
Time bar (total: 2.6s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 1 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 2 |
| 25% | 25% | 74.9% | 0.1% | 0% | 0% | 0% | 3 |
| 28.6% | 25% | 62.4% | 0.1% | 0% | 12.5% | 0% | 4 |
| 46.2% | 37.5% | 43.7% | 0.1% | 0% | 18.7% | 0% | 5 |
| 52.2% | 37.5% | 34.3% | 0.1% | 0% | 28.1% | 0% | 6 |
| 65.1% | 43.7% | 23.4% | 0.1% | 0% | 32.8% | 0% | 7 |
| 70.9% | 43.7% | 18% | 0.1% | 0% | 38.2% | 0% | 8 |
| 79.5% | 46.8% | 12.1% | 0.1% | 0% | 41% | 0% | 9 |
| 83.6% | 46.8% | 9.2% | 0.1% | 0% | 43.9% | 0% | 10 |
| 88.7% | 48.4% | 6.1% | 0.1% | 0% | 45.4% | 0% | 11 |
| 91.3% | 48.4% | 4.6% | 0.1% | 0% | 46.9% | 0% | 12 |
Compiled 6 to 6 computations (0% saved)
| 241.0ms | 8 256× | 0 | valid |
| 16.0ms | 507× | 0 | invalid |
ival-sqrt: 56.0ms (50.1% of total)ival-add: 46.0ms (41.2% of total)ival-true: 6.0ms (5.4% of total)ival-assert: 3.0ms (2.7% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 0 | 0 | - | 0 | - | (sqrt.f64 (+.f64 x y)) |
| 0 | 0 | - | 0 | - | y |
| 0 | 0 | - | 0 | - | (+.f64 x y) |
| 0 | 0 | - | 0 | - | x |
| Predicted + | Predicted - | |
|---|---|---|
| + | 0 | 0 |
| - | 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 256 |
| number | freq |
|---|---|
| 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 1 |
| 18.0ms | 512× | 0 | valid |
Compiled 44 to 24 computations (45.5% saved)
ival-add: 3.0ms (43.6% of total)ival-sqrt: 3.0ms (43.6% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 12 | 24 |
| 1 | 26 | 22 |
| 2 | 41 | 22 |
| 3 | 63 | 22 |
| 4 | 116 | 22 |
| 5 | 155 | 22 |
| 6 | 194 | 22 |
| 7 | 205 | 22 |
| 8 | 207 | 22 |
| 0 | 4 | 4 |
| 0 | 6 | 4 |
| 1 | 7 | 4 |
| 0 | 7 | 4 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(sqrt.f64 (+.f64 x y)) |
| Outputs |
|---|
(sqrt.f64 (+.f64 x y)) |
(sqrt.f64 (+.f64 y x)) |
(sort x y)
Compiled 4 to 4 computations (0% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | (sqrt.f64 (+.f64 x y)) |
Compiled 4 to 4 computations (0% saved)
| 1× | egg-herbie |
Found 2 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 x y) | |
| cost-diff | 0 | (sqrt.f64 (+.f64 x y)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 9 |
| 0 | 6 | 9 |
| 1 | 7 | 9 |
| 0 | 7 | 9 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(sqrt.f64 (+.f64 x y)) |
(+.f64 x y) |
x |
y |
| Outputs |
|---|
(sqrt.f64 (+.f64 x y)) |
(sqrt.f64 (+.f64 y x)) |
(+.f64 x y) |
(+.f64 y x) |
x |
y |
Found 2 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (+.f64 x y) | |
| accuracy | 0.015625 | (sqrt.f64 (+.f64 x y)) |
| 8.0ms | 256× | 0 | valid |
Compiled 20 to 10 computations (50% saved)
ival-sqrt: 2.0ms (61.7% of total)ival-add: 1.0ms (30.8% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
(sqrt.f64 (+.f64 x y)) |
(+.f64 x y) |
| Outputs |
|---|
(sqrt y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
y |
(+ x y) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
x |
(* x (+ 1 (/ y x))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(* y (+ 1 (/ x y))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | ((sqrt (+ x y)) (+ x y)) |
| 1.0ms | y | @ | -inf | ((sqrt (+ x y)) (+ x y)) |
| 1.0ms | x | @ | inf | ((sqrt (+ x y)) (+ x y)) |
| 1.0ms | y | @ | inf | ((sqrt (+ x y)) (+ x y)) |
| 0.0ms | x | @ | 0 | ((sqrt (+ x y)) (+ x y)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 156 | 583 |
| 1 | 454 | 553 |
| 2 | 1425 | 535 |
| 3 | 4629 | 523 |
| 0 | 8199 | 487 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
y |
(+ x y) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
x |
(* x (+ 1 (/ y x))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(* y (+ 1 (/ x y))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
| Outputs |
|---|
(sqrt y) |
(sqrt.f64 y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x (sqrt.f64 y)) |
y |
(+ x y) |
(+.f64 y x) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(*.f64 (fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64)) (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x) |
x |
(* x (+ 1 (/ y x))) |
(+.f64 y x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) y) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) y) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+.f64 y x) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (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 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(*.f64 (fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y) |
(* y (+ 1 (/ x y))) |
(+.f64 y x) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(+.f64 y x) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 7 |
| 0 | 6 | 7 |
| 1 | 22 | 7 |
| 2 | 145 | 7 |
| 3 | 1366 | 7 |
| 0 | 8310 | 7 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(sqrt.f64 (+.f64 x y)) |
(+.f64 x y) |
| Outputs |
|---|
(*.f64 (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (/.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)))) |
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(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64)))) (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64))))) |
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log.f64 (+.f64 y x))))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 y x) #s(literal -1 binary64))) |
(/.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64))))) |
(/.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64))) (fma.f64 (-.f64 y x) y (*.f64 x x)))) |
(/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)) |
(/.f64 (-.f64 (pow.f64 (neg.f64 y) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))) |
(/.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (-.f64 x y)) |
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 y x) y (*.f64 x x))) |
(neg.f64 (neg.f64 (+.f64 y x))) |
(fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) x) |
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) y) |
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y (+.f64 y x) (*.f64 x x)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x y) (+.f64 y x))) (+.f64 y x) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))) |
(fma.f64 (neg.f64 (*.f64 x x)) (/.f64 #s(literal -1 binary64) (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))) |
(fma.f64 #s(literal -1 binary64) (neg.f64 y) x) |
(fma.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (-.f64 x y))) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))) |
(fma.f64 (*.f64 y y) (pow.f64 (-.f64 y x) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 y x)))) |
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))) |
(fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))) |
(-.f64 (/.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x y))) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y))))) (/.f64 (pow.f64 (*.f64 y (/.f64 y (-.f64 x y))) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y)))))) |
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x y) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 y (/.f64 y (-.f64 x y))) #s(literal 2 binary64)) (*.f64 (*.f64 x (/.f64 x (-.f64 x y))) (*.f64 y (/.f64 y (-.f64 x y))))))) (/.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (-.f64 x y) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 y (/.f64 y (-.f64 x y))) #s(literal 2 binary64)) (*.f64 (*.f64 x (/.f64 x (-.f64 x y))) (*.f64 y (/.f64 y (-.f64 x y)))))))) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) (-.f64 x y)) (pow.f64 (-.f64 x y) #s(literal 2 binary64))) (/.f64 (*.f64 (-.f64 x y) (*.f64 y y)) (pow.f64 (-.f64 x y) #s(literal 2 binary64)))) |
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 x y) (fma.f64 y y (*.f64 x x)))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (fma.f64 y y (*.f64 x x))))) |
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (-.f64 x y) (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (*.f64 (-.f64 x y) (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))) |
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (*.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1 binary64) x y)) (neg.f64 (+.f64 y x))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))) (neg.f64 (+.f64 y x))) |
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x))) (-.f64 x y)) (/.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x))) (-.f64 x y))) |
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 x y)) (/.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 x y))) |
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (-.f64 y x) y (*.f64 x x))) (/.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (-.f64 y x) y (*.f64 x x)))) |
(-.f64 (/.f64 (*.f64 y y) (-.f64 y x)) (/.f64 (*.f64 x x) (-.f64 y x))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (+.f64 y x))) |
(-.f64 (*.f64 x (/.f64 x (-.f64 x y))) (*.f64 y (/.f64 y (-.f64 x y)))) |
(-.f64 x (neg.f64 y)) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 y x))) #s(literal -1 binary64))) |
(exp.f64 (log.f64 (+.f64 y x))) |
(+.f64 (/.f64 (*.f64 y y) (-.f64 y x)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 y x)))) |
(+.f64 (*.f64 x (/.f64 x (-.f64 x y))) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))) |
(+.f64 y x) |
(+.f64 x y) |
Compiled 5 667 to 883 computations (84.4% saved)
5 alts after pruning (4 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 243 | 4 | 247 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 243 | 5 | 248 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 49.5% | (/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) |
| ▶ | 49.6% | (sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y))) |
| ✓ | 100.0% | (sqrt.f64 (+.f64 x y)) |
| ▶ | 98.6% | #s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) |
| ▶ | 97.1% | #s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
Compiled 53 to 39 computations (26.4% saved)
| 1× | egg-herbie |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 y x) | |
| cost-diff | 0 | (*.f64 (+.f64 y x) (-.f64 y x)) | |
| cost-diff | 0 | (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) | |
| cost-diff | 0 | (/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) | |
| cost-diff | 0 | (sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y))) | |
| cost-diff | 192 | (fma.f64 #s(literal -1 binary64) x y) | |
| cost-diff | 320 | (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) | |
| cost-diff | 1408 | (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)) | |
| cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) x) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) | |
| cost-diff | 0 | #s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) | |
| cost-diff | 0 | (sqrt.f64 y) | |
| cost-diff | 0 | #s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
Useful iterations: 5 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 26 | 139 |
| 0 | 46 | 146 |
| 1 | 65 | 141 |
| 2 | 92 | 141 |
| 3 | 141 | 141 |
| 4 | 297 | 123 |
| 5 | 609 | 117 |
| 6 | 1421 | 117 |
| 7 | 5029 | 117 |
| 8 | 7427 | 117 |
| 0 | 8077 | 117 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(sqrt.f64 y) |
y |
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(/.f64 #s(literal 1 binary64) y) |
#s(literal 1 binary64) |
y |
(sqrt.f64 y) |
(sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y))) |
(/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)) |
(fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) |
#s(literal -1 binary64) |
(*.f64 x x) |
x |
(*.f64 y y) |
y |
(fma.f64 #s(literal -1 binary64) x y) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) |
(sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) |
(*.f64 (+.f64 y x) (-.f64 y x)) |
(+.f64 y x) |
y |
x |
(-.f64 y x) |
(sqrt.f64 (-.f64 y x)) |
| Outputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(sqrt.f64 y) |
y |
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) |
#s(approx (sqrt (+ x y)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(/.f64 #s(literal 1 binary64) y) |
#s(literal 1 binary64) |
y |
(sqrt.f64 y) |
(sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y))) |
(sqrt.f64 (+.f64 y x)) |
(/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)) |
(+.f64 y x) |
(fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) |
(*.f64 (-.f64 y x) (+.f64 y x)) |
#s(literal -1 binary64) |
(*.f64 x x) |
x |
(*.f64 y y) |
y |
(fma.f64 #s(literal -1 binary64) x y) |
(-.f64 y x) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 y x) (+.f64 y x))) (sqrt.f64 (-.f64 y x))) |
(sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) |
(sqrt.f64 (*.f64 (-.f64 y x) (+.f64 y x))) |
(*.f64 (+.f64 y x) (-.f64 y x)) |
(*.f64 (-.f64 y x) (+.f64 y x)) |
(+.f64 y x) |
y |
x |
(-.f64 y x) |
(sqrt.f64 (-.f64 y x)) |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (*.f64 (+.f64 y x) (-.f64 y x)) | |
| accuracy | 0.015625 | (sqrt.f64 (-.f64 y x)) | |
| accuracy | 0.51953125 | (/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) | |
| accuracy | 31.214516304107754 | (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) | |
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 0.015625 | (sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y))) | |
| accuracy | 2.0000000000000004 | (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) | |
| accuracy | 31.257471928278587 | (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)) | |
| accuracy | 0 | (sqrt.f64 y) | |
| accuracy | 0.01171875 | (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) | |
| accuracy | 0.12109375 | (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) | |
| accuracy | 0.8656999945365534 | #s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) | |
| accuracy | 0 | (sqrt.f64 y) | |
| accuracy | 1.8639498164826163 | #s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
| 42.0ms | 256× | 0 | valid |
Compiled 273 to 55 computations (79.9% saved)
ival-mult: 9.0ms (30.7% of total)ival-sqrt: 9.0ms (30.7% of total)ival-add: 5.0ms (17.1% of total)ival-div: 4.0ms (13.7% of total)ival-sub: 1.0ms (3.4% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(sqrt.f64 y) |
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) |
(*.f64 #s(literal 1/2 binary64) x) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)) |
(fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) |
(fma.f64 #s(literal -1 binary64) x y) |
(sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) |
(sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) |
(*.f64 (+.f64 y x) (-.f64 y x)) |
(+.f64 y x) |
(*.f64 x x) |
(sqrt.f64 (-.f64 y x)) |
| Outputs |
|---|
(sqrt y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(* 1/2 x) |
y |
(+ x y) |
(pow y 2) |
(+ (* -1 (pow x 2)) (pow y 2)) |
(+ y (* -1 x)) |
(+ y (* 1/2 (/ (* x (+ y (* -1 y))) y))) |
(+ y (* x (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/2 (/ (+ y (* -1 y)) y))))) |
(+ y (* x (+ (* 1/2 (/ (+ y (* -1 y)) y)) (* x (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) y)) (* 1/4 (/ (* x (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y)))) (pow y 3)))))))) |
(+ (* x (+ y (* -1 y))) (pow y 2)) |
(+ (* x (+ y (+ (* -1 x) (* -1 y)))) (pow y 2)) |
(pow x 2) |
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* x (sqrt (/ 1 (pow y 3)))))))) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
x |
(* x (+ 1 (/ y x))) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1)) |
(* -1 x) |
(* x (- (/ y x) 1)) |
(* x (sqrt -1)) |
(* x (+ (sqrt -1) (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))) |
(* x (+ (sqrt -1) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1))))))) |
(* x (+ (sqrt -1) (+ (* -1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1)))))))) |
(* (pow x 2) (- (+ (* -1 (/ y x)) (/ y x)) 1)) |
(* (pow x 2) (- (+ (* -1 (/ y x)) (+ (/ y x) (/ (pow y 2) (pow x 2)))) 1)) |
(* (sqrt x) (sqrt -1)) |
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (sqrt -1))) |
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1))))))) |
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) |
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) |
(* (pow x 2) (- (* -1 (/ (+ y (* -1 y)) x)) 1)) |
(* (pow x 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) x)))) x)) 1)) |
(* -1 (* (sqrt x) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(sqrt (/ 1 y)) |
(+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1))) |
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1))))))) |
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1))))))))) |
(+ (* -1 (pow x 2)) (* y (+ x (* -1 x)))) |
(+ (* -1 (pow x 2)) (* y (+ x (+ y (* -1 x))))) |
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1))) |
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1))) |
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1))) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(* y (+ 1 (/ x y))) |
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y)))) |
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))) |
(* (pow y 2) (+ 1 (+ (* -1 (/ x y)) (/ x y)))) |
(* (pow y 2) (+ 1 (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))))) |
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))))))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* -1/2 (/ (+ x (* -1 x)) y)) (pow (sqrt -1) 2)))) |
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2)))) |
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ x (* -1 x)) (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2)))) |
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ x (* -1 x))) (/ (pow x 2) y)) y)))) |
(* -1 (* y (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | y | @ | -inf | ((sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (* (+ y x) (- y x)) (+ y x) (* x x) (sqrt (- y x))) |
| 4.0ms | x | @ | inf | ((sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (* (+ y x) (- y x)) (+ y x) (* x x) (sqrt (- y x))) |
| 3.0ms | x | @ | 0 | ((sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (* (+ y x) (- y x)) (+ y x) (* x x) (sqrt (- y x))) |
| 3.0ms | y | @ | 0 | ((sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (* (+ y x) (- y x)) (+ y x) (* x x) (sqrt (- y x))) |
| 2.0ms | x | @ | -inf | ((sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (* (+ y x) (- y x)) (+ y x) (* x x) (sqrt (- y x))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 500 | 2030 |
| 1 | 1646 | 1660 |
| 2 | 6771 | 1605 |
| 0 | 8191 | 1510 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(* 1/2 x) |
y |
(+ x y) |
(pow y 2) |
(+ (* -1 (pow x 2)) (pow y 2)) |
(+ y (* -1 x)) |
(+ y (* 1/2 (/ (* x (+ y (* -1 y))) y))) |
(+ y (* x (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/2 (/ (+ y (* -1 y)) y))))) |
(+ y (* x (+ (* 1/2 (/ (+ y (* -1 y)) y)) (* x (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) y)) (* 1/4 (/ (* x (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y)))) (pow y 3)))))))) |
(+ (* x (+ y (* -1 y))) (pow y 2)) |
(+ (* x (+ y (+ (* -1 x) (* -1 y)))) (pow y 2)) |
(pow x 2) |
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* x (sqrt (/ 1 (pow y 3)))))))) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
x |
(* x (+ 1 (/ y x))) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1)) |
(* -1 x) |
(* x (- (/ y x) 1)) |
(* x (sqrt -1)) |
(* x (+ (sqrt -1) (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))) |
(* x (+ (sqrt -1) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1))))))) |
(* x (+ (sqrt -1) (+ (* -1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1)))))))) |
(* (pow x 2) (- (+ (* -1 (/ y x)) (/ y x)) 1)) |
(* (pow x 2) (- (+ (* -1 (/ y x)) (+ (/ y x) (/ (pow y 2) (pow x 2)))) 1)) |
(* (sqrt x) (sqrt -1)) |
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (sqrt -1))) |
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1))))))) |
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) |
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) |
(* (pow x 2) (- (* -1 (/ (+ y (* -1 y)) x)) 1)) |
(* (pow x 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) x)))) x)) 1)) |
(* -1 (* (sqrt x) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(sqrt (/ 1 y)) |
(+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1))) |
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1))))))) |
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1))))))))) |
(+ (* -1 (pow x 2)) (* y (+ x (* -1 x)))) |
(+ (* -1 (pow x 2)) (* y (+ x (+ y (* -1 x))))) |
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1))) |
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1))) |
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1))) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(* y (+ 1 (/ x y))) |
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (* -1 (/ x y)))) |
(* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y)))) |
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))) |
(* (pow y 2) (+ 1 (+ (* -1 (/ x y)) (/ x y)))) |
(* (pow y 2) (+ 1 (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))))) |
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))))))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* -1/2 (/ (+ x (* -1 x)) y)) (pow (sqrt -1) 2)))) |
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2)))) |
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ x (* -1 x)) (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2)))) |
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ x (* -1 x))) (/ (pow x 2) y)) y)))) |
(* -1 (* y (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
| Outputs |
|---|
(sqrt y) |
(sqrt.f64 y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x (sqrt.f64 y)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
y |
(+ x y) |
(+.f64 y x) |
(pow y 2) |
(*.f64 y y) |
(+ (* -1 (pow x 2)) (pow y 2)) |
(*.f64 (+.f64 y x) (-.f64 y x)) |
(+ y (* -1 x)) |
(-.f64 y x) |
(+ y (* 1/2 (/ (* x (+ y (* -1 y))) y))) |
y |
(+ y (* x (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/2 (/ (+ y (* -1 y)) y))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 x y) y) |
(+ y (* x (+ (* 1/2 (/ (+ y (* -1 y)) y)) (* x (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) y)) (* 1/4 (/ (* x (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y)))) (pow y 3)))))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 x y) y) |
(+ (* x (+ y (* -1 y))) (pow y 2)) |
(*.f64 y y) |
(+ (* x (+ y (+ (* -1 x) (* -1 y)))) (pow y 2)) |
(*.f64 (+.f64 y x) (-.f64 y x)) |
(pow x 2) |
(*.f64 x x) |
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* x (sqrt (/ 1 (pow y 3)))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) x (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/16 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) x (sqrt.f64 y)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 y y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(*.f64 (+.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (*.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 y y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) |
x |
(* x (+ 1 (/ y x))) |
(fma.f64 (/.f64 y x) x x) |
(* -1 (pow x 2)) |
(*.f64 (neg.f64 x) x) |
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1)) |
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal -1 binary64)) x) x) |
(* -1 x) |
(neg.f64 x) |
(* x (- (/ y x) 1)) |
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) x) |
(* x (sqrt -1)) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x) |
(* x (+ (sqrt -1) (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))) |
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 0 binary64)) |
(* x (+ (sqrt -1) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1))))))) |
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 y (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) x) |
(* x (+ (sqrt -1) (+ (* -1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1)))))))) |
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 y (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) x) |
(* (pow x 2) (- (+ (* -1 (/ y x)) (/ y x)) 1)) |
(*.f64 (neg.f64 x) x) |
(* (pow x 2) (- (+ (* -1 (/ y x)) (+ (/ y x) (/ (pow y 2) (pow x 2)))) 1)) |
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal -1 binary64)) x) x) |
(* (sqrt x) (sqrt -1)) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)) |
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 y y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))) x) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 y (/.f64 y (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))) x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x)) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(fma.f64 (/.f64 y x) x x) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) x) |
(* -1 (* x (sqrt -1))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x) |
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1))))))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x) |
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) |
(*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 y (/.f64 y x)) #s(literal 0 binary64)) x)) (neg.f64 x)) |
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) |
(*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (fma.f64 (*.f64 y (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) #s(literal 0 binary64)) (neg.f64 x)) x)) (neg.f64 x)) |
(* (pow x 2) (- (* -1 (/ (+ y (* -1 y)) x)) 1)) |
(*.f64 (neg.f64 x) x) |
(* (pow x 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) x)))) x)) 1)) |
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal -1 binary64)) x) x) |
(* -1 (* (sqrt x) (sqrt -1))) |
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x)) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x)) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (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 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x (sqrt.f64 (pow.f64 y #s(literal 3 binary64)))) y) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1))) |
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 0 binary64)) |
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1))))))) |
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) y) y (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 0 binary64))) |
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1))))))))) |
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) y) y (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 0 binary64))) |
(+ (* -1 (pow x 2)) (* y (+ x (* -1 x)))) |
(*.f64 (neg.f64 x) x) |
(+ (* -1 (pow x 2)) (* y (+ x (+ y (* -1 x))))) |
(*.f64 (+.f64 y x) (-.f64 y x)) |
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))) |
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 y (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))) |
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(*.f64 (+.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y) |
(* y (+ 1 (/ x y))) |
(fma.f64 (/.f64 x y) y y) |
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) |
(*.f64 (fma.f64 (/.f64 (neg.f64 x) y) (/.f64 x y) #s(literal 1 binary64)) (*.f64 y y)) |
(* y (+ 1 (* -1 (/ x y)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
(* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y)))) |
y |
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 (/.f64 (neg.f64 x) y) (/.f64 x y)) y) |
(* y (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 (/.f64 (neg.f64 x) y) (/.f64 x y)) y) |
(* (pow y 2) (+ 1 (+ (* -1 (/ x y)) (/ x y)))) |
(*.f64 y y) |
(* (pow y 2) (+ 1 (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))))) |
(*.f64 (fma.f64 (/.f64 (neg.f64 x) y) (/.f64 x y) #s(literal 1 binary64)) (*.f64 y y)) |
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))))))) |
(*.f64 (+.f64 (fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (*.f64 (/.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) (neg.f64 y)) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))) (neg.f64 y)) |
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(fma.f64 (/.f64 (neg.f64 x) y) (neg.f64 y) y) |
(* -1 (* y (- (/ x y) 1))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
(* -1 (* y (pow (sqrt -1) 2))) |
y |
(* -1 (* y (+ (* -1/2 (/ (+ x (* -1 x)) y)) (pow (sqrt -1) 2)))) |
y |
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2)))) |
(fma.f64 (/.f64 (*.f64 (*.f64 x (/.f64 x y)) #s(literal -1/2 binary64)) y) y y) |
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ x (* -1 x)) (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2)))) |
(fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) y) y) (neg.f64 y) y) |
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ x (* -1 x))) (/ (pow x 2) y)) y)))) |
(*.f64 (fma.f64 (/.f64 (neg.f64 x) y) (/.f64 x y) #s(literal 1 binary64)) (*.f64 y y)) |
(* -1 (* y (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) (neg.f64 y)) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))) (neg.f64 y)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 26 | 118 |
| 0 | 46 | 125 |
| 1 | 166 | 84 |
| 2 | 1269 | 84 |
| 0 | 8816 | 82 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(sqrt.f64 y) |
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) |
(*.f64 #s(literal 1/2 binary64) x) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)) |
(fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) |
(fma.f64 #s(literal -1 binary64) x y) |
(sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) |
(sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) |
(*.f64 (+.f64 y x) (-.f64 y x)) |
(+.f64 y x) |
(*.f64 x x) |
(sqrt.f64 (-.f64 y x)) |
| Outputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(*.f64 (sqrt.f64 (sqrt.f64 y)) (sqrt.f64 (sqrt.f64 y))) |
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 y) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64)) |
(pow.f64 (sqrt.f64 y) #s(literal 1 binary64)) |
(pow.f64 y #s(literal 1/2 binary64)) |
(/.f64 (neg.f64 (sqrt.f64 y)) #s(literal -1 binary64)) |
(/.f64 (sqrt.f64 (neg.f64 y)) (sqrt.f64 #s(literal -1 binary64))) |
(/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -1/2 binary64))) |
(/.f64 (sqrt.f64 y) #s(literal 1 binary64)) |
(sqrt.f64 y) |
(fabs.f64 (sqrt.f64 y)) |
(exp.f64 (log.f64 (sqrt.f64 y))) |
#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) |
(*.f64 (-.f64 y (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y)) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64))))) |
(*.f64 (neg.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) y)) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))))) |
(*.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 y (*.f64 #s(literal 1/2 binary64) x)))))) |
(*.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) y) (pow.f64 (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y)) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 y (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) (*.f64 #s(literal 1/2 binary64) x))))) |
(*.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 y (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) #s(literal -1 binary64)) |
(/.f64 (-.f64 (*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))) (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y)))) (*.f64 (/.f64 y (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))) (/.f64 y (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))))) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))) (/.f64 y (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))) #s(literal 3 binary64)) (pow.f64 (/.f64 y (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))) #s(literal 3 binary64))) (fma.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))) (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))) (fma.f64 (/.f64 y (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))) (/.f64 y (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))) (*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))) (/.f64 y (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))))))) |
(/.f64 (neg.f64 (-.f64 y (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y))) (neg.f64 (-.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) y))) (neg.f64 (neg.f64 (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 y (*.f64 #s(literal 1/2 binary64) x)))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))) (*.f64 (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y)) y)) (*.f64 (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y)) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y)))) |
(/.f64 (-.f64 y (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y)) (-.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)))) |
(/.f64 (neg.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) y)) (neg.f64 (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y)))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3/2 binary64)))) (neg.f64 (+.f64 y (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) (*.f64 #s(literal 1/2 binary64) x))))) |
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(/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64)) (sqrt.f64 y))) |
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(*.f64 (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 y x) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))) (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 y x))))) |
(*.f64 (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 y x) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(*.f64 (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))) (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 y x) #s(literal -1/2 binary64)))) |
(*.f64 (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 y x)))) |
(*.f64 (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 y x))) (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (/.f64 (sqrt.f64 (-.f64 y x)) (pow.f64 (+.f64 y x) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (+.f64 y x)) (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 (+.f64 y x)) (pow.f64 (+.f64 y x) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (-.f64 y x)) (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 (+.f64 y x)) (pow.f64 (-.f64 y x) #s(literal -1/2 binary64))) (pow.f64 (+.f64 y x) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 (sqrt.f64 (+.f64 y x)) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))) (/.f64 (sqrt.f64 (-.f64 y x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 y x))))) |
(*.f64 (/.f64 (sqrt.f64 (-.f64 y x)) (pow.f64 (-.f64 y x) #s(literal -1/2 binary64))) (/.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(*.f64 (/.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))) (/.f64 (sqrt.f64 (-.f64 y x)) (pow.f64 (-.f64 y x) #s(literal -1/2 binary64)))) |
(*.f64 (/.f64 (sqrt.f64 (+.f64 y x)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 (-.f64 y x) (+.f64 y x)))) |
(*.f64 (/.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 (+.f64 y x))) (sqrt.f64 (-.f64 y x))) |
(*.f64 (/.f64 (sqrt.f64 (-.f64 y x)) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))) (/.f64 (sqrt.f64 (+.f64 y x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 y x))))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 y y (*.f64 x (+.f64 y x)))) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)))) |
(*.f64 (sqrt.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 y y (*.f64 x (+.f64 y x)))) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 y (-.f64 y x) (*.f64 x x)))) |
(*.f64 (sqrt.f64 (*.f64 #s(literal 1 binary64) (/.f64 (+.f64 y x) (-.f64 (neg.f64 x) y)))) (sqrt.f64 (-.f64 x y))) |
(*.f64 (pow.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 y y (*.f64 x (+.f64 y x)))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)))) |
(*.f64 (pow.f64 (*.f64 (/.f64 (+.f64 y x) (fma.f64 y y (*.f64 x (+.f64 y x)))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 y (-.f64 y x) (*.f64 x x)))) |
(*.f64 (pow.f64 (*.f64 #s(literal 1 binary64) (/.f64 (+.f64 y x) (-.f64 (neg.f64 x) y))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 x y))) |
(*.f64 (sqrt.f64 (/.f64 (-.f64 y x) (+.f64 y x))) (/.f64 (sqrt.f64 (+.f64 y x)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (-.f64 y x) #s(literal 1/4 binary64)) (pow.f64 (-.f64 y x) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (neg.f64 x) y)))) |
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)))) |
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) #s(literal 1/2 binary64))) |
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 y y (*.f64 x (+.f64 y x)))))) |
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x))))) |
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (pow.f64 (fma.f64 y y (*.f64 x (+.f64 y x))) #s(literal -1 binary64)))) |
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (pow.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 (pow.f64 (fma.f64 y y (*.f64 x (+.f64 y x))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 (pow.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (+.f64 y x) #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (+.f64 y x)) (pow.f64 (-.f64 y x) #s(literal -1/2 binary64)))) |
(*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 (+.f64 y x)))) |
(*.f64 (sqrt.f64 (-.f64 y x)) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) (pow.f64 (+.f64 y x) #s(literal -1/2 binary64))) |
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (-.f64 y x)))) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 y x))) |
(pow.f64 (exp.f64 (log.f64 (-.f64 y x))) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (-.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (-.f64 y x) #s(literal 1/2 binary64)) |
(/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 y y (*.f64 x (+.f64 y x)))))) |
(/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x))))) |
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 (neg.f64 x) y)))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 y y (*.f64 x (+.f64 y x)))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 y (+.f64 y x) (*.f64 x x))))) |
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))) (sqrt.f64 (-.f64 (neg.f64 x) y))) |
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 y y (*.f64 x (+.f64 y x))))) |
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)))) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 y x))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))) (neg.f64 (sqrt.f64 (+.f64 y x)))) |
(/.f64 (sqrt.f64 (-.f64 y x)) #s(literal 1 binary64)) |
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) (sqrt.f64 (+.f64 y x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (neg.f64 x) y)) (sqrt.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 y y (*.f64 x (+.f64 y x)))) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x))) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1/2 binary64))) |
(neg.f64 (neg.f64 (sqrt.f64 (-.f64 y x)))) |
(sqrt.f64 (-.f64 y x)) |
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (-.f64 y x)))) |
(exp.f64 (-.f64 (*.f64 (log.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal 1/2 binary64)) (*.f64 (log.f64 (+.f64 y x)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (-.f64 y x)) #s(literal 1/2 binary64))) |
Compiled 24 430 to 3 375 computations (86.2% saved)
5 alts after pruning (3 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 940 | 3 | 943 |
| Fresh | 0 | 0 | 0 |
| Picked | 3 | 1 | 4 |
| Done | 0 | 1 | 1 |
| Total | 943 | 5 | 948 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 97.7% | (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) |
| ✓ | 100.0% | (sqrt.f64 (+.f64 x y)) |
| ▶ | 71.0% | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) |
| ▶ | 98.6% | #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) |
| ✓ | 97.1% | #s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
Compiled 62 to 43 computations (30.6% saved)
| 1× | egg-herbie |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (-.f64 y x) | |
| cost-diff | 0 | (sqrt.f64 (-.f64 y x)) | |
| cost-diff | 0 | #s(approx (sqrt (* (+ y x) (- y x))) y) | |
| cost-diff | 0 | (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) | |
| cost-diff | 0 | (/.f64 y x) | |
| cost-diff | 0 | #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) | |
| cost-diff | 896 | (fma.f64 (/.f64 y x) x x) | |
| cost-diff | 0 | (sqrt.f64 y) | |
| cost-diff | 0 | (/.f64 x (sqrt.f64 y)) | |
| cost-diff | 0 | (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) | |
| cost-diff | 0 | #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 29 | 120 |
| 0 | 40 | 114 |
| 1 | 62 | 112 |
| 2 | 94 | 109 |
| 3 | 143 | 103 |
| 4 | 259 | 87 |
| 5 | 770 | 87 |
| 6 | 4070 | 87 |
| 0 | 8684 | 87 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) |
(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) |
(/.f64 x (sqrt.f64 y)) |
x |
(sqrt.f64 y) |
y |
#s(literal 1/2 binary64) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x)) |
(fma.f64 (/.f64 y x) x x) |
(/.f64 y x) |
y |
x |
(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) |
#s(approx (sqrt (* (+ y x) (- y x))) y) |
y |
(sqrt.f64 (-.f64 y x)) |
(-.f64 y x) |
x |
| Outputs |
|---|
#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) |
#s(approx (sqrt (+ x y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) |
(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) |
(/.f64 x (sqrt.f64 y)) |
x |
(sqrt.f64 y) |
y |
#s(literal 1/2 binary64) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+.f64 y x))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x)) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+.f64 y x)) |
(fma.f64 (/.f64 y x) x x) |
(+.f64 y x) |
(/.f64 y x) |
y |
x |
(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) |
#s(approx (sqrt (* (+ y x) (- y x))) y) |
y |
(sqrt.f64 (-.f64 y x)) |
(-.f64 y x) |
x |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (-.f64 y x) | |
| accuracy | 0.015625 | (sqrt.f64 (-.f64 y x)) | |
| accuracy | 0.51953125 | (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) | |
| accuracy | 0.9461280985648626 | #s(approx (sqrt (* (+ y x) (- y x))) y) | |
| accuracy | 0 | (/.f64 y x) | |
| accuracy | 0 | #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x)) | |
| accuracy | 0.015625 | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) | |
| accuracy | 18.18426422457318 | (fma.f64 (/.f64 y x) x x) | |
| accuracy | 0 | (sqrt.f64 y) | |
| accuracy | 0.01171875 | (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) | |
| accuracy | 0.1953125 | (/.f64 x (sqrt.f64 y)) | |
| accuracy | 0.8656999945365534 | #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) |
| 49.0ms | 256× | 0 | valid |
Compiled 217 to 58 computations (73.3% saved)
ival-mult: 11.0ms (30.9% of total)ival-add: 8.0ms (22.5% of total)ival-sqrt: 8.0ms (22.5% of total)ival-div: 7.0ms (19.7% of total)ival-sub: 1.0ms (2.8% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) |
(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) |
(/.f64 x (sqrt.f64 y)) |
(sqrt.f64 y) |
(fma.f64 (/.f64 y x) x x) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x)) |
(/.f64 y x) |
(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) |
#s(approx (sqrt (* (+ y x) (- y x))) y) |
(sqrt.f64 (-.f64 y x)) |
(-.f64 y x) |
| Outputs |
|---|
(sqrt y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(* x (sqrt (/ 1 y))) |
y |
(+ x y) |
(/ y x) |
(+ y (* 1/2 (/ (* x (+ y (* -1 y))) y))) |
(+ y (* x (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/2 (/ (+ y (* -1 y)) y))))) |
(+ y (* x (+ (* 1/2 (/ (+ y (* -1 y)) y)) (* x (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) y)) (* 1/4 (/ (* x (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y)))) (pow y 3)))))))) |
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* x (sqrt (/ 1 (pow y 3)))))))) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(+ y (* -1 x)) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
x |
(* x (+ 1 (/ y x))) |
(* x (sqrt -1)) |
(* x (+ (sqrt -1) (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))) |
(* x (+ (sqrt -1) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1))))))) |
(* x (+ (sqrt -1) (+ (* -1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1)))))))) |
(* (sqrt x) (sqrt -1)) |
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 x) |
(* x (- (/ y x) 1)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (sqrt -1))) |
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1))))))) |
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) |
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) |
(* -1 (* (sqrt x) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1))) |
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1))))))) |
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1))))))))) |
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1))) |
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1))) |
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1))) |
(- y x) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(* y (+ 1 (/ x y))) |
(* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y)))) |
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))) |
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))))))) |
(* y (+ 1 (* -1 (/ x y)))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* y (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* -1/2 (/ (+ x (* -1 x)) y)) (pow (sqrt -1) 2)))) |
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2)))) |
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ x (* -1 x)) (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2)))) |
(* -1 (* y (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(* -1 (* y (- (/ x y) 1))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | y | @ | -inf | ((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (+ (* (/ y x) x) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ y x) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x)) |
| 2.0ms | x | @ | -inf | ((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (+ (* (/ y x) x) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ y x) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x)) |
| 2.0ms | y | @ | inf | ((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (+ (* (/ y x) x) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ y x) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x)) |
| 2.0ms | x | @ | inf | ((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (+ (* (/ y x) x) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ y x) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x)) |
| 2.0ms | x | @ | 0 | ((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (+ (* (/ y x) x) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ y x) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 449 | 1852 |
| 1 | 1488 | 1603 |
| 2 | 6053 | 1478 |
| 0 | 8508 | 1386 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(* x (sqrt (/ 1 y))) |
y |
(+ x y) |
(/ y x) |
(+ y (* 1/2 (/ (* x (+ y (* -1 y))) y))) |
(+ y (* x (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/2 (/ (+ y (* -1 y)) y))))) |
(+ y (* x (+ (* 1/2 (/ (+ y (* -1 y)) y)) (* x (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) y)) (* 1/4 (/ (* x (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y)))) (pow y 3)))))))) |
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* x (sqrt (/ 1 (pow y 3)))))))) |
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(+ y (* -1 x)) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
x |
(* x (+ 1 (/ y x))) |
(* x (sqrt -1)) |
(* x (+ (sqrt -1) (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))) |
(* x (+ (sqrt -1) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1))))))) |
(* x (+ (sqrt -1) (+ (* -1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1)))))))) |
(* (sqrt x) (sqrt -1)) |
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 x) |
(* x (- (/ y x) 1)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (sqrt -1))) |
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1))))))) |
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) |
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) |
(* -1 (* (sqrt x) (sqrt -1))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1))) |
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1))))))) |
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1))))))))) |
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1))) |
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1))) |
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1))) |
(- y x) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(* y (+ 1 (/ x y))) |
(* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y)))) |
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))) |
(* y (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))) |
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))))))) |
(* y (+ 1 (* -1 (/ x y)))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* y (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* -1/2 (/ (+ x (* -1 x)) y)) (pow (sqrt -1) 2)))) |
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2)))) |
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ x (* -1 x)) (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2)))) |
(* -1 (* y (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(* -1 (* y (- (/ x y) 1))) |
| Outputs |
|---|
(sqrt y) |
(sqrt.f64 y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
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(fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) y) y) (neg.f64 y) y) |
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))))))) |
(*.f64 (+.f64 (fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* y (+ 1 (* -1 (/ x y)))) |
(fma.f64 (/.f64 (neg.f64 x) y) y y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (*.f64 (/.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) (neg.f64 y)) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 (*.f64 (/.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))) (neg.f64 y)) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(fma.f64 (/.f64 x y) y y) |
(* -1 (* y (pow (sqrt -1) 2))) |
y |
(* -1 (* y (+ (* -1/2 (/ (+ x (* -1 x)) y)) (pow (sqrt -1) 2)))) |
y |
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2)))) |
(fma.f64 (/.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 x y)) y) y y) |
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ x (* -1 x)) (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2)))) |
(fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) y) y) (neg.f64 y) y) |
(* -1 (* y (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) (neg.f64 y)) |
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))) (neg.f64 y)) |
(* -1 (* y (- (/ x y) 1))) |
(fma.f64 (/.f64 (neg.f64 x) y) y y) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 29 | 113 |
| 0 | 40 | 107 |
| 1 | 170 | 89 |
| 2 | 1381 | 80 |
| 0 | 8951 | 80 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) |
(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) |
(/.f64 x (sqrt.f64 y)) |
(sqrt.f64 y) |
(fma.f64 (/.f64 y x) x x) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x)) |
(/.f64 y x) |
(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) |
#s(approx (sqrt (* (+ y x) (- y x))) y) |
(sqrt.f64 (-.f64 y x)) |
(-.f64 y x) |
| Outputs |
|---|
#s(approx (sqrt (+ x y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) |
(*.f64 (-.f64 y (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y)) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))))) |
(*.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) y)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))))) |
(*.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -3 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y))))) |
(*.f64 (-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) y) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y))) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) |
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -3 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 y (-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (*.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y))) (sqrt.f64 y)))))) |
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -3 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 (fma.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y)) #s(literal -1 binary64))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) #s(literal -1 binary64)) |
(/.f64 (-.f64 (*.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y))))) (*.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (/.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))))) (+.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (/.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) #s(literal 3 binary64)) (pow.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (fma.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (/.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (*.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (/.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))))))) |
(/.f64 (neg.f64 (-.f64 y (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y))) (neg.f64 (-.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) y))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -3 binary64)) (pow.f64 y #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y))) y)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y))))) |
(/.f64 (-.f64 y (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y)) (-.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y))))) |
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) y)) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y))))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -3 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (neg.f64 (+.f64 y (-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (*.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y))) (sqrt.f64 y)))))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -3 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y)))) |
(/.f64 (-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) y) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))) (-.f64 y (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y (-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (*.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y))) (sqrt.f64 y)))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -3 binary64)) (pow.f64 y #s(literal 3/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -3 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (+.f64 y (-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (*.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y))) (sqrt.f64 y))))) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -3 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (fma.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 y #s(literal 1/4 binary64))) (/.f64 x (pow.f64 y #s(literal 1/4 binary64))) (sqrt.f64 y)) |
(fma.f64 (/.f64 x (pow.f64 y #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 y #s(literal 1/4 binary64))) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (sqrt.f64 y)) (sqrt.f64 (sqrt.f64 y)) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))) |
(fma.f64 (*.f64 (neg.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 y)) (sqrt.f64 y)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 y)) (sqrt.f64 y)) |
(fma.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))) |
(fma.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 y)) (sqrt.f64 y)) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 (neg.f64 x) (sqrt.f64 y)) (sqrt.f64 y)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (pow.f64 y #s(literal -1/2 binary64)) (sqrt.f64 y)) |
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y))) (sqrt.f64 y)) |
(fma.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y))) #s(literal -1 binary64)) (neg.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))))) |
(fma.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 y)) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) |
(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 y) #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (sqrt.f64 y)) |
(fma.f64 x (*.f64 (pow.f64 y #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 y)) |
(-.f64 (/.f64 y (-.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y))))) (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (-.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))))) |
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(pow.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64)) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (neg.f64 x) x) (+.f64 y x)) (/.f64 (*.f64 (neg.f64 x) x) (+.f64 y x))) (*.f64 (/.f64 (*.f64 y y) (-.f64 (neg.f64 x) y)) (/.f64 (*.f64 y y) (-.f64 (neg.f64 x) y)))) (fma.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 (*.f64 y y) (-.f64 (neg.f64 x) y)))) |
(/.f64 (-.f64 (*.f64 (*.f64 y (/.f64 y (+.f64 y x))) (*.f64 y (/.f64 y (+.f64 y x)))) (*.f64 (*.f64 x (/.f64 x (+.f64 y x))) (*.f64 x (/.f64 x (+.f64 y x))))) (fma.f64 y (/.f64 y (+.f64 y x)) (*.f64 x (/.f64 x (+.f64 y x))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x))))) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))))) (+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (neg.f64 x) x) (+.f64 y x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 y y) (-.f64 (neg.f64 x) y)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (neg.f64 x) x) (+.f64 y x)) (/.f64 (*.f64 (neg.f64 x) x) (+.f64 y x)) (fma.f64 (/.f64 (*.f64 y y) (-.f64 (neg.f64 x) y)) (/.f64 (*.f64 y y) (-.f64 (neg.f64 x) y)) (*.f64 (/.f64 (*.f64 (neg.f64 x) x) (+.f64 y x)) (/.f64 (*.f64 y y) (-.f64 (neg.f64 x) y)))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 y (/.f64 y (+.f64 y x))) #s(literal 3 binary64)) (pow.f64 (*.f64 x (/.f64 x (+.f64 y x))) #s(literal 3 binary64))) (fma.f64 (*.f64 y (/.f64 y (+.f64 y x))) (*.f64 y (/.f64 y (+.f64 y x))) (fma.f64 (*.f64 x (/.f64 x (+.f64 y x))) (*.f64 x (/.f64 x (+.f64 y x))) (*.f64 (*.f64 y (/.f64 y (+.f64 y x))) (*.f64 x (/.f64 x (+.f64 y x))))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) (*.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 y y (*.f64 x (+.f64 y x)))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 y (+.f64 y x) (*.f64 x x))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 (neg.f64 x) y)) (*.f64 (-.f64 (neg.f64 x) y) (*.f64 y y))) (*.f64 (-.f64 (neg.f64 x) y) (-.f64 (neg.f64 x) y))) |
(/.f64 (-.f64 (*.f64 (*.f64 y y) (+.f64 y x)) (*.f64 (+.f64 y x) (*.f64 x x))) (*.f64 (+.f64 y x) (+.f64 y x))) |
(/.f64 (-.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) (*.f64 (fma.f64 y y (*.f64 x (+.f64 y x))) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (fma.f64 y y (*.f64 x (+.f64 y x))) (fma.f64 y y (*.f64 x (+.f64 y x))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 y y (*.f64 x (+.f64 y x))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)))) |
(/.f64 (-.f64 x y) #s(literal -1 binary64)) |
(/.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (neg.f64 x) y)) |
(/.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (+.f64 y x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) |
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 y y (*.f64 x (+.f64 y x)))) |
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 y (+.f64 y x) (*.f64 x x))) |
(/.f64 (-.f64 y x) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64)))) |
(neg.f64 (-.f64 x y)) |
(fma.f64 (/.f64 y (*.f64 (/.f64 (-.f64 y x) #s(literal -1 binary64)) (pow.f64 (-.f64 y x) #s(literal -1 binary64)))) (/.f64 y (-.f64 (neg.f64 x) y)) (neg.f64 (*.f64 x (/.f64 x (+.f64 y x))))) |
(fma.f64 (/.f64 y (/.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (/.f64 y (fma.f64 y y (*.f64 x (+.f64 y x)))) (neg.f64 (*.f64 x (/.f64 x (+.f64 y x))))) |
(fma.f64 (/.f64 y (/.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (/.f64 y (fma.f64 y (+.f64 y x) (*.f64 x x))) (neg.f64 (*.f64 x (/.f64 x (+.f64 y x))))) |
(fma.f64 (/.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 y (pow.f64 (fma.f64 y (-.f64 y x) (*.f64 x x)) #s(literal -1 binary64))) (neg.f64 (*.f64 x (/.f64 x (+.f64 y x))))) |
(fma.f64 (/.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 y (pow.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) #s(literal -1 binary64))) (neg.f64 (*.f64 x (/.f64 x (+.f64 y x))))) |
(fma.f64 (/.f64 (neg.f64 x) x) (/.f64 y #s(literal -1 binary64)) (neg.f64 x)) |
(fma.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (neg.f64 y) x) (neg.f64 x)) |
(fma.f64 (/.f64 y #s(literal -1 binary64)) (/.f64 (neg.f64 x) x) (neg.f64 x)) |
(fma.f64 (/.f64 y (*.f64 (+.f64 y x) (-.f64 x y))) (/.f64 y (pow.f64 (-.f64 x y) #s(literal -1 binary64))) (neg.f64 (*.f64 x (/.f64 x (+.f64 y x))))) |
(fma.f64 (/.f64 (neg.f64 y) x) (/.f64 x #s(literal -1 binary64)) (neg.f64 x)) |
(fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) |
(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (*.f64 y x) #s(literal -1 binary64)) (neg.f64 x)) |
(fma.f64 (/.f64 y (fma.f64 (neg.f64 x) x (*.f64 y y))) (*.f64 y (-.f64 y x)) (neg.f64 (*.f64 x (/.f64 x (+.f64 y x))))) |
(fma.f64 (pow.f64 x #s(literal -1 binary64)) (*.f64 y x) (neg.f64 x)) |
(fma.f64 #s(literal 1 binary64) y (neg.f64 x)) |
(fma.f64 (*.f64 (neg.f64 x) y) (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) |
(fma.f64 (*.f64 y (-.f64 y x)) (/.f64 y (fma.f64 (neg.f64 x) x (*.f64 y y))) (neg.f64 (*.f64 x (/.f64 x (+.f64 y x))))) |
(fma.f64 (*.f64 y x) (pow.f64 x #s(literal -1 binary64)) (neg.f64 x)) |
(fma.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (fma.f64 y y (*.f64 x (+.f64 y x))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))))) |
(fma.f64 (neg.f64 y) #s(literal -1 binary64) (neg.f64 x)) |
(fma.f64 (*.f64 y y) (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (neg.f64 (*.f64 x (/.f64 x (+.f64 y x))))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 (/.f64 (*.f64 y y) (-.f64 (neg.f64 x) y)))) |
(fma.f64 #s(literal -1 binary64) (neg.f64 y) (neg.f64 x)) |
(fma.f64 #s(literal -1 binary64) x y) |
(fma.f64 (/.f64 y x) x (neg.f64 x)) |
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (neg.f64 x)) |
(fma.f64 y (/.f64 y (+.f64 y x)) (neg.f64 (*.f64 x (/.f64 x (+.f64 y x))))) |
(fma.f64 y #s(literal 1 binary64) (neg.f64 x)) |
(fma.f64 x #s(literal -1 binary64) y) |
(fma.f64 x (/.f64 y x) (neg.f64 x)) |
(-.f64 (/.f64 (/.f64 (*.f64 (neg.f64 x) x) (+.f64 y x)) #s(literal 1 binary64)) (/.f64 (/.f64 (*.f64 y y) (-.f64 (neg.f64 x) y)) #s(literal 1 binary64))) |
(-.f64 (/.f64 (*.f64 y (/.f64 y (+.f64 y x))) #s(literal 1 binary64)) (/.f64 (*.f64 x (/.f64 x (+.f64 y x))) #s(literal 1 binary64))) |
(-.f64 (/.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) #s(literal 1 binary64)) (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) #s(literal 1 binary64))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 (neg.f64 x) y)) (-.f64 x y)) |
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 (neg.f64 y) y))) (+.f64 y x)) (/.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 (neg.f64 y) y))) (+.f64 y x))) |
(-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (+.f64 y x) (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y (+.f64 y x) (*.f64 x x)))) |
(-.f64 (/.f64 (*.f64 (neg.f64 x) x) (+.f64 y x)) (/.f64 (*.f64 y y) (-.f64 (neg.f64 x) y))) |
(-.f64 (*.f64 y (/.f64 y (+.f64 y x))) (*.f64 x (/.f64 x (+.f64 y x)))) |
(-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x))))) |
(-.f64 #s(literal 0 binary64) (-.f64 x y)) |
(-.f64 y x) |
(+.f64 (/.f64 (*.f64 (neg.f64 x) x) (+.f64 y x)) (neg.f64 (/.f64 (*.f64 y y) (-.f64 (neg.f64 x) y)))) |
(+.f64 (*.f64 y (/.f64 y (+.f64 y x))) (neg.f64 (*.f64 x (/.f64 x (+.f64 y x))))) |
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (*.f64 x (+.f64 y x)))))) |
(+.f64 (neg.f64 x) y) |
(+.f64 y (neg.f64 x)) |
Compiled 16 647 to 2 132 computations (87.2% saved)
6 alts after pruning (1 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 539 | 1 | 540 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 3 | 3 |
| Done | 0 | 2 | 2 |
| Total | 539 | 6 | 545 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 97.7% | (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) |
| ✓ | 100.0% | (sqrt.f64 (+.f64 x y)) |
| ✓ | 71.0% | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) |
| ▶ | 77.4% | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x))) |
| ✓ | 98.6% | #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) |
| ✓ | 97.1% | #s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
Compiled 88 to 60 computations (31.8% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 (neg.f64 y) x) | |
| cost-diff | 0 | #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x))) | |
| cost-diff | 1344 | (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x) |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 72 |
| 0 | 22 | 68 |
| 1 | 41 | 64 |
| 2 | 76 | 61 |
| 3 | 181 | 46 |
| 4 | 400 | 30 |
| 5 | 993 | 30 |
| 6 | 3747 | 30 |
| 7 | 7264 | 30 |
| 0 | 8112 | 30 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x)) |
(fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x) |
(*.f64 (neg.f64 y) x) |
(neg.f64 y) |
y |
x |
(/.f64 #s(literal -1 binary64) x) |
#s(literal -1 binary64) |
| Outputs |
|---|
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x))) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+.f64 y x))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x)) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+.f64 y x)) |
(fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x) |
(+.f64 y x) |
(*.f64 (neg.f64 y) x) |
(*.f64 (neg.f64 x) y) |
(neg.f64 y) |
y |
x |
(/.f64 #s(literal -1 binary64) x) |
#s(literal -1 binary64) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (neg.f64 y) | |
| accuracy | 0 | #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x)) | |
| accuracy | 0.015625 | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x))) | |
| accuracy | 14.22729946657694 | (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x) |
| 31.0ms | 256× | 0 | valid |
Compiled 127 to 35 computations (72.4% saved)
ival-mult: 10.0ms (47.7% of total)ival-add: 4.0ms (19.1% of total)ival-div: 3.0ms (14.3% of total)ival-sqrt: 2.0ms (9.5% of total)ival-neg: 1.0ms (4.8% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
(fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x)) |
(*.f64 (neg.f64 y) x) |
(neg.f64 y) |
| Outputs |
|---|
y |
(+ x y) |
(sqrt y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(* -1 (* x y)) |
x |
(* x (+ 1 (/ y x))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(* -1 y) |
(* y (+ 1 (/ x y))) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | y | @ | inf | ((+ (* (* (neg y) x) (/ -1 x)) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (* (neg y) x) (neg y)) |
| 1.0ms | y | @ | -inf | ((+ (* (* (neg y) x) (/ -1 x)) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (* (neg y) x) (neg y)) |
| 1.0ms | x | @ | inf | ((+ (* (* (neg y) x) (/ -1 x)) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (* (neg y) x) (neg y)) |
| 1.0ms | y | @ | 0 | ((+ (* (* (neg y) x) (/ -1 x)) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (* (neg y) x) (neg y)) |
| 1.0ms | x | @ | -inf | ((+ (* (* (neg y) x) (/ -1 x)) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (* (neg y) x) (neg y)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 159 | 589 |
| 1 | 462 | 559 |
| 2 | 1432 | 541 |
| 3 | 4623 | 529 |
| 0 | 8219 | 493 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
y |
(+ x y) |
(sqrt y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(* -1 (* x y)) |
x |
(* x (+ 1 (/ y x))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(* -1 y) |
(* y (+ 1 (/ x y))) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
| Outputs |
|---|
y |
(+ x y) |
(+.f64 x y) |
(sqrt y) |
(sqrt.f64 y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x (sqrt.f64 y)) |
(* -1 (* x y)) |
(*.f64 (neg.f64 x) y) |
x |
(* x (+ 1 (/ y x))) |
(+.f64 x y) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(*.f64 (fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64)) (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+.f64 x y) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 y y) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 y y) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (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 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)) |
(* -1 y) |
(neg.f64 y) |
(* y (+ 1 (/ x y))) |
(+.f64 x y) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(*.f64 (fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(+.f64 x y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 66 |
| 0 | 22 | 62 |
| 1 | 96 | 46 |
| 2 | 688 | 36 |
| 0 | 8584 | 33 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x)) |
(*.f64 (neg.f64 y) x) |
(neg.f64 y) |
| Outputs |
|---|
(*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 x (*.f64 (/.f64 y x) x)) x) #s(literal 2 binary64)))) (-.f64 (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 2 binary64)) (*.f64 (-.f64 x (*.f64 (/.f64 y x) x)) x))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (-.f64 x (*.f64 (/.f64 y x) x)) x) #s(literal 3 binary64)) (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 x (*.f64 (/.f64 y x) x)) x) (-.f64 (*.f64 (-.f64 x (*.f64 (/.f64 y x) x)) x) (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 2 binary64))) (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 4 binary64)))) |
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 2 binary64))) (fma.f64 (neg.f64 x) x (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 2 binary64)))) (fma.f64 (/.f64 y x) x x)) |
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 2 binary64))) (-.f64 (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (fma.f64 (/.f64 y x) x x) (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 2 binary64)))) |
(*.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) y #s(literal 1 binary64)) x) |
(*.f64 (-.f64 (*.f64 x x) (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 (/.f64 y x) x)))) |
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (/.f64 (neg.f64 x) x) y x)) (fma.f64 (neg.f64 x) x (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (fma.f64 (*.f64 (/.f64 y x) x) (fma.f64 (/.f64 y x) x (neg.f64 x)) (*.f64 x x)) #s(literal -1 binary64)) (-.f64 (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (neg.f64 x) x (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (neg.f64 x) x) y x))) |
(*.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 (/.f64 y x) x) (fma.f64 (/.f64 y x) x (neg.f64 x)) (*.f64 x x))))) |
(*.f64 (fma.f64 (neg.f64 x) x (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (/.f64 (neg.f64 x) x) y x))) |
(*.f64 (fma.f64 (*.f64 (/.f64 y x) x) (fma.f64 (/.f64 y x) x (neg.f64 x)) (*.f64 x x)) (/.f64 (fma.f64 (/.f64 y x) x x) (fma.f64 (*.f64 (/.f64 y x) x) (fma.f64 (/.f64 y x) x (neg.f64 x)) (*.f64 x x)))) |
(*.f64 (fma.f64 (*.f64 (/.f64 y x) x) (fma.f64 (/.f64 y x) x (neg.f64 x)) (*.f64 x x)) (*.f64 (fma.f64 (/.f64 y x) x x) (pow.f64 (fma.f64 (*.f64 (/.f64 y x) x) (fma.f64 (/.f64 y x) x (neg.f64 x)) (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (-.f64 (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (*.f64 (/.f64 y x) x) (fma.f64 (/.f64 y x) x (neg.f64 x)) (*.f64 x x)) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (fma.f64 (/.f64 y x) x x)) |
(*.f64 (fma.f64 (/.f64 y x) x x) (/.f64 (fma.f64 (/.f64 y x) x (neg.f64 x)) (fma.f64 (/.f64 y x) x (neg.f64 x)))) |
(*.f64 (fma.f64 (/.f64 y x) x x) (*.f64 (fma.f64 (/.f64 y x) x (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 (/.f64 (neg.f64 x) x) y x)))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 y x) x x)) #s(literal -1 binary64)) |
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (/.f64 (neg.f64 x) x) y x))) (fma.f64 x x (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 2 binary64)))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (/.f64 (neg.f64 x) x) y x))) (fma.f64 (*.f64 x x) (fma.f64 x x (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 2 binary64))) (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 4 binary64)))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (*.f64 (/.f64 y x) x) (fma.f64 (/.f64 y x) x (neg.f64 x)) (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) |
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 9 binary64))) (pow.f64 (fma.f64 (*.f64 (/.f64 y x) x) (fma.f64 (/.f64 y x) x (neg.f64 x)) (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (-.f64 (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 (*.f64 x y) (/.f64 x x)) #s(literal 3 binary64)))) |
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(/.f64 (*.f64 (pow.f64 (neg.f64 y) #s(literal 3 binary64)) x) (*.f64 y y)) |
(/.f64 (*.f64 x y) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 x y))) |
(/.f64 (*.f64 x (neg.f64 y)) #s(literal 1 binary64)) |
(/.f64 y (/.f64 #s(literal -1 binary64) x)) |
(neg.f64 (*.f64 x y)) |
(fma.f64 #s(literal 0 binary64) x (*.f64 x (neg.f64 y))) |
(fma.f64 x #s(literal 0 binary64) (*.f64 x (neg.f64 y))) |
(-.f64 #s(literal 0 binary64) (*.f64 x y)) |
(+.f64 (*.f64 x #s(literal 0 binary64)) (*.f64 x (neg.f64 y))) |
(+.f64 (*.f64 #s(literal 0 binary64) x) (*.f64 x (neg.f64 y))) |
(+.f64 #s(literal 0 binary64) (*.f64 x (neg.f64 y))) |
(*.f64 (*.f64 (neg.f64 y) y) (/.f64 #s(literal 1 binary64) y)) |
(*.f64 (pow.f64 (neg.f64 y) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y y))) |
(*.f64 #s(literal -1 binary64) y) |
(*.f64 y #s(literal -1 binary64)) |
(/.f64 (neg.f64 (pow.f64 (neg.f64 y) #s(literal 3 binary64))) (*.f64 (neg.f64 y) y)) |
(/.f64 (*.f64 (neg.f64 y) y) (-.f64 #s(literal 0 binary64) (neg.f64 y))) |
(/.f64 (*.f64 (neg.f64 y) y) y) |
(/.f64 (pow.f64 (neg.f64 y) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 y y) (*.f64 #s(literal 0 binary64) (neg.f64 y))))) |
(/.f64 (pow.f64 (neg.f64 y) #s(literal 3 binary64)) (*.f64 y y)) |
(/.f64 #s(literal 1 binary64) (/.f64 y (*.f64 (neg.f64 y) y))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 y y) (pow.f64 (neg.f64 y) #s(literal 3 binary64)))) |
(/.f64 (*.f64 y y) (neg.f64 y)) |
(neg.f64 y) |
(fma.f64 (*.f64 (neg.f64 y) y) (/.f64 #s(literal 1 binary64) y) #s(literal 0 binary64)) |
(fma.f64 (pow.f64 (neg.f64 y) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal 0 binary64)) |
(fma.f64 #s(literal -1 binary64) y #s(literal 0 binary64)) |
(fma.f64 y #s(literal -1 binary64) #s(literal 0 binary64)) |
(-.f64 (/.f64 #s(literal 0 binary64) y) (*.f64 y #s(literal 1 binary64))) |
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 y y)) (/.f64 (pow.f64 y #s(literal 3 binary64)) (*.f64 y y))) |
(-.f64 #s(literal 0 binary64) y) |
(+.f64 #s(literal 0 binary64) (neg.f64 y)) |
(+.f64 (neg.f64 y) #s(literal 0 binary64)) |
Compiled 7 014 to 883 computations (87.4% saved)
6 alts after pruning (0 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 190 | 0 | 190 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 5 | 5 |
| Total | 190 | 6 | 196 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 97.7% | (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) |
| ✓ | 100.0% | (sqrt.f64 (+.f64 x y)) |
| ✓ | 71.0% | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) |
| ✓ | 77.4% | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x))) |
| ✓ | 98.6% | #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) |
| ✓ | 97.1% | #s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
Compiled 218 to 115 computations (47.2% saved)
| Inputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(sqrt.f64 (+.f64 x y)) |
(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x))) |
#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) |
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) |
(sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) |
| Outputs |
|---|
(sqrt.f64 (+.f64 x y)) |
4 calls:
| 4.0ms | (sqrt.f64 (+.f64 x y)) |
| 4.0ms | (+.f64 x y) |
| 4.0ms | y |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | y |
| 100.0% | 1 | (sqrt.f64 (+.f64 x y)) |
| 100.0% | 1 | (+.f64 x y) |
Compiled 9 to 11 computations (-22.2% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
| Outputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
4 calls:
| 2.0ms | (sqrt.f64 (+.f64 x y)) |
| 2.0ms | (+.f64 x y) |
| 2.0ms | x |
| 2.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.1% | 1 | x |
| 97.1% | 1 | y |
| 97.1% | 1 | (sqrt.f64 (+.f64 x y)) |
| 97.1% | 1 | (+.f64 x y) |
Compiled 9 to 11 computations (-22.2% saved)
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 11 |
| 1 | 9 | 11 |
| 1× | saturated |
| Inputs |
|---|
(sqrt.f64 (+.f64 x y)) |
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
| Outputs |
|---|
(sqrt.f64 (+.f64 x y)) |
(sqrt.f64 (+.f64 y x)) |
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 156 | 583 |
| 1 | 454 | 553 |
| 2 | 1425 | 535 |
| 3 | 4629 | 523 |
| 0 | 8199 | 487 |
| 1× | done |
| 1× | iter limit |
| 1× | node limit |
Compiled 13 to 11 computations (15.4% saved)
(sort x y)
Compiled 46 to 40 computations (13% saved)
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