
Time bar (total: 5.9s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 1 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 2 |
| 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)
| 447.0ms | 8 256× | 0 | valid |
| 16.0ms | 493× | 0 | invalid |
ival-add: 100.0ms (50% of total)ival-sqrt: 90.0ms (45% of total)ival-true: 7.0ms (3.5% of total)ival-assert: 3.0ms (1.5% 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 |
| 19.0ms | 512× | 0 | valid |
Compiled 26 to 16 computations (38.5% saved)
ival-add: 3.0ms (43.4% of total)ival-sqrt: 3.0ms (43.4% 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 | 159 | 22 |
| 6 | 206 | 22 |
| 7 | 217 | 22 |
| 8 | 220 | 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 | 0.0 | (+.f64 x y) | |
| accuracy | 0.01171875 | (sqrt.f64 (+.f64 x y)) |
| 10.0ms | 256× | 0 | valid |
Compiled 11 to 6 computations (45.5% saved)
ival-sqrt: 3.0ms (68.1% of total)ival-add: 1.0ms (22.7% 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 | 1431 | 535 |
| 3 | 4702 | 523 |
| 0 | 8271 | 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 | 1374 | 7 |
| 0 | 8331 | 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 |
|---|---|---|
| ▶ | 47.7% | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))))) |
| ▶ | 100.0% | (sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))) |
| ▶ | 47.7% | (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)) |
| ▶ | 98.1% | #s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
Compiled 56 to 38 computations (32.1% saved)
| 1× | egg-herbie |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (-.f64 y x) | |
| cost-diff | 0 | (sqrt.f64 (-.f64 y x)) | |
| cost-diff | 0 | (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x)))) | |
| cost-diff | 2 | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))))) | |
| cost-diff | 0 | (/.f64 x (-.f64 x y)) | |
| cost-diff | 0 | (sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))) | |
| cost-diff | 1 | (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))) | |
| cost-diff | 11 | (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))) | |
| 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 | 1 | (fma.f64 #s(literal -1 binary64) x y) | |
| cost-diff | 1 | (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) | |
| cost-diff | 8 | (/.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 y) | |
| cost-diff | 0 | #s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 28 | 175 |
| 0 | 52 | 176 |
| 1 | 81 | 169 |
| 2 | 129 | 166 |
| 3 | 218 | 166 |
| 4 | 466 | 126 |
| 5 | 1168 | 126 |
| 6 | 3068 | 126 |
| 7 | 5451 | 126 |
| 8 | 7004 | 126 |
| 9 | 7612 | 126 |
| 0 | 8006 | 126 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(sqrt.f64 y) |
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) |
(sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (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))))) |
x |
(/.f64 x (-.f64 x y)) |
(-.f64 x y) |
y |
(neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))) |
(*.f64 y (/.f64 y (-.f64 x y))) |
(/.f64 y (-.f64 x y)) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))))) |
#s(literal 1 binary64) |
(/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x)))) |
(sqrt.f64 (-.f64 y x)) |
(-.f64 y x) |
y |
x |
(sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) |
(*.f64 (+.f64 y x) (-.f64 y x)) |
(+.f64 y x) |
| Outputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(sqrt.f64 y) |
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) |
(sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))) |
(sqrt.f64 (+.f64 y x)) |
(fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))) |
(+.f64 y x) |
x |
(/.f64 x (-.f64 x y)) |
(-.f64 x y) |
y |
(neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))) |
(*.f64 (/.f64 y (-.f64 y x)) y) |
(*.f64 y (/.f64 y (-.f64 x y))) |
(*.f64 (/.f64 y (-.f64 x y)) y) |
(/.f64 y (-.f64 x y)) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) |
#s(literal 1 binary64) |
(/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x)))) |
(sqrt.f64 (-.f64 y x)) |
(-.f64 y x) |
y |
x |
(sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) |
(*.f64 (+.f64 y x) (-.f64 y x)) |
(+.f64 y x) |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0 | (sqrt.f64 (-.f64 y x)) | |
| accuracy | 0.265625 | (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x)))) | |
| accuracy | 0.26953125 | (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))))) | |
| accuracy | 32.03693098018467 | (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) | |
| accuracy | 0.00390625 | (*.f64 y (/.f64 y (-.f64 x y))) | |
| accuracy | 0.00390625 | (sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))) | |
| accuracy | 0.0078125 | (/.f64 y (-.f64 x y)) | |
| accuracy | 0.0078125 | (/.f64 x (-.f64 x y)) | |
| accuracy | 0.0 | (*.f64 x x) | |
| accuracy | 0.00390625 | (sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y))) | |
| accuracy | 2.7968750000000004 | (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) | |
| accuracy | 32.07597674243 | (/.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x x) (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)) | |
| accuracy | 0.0 | (sqrt.f64 y) | |
| accuracy | 0.8249251558200901 | #s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
| 116.0ms | 254× | 0 | valid |
| 2.0ms | 2× | 5 | exit |
Compiled 182 to 32 computations (82.4% saved)
ival-mult: 10.0ms (27.2% of total)ival-sqrt: 9.0ms (24.5% of total)ival-div: 7.0ms (19% of total)ival-add: 6.0ms (16.3% of total)ival-sub: 2.0ms (5.4% of total)ival-neg: 1.0ms (2.7% of total)adjust: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(sqrt.f64 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))) |
(fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))) |
(neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))) |
(sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))) |
(/.f64 x (-.f64 x y)) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))))) |
(/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x)))) |
(sqrt.f64 (-.f64 y x)) |
(-.f64 y x) |
(*.f64 x x) |
(/.f64 y (-.f64 x y)) |
(*.f64 y (/.f64 y (-.f64 x y))) |
(sqrt.f64 (*.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)))))))))) |
y |
(+ x y) |
(pow y 2) |
(+ (* -1 (pow x 2)) (pow y 2)) |
(+ y (* -1 x)) |
(- x (* -1 y)) |
(- (* x (+ 1 (/ x y))) (* -1 y)) |
(- (* x (+ 1 (* x (+ (/ 1 y) (/ x (pow y 2)))))) (* -1 y)) |
(* -1 (/ x y)) |
(* x (- (* -1 (/ x (pow y 2))) (/ 1 y))) |
(* x (- (* x (- (* -1 (/ x (pow y 3))) (/ 1 (pow y 2)))) (/ 1 y))) |
(* x (- (* x (- (* x (- (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))) |
(sqrt (/ 1 y)) |
(+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))) |
(+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* x (sqrt (/ 1 (pow y 5)))))))) |
(+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* x (+ (* -5/16 (* x (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5))))))))) |
(+ (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)))))))))) |
(pow x 2) |
-1 |
(- (* -1 (/ x y)) 1) |
(- (* x (- (* -1 (/ x (pow y 2))) (/ 1 y))) 1) |
(- (* x (- (* x (- (* -1 (/ x (pow y 3))) (/ 1 (pow y 2)))) (/ 1 y))) 1) |
(* -1 y) |
(+ (* -1 x) (* -1 y)) |
(+ (* -1 y) (* x (- (* -1 (/ x y)) 1))) |
(+ (* -1 y) (* x (- (* x (- (* -1 (/ x (pow y 2))) (/ 1 y))) 1))) |
(+ 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 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 (pow x 2)) |
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1)) |
(* -1 x) |
(* x (- (/ y x) 1)) |
(* x (- (+ 1 (* -1 (/ (+ (* -1 (pow y 2)) (pow y 2)) (pow x 2)))) (* -1 (/ y x)))) |
(* -1 (/ (pow y 2) x)) |
(/ (- (* -1 (/ (pow y 3) x)) (pow y 2)) x) |
(/ (- (+ (* -1 (/ (pow y 3) x)) (* -1 (/ (pow y 4) (pow x 2)))) (pow y 2)) x) |
(/ (- (+ (* -1 (/ (pow y 3) x)) (+ (* -1 (/ (pow y 4) (pow x 2))) (* -1 (/ (pow y 5) (pow x 3))))) (pow y 2)) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (pow y 2)) (pow y 2)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (pow y 2)) (pow y 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
1 |
(+ 1 (/ y x)) |
(- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ y x))) |
(- (+ 1 (/ (pow y 3) (pow x 3))) (+ (* -1 (/ y x)) (* -1 (/ (pow y 2) (pow x 2))))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* 1/4 (* x (pow y 2))) (pow y 3)))) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2)))))) |
(* (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)))))) |
(/ y x) |
(/ (+ y (/ (pow y 2) x)) x) |
(/ (- (+ y (/ (pow y 3) (pow x 2))) (* -1 (/ (pow y 2) x))) x) |
(/ (- (+ y (/ (pow y 4) (pow x 3))) (+ (* -1 (/ (pow y 2) x)) (* -1 (/ (pow y 3) (pow x 2))))) x) |
(/ (pow y 2) x) |
(/ (+ (/ (pow y 3) x) (pow y 2)) x) |
(/ (- (+ (/ (pow y 4) (pow x 2)) (pow y 2)) (* -1 (/ (pow y 3) x))) x) |
(/ (- (+ (/ (pow y 5) (pow x 3)) (pow y 2)) (+ (* -1 (/ (pow y 3) x)) (* -1 (/ (pow y 4) (pow x 2))))) 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)))))))) |
(* -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))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 4) x)) (pow y 3)) x)) (* -1 (pow y 2))) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 5) x) (* -1 (pow y 4))) x)) (pow y 3)) x)) (* -1 (pow y 2))) x)) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (+ (* -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) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) y) x))) |
(+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x)) y) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (pow y 2))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))) (pow y 3))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(* -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 (/ (+ (* -1 y) (* -1 (/ (pow y 2) x))) x)) |
(* -1 (/ (+ (* -1 y) (* -1 (/ (+ (/ (pow y 3) x) (pow y 2)) x))) x)) |
(* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (pow y 4) x)) (* -1 (pow y 3))) x)) (pow y 2)) x))) x)) |
(* -1 (/ (+ (* -1 (/ (pow y 3) x)) (* -1 (pow y 2))) x)) |
(* -1 (/ (+ (* -1 (/ (+ (/ (pow y 4) x) (pow y 3)) x)) (* -1 (pow y 2))) x)) |
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (pow y 5) x)) (* -1 (pow y 4))) x)) (pow y 3)) x)) (* -1 (pow y 2))) 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))))) |
(+ (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))))))) |
(* (pow y 2) (- (* -1 (/ y (pow x 2))) (/ 1 x))) |
(* (pow y 2) (- (* y (- (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))) |
(* (pow y 2) (- (* y (- (* y (- (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))) |
(+ 1 (* y (+ (/ 1 x) (/ y (pow x 2))))) |
(+ 1 (* y (+ (* y (+ (/ 1 (pow x 2)) (/ y (pow x 3)))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) y))))) |
(+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* y (+ (* -5/16 (* (sqrt (/ 1 (pow x 7))) y)) (* 3/8 (sqrt (/ 1 (pow x 5))))))))) |
(+ (* 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 (+ (/ 1 x) (/ y (pow x 2)))) |
(* y (+ (* y (+ (/ 1 (pow x 2)) (/ y (pow x 3)))) (/ 1 x))) |
(* y (+ (* y (+ (* y (+ (/ 1 (pow x 3)) (/ y (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x))) |
(* (pow y 2) (+ (/ 1 x) (/ y (pow x 2)))) |
(* (pow y 2) (+ (* y (+ (/ 1 (pow x 2)) (/ y (pow x 3)))) (/ 1 x))) |
(* (pow y 2) (+ (* y (+ (* y (+ (/ 1 (pow x 3)) (/ y (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x))) |
(+ (* 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))))))))) |
(* 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 (/ (pow x 2) (pow y 2))) (+ (/ x y) (/ (pow x 2) (pow y 2)))))) |
(* y (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (+ (/ x y) (+ (/ (pow x 2) (pow y 2)) (/ (pow x 3) (pow y 3)))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 2)) (pow x 2))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 2)) (pow x 2)))))))) |
(/ (+ (* -1 x) (* -1 (/ (pow x 2) y))) y) |
(/ (- (+ (* -1 x) (* -1 (/ (pow x 3) (pow y 2)))) (/ (pow x 2) y)) y) |
(/ (- (+ (* -1 x) (* -1 (/ (pow x 4) (pow y 3)))) (+ (/ (pow x 2) y) (/ (pow x 3) (pow y 2)))) y) |
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))) |
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 2) y)) (pow x 3)))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) |
(* 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 (/ (pow x 2) (pow y 2))) (+ 1 (/ x y))) |
(- (* -1 (/ (pow x 3) (pow y 3))) (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2))))) |
(* y (- (* -1 (/ x y)) 1)) |
(* y (- (* -1 (/ (pow x 2) (pow y 2))) (+ 1 (/ x y)))) |
(* y (- (* -1 (/ (pow x 3) (pow y 3))) (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2)))))) |
(* 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))))))) |
(* -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))) |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) y))) y)) 1))) |
(* -1 (* y (- (* -1 (/ (+ x (/ (pow x 2) y)) y)) 1))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ (+ (* -1 (/ (pow x 3) y)) (* -1 (pow x 2))) y))) y)) 1))) |
(* -1 (* y (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 2)) (pow x 2)))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1 (/ (+ (* 1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt y))) (* 1/2 (* (sqrt y) (+ (* -1 (pow x 2)) (pow x 2))))) (pow y 3))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (/ (+ x (/ (pow x 2) y)) y)) |
(* -1 (/ (+ x (* -1 (/ (- (* -1 (/ (pow x 3) y)) (pow x 2)) y))) y)) |
(* -1 (/ (+ x (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (* -1 (pow x 3))) y)) (pow x 2)) y))) y)) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (* (pow x 2) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))) (pow x 3))))) (pow y 3))) (+ (* -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))))) |
(* -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 (/ (- (/ (pow x 2) y) (* -1 x)) y)) 1) |
(- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow x 3) y)) (pow x 2)) y)) (* -1 x)) y)) 1) |
(* -1 (* y (+ 1 (/ x y)))) |
(* -1 (* y (+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) y)) x) y))))) |
(* -1 (* y (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (* -1 (pow x 2))) y)) x) y))))) |
(* -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)))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 56.0ms | x | @ | inf | ((sqrt (+ x y)) (sqrt 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))) (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y))))) (neg (* y (/ y (- x y)))) (sqrt (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y)))))) (/ x (- x y)) (/ 1 (/ (sqrt (- y x)) (sqrt (* (+ y x) (- y x))))) (/ (sqrt (- y x)) (sqrt (* (+ y x) (- y x)))) (sqrt (- y x)) (- y x) (* x x) (/ y (- x y)) (* y (/ y (- x y))) (sqrt (* (+ y x) (- y x)))) |
| 14.0ms | y | @ | inf | ((sqrt (+ x y)) (sqrt 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))) (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y))))) (neg (* y (/ y (- x y)))) (sqrt (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y)))))) (/ x (- x y)) (/ 1 (/ (sqrt (- y x)) (sqrt (* (+ y x) (- y x))))) (/ (sqrt (- y x)) (sqrt (* (+ y x) (- y x)))) (sqrt (- y x)) (- y x) (* x x) (/ y (- x y)) (* y (/ y (- x y))) (sqrt (* (+ y x) (- y x)))) |
| 6.0ms | y | @ | -inf | ((sqrt (+ x y)) (sqrt 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))) (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y))))) (neg (* y (/ y (- x y)))) (sqrt (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y)))))) (/ x (- x y)) (/ 1 (/ (sqrt (- y x)) (sqrt (* (+ y x) (- y x))))) (/ (sqrt (- y x)) (sqrt (* (+ y x) (- y x)))) (sqrt (- y x)) (- y x) (* x x) (/ y (- x y)) (* y (/ y (- x y))) (sqrt (* (+ y x) (- y x)))) |
| 6.0ms | y | @ | 0 | ((sqrt (+ x y)) (sqrt 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))) (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y))))) (neg (* y (/ y (- x y)))) (sqrt (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y)))))) (/ x (- x y)) (/ 1 (/ (sqrt (- y x)) (sqrt (* (+ y x) (- y x))))) (/ (sqrt (- y x)) (sqrt (* (+ y x) (- y x)))) (sqrt (- y x)) (- y x) (* x x) (/ y (- x y)) (* y (/ y (- x y))) (sqrt (* (+ y x) (- y x)))) |
| 6.0ms | x | @ | -inf | ((sqrt (+ x y)) (sqrt 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))) (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y))))) (neg (* y (/ y (- x y)))) (sqrt (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y)))))) (/ x (- x y)) (/ 1 (/ (sqrt (- y x)) (sqrt (* (+ y x) (- y x))))) (/ (sqrt (- y x)) (sqrt (* (+ y x) (- y x)))) (sqrt (- y x)) (- y x) (* x x) (/ y (- x y)) (* y (/ y (- x y))) (sqrt (* (+ y x) (- y x)))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 860 | 4246 |
| 1 | 2857 | 3675 |
| 0 | 9152 | 3452 |
| 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) |
(pow y 2) |
(+ (* -1 (pow x 2)) (pow y 2)) |
(+ y (* -1 x)) |
(- x (* -1 y)) |
(- (* x (+ 1 (/ x y))) (* -1 y)) |
(- (* x (+ 1 (* x (+ (/ 1 y) (/ x (pow y 2)))))) (* -1 y)) |
(* -1 (/ x y)) |
(* x (- (* -1 (/ x (pow y 2))) (/ 1 y))) |
(* x (- (* x (- (* -1 (/ x (pow y 3))) (/ 1 (pow y 2)))) (/ 1 y))) |
(* x (- (* x (- (* x (- (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))) |
(sqrt (/ 1 y)) |
(+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))) |
(+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* x (sqrt (/ 1 (pow y 5)))))))) |
(+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* x (+ (* -5/16 (* x (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5))))))))) |
(+ (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)))))))))) |
(pow x 2) |
-1 |
(- (* -1 (/ x y)) 1) |
(- (* x (- (* -1 (/ x (pow y 2))) (/ 1 y))) 1) |
(- (* x (- (* x (- (* -1 (/ x (pow y 3))) (/ 1 (pow y 2)))) (/ 1 y))) 1) |
(* -1 y) |
(+ (* -1 x) (* -1 y)) |
(+ (* -1 y) (* x (- (* -1 (/ x y)) 1))) |
(+ (* -1 y) (* x (- (* x (- (* -1 (/ x (pow y 2))) (/ 1 y))) 1))) |
(+ 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 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 (pow x 2)) |
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1)) |
(* -1 x) |
(* x (- (/ y x) 1)) |
(* x (- (+ 1 (* -1 (/ (+ (* -1 (pow y 2)) (pow y 2)) (pow x 2)))) (* -1 (/ y x)))) |
(* -1 (/ (pow y 2) x)) |
(/ (- (* -1 (/ (pow y 3) x)) (pow y 2)) x) |
(/ (- (+ (* -1 (/ (pow y 3) x)) (* -1 (/ (pow y 4) (pow x 2)))) (pow y 2)) x) |
(/ (- (+ (* -1 (/ (pow y 3) x)) (+ (* -1 (/ (pow y 4) (pow x 2))) (* -1 (/ (pow y 5) (pow x 3))))) (pow y 2)) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (pow y 2)) (pow y 2)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (pow y 2)) (pow y 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
1 |
(+ 1 (/ y x)) |
(- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ y x))) |
(- (+ 1 (/ (pow y 3) (pow x 3))) (+ (* -1 (/ y x)) (* -1 (/ (pow y 2) (pow x 2))))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* 1/4 (* x (pow y 2))) (pow y 3)))) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2)))))) |
(* (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)))))) |
(/ y x) |
(/ (+ y (/ (pow y 2) x)) x) |
(/ (- (+ y (/ (pow y 3) (pow x 2))) (* -1 (/ (pow y 2) x))) x) |
(/ (- (+ y (/ (pow y 4) (pow x 3))) (+ (* -1 (/ (pow y 2) x)) (* -1 (/ (pow y 3) (pow x 2))))) x) |
(/ (pow y 2) x) |
(/ (+ (/ (pow y 3) x) (pow y 2)) x) |
(/ (- (+ (/ (pow y 4) (pow x 2)) (pow y 2)) (* -1 (/ (pow y 3) x))) x) |
(/ (- (+ (/ (pow y 5) (pow x 3)) (pow y 2)) (+ (* -1 (/ (pow y 3) x)) (* -1 (/ (pow y 4) (pow x 2))))) 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)))))))) |
(* -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))) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 4) x)) (pow y 3)) x)) (* -1 (pow y 2))) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 5) x) (* -1 (pow y 4))) x)) (pow y 3)) x)) (* -1 (pow y 2))) x)) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (+ (* -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) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) y) x))) |
(+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x)) y) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (pow y 2))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))) (pow y 3))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(* -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 (/ (+ (* -1 y) (* -1 (/ (pow y 2) x))) x)) |
(* -1 (/ (+ (* -1 y) (* -1 (/ (+ (/ (pow y 3) x) (pow y 2)) x))) x)) |
(* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (pow y 4) x)) (* -1 (pow y 3))) x)) (pow y 2)) x))) x)) |
(* -1 (/ (+ (* -1 (/ (pow y 3) x)) (* -1 (pow y 2))) x)) |
(* -1 (/ (+ (* -1 (/ (+ (/ (pow y 4) x) (pow y 3)) x)) (* -1 (pow y 2))) x)) |
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (pow y 5) x)) (* -1 (pow y 4))) x)) (pow y 3)) x)) (* -1 (pow y 2))) 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))))) |
(+ (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))))))) |
(* (pow y 2) (- (* -1 (/ y (pow x 2))) (/ 1 x))) |
(* (pow y 2) (- (* y (- (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))) |
(* (pow y 2) (- (* y (- (* y (- (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))) |
(+ 1 (* y (+ (/ 1 x) (/ y (pow x 2))))) |
(+ 1 (* y (+ (* y (+ (/ 1 (pow x 2)) (/ y (pow x 3)))) (/ 1 x)))) |
(+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) y))))) |
(+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* y (+ (* -5/16 (* (sqrt (/ 1 (pow x 7))) y)) (* 3/8 (sqrt (/ 1 (pow x 5))))))))) |
(+ (* 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 (+ (/ 1 x) (/ y (pow x 2)))) |
(* y (+ (* y (+ (/ 1 (pow x 2)) (/ y (pow x 3)))) (/ 1 x))) |
(* y (+ (* y (+ (* y (+ (/ 1 (pow x 3)) (/ y (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x))) |
(* (pow y 2) (+ (/ 1 x) (/ y (pow x 2)))) |
(* (pow y 2) (+ (* y (+ (/ 1 (pow x 2)) (/ y (pow x 3)))) (/ 1 x))) |
(* (pow y 2) (+ (* y (+ (* y (+ (/ 1 (pow x 3)) (/ y (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x))) |
(+ (* 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))))))))) |
(* 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 (/ (pow x 2) (pow y 2))) (+ (/ x y) (/ (pow x 2) (pow y 2)))))) |
(* y (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (+ (/ x y) (+ (/ (pow x 2) (pow y 2)) (/ (pow x 3) (pow y 3)))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 2)) (pow x 2))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 2)) (pow x 2)))))))) |
(/ (+ (* -1 x) (* -1 (/ (pow x 2) y))) y) |
(/ (- (+ (* -1 x) (* -1 (/ (pow x 3) (pow y 2)))) (/ (pow x 2) y)) y) |
(/ (- (+ (* -1 x) (* -1 (/ (pow x 4) (pow y 3)))) (+ (/ (pow x 2) y) (/ (pow x 3) (pow y 2)))) y) |
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))) |
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 2) y)) (pow x 3)))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) |
(* 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 (/ (pow x 2) (pow y 2))) (+ 1 (/ x y))) |
(- (* -1 (/ (pow x 3) (pow y 3))) (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2))))) |
(* y (- (* -1 (/ x y)) 1)) |
(* y (- (* -1 (/ (pow x 2) (pow y 2))) (+ 1 (/ x y)))) |
(* y (- (* -1 (/ (pow x 3) (pow y 3))) (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2)))))) |
(* 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))))))) |
(* -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))) |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) y))) y)) 1))) |
(* -1 (* y (- (* -1 (/ (+ x (/ (pow x 2) y)) y)) 1))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ (+ (* -1 (/ (pow x 3) y)) (* -1 (pow x 2))) y))) y)) 1))) |
(* -1 (* y (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 2)) (pow x 2)))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1 (/ (+ (* 1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt y))) (* 1/2 (* (sqrt y) (+ (* -1 (pow x 2)) (pow x 2))))) (pow y 3))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (/ (+ x (/ (pow x 2) y)) y)) |
(* -1 (/ (+ x (* -1 (/ (- (* -1 (/ (pow x 3) y)) (pow x 2)) y))) y)) |
(* -1 (/ (+ x (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (* -1 (pow x 3))) y)) (pow x 2)) y))) y)) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (* (pow x 2) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))) (pow x 3))))) (pow y 3))) (+ (* -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))))) |
(* -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 (/ (- (/ (pow x 2) y) (* -1 x)) y)) 1) |
(- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow x 3) y)) (pow x 2)) y)) (* -1 x)) y)) 1) |
(* -1 (* y (+ 1 (/ x y)))) |
(* -1 (* y (+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) y)) x) y))))) |
(* -1 (* y (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (* -1 (pow x 2))) y)) x) y))))) |
(* -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)))) |
| Outputs |
|---|
(sqrt y) |
(sqrt.f64 y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (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 x #s(literal -1/8 binary64)) (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) |
(pow y 2) |
(*.f64 y y) |
(+ (* -1 (pow x 2)) (pow y 2)) |
(fma.f64 (neg.f64 x) x (*.f64 y y)) |
(+ y (* -1 x)) |
(-.f64 y x) |
(- x (* -1 y)) |
(+.f64 y x) |
(- (* x (+ 1 (/ x y))) (* -1 y)) |
(fma.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) x y) |
(- (* x (+ 1 (* x (+ (/ 1 y) (/ x (pow y 2)))))) (* -1 y)) |
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(* y (+ 1 (+ (* -1 (/ (pow x 2) (pow y 2))) (+ (/ x y) (/ (pow x 2) (pow y 2)))))) |
(fma.f64 (-.f64 (fma.f64 (/.f64 x y) (/.f64 x y) (/.f64 x y)) (*.f64 (/.f64 x y) (/.f64 x y))) y y) |
(* y (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2))))) |
(fma.f64 (fma.f64 (/.f64 x y) (/.f64 x y) (/.f64 x y)) y y) |
(* y (+ 1 (+ (/ x y) (+ (/ (pow x 2) (pow y 2)) (/ (pow x 3) (pow y 3)))))) |
(fma.f64 (+.f64 (fma.f64 (/.f64 x y) (/.f64 x y) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (/.f64 x y)) y y) |
(* y (+ (sqrt (/ 1 y)) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 2)) (pow x 2))))))) |
(*.f64 (fma.f64 #s(literal 0 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))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 2)) (pow x 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 #s(literal 0 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 x) (* -1 (/ (pow x 2) y))) y) |
(/.f64 (neg.f64 (+.f64 (/.f64 (*.f64 x x) y) x)) y) |
(/ (- (+ (* -1 x) (* -1 (/ (pow x 3) (pow y 2)))) (/ (pow x 2) y)) y) |
(/.f64 (-.f64 (-.f64 (neg.f64 x) (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 y y))) (/.f64 (*.f64 x x) y)) y) |
(/ (- (+ (* -1 x) (* -1 (/ (pow x 4) (pow y 3)))) (+ (/ (pow x 2) y) (/ (pow x 3) (pow y 2)))) y) |
(/.f64 (-.f64 (-.f64 (-.f64 (neg.f64 x) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 3 binary64)))) (/.f64 (*.f64 x x) y)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 y y))) y) |
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))) |
(fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) |
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 2) y)) (pow x 3)))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) |
(fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) x (*.f64 (fma.f64 (*.f64 (*.f64 x x) y) #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))))) (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) |
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(*.f64 (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (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 #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 x #s(literal -1/2 binary64)) (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 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (*.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y) |
(- (* -1 (/ (pow x 2) (pow y 2))) (+ 1 (/ x y))) |
(neg.f64 (fma.f64 (/.f64 x y) (/.f64 x y) (+.f64 (/.f64 x y) #s(literal 1 binary64)))) |
(- (* -1 (/ (pow x 3) (pow y 3))) (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2))))) |
(-.f64 (/.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (/.f64 x y) (/.f64 x y) (+.f64 (/.f64 x y) #s(literal 1 binary64)))) |
(* y (- (* -1 (/ x y)) 1)) |
(neg.f64 (fma.f64 (/.f64 x y) y y)) |
(* y (- (* -1 (/ (pow x 2) (pow y 2))) (+ 1 (/ x y)))) |
(*.f64 (neg.f64 (fma.f64 (/.f64 x y) (/.f64 x y) (+.f64 (/.f64 x y) #s(literal 1 binary64)))) y) |
(* y (- (* -1 (/ (pow x 3) (pow y 3))) (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2)))))) |
(*.f64 (-.f64 (/.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (/.f64 x y) (/.f64 x y) (+.f64 (/.f64 x y) #s(literal 1 binary64)))) y) |
(* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y)))) |
(fma.f64 (/.f64 #s(literal 0 binary64) y) 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 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 0 binary64)) y) (/.f64 #s(literal 0 binary64) y)) 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 (fma.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 0 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 0 binary64)) y) (/.f64 #s(literal 0 binary64) y))) y y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1 binary64) (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)))) (*.f64 #s(literal -1 binary64) (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))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x x) #s(literal -1 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)))) (*.f64 #s(literal -1 binary64) (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 #s(literal -1/8 binary64) (/.f64 (*.f64 x x) #s(literal -1 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)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 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) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))) (neg.f64 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 (- (* -1 (/ (+ x (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) y))) y)) 1))) |
(fma.f64 (/.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 #s(literal 0 binary64) y)) y) (neg.f64 y) y) |
(* -1 (* y (- (* -1 (/ (+ x (/ (pow x 2) y)) y)) 1))) |
(fma.f64 (/.f64 (+.f64 (/.f64 (*.f64 x x) y) x) y) y y) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ (+ (* -1 (/ (pow x 3) y)) (* -1 (pow x 2))) y))) y)) 1))) |
(neg.f64 (neg.f64 (fma.f64 (/.f64 (-.f64 x (/.f64 (neg.f64 (fma.f64 x x (/.f64 (pow.f64 x #s(literal 3 binary64)) y))) y)) y) y y))) |
(* -1 (* y (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 2)) (pow x 2)))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 #s(literal 0 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)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) (neg.f64 y)) |
(* -1 (* y (+ (* -1 (/ (+ (* 1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt y))) (* 1/2 (* (sqrt y) (+ (* -1 (pow x 2)) (pow x 2))))) (pow y 3))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(*.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (/.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 y)) (/.f64 (*.f64 x x) #s(literal -1 binary64)) (*.f64 #s(literal 0 binary64) (sqrt.f64 y))) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 y)) |
(* -1 (/ (+ x (/ (pow x 2) y)) y)) |
(/.f64 (neg.f64 (+.f64 (/.f64 (*.f64 x x) y) x)) y) |
(* -1 (/ (+ x (* -1 (/ (- (* -1 (/ (pow x 3) y)) (pow x 2)) y))) y)) |
(/.f64 (neg.f64 (-.f64 x (/.f64 (neg.f64 (fma.f64 x x (/.f64 (pow.f64 x #s(literal 3 binary64)) y))) y))) y) |
(* -1 (/ (+ x (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (* -1 (pow x 3))) y)) (pow x 2)) y))) y)) |
(/.f64 (-.f64 x (/.f64 (-.f64 (/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (pow.f64 x #s(literal 3 binary64))) (neg.f64 y)) (*.f64 x x)) y)) (neg.f64 y)) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) |
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) |
(+ (* -1 (/ (+ (* -1/2 (* (pow x 2) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))) (pow x 3))))) (pow y 3))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 (*.f64 (*.f64 x x) y) #s(literal -1 binary64)) #s(literal -1/4 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 y)) (*.f64 x x))) (neg.f64 (pow.f64 y #s(literal 3 binary64)))))) |
(* -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 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 #s(literal -1 binary64) (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))))) (+ (* 1/2 (* (* 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 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 #s(literal -1 binary64) (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 #s(literal -1/16 binary64) (pow.f64 x #s(literal 3 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 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))) (neg.f64 y)) |
(- (* -1 (/ (- (/ (pow x 2) y) (* -1 x)) y)) 1) |
(fma.f64 (/.f64 (+.f64 (/.f64 (*.f64 x x) y) x) y) #s(literal -1 binary64) #s(literal -1 binary64)) |
(- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow x 3) y)) (pow x 2)) y)) (* -1 x)) y)) 1) |
(fma.f64 (/.f64 (-.f64 x (/.f64 (neg.f64 (fma.f64 x x (/.f64 (pow.f64 x #s(literal 3 binary64)) y))) y)) y) #s(literal -1 binary64) #s(literal -1 binary64)) |
(* -1 (* y (+ 1 (/ x y)))) |
(neg.f64 (fma.f64 (/.f64 x y) y y)) |
(* -1 (* y (+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) y)) x) y))))) |
(neg.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (*.f64 x x) y) x) y) y y)) |
(* -1 (* y (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (* -1 (pow x 2))) y)) x) y))))) |
(neg.f64 (fma.f64 (/.f64 (-.f64 x (/.f64 (neg.f64 (fma.f64 x x (/.f64 (pow.f64 x #s(literal 3 binary64)) y))) y)) y) y y)) |
(* -1 (* y (pow (sqrt -1) 2))) |
y |
(* -1 (* y (+ (* -1/2 (/ (+ x (* -1 x)) y)) (pow (sqrt -1) 2)))) |
(fma.f64 (/.f64 #s(literal 0 binary64) y) (neg.f64 y) 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)))) |
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (/.f64 (fma.f64 x x #s(literal 0 binary64)) y) #s(literal -1/2 binary64) #s(literal 0 binary64)) y)) (neg.f64 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)))) |
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) y)) (neg.f64 y)) y)) (neg.f64 y)) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 28 | 150 |
| 0 | 52 | 138 |
| 1 | 197 | 85 |
| 2 | 1605 | 84 |
| 0 | 8489 | 84 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(sqrt.f64 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))) |
(fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))) |
(neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))) |
(sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))) |
(/.f64 x (-.f64 x y)) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))))) |
(/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x)))) |
(sqrt.f64 (-.f64 y x)) |
(-.f64 y x) |
(*.f64 x x) |
(/.f64 y (-.f64 x y)) |
(*.f64 y (/.f64 y (-.f64 x y))) |
(sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) |
| Outputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64))) |
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 1/2 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 y #s(literal 1/2 binary64)) |
(sqrt.f64 y) |
(exp.f64 (*.f64 (log.f64 y) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 (-.f64 y x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 (neg.f64 y) y)) #s(literal -1 binary64))) |
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(*.f64 y (/.f64 y (-.f64 x y))) |
(pow.f64 (/.f64 (-.f64 x y) (*.f64 y y)) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) y)) (neg.f64 (/.f64 (-.f64 x y) y))) |
(/.f64 (neg.f64 (*.f64 y (neg.f64 y))) (-.f64 x y)) |
(/.f64 (neg.f64 (*.f64 y #s(literal 1 binary64))) (neg.f64 (/.f64 (-.f64 x y) y))) |
(/.f64 (neg.f64 (*.f64 (neg.f64 y) y)) (-.f64 x y)) |
(/.f64 (neg.f64 (neg.f64 (*.f64 y y))) (-.f64 x y)) |
(/.f64 (/.f64 (*.f64 y y) (*.f64 (+.f64 y x) (-.f64 x y))) (pow.f64 (+.f64 y x) #s(literal -1 binary64))) |
(/.f64 (*.f64 #s(literal 1 binary64) y) (/.f64 (-.f64 x y) y)) |
(/.f64 (*.f64 y (neg.f64 y)) (-.f64 y x)) |
(/.f64 (*.f64 y #s(literal 1 binary64)) (/.f64 (-.f64 x y) y)) |
(/.f64 (*.f64 (neg.f64 y) y) (-.f64 y x)) |
(/.f64 (neg.f64 (*.f64 y y)) (-.f64 y x)) |
(/.f64 (neg.f64 y) (neg.f64 (/.f64 (-.f64 x y) y))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 x y) y) (*.f64 #s(literal 1 binary64) y))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y x) (*.f64 y (neg.f64 y)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 x y) y) (*.f64 y #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y x) (*.f64 (neg.f64 y) y))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 x y) (*.f64 y y)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 x y) y) y)) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (*.f64 y y))) |
(/.f64 (*.f64 y y) (-.f64 x y)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x y) (*.f64 y y)))) |
(/.f64 y (/.f64 (-.f64 x y) y)) |
(*.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 (neg.f64 y) y))))) |
(*.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 (neg.f64 y) y)) #s(literal -1 binary64)))) |
(*.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 (neg.f64 y) y)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))) |
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (pow.f64 (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))) |
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (pow.f64 (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 (-.f64 y x))) |
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (+.f64 y x))) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))) |
(pow.f64 (exp.f64 (log.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) |
(pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) |
(pow.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal 1 binary64)) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 (neg.f64 y) y))))) |
(/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 y x))) (sqrt.f64 (-.f64 x y))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 y x))) (sqrt.f64 (fma.f64 y (-.f64 y x) (*.f64 x x)))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 y x))) (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (+.f64 y x))) (sqrt.f64 (-.f64 (neg.f64 x) y))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 y x))) (sqrt.f64 (fma.f64 y y (*.f64 x (+.f64 y x))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 y x))) (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (fma.f64 (neg.f64 x) x (*.f64 y y)))) (sqrt.f64 (+.f64 y x))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (*.f64 (+.f64 y x) (-.f64 x y)))) (sqrt.f64 (-.f64 (neg.f64 x) y))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 y y (*.f64 x (+.f64 y x))))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 y x) (*.f64 (+.f64 y x) (-.f64 x y)))) (sqrt.f64 (-.f64 x y))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 y x) (fma.f64 (neg.f64 x) x (*.f64 y y)))) (sqrt.f64 (-.f64 y x))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 y x) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 y (-.f64 y x) (*.f64 x x)))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 y x) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y))))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (hypot.f64 y x)) |
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (neg.f64 x) x (*.f64 (neg.f64 y) y))))) |
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (fma.f64 (neg.f64 x) x (*.f64 y y)))) (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x)))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (fma.f64 (neg.f64 x) x (*.f64 y y)))) (sqrt.f64 (*.f64 (-.f64 (neg.f64 x) y) (-.f64 y x)))) |
(/.f64 (sqrt.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (-.f64 x y) (-.f64 (neg.f64 x) y)))) |
(/.f64 (sqrt.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (-.f64 (neg.f64 x) y) (-.f64 x y)))) |
(/.f64 (sqrt.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (-.f64 x y) (fma.f64 y y (*.f64 x (+.f64 y x)))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (-.f64 x y) (fma.f64 y (+.f64 y x) (*.f64 x x))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (-.f64 (neg.f64 x) y) (fma.f64 y (-.f64 y x) (*.f64 x x))))) |
(/.f64 (sqrt.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (-.f64 (neg.f64 x) y) (fma.f64 y y (*.f64 x (-.f64 x y)))))) |
(/.f64 (sqrt.f64 (*.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))))) (sqrt.f64 (*.f64 (-.f64 y x) (fma.f64 y y (*.f64 x (+.f64 y x)))))) |
(/.f64 (sqrt.f64 (*.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))))) (sqrt.f64 (*.f64 (-.f64 y x) (fma.f64 y (+.f64 y x) (*.f64 x x))))) |
(/.f64 (sqrt.f64 (*.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))))) (sqrt.f64 (*.f64 (+.f64 y x) (fma.f64 y (-.f64 y x) (*.f64 x x))))) |
(/.f64 (sqrt.f64 (*.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))))) (sqrt.f64 (*.f64 (+.f64 y x) (fma.f64 y y (*.f64 x (-.f64 x y)))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 (+.f64 y x) (-.f64 x y)))) (sqrt.f64 (*.f64 (fma.f64 y y (*.f64 x (-.f64 x y))) (-.f64 (neg.f64 x) y)))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 (+.f64 y x) (-.f64 x y)))) (sqrt.f64 (*.f64 (fma.f64 y y (*.f64 x (+.f64 y x))) (-.f64 x y)))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 (+.f64 y x) (-.f64 x y)))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (fma.f64 y (-.f64 y x) (*.f64 x x)) (fma.f64 y y (*.f64 x (+.f64 y x)))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (fma.f64 y (-.f64 y x) (*.f64 x x)) (fma.f64 y (+.f64 y x) (*.f64 x x))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (fma.f64 y y (*.f64 x (-.f64 x y))) (fma.f64 y y (*.f64 x (+.f64 y x)))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (fma.f64 y y (*.f64 x (-.f64 x y))) (fma.f64 y (+.f64 y x) (*.f64 x x))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (fma.f64 y y (*.f64 x (+.f64 y x))) (fma.f64 y (-.f64 y x) (*.f64 x x))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (fma.f64 y y (*.f64 x (+.f64 y x))) (fma.f64 y y (*.f64 x (-.f64 x y)))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) (fma.f64 y (-.f64 y x) (*.f64 x x))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) (fma.f64 y y (*.f64 x (-.f64 x y)))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (*.f64 (+.f64 y x) (-.f64 x y)))) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y)))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (neg.f64 x) x (*.f64 y y)))) (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) |
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 (neg.f64 y) y)))) |
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64)))))) |
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64))))))) |
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))) |
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))) #s(literal -1 binary64)) |
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal 1 binary64)) |
(/.f64 (sqrt.f64 (-.f64 y x)) (pow.f64 (+.f64 y x) #s(literal -1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 (neg.f64 y) y))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal -1/2 binary64))) |
(sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) |
(exp.f64 (fma.f64 (log.f64 (pow.f64 (+.f64 y x) #s(literal -1/2 binary64))) #s(literal -1 binary64) (*.f64 (log.f64 (-.f64 y x)) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (+.f64 y x)) #s(literal 1/2 binary64) (*.f64 (log.f64 (-.f64 y x)) #s(literal 1/2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (-.f64 y x)) #s(literal 1/2 binary64) (*.f64 (log.f64 (pow.f64 (+.f64 y x) #s(literal -1/2 binary64))) #s(literal -1 binary64)))) |
(exp.f64 (fma.f64 (log.f64 (-.f64 y x)) #s(literal 1/2 binary64) (*.f64 (log.f64 (+.f64 y x)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal -1/2 binary64))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal 1/2 binary64))) |
Compiled 34 576 to 5 018 computations (85.5% saved)
5 alts after pruning (3 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 257 | 3 | 1 260 |
| Fresh | 0 | 0 | 0 |
| Picked | 3 | 1 | 4 |
| Done | 0 | 1 | 1 |
| Total | 1 260 | 5 | 1 265 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | (sqrt.f64 (fma.f64 (/.f64 y (-.f64 y x)) y (*.f64 (/.f64 x (-.f64 x y)) x))) |
| ✓ | 100.0% | (sqrt.f64 (+.f64 x y)) |
| ▶ | 73.4% | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) |
| ▶ | 100.0% | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y))) |
| ✓ | 98.1% | #s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
Compiled 72 to 47 computations (34.7% saved)
| 1× | egg-herbie |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (-.f64 y x) | |
| cost-diff | 0 | (/.f64 y (-.f64 y x)) | |
| cost-diff | 0 | (sqrt.f64 (fma.f64 (/.f64 y (-.f64 y x)) y (*.f64 (/.f64 x (-.f64 x y)) x))) | |
| cost-diff | 11 | (fma.f64 (/.f64 y (-.f64 y x)) y (*.f64 (/.f64 x (-.f64 x 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 | 3 | (fma.f64 (/.f64 y x) x x) | |
| cost-diff | 0 | (/.f64 x y) | |
| cost-diff | 0 | #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y))) | |
| cost-diff | 3 | (fma.f64 (/.f64 x y) y y) |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 166 |
| 0 | 41 | 146 |
| 1 | 70 | 142 |
| 2 | 89 | 135 |
| 3 | 121 | 121 |
| 4 | 181 | 78 |
| 5 | 812 | 78 |
| 6 | 4806 | 78 |
| 0 | 8436 | 78 |
| 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 x y) y y))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y)) |
(fma.f64 (/.f64 x y) y y) |
(/.f64 x y) |
x |
y |
(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 |
(sqrt.f64 (fma.f64 (/.f64 y (-.f64 y x)) y (*.f64 (/.f64 x (-.f64 x y)) x))) |
(fma.f64 (/.f64 y (-.f64 y x)) y (*.f64 (/.f64 x (-.f64 x y)) x)) |
(/.f64 y (-.f64 y x)) |
y |
(-.f64 y x) |
x |
(*.f64 (/.f64 x (-.f64 x y)) x) |
(/.f64 x (-.f64 x y)) |
(-.f64 x y) |
| Outputs |
|---|
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y))) |
(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 x y) y y)) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+.f64 y x)) |
(fma.f64 (/.f64 x y) y y) |
(+.f64 y x) |
(/.f64 x y) |
x |
y |
(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 |
(sqrt.f64 (fma.f64 (/.f64 y (-.f64 y x)) y (*.f64 (/.f64 x (-.f64 x y)) x))) |
(sqrt.f64 (+.f64 y x)) |
(fma.f64 (/.f64 y (-.f64 y x)) y (*.f64 (/.f64 x (-.f64 x y)) x)) |
(+.f64 y x) |
(/.f64 y (-.f64 y x)) |
y |
(-.f64 y x) |
x |
(*.f64 (/.f64 x (-.f64 x y)) x) |
(/.f64 x (-.f64 x y)) |
(-.f64 x y) |
Found 12 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0078125 | (fma.f64 (/.f64 y (-.f64 y x)) y (*.f64 (/.f64 x (-.f64 x y)) x)) | |
| accuracy | 0.0078125 | (/.f64 y (-.f64 y x)) | |
| accuracy | 0.0078125 | (/.f64 x (-.f64 x y)) | |
| accuracy | 0.17578125 | (*.f64 (/.f64 x (-.f64 x y)) x) | |
| accuracy | 0.0 | (/.f64 y x) | |
| accuracy | 0.0 | #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x)) | |
| accuracy | 0.00390625 | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) | |
| accuracy | 16.569870356304065 | (fma.f64 (/.f64 y x) x x) | |
| accuracy | 0.0 | (fma.f64 (/.f64 x y) y y) | |
| accuracy | 0.0 | (/.f64 x y) | |
| accuracy | 0.0 | #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y)) | |
| accuracy | 0.00390625 | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y))) |
| 77.0ms | 254× | 0 | valid |
| 2.0ms | 2× | 5 | exit |
Compiled 144 to 27 computations (81.3% saved)
ival-mult: 19.0ms (41.5% of total)ival-div: 14.0ms (30.6% of total)ival-add: 5.0ms (10.9% of total)ival-sqrt: 3.0ms (6.6% of total)ival-sub: 2.0ms (4.4% of total)adjust: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(fma.f64 (/.f64 x y) y y) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y)) |
(/.f64 x 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) |
(fma.f64 (/.f64 y (-.f64 y x)) y (*.f64 (/.f64 x (-.f64 x y)) x)) |
(sqrt.f64 (fma.f64 (/.f64 y (-.f64 y x)) y (*.f64 (/.f64 x (-.f64 x y)) x))) |
(/.f64 y (-.f64 y x)) |
(-.f64 y x) |
(*.f64 (/.f64 x (-.f64 x y)) x) |
(/.f64 x (-.f64 x 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)))))))))) |
(/ x y) |
(/ y x) |
1 |
(+ 1 (/ x y)) |
(+ 1 (* x (+ (/ 1 y) (/ x (pow y 2))))) |
(+ 1 (* x (+ (* x (+ (/ 1 (pow y 2)) (/ x (pow y 3)))) (/ 1 y)))) |
(+ y (* -1 x)) |
(* -1 (/ (pow x 2) y)) |
(* (pow x 2) (- (* -1 (/ x (pow y 2))) (/ 1 y))) |
(* (pow x 2) (- (* x (- (* -1 (/ x (pow y 3))) (/ 1 (pow y 2)))) (/ 1 y))) |
(* (pow x 2) (- (* x (- (* x (- (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))) |
(* -1 (/ x y)) |
(* x (- (* -1 (/ x (pow y 2))) (/ 1 y))) |
(* x (- (* x (- (* -1 (/ x (pow y 3))) (/ 1 (pow y 2)))) (/ 1 y))) |
(* x (- (* x (- (* x (- (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 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)))))) |
(* x (- (+ 1 (* -1 (/ (+ (* -1 (pow y 3)) (pow y 3)) (pow x 3)))) (* -1 (/ y x)))) |
(* x (- (+ 1 (* -1 (/ (+ (* -1 (pow y 4)) (pow y 4)) (pow x 4)))) (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 3) (pow x 3))) (/ (pow y 3) (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* -1 (pow y 3)) (+ (* 1/4 (* x (pow y 2))) (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* -1 (pow y 3)) (+ (* 1/4 (* x (pow y 2))) (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 9))) (+ (* -1 (pow y 4)) (pow y 4)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(* -1 (/ y x)) |
(/ (+ (* -1 y) (* -1 (/ (pow y 2) x))) x) |
(/ (- (+ (* -1 y) (* -1 (/ (pow y 3) (pow x 2)))) (/ (pow y 2) x)) x) |
(/ (- (+ (* -1 y) (* -1 (/ (pow y 4) (pow x 3)))) (+ (/ (pow y 2) x) (/ (pow y 3) (pow x 2)))) x) |
(* -1 x) |
(* x (- (/ y x) 1)) |
(* x (- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ y x)))) |
(* x (- (+ 1 (/ (pow y 3) (pow x 3))) (+ (* -1 (/ y x)) (* -1 (/ (pow y 2) (pow x 2)))))) |
(+ 1 (/ y x)) |
(- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ y x))) |
(- (+ 1 (/ (pow y 3) (pow x 3))) (+ (* -1 (/ y x)) (* -1 (/ (pow y 2) (pow x 2))))) |
(* -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))))))) |
(* -1 (* x (- (* -1 (/ (+ y (* -1 (/ (+ (* -1 (pow y 2)) (pow y 2)) x))) x)) 1))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (pow y 2)) (pow y 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (* (sqrt x) (/ (pow y 2) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt x) (+ (* -1 (pow y 2)) (pow y 2))))) (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (/ (+ y (/ (pow y 2) x)) x)) |
(* -1 (/ (+ y (* -1 (/ (- (* -1 (/ (pow y 3) x)) (pow y 2)) x))) x)) |
(* -1 (/ (+ y (* -1 (/ (- (* -1 (/ (- (/ (pow y 4) x) (* -1 (pow y 3))) x)) (pow y 2)) x))) x)) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (- (* -1 (/ (- (/ (pow y 2) x) (* -1 y)) x)) 1))) |
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 3) x)) (pow y 2)) x)) (* -1 y)) x)) 1))) |
(+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) y) x))) |
(+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x)) 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))))))) |
(* y (- (* -1 (/ y (pow x 2))) (/ 1 x))) |
(* y (- (* y (- (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))) |
(* y (- (* y (- (* y (- (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))) |
(- y x) |
(+ x (* y (+ 1 (/ y x)))) |
(+ x (* y (+ 1 (* y (+ (/ 1 x) (/ y (pow x 2))))))) |
(+ 1 (* y (+ (/ 1 x) (/ y (pow x 2))))) |
(+ 1 (* y (+ (* y (+ (/ 1 (pow x 2)) (/ y (pow x 3)))) (/ 1 x)))) |
(* 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))))))))) |
(* y (- (+ 1 (* -1 (/ (+ (* -1 (pow x 3)) (pow x 3)) (pow y 3)))) (* -1 (/ x y)))) |
(* y (- (+ 1 (* -1 (/ (+ (* -1 (pow x 4)) (pow x 4)) (pow y 4)))) (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 3) (pow y 3))) (/ (pow x 3) (pow y 3)))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* -1 (pow x 3)) (+ (* 1/4 (* (pow x 2) y)) (pow x 3))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* -1 (pow x 3)) (+ (* 1/4 (* (pow x 2) y)) (pow x 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 9))) (+ (* -1 (pow x 4)) (pow x 4)))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(- (+ 1 (/ (pow x 2) (pow y 2))) (* -1 (/ x y))) |
(- (+ 1 (/ (pow x 3) (pow y 3))) (+ (* -1 (/ x y)) (* -1 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (* -1 (/ x y)))) |
(/ (+ (* -1 (/ (pow x 3) y)) (* -1 (pow x 2))) y) |
(/ (- (+ (* -1 (/ (pow x 4) (pow y 2))) (* -1 (pow x 2))) (/ (pow x 3) y)) y) |
(/ (- (+ (* -1 (/ (pow x 5) (pow y 3))) (* -1 (pow x 2))) (+ (/ (pow x 3) y) (/ (pow x 4) (pow y 2)))) y) |
(/ (+ (* -1 x) (* -1 (/ (pow x 2) y))) y) |
(/ (- (+ (* -1 x) (* -1 (/ (pow x 3) (pow y 2)))) (/ (pow x 2) y)) y) |
(/ (- (+ (* -1 x) (* -1 (/ (pow x 4) (pow y 3)))) (+ (/ (pow x 2) y) (/ (pow x 3) (pow y 2)))) y) |
(* -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))))))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) y))) y)) 1))) |
(* -1 (* y (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 2)) (pow x 2)))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1 (/ (+ (* 1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt y))) (* 1/2 (* (sqrt y) (+ (* -1 (pow x 2)) (pow x 2))))) (pow y 3))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) y)) x) y))) |
(+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (* -1 (pow x 2))) y)) x) y))) |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (/ (+ (/ (pow x 3) y) (pow x 2)) y)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow x 4) y)) (pow x 3)) y)) (pow x 2)) y)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ (pow x 5) y) (* -1 (pow x 4))) y)) (pow x 3)) y)) (pow x 2)) y)) |
(* -1 (/ (+ x (/ (pow x 2) y)) y)) |
(* -1 (/ (+ x (* -1 (/ (- (* -1 (/ (pow x 3) y)) (pow x 2)) y))) y)) |
(* -1 (/ (+ x (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (* -1 (pow x 3))) y)) (pow x 2)) y))) y)) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | x | @ | inf | ((+ (* (/ x y) y) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ x y) (+ (* (/ y x) x) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ y x) (+ (* (/ y (- y x)) y) (* (/ x (- x y)) x)) (sqrt (+ (* (/ y (- y x)) y) (* (/ x (- x y)) x))) (/ y (- y x)) (- y x) (* (/ x (- x y)) x) (/ x (- x y))) |
| 2.0ms | y | @ | inf | ((+ (* (/ x y) y) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ x y) (+ (* (/ y x) x) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ y x) (+ (* (/ y (- y x)) y) (* (/ x (- x y)) x)) (sqrt (+ (* (/ y (- y x)) y) (* (/ x (- x y)) x))) (/ y (- y x)) (- y x) (* (/ x (- x y)) x) (/ x (- x y))) |
| 2.0ms | x | @ | -inf | ((+ (* (/ x y) y) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ x y) (+ (* (/ y x) x) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ y x) (+ (* (/ y (- y x)) y) (* (/ x (- x y)) x)) (sqrt (+ (* (/ y (- y x)) y) (* (/ x (- x y)) x))) (/ y (- y x)) (- y x) (* (/ x (- x y)) x) (/ x (- x y))) |
| 2.0ms | x | @ | 0 | ((+ (* (/ x y) y) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ x y) (+ (* (/ y x) x) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ y x) (+ (* (/ y (- y x)) y) (* (/ x (- x y)) x)) (sqrt (+ (* (/ y (- y x)) y) (* (/ x (- x y)) x))) (/ y (- y x)) (- y x) (* (/ x (- x y)) x) (/ x (- x y))) |
| 2.0ms | y | @ | -inf | ((+ (* (/ x y) y) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ x y) (+ (* (/ y x) x) x) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (/ y x) (+ (* (/ y (- y x)) y) (* (/ x (- x y)) x)) (sqrt (+ (* (/ y (- y x)) y) (* (/ x (- x y)) x))) (/ y (- y x)) (- y x) (* (/ x (- x y)) x) (/ x (- x y))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 514 | 1919 |
| 1 | 1620 | 1747 |
| 2 | 5360 | 1643 |
| 0 | 8609 | 1534 |
| 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)))))))))) |
(/ x y) |
(/ y x) |
1 |
(+ 1 (/ x y)) |
(+ 1 (* x (+ (/ 1 y) (/ x (pow y 2))))) |
(+ 1 (* x (+ (* x (+ (/ 1 (pow y 2)) (/ x (pow y 3)))) (/ 1 y)))) |
(+ y (* -1 x)) |
(* -1 (/ (pow x 2) y)) |
(* (pow x 2) (- (* -1 (/ x (pow y 2))) (/ 1 y))) |
(* (pow x 2) (- (* x (- (* -1 (/ x (pow y 3))) (/ 1 (pow y 2)))) (/ 1 y))) |
(* (pow x 2) (- (* x (- (* x (- (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))) |
(* -1 (/ x y)) |
(* x (- (* -1 (/ x (pow y 2))) (/ 1 y))) |
(* x (- (* x (- (* -1 (/ x (pow y 3))) (/ 1 (pow y 2)))) (/ 1 y))) |
(* x (- (* x (- (* x (- (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 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)))))) |
(* x (- (+ 1 (* -1 (/ (+ (* -1 (pow y 3)) (pow y 3)) (pow x 3)))) (* -1 (/ y x)))) |
(* x (- (+ 1 (* -1 (/ (+ (* -1 (pow y 4)) (pow y 4)) (pow x 4)))) (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 3) (pow x 3))) (/ (pow y 3) (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* -1 (pow y 3)) (+ (* 1/4 (* x (pow y 2))) (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* -1 (pow y 3)) (+ (* 1/4 (* x (pow y 2))) (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 9))) (+ (* -1 (pow y 4)) (pow y 4)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(* -1 (/ y x)) |
(/ (+ (* -1 y) (* -1 (/ (pow y 2) x))) x) |
(/ (- (+ (* -1 y) (* -1 (/ (pow y 3) (pow x 2)))) (/ (pow y 2) x)) x) |
(/ (- (+ (* -1 y) (* -1 (/ (pow y 4) (pow x 3)))) (+ (/ (pow y 2) x) (/ (pow y 3) (pow x 2)))) x) |
(* -1 x) |
(* x (- (/ y x) 1)) |
(* x (- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ y x)))) |
(* x (- (+ 1 (/ (pow y 3) (pow x 3))) (+ (* -1 (/ y x)) (* -1 (/ (pow y 2) (pow x 2)))))) |
(+ 1 (/ y x)) |
(- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ y x))) |
(- (+ 1 (/ (pow y 3) (pow x 3))) (+ (* -1 (/ y x)) (* -1 (/ (pow y 2) (pow x 2))))) |
(* -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))))))) |
(* -1 (* x (- (* -1 (/ (+ y (* -1 (/ (+ (* -1 (pow y 2)) (pow y 2)) x))) x)) 1))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (pow y 2)) (pow y 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (* (sqrt x) (/ (pow y 2) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt x) (+ (* -1 (pow y 2)) (pow y 2))))) (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (/ (+ y (/ (pow y 2) x)) x)) |
(* -1 (/ (+ y (* -1 (/ (- (* -1 (/ (pow y 3) x)) (pow y 2)) x))) x)) |
(* -1 (/ (+ y (* -1 (/ (- (* -1 (/ (- (/ (pow y 4) x) (* -1 (pow y 3))) x)) (pow y 2)) x))) x)) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(* -1 (* x (- (* -1 (/ (- (/ (pow y 2) x) (* -1 y)) x)) 1))) |
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 3) x)) (pow y 2)) x)) (* -1 y)) x)) 1))) |
(+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) y) x))) |
(+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x)) 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))))))) |
(* y (- (* -1 (/ y (pow x 2))) (/ 1 x))) |
(* y (- (* y (- (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))) |
(* y (- (* y (- (* y (- (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))) |
(- y x) |
(+ x (* y (+ 1 (/ y x)))) |
(+ x (* y (+ 1 (* y (+ (/ 1 x) (/ y (pow x 2))))))) |
(+ 1 (* y (+ (/ 1 x) (/ y (pow x 2))))) |
(+ 1 (* y (+ (* y (+ (/ 1 (pow x 2)) (/ y (pow x 3)))) (/ 1 x)))) |
(* 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))))))))) |
(* y (- (+ 1 (* -1 (/ (+ (* -1 (pow x 3)) (pow x 3)) (pow y 3)))) (* -1 (/ x y)))) |
(* y (- (+ 1 (* -1 (/ (+ (* -1 (pow x 4)) (pow x 4)) (pow y 4)))) (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 3) (pow y 3))) (/ (pow x 3) (pow y 3)))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* -1 (pow x 3)) (+ (* 1/4 (* (pow x 2) y)) (pow x 3))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* -1 (pow x 3)) (+ (* 1/4 (* (pow x 2) y)) (pow x 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 9))) (+ (* -1 (pow x 4)) (pow x 4)))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(- (+ 1 (/ (pow x 2) (pow y 2))) (* -1 (/ x y))) |
(- (+ 1 (/ (pow x 3) (pow y 3))) (+ (* -1 (/ x y)) (* -1 (/ (pow x 2) (pow y 2))))) |
(* y (+ 1 (* -1 (/ x y)))) |
(/ (+ (* -1 (/ (pow x 3) y)) (* -1 (pow x 2))) y) |
(/ (- (+ (* -1 (/ (pow x 4) (pow y 2))) (* -1 (pow x 2))) (/ (pow x 3) y)) y) |
(/ (- (+ (* -1 (/ (pow x 5) (pow y 3))) (* -1 (pow x 2))) (+ (/ (pow x 3) y) (/ (pow x 4) (pow y 2)))) y) |
(/ (+ (* -1 x) (* -1 (/ (pow x 2) y))) y) |
(/ (- (+ (* -1 x) (* -1 (/ (pow x 3) (pow y 2)))) (/ (pow x 2) y)) y) |
(/ (- (+ (* -1 x) (* -1 (/ (pow x 4) (pow y 3)))) (+ (/ (pow x 2) y) (/ (pow x 3) (pow y 2)))) y) |
(* -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))))))) |
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) y))) y)) 1))) |
(* -1 (* y (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 2)) (pow x 2)))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1 (/ (+ (* 1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt y))) (* 1/2 (* (sqrt y) (+ (* -1 (pow x 2)) (pow x 2))))) (pow y 3))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) y)) x) y))) |
(+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (* -1 (pow x 2))) y)) x) y))) |
(* -1 (* y (- (/ x y) 1))) |
(* -1 (/ (+ (/ (pow x 3) y) (pow x 2)) y)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow x 4) y)) (pow x 3)) y)) (pow x 2)) y)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ (pow x 5) y) (* -1 (pow x 4))) y)) (pow x 3)) y)) (pow x 2)) y)) |
(* -1 (/ (+ x (/ (pow x 2) y)) y)) |
(* -1 (/ (+ x (* -1 (/ (- (* -1 (/ (pow x 3) y)) (pow x 2)) y))) y)) |
(* -1 (/ (+ x (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (* -1 (pow x 3))) y)) (pow x 2)) y))) y)) |
| Outputs |
|---|
y |
(+ x y) |
(+.f64 y x) |
(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)) |
(/ x y) |
(/.f64 x y) |
(/ y x) |
(/.f64 y x) |
1 |
#s(literal 1 binary64) |
(+ 1 (/ x y)) |
(+.f64 (/.f64 x y) #s(literal 1 binary64)) |
(+ 1 (* x (+ (/ 1 y) (/ x (pow y 2))))) |
(fma.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) (/.f64 x y) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* x (+ (/ 1 (pow y 2)) (/ x (pow y 3)))) (/ 1 y)))) |
(fma.f64 (/.f64 (/.f64 x y) y) (fma.f64 x (/.f64 x y) x) (+.f64 (/.f64 x y) #s(literal 1 binary64))) |
(+ y (* -1 x)) |
(-.f64 y x) |
(* -1 (/ (pow x 2) y)) |
(*.f64 (neg.f64 x) (/.f64 x y)) |
(* (pow x 2) (- (* -1 (/ x (pow y 2))) (/ 1 y))) |
(/.f64 (*.f64 x (*.f64 x (-.f64 #s(literal -1 binary64) (/.f64 x y)))) y) |
(* (pow x 2) (- (* x (- (* -1 (/ x (pow y 3))) (/ 1 (pow y 2)))) (/ 1 y))) |
(*.f64 (fma.f64 (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 y y))) x (/.f64 #s(literal -1 binary64) y)) (*.f64 x x)) |
(* (pow x 2) (- (* x (- (* x (- (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))) |
(*.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 3 binary64))) (/.f64 x (pow.f64 y #s(literal 4 binary64)))) x (/.f64 #s(literal -1 binary64) (*.f64 y y))) x (/.f64 #s(literal -1 binary64) y)) (*.f64 x x)) |
(* -1 (/ x y)) |
(/.f64 (neg.f64 x) y) |
(* x (- (* -1 (/ x (pow y 2))) (/ 1 y))) |
(*.f64 (/.f64 x y) (-.f64 #s(literal -1 binary64) (/.f64 x y))) |
(* x (- (* x (- (* -1 (/ x (pow y 3))) (/ 1 (pow y 2)))) (/ 1 y))) |
(*.f64 (fma.f64 (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 y y))) x (/.f64 #s(literal -1 binary64) y)) x) |
(* x (- (* x (- (* x (- (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))) |
(*.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 3 binary64))) (/.f64 x (pow.f64 y #s(literal 4 binary64)))) x (/.f64 #s(literal -1 binary64) (*.f64 y y))) x (/.f64 #s(literal -1 binary64) y)) x) |
x |
(* x (+ 1 (/ y x))) |
(fma.f64 (/.f64 y x) x 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 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #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 y y) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64)) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 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 (- (+ 1 (* -1 (/ (+ (* -1 (pow y 3)) (pow y 3)) (pow x 3)))) (* -1 (/ y x)))) |
(fma.f64 (/.f64 y x) x x) |
(* x (- (+ 1 (* -1 (/ (+ (* -1 (pow y 4)) (pow y 4)) (pow x 4)))) (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 3) (pow x 3))) (/ (pow y 3) (pow x 3)))))) |
(fma.f64 (/.f64 y x) x x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* -1 (pow y 3)) (+ (* 1/4 (* x (pow y 2))) (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 y y) x) #s(literal 1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 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)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* -1 (pow y 3)) (+ (* 1/4 (* x (pow y 2))) (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 9))) (+ (* -1 (pow y 4)) (pow y 4)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (*.f64 (*.f64 (*.f64 y y) x) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 0 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 (/ y x)) |
(/.f64 y (neg.f64 x)) |
(/ (+ (* -1 y) (* -1 (/ (pow y 2) x))) x) |
(*.f64 (/.f64 y x) (-.f64 #s(literal -1 binary64) (/.f64 y x))) |
(/ (- (+ (* -1 y) (* -1 (/ (pow y 3) (pow x 2)))) (/ (pow y 2) x)) x) |
(/.f64 (*.f64 y (fma.f64 (/.f64 y x) (-.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal -1 binary64))) x) |
(/ (- (+ (* -1 y) (* -1 (/ (pow y 4) (pow x 3)))) (+ (/ (pow y 2) x) (/ (pow y 3) (pow x 2)))) x) |
(/.f64 (-.f64 (/.f64 (neg.f64 (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (/.f64 y x) (fma.f64 (/.f64 y x) y y) y)) x) |
(* -1 x) |
(neg.f64 x) |
(* x (- (/ y x) 1)) |
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) x) |
(* x (- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ y x)))) |
(fma.f64 (/.f64 (fma.f64 (/.f64 y x) y y) x) x x) |
(* x (- (+ 1 (/ (pow y 3) (pow x 3))) (+ (* -1 (/ y x)) (* -1 (/ (pow y 2) (pow x 2)))))) |
(*.f64 (+.f64 (/.f64 (fma.f64 (/.f64 y x) (fma.f64 (/.f64 y x) y y) y) x) #s(literal 1 binary64)) x) |
(+ 1 (/ y x)) |
(+.f64 (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ y x))) |
(fma.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(- (+ 1 (/ (pow y 3) (pow x 3))) (+ (* -1 (/ y x)) (* -1 (/ (pow y 2) (pow x 2))))) |
(+.f64 (/.f64 (fma.f64 (/.f64 y x) (fma.f64 (/.f64 y x) y y) y) x) #s(literal 1 binary64)) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(fma.f64 (/.f64 y x) x 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 (/ (+ y (* -1 (/ (+ (* -1 (pow y 2)) (pow y 2)) x))) x)) 1))) |
(fma.f64 (/.f64 y x) x x) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (pow y 2)) (pow y 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)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x)) |
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (* (sqrt x) (/ (pow y 2) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt x) (+ (* -1 (pow y 2)) (pow y 2))))) (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (-.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)))) (/.f64 (*.f64 (sqrt.f64 x) (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 y y) #s(literal -1 binary64)) #s(literal 0 binary64))) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 x)) |
(* -1 (/ (+ y (/ (pow y 2) x)) x)) |
(*.f64 (/.f64 y x) (-.f64 #s(literal -1 binary64) (/.f64 y x))) |
(* -1 (/ (+ y (* -1 (/ (- (* -1 (/ (pow y 3) x)) (pow y 2)) x))) x)) |
(/.f64 (*.f64 y (fma.f64 (/.f64 y x) (-.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal -1 binary64))) x) |
(* -1 (/ (+ y (* -1 (/ (- (* -1 (/ (- (/ (pow y 4) x) (* -1 (pow y 3))) x)) (pow y 2)) x))) x)) |
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (pow.f64 y #s(literal 3 binary64))) x) (*.f64 y y)) x) y) (neg.f64 x)) |
(* -1 (* x (+ 1 (* -1 (/ y x))))) |
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) x) |
(* -1 (* x (- (* -1 (/ (- (/ (pow y 2) x) (* -1 y)) x)) 1))) |
(fma.f64 (/.f64 (fma.f64 (/.f64 y x) y y) x) x x) |
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 3) x)) (pow y 2)) x)) (* -1 y)) x)) 1))) |
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (/.f64 y x) (fma.f64 (/.f64 y x) y y) y) x)) (neg.f64 x)) |
(+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) y) x))) |
(fma.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x)) y) x))) |
(+.f64 (/.f64 (fma.f64 (/.f64 y x) (fma.f64 (/.f64 y x) y y) y) x) #s(literal 1 binary64)) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (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 (- (* -1 (/ y (pow x 2))) (/ 1 x))) |
(*.f64 (/.f64 y x) (-.f64 #s(literal -1 binary64) (/.f64 y x))) |
(* y (- (* y (- (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))) |
(*.f64 (fma.f64 (*.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 x x))) y (/.f64 #s(literal -1 binary64) x)) y) |
(* y (- (* y (- (* y (- (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))) |
(*.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 y (pow.f64 x #s(literal 4 binary64)))) y (/.f64 #s(literal -1 binary64) (*.f64 x x))) y (/.f64 #s(literal -1 binary64) x)) y) |
(- y x) |
(-.f64 y x) |
(+ x (* y (+ 1 (/ y x)))) |
(fma.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) y x) |
(+ x (* y (+ 1 (* y (+ (/ 1 x) (/ y (pow x 2))))))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) (/.f64 y x) #s(literal 1 binary64)) y x) |
(+ 1 (* y (+ (/ 1 x) (/ y (pow x 2))))) |
(fma.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) (/.f64 y x) #s(literal 1 binary64)) |
(+ 1 (* y (+ (* y (+ (/ 1 (pow x 2)) (/ y (pow x 3)))) (/ 1 x)))) |
(fma.f64 (/.f64 (/.f64 y x) x) (fma.f64 (/.f64 y x) y y) (+.f64 (/.f64 y x) #s(literal 1 binary64))) |
(* y (+ 1 (/ x y))) |
(fma.f64 (/.f64 x y) 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)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) 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)))) (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 #s(literal -1/8 binary64) x) x) (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 (* -1 (/ (+ (* -1 (pow x 3)) (pow x 3)) (pow y 3)))) (* -1 (/ x y)))) |
(fma.f64 (/.f64 x y) y y) |
(* y (- (+ 1 (* -1 (/ (+ (* -1 (pow x 4)) (pow x 4)) (pow y 4)))) (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 3) (pow y 3))) (/ (pow x 3) (pow y 3)))))) |
(fma.f64 (/.f64 x y) y y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* -1 (pow x 3)) (+ (* 1/4 (* (pow x 2) y)) (pow x 3))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 x x) y) #s(literal 1/4 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)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* -1 (pow x 3)) (+ (* 1/4 (* (pow x 2) y)) (pow x 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 9))) (+ (* -1 (pow x 4)) (pow x 4)))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (*.f64 (*.f64 (*.f64 x x) y) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) #s(literal 0 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 (/ (pow x 2) (pow y 2))) (* -1 (/ x y))) |
(fma.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) (/.f64 x y) #s(literal 1 binary64)) |
(- (+ 1 (/ (pow x 3) (pow y 3))) (+ (* -1 (/ x y)) (* -1 (/ (pow x 2) (pow y 2))))) |
(fma.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) (/.f64 x y) (+.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1 binary64))) |
(* y (+ 1 (* -1 (/ x y)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
(/ (+ (* -1 (/ (pow x 3) y)) (* -1 (pow x 2))) y) |
(/.f64 (*.f64 x (*.f64 x (-.f64 #s(literal -1 binary64) (/.f64 x y)))) y) |
(/ (- (+ (* -1 (/ (pow x 4) (pow y 2))) (* -1 (pow x 2))) (/ (pow x 3) y)) y) |
(/.f64 (neg.f64 (fma.f64 x x (/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (pow.f64 x #s(literal 3 binary64))) y))) y) |
(/ (- (+ (* -1 (/ (pow x 5) (pow y 3))) (* -1 (pow x 2))) (+ (/ (pow x 3) y) (/ (pow x 4) (pow y 2)))) y) |
(/.f64 (-.f64 (neg.f64 (fma.f64 x x (/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (pow.f64 x #s(literal 3 binary64))) y))) (/.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 y #s(literal 3 binary64)))) y) |
(/ (+ (* -1 x) (* -1 (/ (pow x 2) y))) y) |
(*.f64 (/.f64 x y) (-.f64 #s(literal -1 binary64) (/.f64 x y))) |
(/ (- (+ (* -1 x) (* -1 (/ (pow x 3) (pow y 2)))) (/ (pow x 2) y)) y) |
(/.f64 (fma.f64 (/.f64 x y) (fma.f64 x (/.f64 x y) x) x) (neg.f64 y)) |
(/ (- (+ (* -1 x) (* -1 (/ (pow x 4) (pow y 3)))) (+ (/ (pow x 2) y) (/ (pow x 3) (pow y 2)))) y) |
(/.f64 (+.f64 (/.f64 (fma.f64 x x (/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (pow.f64 x #s(literal 3 binary64))) y)) y) x) (neg.f64 y)) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(fma.f64 (/.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)))) (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))))) (+ (* 1/2 (* 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 (/ (+ x (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) y))) y)) 1))) |
(fma.f64 (/.f64 x y) y y) |
(* -1 (* y (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 2)) (pow x 2)))) (+ (* 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)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (neg.f64 y)) |
(* -1 (* y (+ (* -1 (/ (+ (* 1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt y))) (* 1/2 (* (sqrt y) (+ (* -1 (pow x 2)) (pow x 2))))) (pow y 3))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(*.f64 (-.f64 (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)))) (/.f64 (*.f64 (sqrt.f64 y) (fma.f64 (/.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1/8 binary64) #s(literal 0 binary64))) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 y)) |
(+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) y)) x) y))) |
(fma.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) (/.f64 x y) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (* -1 (pow x 2))) y)) x) y))) |
(+.f64 (/.f64 (fma.f64 (/.f64 x y) (fma.f64 x (/.f64 x y) x) x) y) #s(literal 1 binary64)) |
(* -1 (* y (- (/ x y) 1))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
(* -1 (/ (+ (/ (pow x 3) y) (pow x 2)) y)) |
(/.f64 (*.f64 x (*.f64 x (-.f64 #s(literal -1 binary64) (/.f64 x y)))) y) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow x 4) y)) (pow x 3)) y)) (pow x 2)) y)) |
(/.f64 (neg.f64 (fma.f64 x x (/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (pow.f64 x #s(literal 3 binary64))) y))) y) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ (pow x 5) y) (* -1 (pow x 4))) y)) (pow x 3)) y)) (pow x 2)) y)) |
(/.f64 (fma.f64 x x (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 5 binary64)) y) (pow.f64 x #s(literal 4 binary64))) y) (pow.f64 x #s(literal 3 binary64))) y)) (neg.f64 y)) |
(* -1 (/ (+ x (/ (pow x 2) y)) y)) |
(*.f64 (/.f64 x y) (-.f64 #s(literal -1 binary64) (/.f64 x y))) |
(* -1 (/ (+ x (* -1 (/ (- (* -1 (/ (pow x 3) y)) (pow x 2)) y))) y)) |
(/.f64 (fma.f64 (/.f64 x y) (fma.f64 x (/.f64 x y) x) x) (neg.f64 y)) |
(* -1 (/ (+ x (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (* -1 (pow x 3))) y)) (pow x 2)) y))) y)) |
(/.f64 (+.f64 (/.f64 (fma.f64 x x (/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (pow.f64 x #s(literal 3 binary64))) y)) y) x) (neg.f64 y)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 157 |
| 0 | 41 | 145 |
| 1 | 181 | 109 |
| 2 | 1431 | 103 |
| 0 | 8680 | 97 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (/.f64 x y) y y) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y)) |
(/.f64 x 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) |
(fma.f64 (/.f64 y (-.f64 y x)) y (*.f64 (/.f64 x (-.f64 x y)) x)) |
(sqrt.f64 (fma.f64 (/.f64 y (-.f64 y x)) y (*.f64 (/.f64 x (-.f64 x y)) x))) |
(/.f64 y (-.f64 y x)) |
(-.f64 y x) |
(*.f64 (/.f64 x (-.f64 x y)) x) |
(/.f64 x (-.f64 x y)) |
| Outputs |
|---|
(*.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 y (-.f64 y (*.f64 x #s(literal 1 binary64))) (*.f64 x x))))) |
(*.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x #s(literal 1 binary64) (neg.f64 y))))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
(*.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (pow.f64 (fma.f64 x #s(literal 1 binary64) (neg.f64 y)) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1 binary64) y)) |
(*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y y (-.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 1 binary64)) y))))) |
(*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 y (-.f64 y (*.f64 x #s(literal 1 binary64))) (*.f64 x x)) #s(literal -1 binary64))) |
(*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (-.f64 y (*.f64 x #s(literal 1 binary64))))) |
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1 binary64) y)) #s(literal -1 binary64)) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (fma.f64 x #s(literal 1 binary64) (neg.f64 y))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 y y) (fma.f64 x #s(literal 1 binary64) (neg.f64 y))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x x) (fma.f64 x #s(literal 1 binary64) (neg.f64 y))) (/.f64 (*.f64 x x) (fma.f64 x #s(literal 1 binary64) (neg.f64 y))) (fma.f64 (/.f64 (*.f64 y y) (fma.f64 x #s(literal 1 binary64) (neg.f64 y))) (/.f64 (*.f64 y y) (fma.f64 x #s(literal 1 binary64) (neg.f64 y))) (*.f64 (/.f64 (*.f64 x x) (fma.f64 x #s(literal 1 binary64) (neg.f64 y))) (/.f64 (*.f64 y y) (fma.f64 x #s(literal 1 binary64) (neg.f64 y))))))) |
(/.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 (*.f64 x #s(literal 1 binary64))) (*.f64 x x))))) |
(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 x y)))) (neg.f64 (neg.f64 (fma.f64 x #s(literal 1 binary64) (neg.f64 y))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (fma.f64 x #s(literal 1 binary64) (neg.f64 y))) (*.f64 (fma.f64 x #s(literal 1 binary64) (neg.f64 y)) (*.f64 y y))) (*.f64 (fma.f64 x #s(literal 1 binary64) (neg.f64 y)) (fma.f64 x #s(literal 1 binary64) (neg.f64 y)))) |
(/.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 (*.f64 x x) (*.f64 (*.f64 x #s(literal 1 binary64)) y))))) |
(/.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 (*.f64 x #s(literal 1 binary64))) (*.f64 x x)))) |
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (neg.f64 (fma.f64 x #s(literal 1 binary64) (neg.f64 y)))) |
(/.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (neg.f64 (-.f64 y (*.f64 x #s(literal 1 binary64))))) |
(/.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (fma.f64 x #s(literal 1 binary64) (neg.f64 y))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y (*.f64 x #s(literal 1 binary64))) (*.f64 (+.f64 y x) (-.f64 y x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1 binary64) y)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y (-.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 1 binary64)) y))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1 binary64) y))) |
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 y y (-.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 1 binary64)) y)))) |
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 y (-.f64 y (*.f64 x #s(literal 1 binary64))) (*.f64 x x))) |
(/.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (-.f64 y (*.f64 x #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1 binary64) y)))) |
(fma.f64 (/.f64 y (pow.f64 (neg.f64 x) #s(literal -1 binary64))) (pow.f64 (neg.f64 y) #s(literal -1 binary64)) y) |
(fma.f64 (/.f64 y (pow.f64 x #s(literal -1 binary64))) (pow.f64 y #s(literal -1 binary64)) y) |
(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 x) #s(literal -1 binary64))) (/.f64 y (neg.f64 y)) y) |
(fma.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (neg.f64 y) y) y) |
(fma.f64 (/.f64 y #s(literal -1 binary64)) (/.f64 (neg.f64 x) y) y) |
(fma.f64 (/.f64 y (neg.f64 y)) (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 x) #s(literal -1 binary64))) y) |
(fma.f64 (*.f64 #s(literal 1 binary64) y) (/.f64 x y) y) |
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(*.f64 (/.f64 x (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (neg.f64 x) (pow.f64 (fma.f64 y y (*.f64 x (+.f64 y x))) #s(literal -1 binary64)))) |
(*.f64 (/.f64 x (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (neg.f64 x) (pow.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 x (-.f64 y x))) |
(*.f64 (/.f64 (neg.f64 x) (*.f64 (+.f64 y x) (-.f64 y x))) (/.f64 x (pow.f64 (+.f64 y x) #s(literal -1 binary64)))) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 (+.f64 y x) (-.f64 y x))) (/.f64 (*.f64 x x) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64)) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) |
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 x)) (-.f64 y x))) |
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 x (-.f64 y x))) |
(*.f64 (/.f64 (*.f64 x x) #s(literal -1 binary64)) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (/.f64 (*.f64 (neg.f64 x) x) (pow.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 y x) (-.f64 y x))) (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 y y (*.f64 x (+.f64 y x))) #s(literal -1 binary64)))) |
(*.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (/.f64 x (*.f64 (+.f64 y x) (-.f64 x y))) (/.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (+.f64 y x)))) |
(*.f64 (/.f64 x (*.f64 (+.f64 y x) (-.f64 x y))) (/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 x)) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))) |
(*.f64 (/.f64 x (*.f64 (+.f64 y x) (-.f64 x y))) (/.f64 x (pow.f64 (+.f64 y x) #s(literal -1 binary64)))) |
(*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 x)) (pow.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (/.f64 x (pow.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (*.f64 (/.f64 x (+.f64 y x)) (/.f64 x (-.f64 x y))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 y x)))) |
(*.f64 (*.f64 (/.f64 x (+.f64 y x)) (/.f64 x (-.f64 x y))) (+.f64 y x)) |
(*.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(*.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))) |
(*.f64 (pow.f64 (*.f64 (+.f64 y x) (-.f64 x y)) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))) |
(*.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (pow.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 x (-.f64 x y))) |
(*.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 x (-.f64 x y))) |
(*.f64 (pow.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 y x)))) |
(*.f64 (pow.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 x) x) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))) |
(*.f64 (/.f64 x (*.f64 (+.f64 y x) (-.f64 y x))) (/.f64 (neg.f64 x) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))) |
(*.f64 (/.f64 x (*.f64 (+.f64 y x) (-.f64 y x))) (/.f64 x (/.f64 #s(literal -1 binary64) (+.f64 y x)))) |
(*.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (/.f64 x (pow.f64 x #s(literal -1 binary64)))) |
(*.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 x y)) x)) |
(*.f64 (/.f64 x (-.f64 x y)) (*.f64 x #s(literal 1 binary64))) |
(*.f64 (/.f64 x (-.f64 x y)) x) |
(*.f64 (*.f64 (neg.f64 x) x) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) |
(*.f64 (*.f64 x x) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) |
(*.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) (-.f64 y x))) |
(*.f64 x (/.f64 x (-.f64 x y))) |
(pow.f64 (/.f64 (-.f64 x y) (*.f64 x x)) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) x)) (neg.f64 (/.f64 (-.f64 x y) x))) |
(/.f64 (neg.f64 (*.f64 x #s(literal 1 binary64))) (neg.f64 (/.f64 (-.f64 x y) x))) |
(/.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 (-.f64 x y) x)) |
(/.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 (-.f64 x y) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 x y) x) (*.f64 #s(literal 1 binary64) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 x y) x) (*.f64 x #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 x y) (*.f64 x x)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 x y) x) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (*.f64 x x))) |
(/.f64 (neg.f64 x) (neg.f64 (/.f64 (-.f64 x y) x))) |
(/.f64 (*.f64 (neg.f64 x) x) (-.f64 y x)) |
(/.f64 (*.f64 x x) (-.f64 x y)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x y) (*.f64 x x)))) |
(/.f64 x (/.f64 (-.f64 x y) x)) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 y x)) (/.f64 (*.f64 x x) (-.f64 y x))) |
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 x (pow.f64 (fma.f64 y y (*.f64 x (+.f64 y x))) #s(literal -1 binary64)))) |
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 x (pow.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (/.f64 x (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 y y (*.f64 x (+.f64 y x))) #s(literal -1 binary64)))) |
(*.f64 (/.f64 x (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 (+.f64 y x) (-.f64 y x))) (/.f64 x (pow.f64 (+.f64 y x) #s(literal -1 binary64)))) |
(*.f64 (/.f64 x #s(literal -1 binary64)) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) |
(*.f64 (/.f64 x (*.f64 (+.f64 y x) (-.f64 x y))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 y x)))) |
(*.f64 (/.f64 x (*.f64 (+.f64 y x) (-.f64 x y))) (+.f64 y x)) |
(*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (/.f64 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))) |
(*.f64 (*.f64 x #s(literal 1 binary64)) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal -1 binary64)) (/.f64 x (/.f64 #s(literal -1 binary64) (+.f64 y x)))) |
(*.f64 (/.f64 x (*.f64 (+.f64 y x) (-.f64 y x))) (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))) |
(*.f64 (neg.f64 (neg.f64 x)) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (*.f64 x #s(literal 1 binary64))) |
(*.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) x) |
(*.f64 #s(literal 1 binary64) (/.f64 x (-.f64 x y))) |
(*.f64 (neg.f64 x) (pow.f64 (-.f64 y x) #s(literal -1 binary64))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (-.f64 x y) x)))) |
(*.f64 #s(literal -1 binary64) (/.f64 x (-.f64 y x))) |
(*.f64 x (pow.f64 (-.f64 x y) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (-.f64 x y) x) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (*.f64 x #s(literal 1 binary64))) (-.f64 y x)) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 x))) (-.f64 y x)) |
(/.f64 (*.f64 x #s(literal 1 binary64)) (-.f64 x y)) |
(/.f64 (neg.f64 (neg.f64 x)) (-.f64 x y)) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (*.f64 x #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (-.f64 x y) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) x)) |
(/.f64 (neg.f64 x) (-.f64 y x)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x y) x))) |
(/.f64 x (-.f64 x y)) |
(neg.f64 (/.f64 x (-.f64 y x))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 y x)) (/.f64 x (-.f64 y x))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 x y) x)) #s(literal -1 binary64))) |
Compiled 21 249 to 2 990 computations (85.9% saved)
5 alts after pruning (1 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 727 | 1 | 728 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 2 | 3 |
| Done | 0 | 2 | 2 |
| Total | 728 | 5 | 733 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (sqrt.f64 (+.f64 x y)) |
| ✓ | 73.4% | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) |
| ✓ | 100.0% | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y))) |
| ▶ | 100.0% | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))) |
| ✓ | 98.1% | #s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
Compiled 81 to 54 computations (33.3% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 #s(literal 1 binary64) (/.f64 x y)) | |
| cost-diff | 0 | #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))) | |
| cost-diff | 4 | (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 65 |
| 0 | 20 | 61 |
| 1 | 31 | 57 |
| 2 | 44 | 57 |
| 3 | 67 | 57 |
| 4 | 157 | 29 |
| 5 | 390 | 29 |
| 6 | 1317 | 29 |
| 7 | 5299 | 29 |
| 0 | 8165 | 29 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y)) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
(+.f64 #s(literal 1 binary64) (/.f64 x y)) |
#s(literal 1 binary64) |
(/.f64 x y) |
x |
y |
| Outputs |
|---|
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))) |
(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)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y)) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+.f64 y x)) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
(+.f64 y x) |
(+.f64 #s(literal 1 binary64) (/.f64 x y)) |
(-.f64 (/.f64 x y) #s(literal -1 binary64)) |
#s(literal 1 binary64) |
(/.f64 x y) |
x |
y |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0 | (+.f64 #s(literal 1 binary64) (/.f64 x y)) | |
| accuracy | 0.0 | #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y)) | |
| accuracy | 0.00390625 | (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y) | |
| accuracy | 0.00390625 | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))) |
| 87.0ms | 254× | 0 | valid |
| 1.0ms | 2× | 5 | exit |
Compiled 51 to 17 computations (66.7% saved)
ival-mult: 71.0ms (88.8% of total)ival-div: 3.0ms (3.8% of total)ival-add: 3.0ms (3.8% of total)ival-sqrt: 2.0ms (2.5% of total)adjust: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y)) |
(+.f64 #s(literal 1 binary64) (/.f64 x 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 |
(+ 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)))))) |
(/ x y) |
(* x (+ (/ 1 x) (/ 1 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))))))) |
(/ (+ x y) 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 | |
|---|---|---|---|---|
| 5.0ms | y | @ | inf | ((* (+ 1 (/ x y)) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+ 1 (/ x y))) |
| 1.0ms | y | @ | -inf | ((* (+ 1 (/ x y)) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+ 1 (/ x y))) |
| 1.0ms | x | @ | inf | ((* (+ 1 (/ x y)) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+ 1 (/ x y))) |
| 1.0ms | x | @ | -inf | ((* (+ 1 (/ x y)) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+ 1 (/ x y))) |
| 1.0ms | x | @ | 0 | ((* (+ 1 (/ x y)) y) (sqrt (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y))) (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (+ 1 (/ x y))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 159 | 602 |
| 1 | 465 | 572 |
| 2 | 1448 | 554 |
| 3 | 4758 | 542 |
| 0 | 8220 | 506 |
| 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 |
(+ 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)))))) |
(/ x y) |
(* x (+ (/ 1 x) (/ 1 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))))))) |
(/ (+ x y) 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 y x) |
(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 |
#s(literal 1 binary64) |
(+ 1 (/ x y)) |
(-.f64 (/.f64 x y) #s(literal -1 binary64)) |
x |
(* x (+ 1 (/ y x))) |
(+.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 y) |
(/.f64 x y) |
(* x (+ (/ 1 x) (/ 1 y))) |
(-.f64 (/.f64 x y) #s(literal -1 binary64)) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+.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 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)) |
(/ (+ x y) y) |
(-.f64 (/.f64 x y) #s(literal -1 binary64)) |
(* y (+ 1 (/ x y))) |
(+.f64 y 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) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(+.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) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 59 |
| 0 | 20 | 55 |
| 1 | 86 | 39 |
| 2 | 645 | 35 |
| 0 | 8893 | 32 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))) |
#s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y)) |
(+.f64 #s(literal 1 binary64) (/.f64 x y)) |
| Outputs |
|---|
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64))) y) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 3 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64))) (/.f64 x y))) |
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64))) y) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64)))) (+.f64 (/.f64 x y) #s(literal 1 binary64))) |
(*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1 binary64)) y) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64))) #s(literal 2 binary64)))) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64))) (/.f64 x y))) |
(*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1 binary64)) y) (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64))) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64)))))) |
(*.f64 (/.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 3 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64))) (/.f64 x y))) |
(*.f64 (/.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64)))) (+.f64 (/.f64 x y) #s(literal 1 binary64))) |
(*.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) y y) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64))) #s(literal 2 binary64)))) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64))) (/.f64 x y))) |
(*.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) y y) (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64))) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64)))))) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64))) y) (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) #s(literal -1 binary64))) |
(*.f64 (*.f64 (+.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1 binary64)) y) (pow.f64 (fma.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(*.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64)))) (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) y y) (pow.f64 (fma.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64))) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) #s(literal -1 binary64)) y)) |
(*.f64 (+.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) y)) |
(*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y) |
(*.f64 y (+.f64 (/.f64 x y) #s(literal 1 binary64))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1 binary64)) y) (-.f64 (/.f64 x y) #s(literal 1 binary64))) |
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64))) y) (+.f64 #s(literal -1 binary64) (/.f64 x y))) |
(/.f64 (*.f64 (neg.f64 (+.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1 binary64))) y) (neg.f64 (fma.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (*.f64 y (-.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (/.f64 x y) #s(literal 1 binary64))) |
(/.f64 (*.f64 y (+.f64 #s(literal -1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64)))) (+.f64 #s(literal -1 binary64) (/.f64 x y))) |
(/.f64 (*.f64 y (neg.f64 (+.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 x y) y) (*.f64 (/.f64 x y) y)) (*.f64 y y)) (-.f64 (*.f64 (/.f64 x y) y) y)) |
(/.f64 (-.f64 (*.f64 y y) (*.f64 (*.f64 (/.f64 x y) y) (*.f64 (/.f64 x y) y))) (-.f64 y (*.f64 (/.f64 x y) y))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x y) y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 x y) y) (*.f64 (/.f64 x y) y) (-.f64 (*.f64 y y) (*.f64 (*.f64 (/.f64 x y) y) y)))) |
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (*.f64 (/.f64 x y) y) #s(literal 3 binary64))) (fma.f64 y y (-.f64 (*.f64 (*.f64 (/.f64 x y) y) (*.f64 (/.f64 x y) y)) (*.f64 y (*.f64 (/.f64 x y) y))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64))) y)) (+.f64 #s(literal -1 binary64) (/.f64 x y))) |
(/.f64 (neg.f64 (*.f64 (+.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1 binary64)) y)) (neg.f64 (fma.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64))))) (+.f64 #s(literal -1 binary64) (/.f64 x y))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) y y)) (neg.f64 (fma.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64))) y) (-.f64 #s(literal 1 binary64) (/.f64 x y))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1 binary64)) y) (-.f64 (+.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 x y))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1 binary64)) y) (fma.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(/.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (/.f64 x y))) |
(/.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) y y) (-.f64 (+.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 x y))) |
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(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) #s(literal -1 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x y)))) |
(-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) y)) |
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x y))))) |
(+.f64 (/.f64 x y) #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) (/.f64 x y)) |
Compiled 6 018 to 794 computations (86.8% saved)
5 alts after pruning (0 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 164 | 0 | 164 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 4 | 4 |
| Total | 164 | 5 | 169 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (sqrt.f64 (+.f64 x y)) |
| ✓ | 73.4% | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) |
| ✓ | 100.0% | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y))) |
| ✓ | 100.0% | (sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))) |
| ✓ | 98.1% | #s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
Compiled 222 to 108 computations (51.4% saved)
| Inputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(sqrt.f64 (+.f64 x y)) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y))) |
(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 (+.f64 #s(literal 1 binary64) (/.f64 x y)) 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 (fma.f64 (/.f64 y (-.f64 y x)) y (*.f64 (/.f64 x (-.f64 x y)) x))) |
(sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))))) |
| Outputs |
|---|
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))) |
4 calls:
| 22.0ms | (sqrt.f64 (+.f64 x y)) |
| 3.0ms | y |
| 3.0ms | (+.f64 x y) |
| 3.0ms | 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)
| Inputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(sqrt.f64 (+.f64 x y)) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y))) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 y x) x x))) |
| Outputs |
|---|
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y))) |
4 calls:
| 2.0ms | (sqrt.f64 (+.f64 x y)) |
| 2.0ms | (+.f64 x y) |
| 2.0ms | y |
| 2.0ms | 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)
| Inputs |
|---|
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
(sqrt.f64 (+.f64 x y)) |
| Outputs |
|---|
(sqrt.f64 (+.f64 x y)) |
4 calls:
| 1.0ms | (+.f64 x y) |
| 1.0ms | (sqrt.f64 (+.f64 x y)) |
| 1.0ms | x |
| 1.0ms | y |
| 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 | x |
| 1.0ms | (sqrt.f64 (+.f64 x y)) |
| 1.0ms | (+.f64 x y) |
| 1.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.1% | 1 | x |
| 98.1% | 1 | y |
| 98.1% | 1 | (sqrt.f64 (+.f64 x y)) |
| 98.1% | 1 | (+.f64 x y) |
Compiled 9 to 11 computations (-22.2% saved)
| 1× | egg-herbie |
Useful iterations: 5 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 54 |
| 1 | 35 | 50 |
| 2 | 40 | 50 |
| 3 | 54 | 50 |
| 4 | 104 | 38 |
| 5 | 265 | 34 |
| 6 | 841 | 34 |
| 7 | 5806 | 34 |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y))) |
(sqrt.f64 (+.f64 x y)) |
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
| Outputs |
|---|
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))) |
(sqrt.f64 #s(approx (/ (+ (* -1 (* x x)) (* y y)) (+ (* -1 x) y)) (fma.f64 (/.f64 x y) y y))) |
(sqrt.f64 (+.f64 x y)) |
#s(approx (sqrt (+ x y)) (sqrt.f64 y)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 7 |
| 0 | 6 | 7 |
| 1 | 22 | 7 |
| 2 | 145 | 7 |
| 3 | 1374 | 7 |
| 0 | 8331 | 7 |
| 0 | 156 | 583 |
| 1 | 454 | 553 |
| 2 | 1431 | 535 |
| 3 | 4702 | 523 |
| 0 | 8271 | 487 |
| 0 | 860 | 4246 |
| 1 | 2857 | 3675 |
| 0 | 9152 | 3452 |
| 0 | 25 | 157 |
| 0 | 41 | 145 |
| 1 | 181 | 109 |
| 2 | 1431 | 103 |
| 0 | 8680 | 97 |
| 1× | done |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 133 to 74 computations (44.4% saved)
Compiled 220 to 122 computations (44.5% saved)
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