Time bar (total: 2.3s)
| 1× | search |
| True | Other | False | Iter |
|---|---|---|---|
| 0% | 99.9% | 0.1% | 0 |
| 0% | 99.9% | 0.1% | 1 |
| 0% | 99.9% | 0.1% | 2 |
| 0% | 99.9% | 0.1% | 3 |
| 0% | 87.4% | 12.6% | 4 |
| 6.2% | 74.9% | 18.8% | 5 |
| 12.5% | 59.3% | 28.2% | 6 |
| 23.4% | 43.7% | 32.9% | 7 |
| 28.1% | 33.6% | 38.3% | 8 |
| 35.5% | 23.4% | 41.1% | 9 |
| 38.2% | 17.8% | 44% | 10 |
| 42.4% | 12.1% | 45.5% | 11 |
| 43.9% | 9.1% | 47% | 12 |
| 46.1% | 6.1% | 47.7% | 13 |
| 46.9% | 4.6% | 48.5% | 14 |
Compiled 7 to 5 computations (28.6% saved)
| 737.0ms | 8256× | body | 128 | valid |
| 19.0ms | 269× | body | 128 | invalid |
| 2× | egg-herbie |
| 1× | swap-x-y |
| 1× | +-commutative_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 7 | 12 |
| 1 | 7 | 12 |
| 0 | 2 | 2 |
| 1 | 2 | 2 |
| 1× | unsound |
| 1× | saturated |
| Inputs |
|---|
0 |
1 |
| Outputs |
|---|
0 |
1 |
0 |
| Inputs |
|---|
(sqrt.f64 (+.f64 x y)) |
(sqrt.f64 (+.f64 y x)) |
| Outputs |
|---|
(sqrt.f64 (+.f64 x y)) |
(sqrt.f64 (+.f64 y x)) |
(sqrt.f64 (+.f64 x y)) |
(sort x y)
Compiled 6 to 4 computations (33.3% saved)
| 1× | egg-herbie |
| 1× | +-commutative_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 6 |
| 1 | 6 | 6 |
| 1× | saturated |
| Inputs |
|---|
(sqrt.f64 (+.f64 x y)) |
| Outputs |
|---|
(sqrt.f64 (+.f64 x y)) |
Compiled 6 to 4 computations (33.3% saved)
2 alts after pruning (2 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 0 | 1 | 1 |
| Fresh | 0 | 1 | 1 |
| Picked | 0 | 0 | 0 |
| Done | 0 | 0 | 0 |
| Total | 0 | 2 | 2 |
| Status | Error | Program |
|---|---|---|
| ▶ | 0.0b | (sqrt.f64 (+.f64 x y)) |
Compiled 12 to 8 computations (33.3% saved)
Found 1 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (sqrt.f64 (+.f64 x y)) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | inf | (sqrt.f64 (+.f64 x y)) |
| 1.0ms | x | @ | 0 | (sqrt.f64 (+.f64 x y)) |
| 1.0ms | y | @ | inf | (sqrt.f64 (+.f64 x y)) |
| 1.0ms | y | @ | 0 | (sqrt.f64 (+.f64 x y)) |
| 1.0ms | x | @ | -inf | (sqrt.f64 (+.f64 x y)) |
| 1× | batch-egg-rewrite |
| 592× | pow1_binary64 |
| 553× | add-log-exp_binary64 |
| 553× | log1p-expm1-u_binary64 |
| 553× | expm1-log1p-u_binary64 |
| 58× | add-sqr-sqrt_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 6 |
| 1 | 109 | 6 |
| 2 | 1503 | 6 |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 (+.f64 x y)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) (cbrt.f64 (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x y) 1/4) (pow.f64 (+.f64 x y) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 y y))) (sqrt.f64 (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 x x (*.f64 y (-.f64 y x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x y) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x y) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 y) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 x) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x y)))))))) |
| 1× | egg-herbie |
| 679× | fma-def_binary64 |
| 451× | associate-*l*_binary64 |
| 329× | associate-*r*_binary64 |
| 260× | associate-/r*_binary64 |
| 236× | distribute-rgt-out_binary64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 51 | 210 |
| 1 | 130 | 204 |
| 2 | 339 | 204 |
| 3 | 956 | 198 |
| 4 | 2820 | 198 |
| 5 | 4232 | 198 |
| 6 | 4796 | 198 |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 y) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(+.f64 (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))) |
(+.f64 (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (*.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))) (sqrt.f64 y)))) |
(sqrt.f64 x) |
(+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))))) |
(+.f64 (*.f64 -1/8 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))) |
(+.f64 (*.f64 -1/8 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 1/16 (*.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))))))) |
| Outputs |
|---|
(sqrt.f64 y) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(+.f64 (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))) |
(fma.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x x)) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))) |
(fma.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (*.f64 x x) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))) |
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x (*.f64 x -1/8)) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))) |
(fma.f64 x (fma.f64 -1/8 (*.f64 x (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 y)))) (sqrt.f64 y)) |
(+.f64 (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (*.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))) (sqrt.f64 y)))) |
(fma.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x x)) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y)))) |
(fma.f64 -1/8 (*.f64 x (*.f64 x (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y)))) |
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x (*.f64 x -1/8)) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (*.f64 1/16 (pow.f64 x 3)) (sqrt.f64 y)))) |
(fma.f64 x (fma.f64 -1/8 (*.f64 x (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 y)))) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y))) |
(sqrt.f64 x) |
(+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))))) |
(fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) |
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) |
(+.f64 (*.f64 -1/8 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))) |
(fma.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 y y)) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))) |
(fma.f64 (*.f64 -1/8 (*.f64 y y)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))) |
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 y (*.f64 y -1/8)) (sqrt.f64 x))) |
(+.f64 (*.f64 -1/8 (*.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 1/16 (*.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))))))) |
(fma.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 y y)) (fma.f64 1/16 (*.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))))))) |
(fma.f64 -1/8 (*.f64 y (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (fma.f64 1/16 (*.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)))) |
(fma.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 y y)) (fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 (pow.f64 y 3) 1/16) (sqrt.f64 x)))) |
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 (pow.f64 y 3) 1/16) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 y (*.f64 y -1/8)) (sqrt.f64 x)))) |
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 y (*.f64 y (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (fma.f64 (pow.f64 y 3) (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (sqrt.f64 x)))) |
Compiled 481 to 285 computations (40.7% saved)
2 alts after pruning (1 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 38 | 1 | 39 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 38 | 2 | 40 |
| Status | Error | Program |
|---|---|---|
| ▶ | 1.0b | (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
| ✓ | 0.0b | (sqrt.f64 (+.f64 x y)) |
Compiled 30 to 22 computations (26.7% saved)
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
| ✓ | 0.1b | (sqrt.f64 (/.f64 1 y)) |
| ✓ | 0.2b | (*.f64 (sqrt.f64 (/.f64 1 y)) x) |
15 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | y | @ | -inf | (*.f64 (sqrt.f64 (/.f64 1 y)) x) |
| 1.0ms | x | @ | inf | (*.f64 (sqrt.f64 (/.f64 1 y)) x) |
| 1.0ms | y | @ | 0 | (*.f64 (sqrt.f64 (/.f64 1 y)) x) |
| 1.0ms | x | @ | 0 | (*.f64 (sqrt.f64 (/.f64 1 y)) x) |
| 1.0ms | y | @ | inf | (*.f64 (sqrt.f64 (/.f64 1 y)) x) |
| 1× | batch-egg-rewrite |
| 835× | pow1_binary64 |
| 768× | log1p-expm1-u_binary64 |
| 768× | expm1-log1p-u_binary64 |
| 93× | add-sqr-sqrt_binary64 |
| 89× | *-un-lft-identity_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 30 |
| 1 | 198 | 22 |
| 2 | 2192 | 22 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(sqrt.f64 (/.f64 1 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (sqrt.f64 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sqrt.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (sqrt.f64 y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (sqrt.f64 y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (/.f64 (pow.f64 y -1/2) y) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (/.f64 (pow.f64 y -1/2) y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 x (sqrt.f64 y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (sqrt.f64 y)))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 y -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 y -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 y -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 y -1/2)) (cbrt.f64 (/.f64 1 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 y)) (cbrt.f64 (pow.f64 y -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 y -1/2)) (sqrt.f64 (pow.f64 y -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 y -2))) (sqrt.f64 (cbrt.f64 (/.f64 1 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (pow.f64 y -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 y -2)) 1/2) (pow.f64 (cbrt.f64 (/.f64 1 y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 y) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (/.f64 1 y)) (cbrt.f64 (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 y -1/2)) (pow.f64 y 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 y -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 y) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 y -1/2) y) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 y -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 y -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 y -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 y -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 y -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 y -1/2) y))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 y -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 y -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 y -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 y -1/2))))))) |
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) 1) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) 2) (cbrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) 3) (pow.f64 y 3/2)) (+.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) (-.f64 y (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))))))) |
| 1× | egg-herbie |
| 6× | fma-def_binary64 |
| 5× | *-commutative_binary64 |
| 3× | associate-*r*_binary64 |
| 3× | associate-*l*_binary64 |
| 1× | +-commutative_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 11 | 162 |
| 1 | 19 | 162 |
| 2 | 28 | 162 |
| 3 | 34 | 162 |
| 1× | saturated |
| Inputs |
|---|
(sqrt.f64 y) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
| Outputs |
|---|
(sqrt.f64 y) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
Compiled 910 to 486 computations (46.6% saved)
3 alts after pruning (1 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 73 | 1 | 74 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 1 | 1 |
| Total | 73 | 3 | 76 |
| Status | Error | Program |
|---|---|---|
| ✓ | 1.0b | (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
| ▶ | 1.5b | (/.f64 (-.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y))) |
| ✓ | 0.0b | (sqrt.f64 (+.f64 x y)) |
Compiled 72 to 41 computations (43.1% saved)
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y)) |
| ✓ | 0.3b | (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) |
| ✓ | 0.3b | (/.f64 x (sqrt.f64 y)) |
| ✓ | 0.5b | (/.f64 (-.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y))) |
24 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 5.0ms | y | @ | -inf | (/.f64 (-.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y))) |
| 3.0ms | y | @ | 0 | (/.f64 (-.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y))) |
| 2.0ms | y | @ | inf | (/.f64 (-.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y))) |
| 2.0ms | y | @ | -inf | (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) |
| 1.0ms | x | @ | 0 | (/.f64 (-.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y))) |
| 1× | batch-egg-rewrite |
| 339× | fma-neg_binary64 |
| 234× | expm1-udef_binary64 |
| 234× | log1p-udef_binary64 |
| 137× | add-sqr-sqrt_binary64 |
| 133× | *-un-lft-identity_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 11 | 63 |
| 1 | 263 | 42 |
| 2 | 4097 | 42 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y))) |
(/.f64 x (sqrt.f64 y)) |
(*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) |
(-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (/.f64 (*.f64 x x) y) 1/4) (fma.f64 (/.f64 x (sqrt.f64 y)) 1/2 (neg.f64 (sqrt.f64 y)))) (neg.f64 (/.f64 y (fma.f64 (/.f64 x (sqrt.f64 y)) 1/2 (neg.f64 (sqrt.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (/.f64 (*.f64 x x) y) 1/4) (fma.f64 (/.f64 x (sqrt.f64 y)) 1/2 (neg.f64 (sqrt.f64 y)))) (/.f64 y (fma.f64 (/.f64 x (sqrt.f64 y)) 1/2 (neg.f64 (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (/.f64 x (sqrt.f64 y)) 1/2 (sqrt.f64 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) y) 1/4) y) (/.f64 1 (fma.f64 (/.f64 x (sqrt.f64 y)) 1/2 (neg.f64 (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (/.f64 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| 1× | egg-herbie |
| 387× | fma-def_binary64 |
| 332× | distribute-rgt-neg-in_binary64 |
| 264× | *-commutative_binary64 |
| 245× | fma-neg_binary64 |
| 242× | unswap-sqr_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 19 | 661 |
| 1 | 38 | 652 |
| 2 | 65 | 652 |
| 3 | 122 | 652 |
| 4 | 319 | 652 |
| 5 | 1070 | 652 |
| 6 | 2659 | 652 |
| 7 | 4300 | 652 |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 y) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 -1 (sqrt.f64 y)) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
| Outputs |
|---|
(sqrt.f64 y) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (sqrt.f64 y)) |
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (sqrt.f64 y)) |
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (sqrt.f64 y)) |
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (sqrt.f64 y)) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 (sqrt.f64 (/.f64 1 y)) x) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 1/4 (/.f64 (pow.f64 x 2) y)) |
(*.f64 1/4 (/.f64 (*.f64 x x) y)) |
(*.f64 1/4 (/.f64 x (/.f64 y x))) |
(/.f64 x (/.f64 (/.f64 y 1/4) x)) |
(*.f64 x (*.f64 x (/.f64 1/4 y))) |
(*.f64 x (/.f64 x (/.f64 y 1/4))) |
(*.f64 -1 (sqrt.f64 y)) |
(neg.f64 (sqrt.f64 y)) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 -1 (sqrt.f64 y) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (neg.f64 (sqrt.f64 y))) |
(-.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (neg.f64 (sqrt.f64 y))) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 -1 (sqrt.f64 y) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (neg.f64 (sqrt.f64 y))) |
(-.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (neg.f64 (sqrt.f64 y))) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 -1 (sqrt.f64 y) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (neg.f64 (sqrt.f64 y))) |
(-.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (neg.f64 (sqrt.f64 y))) |
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 -1 (sqrt.f64 y) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (neg.f64 (sqrt.f64 y))) |
(-.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (neg.f64 (sqrt.f64 y))) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 -1 (sqrt.f64 y) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (neg.f64 (sqrt.f64 y))) |
(-.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (neg.f64 (sqrt.f64 y))) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 -1 (sqrt.f64 y) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (neg.f64 (sqrt.f64 y))) |
(-.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (neg.f64 (sqrt.f64 y))) |
(*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 -1 (sqrt.f64 y) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (neg.f64 (sqrt.f64 y))) |
(-.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (neg.f64 (sqrt.f64 y))) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 -1 (sqrt.f64 y) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (neg.f64 (sqrt.f64 y))) |
(-.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (neg.f64 (sqrt.f64 y))) |
(+.f64 (*.f64 -1 (sqrt.f64 y)) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 -1 (sqrt.f64 y) (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x))) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (neg.f64 (sqrt.f64 y))) |
(-.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 1/2 x) (neg.f64 (sqrt.f64 y))) |
Compiled 7425 to 3141 computations (57.7% saved)
3 alts after pruning (0 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 257 | 0 | 257 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 2 | 2 |
| Total | 257 | 3 | 260 |
| Status | Error | Program |
|---|---|---|
| ✓ | 1.0b | (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
| ✓ | 1.5b | (/.f64 (-.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y))) |
| ✓ | 0.0b | (sqrt.f64 (+.f64 x y)) |
Compiled 45 to 27 computations (40% saved)
Total -1.5b remaining (-19768.8%)
Threshold costs -1.5b (-19768.8%)
| Inputs |
|---|
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (*.f64 (/.f64 x (sqrt.f64 y)) 1/2)) y) (-.f64 (*.f64 (/.f64 x (sqrt.f64 y)) 1/2) (sqrt.f64 y))) |
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) |
(sqrt.f64 (+.f64 x y)) |
| Outputs |
|---|
(sqrt.f64 (+.f64 x y)) |
| Time | Error | Segments | Branch |
| 5.0ms | 0.0b | 1 | x |
| 4.0ms | 0.0b | 1 | y |
| 4.0ms | 0.0b | 1 | (sqrt.f64 (+.f64 x y)) |
| 4.0ms | 0.0b | 1 | (+.f64 x y) |
Compiled 58 to 33 computations (43.1% saved)
| 1× | egg-herbie |
| 1× | +-commutative_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 6 |
| 1 | 6 | 6 |
| 1× | saturated |
| Inputs |
|---|
(sqrt.f64 (+.f64 x y)) |
| Outputs |
|---|
(sqrt.f64 (+.f64 x y)) |
| 1× | done |
(sort x y)
Compiled 24 to 16 computations (33.3% saved)
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