) |
(*.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 x #s(literal -1/144 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))))) |
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))) |
(*.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (+.f64 (/.f64 (*.f64 x #s(literal 1/3456 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/144 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(*.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal 1/6 binary64)))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(*.f64 x (*.f64 x (+.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal 1/6 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/6 binary64)) #s(literal 5 binary64))))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal -1/6 binary64))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) #s(literal 3/16 binary64)))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) #s(literal 3/16 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/128 binary64)) (pow.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal 5 binary64)))))))) |
(* 1/2 (pow x 2)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (* 1/6 x))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (* 1/6 x))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x x)) |
(* (pow x 2) (+ 1/2 (* 1/6 x))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x x)) |
(* 1/6 (pow x 3)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x x)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x x)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x x)) |
(* 1/6 (pow x 3)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x x)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x x)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x x)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* 1/6 x))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* x (+ 1/2 (* 1/6 x))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* x (+ 1/2 (* 1/6 x))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* 1/6 x)) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
(+ 1/2 (* 1/6 x)) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
(+ 1/2 (* 1/6 x)) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
(sqrt 2) |
(sqrt.f64 #s(literal 2 binary64)) |
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 3/16 binary64) x) (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)))))) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal 7/192 binary64) x) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))))) |
(* (sqrt (/ 1 (pow x 3))) (sqrt 48)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 48 binary64))) |
(/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))) x) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 288 binary64) (sqrt.f64 #s(literal 48 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 48 binary64)))) x) |
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48)))) x) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 48 binary64))) (/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal -576 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 288 binary64))) (sqrt.f64 #s(literal 48 binary64)))) x) |
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (+ (* 3456 (* (sqrt (/ 1 (pow x 9))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))))) x) |
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 48 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 48 binary64))) (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal -576 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 288 binary64))) (*.f64 #s(literal 3456 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 9 binary64)))))))) x) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -48) (sqrt -1)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -48 binary64))))) |
(* -1 (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -48)))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x)) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 #s(literal -48 binary64))) #s(literal -288 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -48 binary64))))) x) |
(* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 576 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x)) |
(/.f64 (-.f64 (/.f64 (/.f64 (*.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -48 binary64))) x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 576 binary64)) (*.f64 (sqrt.f64 x) #s(literal -288 binary64)))) x) x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -48 binary64))))) x) |
(* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* -1 (/ (+ (* -576 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 3456 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) x))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x)) |
(/.f64 (-.f64 (/.f64 (-.f64 (*.f64 (sqrt.f64 x) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -288 binary64)) (sqrt.f64 #s(literal -48 binary64)))) (*.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -48 binary64))) x) (+.f64 (*.f64 (sqrt.f64 x) #s(literal -576 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 3456 binary64))))) (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -48 binary64))))) x) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/4 x)) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64))) |
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64))))) |
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64))))) |
(* 1/48 (pow x 3)) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/48 binary64))) |
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 x (*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x)) |
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x x))))) |
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x x))))) |
(* 1/48 (pow x 3)) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/48 binary64))) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48))) |
(*.f64 x (*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x)) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3)))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x x))))) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3)))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x x))))) |
(* -1/4 x) |
(/.f64 x #s(literal -4 binary64)) |
(* x (- (* 1/48 (pow x 2)) 1/4)) |
(*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64)))) |
(* x (- (* 1/48 (pow x 2)) 1/4)) |
(*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64)))) |
(* x (- (* 1/48 (pow x 2)) 1/4)) |
(*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64)))) |
(* 1/48 (pow x 3)) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/48 binary64))) |
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 x (*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x)) |
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 x (*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x)) |
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 x (*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x)) |
(* 1/48 (pow x 3)) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/48 binary64))) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48))) |
(*.f64 x (*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x)) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48))) |
(*.f64 x (*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x)) |
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48))) |
(*.f64 x (*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x)) |
-1/4 |
#s(literal -1/4 binary64) |
(- (* 1/48 (pow x 2)) 1/4) |
(+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64))) |
(- (* 1/48 (pow x 2)) 1/4) |
(+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64))) |
(- (* 1/48 (pow x 2)) 1/4) |
(+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64))) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x) |
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) x) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(* 1/48 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/48 binary64)) |
(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) |
Compiled 15 450 to 2 167 computations (86% saved)
11 alts after pruning (4 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 701 | 2 | 703 |
| Fresh | 1 | 2 | 3 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 3 | 3 |
| Total | 703 | 11 | 714 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
| ✓ | 61.7% | (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))) #s(literal -1/2 binary64)) |
| ✓ | 63.6% | (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) |
| ▶ | 2.3% | (*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x) |
| ▶ | 2.8% | (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
| ✓ | 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| ✓ | 60.6% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ▶ | 2.1% | (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) |
| ▶ | 2.0% | (sqrt.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) |
| ✓ | 2.1% | (sqrt.f64 x) |
| ✓ | 68.1% | (sqrt.f64 #s(literal 2 binary64)) |
Compiled 85 to 66 computations (22.4% saved)
| 1× | egg-herbie |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 x #s(literal 1/6 binary64)) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
| ✓ | cost-diff | 0 | (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x) |
| ✓ | cost-diff | 0 | (sqrt.f64 #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
| ✓ | cost-diff | 0 | (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) |
| ✓ | cost-diff | 0 | (*.f64 x #s(literal 1/6 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (*.f64 x #s(literal 1/6 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) |
| ✓ | cost-diff | 0 | (sqrt.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) |
| 208× | accelerator-lowering-fma.f32 |
| 208× | accelerator-lowering-fma.f64 |
| 158× | *-lowering-*.f32 |
| 158× | *-lowering-*.f64 |
| 56× | associate-*r* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 109 |
| 1 | 43 | 109 |
| 2 | 72 | 105 |
| 3 | 154 | 105 |
| 4 | 195 | 105 |
| 5 | 195 | 105 |
| 0 | 195 | 94 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(sqrt (* x (* x (* x 1/6)))) |
(* x (* x (* x 1/6))) |
x |
(* x (* x 1/6)) |
(* x 1/6) |
1/6 |
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))) |
(* x (+ 1 (* x (+ 1/2 (* x 1/6))))) |
x |
(+ 1 (* x (+ 1/2 (* x 1/6)))) |
1 |
(* x (+ 1/2 (* x 1/6))) |
(+ 1/2 (* x 1/6)) |
1/2 |
(* x 1/6) |
1/6 |
(* x (sqrt 1/2)) |
x |
(sqrt 1/2) |
1/2 |
(* (pow (+ 1/2 (* x 1/6)) 1/2) x) |
(pow (+ 1/2 (* x 1/6)) 1/2) |
(+ 1/2 (* x 1/6)) |
1/2 |
(* x 1/6) |
x |
1/6 |
| Outputs |
|---|
(sqrt (* x (* x (* x 1/6)))) |
(sqrt.f64 (*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))) |
(* x (* x (* x 1/6))) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
x |
(* x (* x 1/6)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* x 1/6) |
(*.f64 x #s(literal 1/6 binary64)) |
1/6 |
#s(literal 1/6 binary64) |
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))) |
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) |
(* x (+ 1 (* x (+ 1/2 (* x 1/6))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) |
x |
(+ 1 (* x (+ 1/2 (* x 1/6)))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) |
1 |
#s(literal 1 binary64) |
(* x (+ 1/2 (* x 1/6))) |
(*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) |
(+ 1/2 (* x 1/6)) |
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(* x 1/6) |
(*.f64 x #s(literal 1/6 binary64)) |
1/6 |
#s(literal 1/6 binary64) |
(* x (sqrt 1/2)) |
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
x |
(sqrt 1/2) |
(sqrt.f64 #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(* (pow (+ 1/2 (* x 1/6)) 1/2) x) |
(*.f64 x (pow.f64 (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) |
(pow (+ 1/2 (* x 1/6)) 1/2) |
(pow.f64 (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) |
(+ 1/2 (* x 1/6)) |
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(* x 1/6) |
(*.f64 x #s(literal 1/6 binary64)) |
x |
1/6 |
#s(literal 1/6 binary64) |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) |
| ✓ | accuracy | 99.9% | (*.f64 x #s(literal 1/6 binary64)) |
| ✓ | accuracy | 99.8% | (*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 #s(literal 1/2 binary64)) |
| ✓ | accuracy | 99.8% | (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) |
| ✓ | accuracy | 100.0% | (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
| ✓ | accuracy | 100.0% | (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) |
| ✓ | accuracy | 99.9% | (*.f64 x #s(literal 1/6 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) |
| ✓ | accuracy | 99.9% | (*.f64 x (*.f64 x #s(literal 1/6 binary64))) |
| ✓ | accuracy | 99.9% | (*.f64 x #s(literal 1/6 binary64)) |
| ✓ | accuracy | 90.1% | (sqrt.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) |
| 30.0ms | 178× | 0 | invalid |
| 10.0ms | 78× | 0 | valid |
Compiled 113 to 19 computations (83.2% saved)
ival-mult: 15.0ms (54.5% of total)ival-sqrt: 6.0ms (21.8% of total)const: 4.0ms (14.5% of total)ival-add: 2.0ms (7.3% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (sqrt (* x (* x (* x 1/6))))> |
#<alt (* x (* x (* x 1/6)))> |
#<alt (* x (* x 1/6))> |
#<alt (* x 1/6)> |
#<alt (sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))> |
#<alt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))> |
#<alt (+ 1 (* x (+ 1/2 (* x 1/6))))> |
#<alt (* x (+ 1/2 (* x 1/6)))> |
#<alt (* x (sqrt 1/2))> |
#<alt (sqrt 1/2)> |
#<alt (* (pow (+ 1/2 (* x 1/6)) 1/2) x)> |
#<alt (pow (+ 1/2 (* x 1/6)) 1/2)> |
#<alt (+ 1/2 (* x 1/6))> |
| Outputs |
|---|
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))> |
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))> |
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))> |
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (* 1/6 x)> |
#<alt (sqrt x)> |
#<alt (+ (sqrt x) (* 1/4 (sqrt (pow x 3))))> |
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))> |
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))> |
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))> |
#<alt (* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6)))> |
#<alt (* (pow x 2) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))> |
#<alt (* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* 1/32 (* (sqrt x) (/ (pow (sqrt -1) 2) (pow (sqrt 1/6) 3)))) (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/2 x)))> |
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))> |
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 x))> |
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))> |
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))> |
#<alt (* 1/2 x)> |
#<alt (* x (+ 1/2 (* 1/6 x)))> |
#<alt (* x (+ 1/2 (* 1/6 x)))> |
#<alt (* x (+ 1/2 (* 1/6 x)))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* 1/6 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (sqrt 1/2))> |
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))> |
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))> |
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))> |
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))> |
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))> |
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))> |
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))> |
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))> |
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6))))))> |
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))))))> |
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3))))))))> |
#<alt (sqrt 1/2)> |
#<alt (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))> |
#<alt (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))> |
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))> |
#<alt (* (sqrt x) (sqrt 1/6))> |
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))> |
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))> |
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))> |
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))> |
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))> |
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))> |
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))))> |
#<alt 1/2> |
#<alt (+ 1/2 (* 1/6 x))> |
#<alt (+ 1/2 (* 1/6 x))> |
#<alt (+ 1/2 (* 1/6 x))> |
#<alt (* 1/6 x)> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* 1/6 x)> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))> |
36 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | 0 | (sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))) |
| 1.0ms | x | @ | 0 | (sqrt (* x (* x (* x 1/6)))) |
| 1.0ms | x | @ | -inf | (sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))) |
| 1.0ms | x | @ | -inf | (* (pow (+ 1/2 (* x 1/6)) 1/2) x) |
| 0.0ms | x | @ | 0 | (* x (sqrt 1/2)) |
| 1× | batch-egg-rewrite |
| 4 876× | accelerator-lowering-fma.f32 |
| 4 876× | accelerator-lowering-fma.f64 |
| 4 606× | *-lowering-*.f32 |
| 4 606× | *-lowering-*.f64 |
| 1 870× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 87 |
| 1 | 85 | 87 |
| 2 | 525 | 83 |
| 3 | 4815 | 83 |
| 0 | 8403 | 73 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt (* x (* x (* x 1/6)))) |
(* x (* x (* x 1/6))) |
(* x (* x 1/6)) |
(* x 1/6) |
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))) |
(* x (+ 1 (* x (+ 1/2 (* x 1/6))))) |
(+ 1 (* x (+ 1/2 (* x 1/6)))) |
(* x (+ 1/2 (* x 1/6))) |
(* x (sqrt 1/2)) |
(sqrt 1/2) |
(* (pow (+ 1/2 (* x 1/6)) 1/2) x) |
(pow (+ 1/2 (* x 1/6)) 1/2) |
(+ 1/2 (* x 1/6)) |
| Outputs |
|---|
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1/4 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(exp.f64 (+.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1/2 binary64)))) |
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1/2 binary64)) (*.f64 (log.f64 x) #s(literal 1/2 binary64)))) |
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)))) |
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/2 binary64)))) |
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) #s(literal 1/4 binary64)) (*.f64 (log.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) #s(literal 1/4 binary64)))) |
(sqrt.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) |
(pow.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) #s(literal 1/4 binary64)) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))) |
(*.f64 x (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 x) (*.f64 x (sqrt.f64 #s(literal 1/6 binary64)))) |
(*.f64 (*.f64 x (sqrt.f64 #s(literal 1/6 binary64))) (sqrt.f64 x)) |
(*.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x) |
(*.f64 (pow.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 1/6 binary64))) |
(exp.f64 (log.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))) |
(*.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 x x)) |
(*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) x) |
(*.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) |
(*.f64 (*.f64 x x) (*.f64 x #s(literal 1/6 binary64))) |
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)) |
(*.f64 (*.f64 x (*.f64 x x)) (exp.f64 (log.f64 #s(literal 1/6 binary64)))) |
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))) |
(*.f64 (exp.f64 (log.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) (exp.f64 (log.f64 x))) |
(*.f64 x (*.f64 x #s(literal 1/6 binary64))) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(*.f64 (*.f64 x #s(literal 1/6 binary64)) x) |
(*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))) |
(*.f64 (*.f64 x x) #s(literal 1/6 binary64)) |
(exp.f64 (log.f64 (*.f64 x #s(literal 1/6 binary64)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64))) |
(pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1 binary64)) |
(*.f64 x #s(literal 1/6 binary64)) |
(*.f64 #s(literal 1/6 binary64) x) |
(*.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/6 binary64))) |
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 #s(literal 1/6 binary64)))) |
(*.f64 (exp.f64 (log.f64 #s(literal 1/6 binary64))) (exp.f64 (log.f64 x))) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) #s(literal 1/4 binary64))) #s(literal 2 binary64))) |
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(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64)))) |
(*.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64)))))) |
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) |
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64)))) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) (*.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) (-.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) #s(literal 1/4 binary64))))) |
(*.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) (-.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))) |
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) (-.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))) |
| 1× | egg-herbie |
| 13 902× | accelerator-lowering-fma.f32 |
| 13 902× | accelerator-lowering-fma.f64 |
| 5 444× | *-lowering-*.f32 |
| 5 444× | *-lowering-*.f64 |
| 2 584× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 198 | 1650 |
| 1 | 635 | 1558 |
| 2 | 2171 | 1501 |
| 3 | 5001 | 1451 |
| 0 | 8473 | 1365 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 2)) |
(* 1/6 (pow x 2)) |
(* 1/6 (pow x 2)) |
(* 1/6 (pow x 2)) |
(* 1/6 (pow x 2)) |
(* 1/6 (pow x 2)) |
(* 1/6 (pow x 2)) |
(* 1/6 (pow x 2)) |
(* 1/6 (pow x 2)) |
(* 1/6 (pow x 2)) |
(* 1/6 (pow x 2)) |
(* 1/6 (pow x 2)) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(* 1/6 x) |
(sqrt x) |
(+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x)))))))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6))) |
(* (pow x 2) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))) |
(* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* 1/32 (* (sqrt x) (/ (pow (sqrt -1) 2) (pow (sqrt 1/6) 3)))) (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))) |
x |
(* x (+ 1 (* 1/2 x))) |
(* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) |
(* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(+ 1 (* x (+ 1/2 (* 1/6 x)))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/6 x))) |
(* x (+ 1/2 (* 1/6 x))) |
(* x (+ 1/2 (* 1/6 x))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* 1/6 (pow x 2)) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (sqrt 1/2)) |
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))) |
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))) |
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))) |
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))))) |
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3))))))) |
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))))))) |
(sqrt 1/2) |
(+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))) |
(+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))) |
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))) |
(* (sqrt x) (sqrt 1/6)) |
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6)))) |
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))) |
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))) |
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))) |
1/2 |
(+ 1/2 (* 1/6 x)) |
(+ 1/2 (* 1/6 x)) |
(+ 1/2 (* 1/6 x)) |
(* 1/6 x) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* 1/6 x) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
| Outputs |
|---|
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x))))) |
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x))))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* 1/6 (pow x 2)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x x)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) |
(+.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) #s(literal 1/4 binary64))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))))) |
(+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1 binary64)) (sqrt.f64 x))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x)))))))) |
(+.f64 (sqrt.f64 x) (*.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 5/96 binary64) x))))) |
(* (sqrt (pow x 3)) (sqrt 1/6)) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (sqrt.f64 #s(literal 1/6 binary64))))) |
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))) |
(*.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal 1/6 binary64))) #s(literal 5/16 binary64)))) |
(* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6))) |
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) |
(* (pow x 2) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))) |
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(* (pow x 2) (+ (* -1 (/ (+ (* 1/32 (* (sqrt x) (/ (pow (sqrt -1) 2) (pow (sqrt 1/6) 3)))) (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))) |
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x |
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(* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) |
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(* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) |
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(* 1/6 (pow x 3)) |
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(*.f64 (*.f64 x x) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) |
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1 |
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(* 1/6 (pow x 2)) |
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(* 1/6 (pow x 2)) |
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(* 1/2 x) |
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(sqrt 1/2) |
(sqrt.f64 #s(literal 1/2 binary64)) |
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(* (sqrt x) (sqrt 1/6)) |
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x)) |
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(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))) |
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1/2 |
#s(literal 1/2 binary64) |
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(+ 1/2 (* 1/6 x)) |
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) |
(* 1/6 x) |
(*.f64 x #s(literal 1/6 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) |
(* x (+ 1/6 (* 1/2 (/ 1 x)))) |
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) |
Compiled 17 358 to 2 225 computations (87.2% saved)
11 alts after pruning (2 fresh and 9 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 734 | 2 | 736 |
| Fresh | 0 | 0 | 0 |
| Picked | 2 | 2 | 4 |
| Done | 0 | 7 | 7 |
| Total | 736 | 11 | 747 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
| ✓ | 61.7% | (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))) #s(literal -1/2 binary64)) |
| ✓ | 63.6% | (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) |
| 1.4% | (*.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x) | |
| 2.3% | (*.f64 (sqrt.f64 (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x) | |
| ✓ | 2.8% | (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) |
| ✓ | 100.0% | (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| ✓ | 60.6% | (sqrt.f64 (+.f64 #s(literal 2 binary64) x)) |
| ✓ | 2.1% | (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) |
| ✓ | 2.1% | (sqrt.f64 x) |
| ✓ | 68.1% | (sqrt.f64 #s(literal 2 binary64)) |
Compiled 236 to 133 computations (43.6% 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))) |
(*.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x) |
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) |
(sqrt.f64 (*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))) |
(sqrt.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) |
(*.f64 (sqrt.f64 (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x) |
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x) |
(sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))) |
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) |
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))) #s(literal -1/2 binary64)) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) |
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 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 |
|---|
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
3 calls:
| 6.0ms | (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) |
| 5.0ms | x |
| 5.0ms | (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)
| 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))) |
(*.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x) |
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) |
(sqrt.f64 (*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))) |
(sqrt.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) |
(*.f64 (sqrt.f64 (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x) |
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x) |
(sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))) |
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) |
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))) #s(literal -1/2 binary64)) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) |
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
| Outputs |
|---|
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
1 calls:
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
Compiled 2 to 1 computations (50% saved)
Total -42.7b remaining (-208.9%)
Threshold costs -42.7b (-208.9%)
| 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))) |
(*.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x) |
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) |
(sqrt.f64 (*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))) |
(sqrt.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))) |
(*.f64 (sqrt.f64 (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x) |
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x) |
(sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))) |
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) |
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 x x))))) #s(literal -1/2 binary64)) |
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) |
| Outputs |
|---|
(sqrt.f64 #s(literal 2 binary64)) |
1 calls:
| 9.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 68.1% | 1 | x |
Compiled 2 to 1 computations (50% saved)
| 1× | egg-herbie |
| 6× | +-commutative_binary64 |
| 4× | sub-neg_binary64 |
| 2× | 1-exp_binary64 |
| 2× | neg-sub0_binary64 |
| 2× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 12 | 15 |
| 1 | 18 | 15 |
| 2 | 21 | 15 |
| 3 | 22 | 15 |
| 4 | 23 | 15 |
| 1× | saturated |
| Inputs |
|---|
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
| Outputs |
|---|
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)) |
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) |
(sqrt.f64 #s(literal 2 binary64)) |
| 15 504× | accelerator-lowering-fma.f32 |
| 15 504× | accelerator-lowering-fma.f64 |
| 4 704× | *-lowering-*.f32 |
| 4 704× | *-lowering-*.f64 |
| 4 562× | accelerator-lowering-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 77 | 444 |
| 1 | 252 | 410 |
| 2 | 663 | 410 |
| 3 | 1429 | 404 |
| 4 | 2558 | 324 |
| 5 | 5941 | 289 |
| 0 | 8294 | 234 |
| 0 | 10 | 33 |
| 1 | 56 | 19 |
| 2 | 421 | 19 |
| 3 | 4985 | 19 |
| 0 | 8093 | 15 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 34 to 27 computations (20.6% saved)
Compiled 58 to 44 computations (24.1% saved)
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