Time bar (total: 1.1s)
| 1× | search |
| True | Other | False | Iter |
|---|---|---|---|
| 0% | 100% | 0% | 0 |
| 0% | 100% | 0% | 1 |
| 0% | 100% | 0% | 2 |
| 0% | 50% | 50% | 3 |
| 25% | 25% | 50% | 4 |
| 37.5% | 12.5% | 50% | 5 |
| 43.7% | 6.2% | 50% | 6 |
| 46.9% | 3.1% | 50% | 7 |
| 48.4% | 1.6% | 50% | 8 |
| 49.2% | 0.8% | 50% | 9 |
| 49.6% | 0.4% | 50% | 10 |
| 49.8% | 0.2% | 50% | 11 |
| 49.9% | 0.1% | 50% | 12 |
| 49.9% | 0% | 50% | 13 |
| 49.9% | 0% | 50% | 14 |
Compiled 8 to 6 computations (25% saved)
| 693.0ms | 8256× | body | 128 | valid |
Compiled 16 to 12 computations (25% saved)
| 2× | egg-herbie |
| 492× | fma-neg_binary64 |
| 454× | unsub-neg_binary64 |
| 411× | distribute-rgt-in_binary64 |
| 370× | fma-def_binary64 |
| 363× | distribute-neg-in_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 9 |
| 1 | 13 | 9 |
| 2 | 20 | 9 |
| 3 | 31 | 9 |
| 4 | 48 | 9 |
| 5 | 76 | 9 |
| 6 | 123 | 9 |
| 7 | 318 | 9 |
| 8 | 657 | 9 |
| 9 | 1421 | 9 |
| 10 | 2745 | 9 |
| 11 | 4127 | 9 |
| 0 | 1 | 1 |
| 1× | saturated |
| 1× | node limit |
| Inputs |
|---|
0 |
| Outputs |
|---|
0 |
| Inputs |
|---|
(sqrt.f64 (-.f64 1 (*.f64 x x))) |
| Outputs |
|---|
(sqrt.f64 (-.f64 1 (*.f64 x x))) |
Compiled 7 to 5 computations (28.6% saved)
| 1× | egg-herbie |
| 492× | fma-neg_binary64 |
| 454× | unsub-neg_binary64 |
| 411× | distribute-rgt-in_binary64 |
| 370× | fma-def_binary64 |
| 363× | distribute-neg-in_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 9 |
| 1 | 13 | 9 |
| 2 | 20 | 9 |
| 3 | 31 | 9 |
| 4 | 48 | 9 |
| 5 | 76 | 9 |
| 6 | 123 | 9 |
| 7 | 318 | 9 |
| 8 | 657 | 9 |
| 9 | 1421 | 9 |
| 10 | 2745 | 9 |
| 11 | 4127 | 9 |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 (-.f64 1 (*.f64 x x))) |
| Outputs |
|---|
(sqrt.f64 (-.f64 1 (*.f64 x x))) |
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 1 (*.f64 x x))) |
Compiled 21 to 15 computations (28.6% saved)
Found 1 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (sqrt.f64 (-.f64 1 (*.f64 x x))) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (sqrt.f64 (-.f64 1 (*.f64 x x))) |
| 1.0ms | x | @ | inf | (sqrt.f64 (-.f64 1 (*.f64 x x))) |
| 1.0ms | x | @ | 0 | (sqrt.f64 (-.f64 1 (*.f64 x x))) |
| 1× | batch-egg-rewrite |
| 580× | pow1_binary64 |
| 544× | add-log-exp_binary64 |
| 543× | log1p-expm1-u_binary64 |
| 543× | expm1-log1p-u_binary64 |
| 531× | add-exp-log_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 9 |
| 1 | 126 | 9 |
| 2 | 1543 | 9 |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 (-.f64 1 (*.f64 x x))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (*.f64 x (neg.f64 x))) 1/2)))))) |
| 1× | egg-herbie |
| 591× | fma-def_binary64 |
| 439× | cancel-sign-sub-inv_binary64 |
| 315× | fma-neg_binary64 |
| 217× | associate-/l/_binary64 |
| 193× | associate-*r/_binary64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 47 | 268 |
| 1 | 152 | 255 |
| 2 | 451 | 246 |
| 3 | 1698 | 240 |
| 1× | node limit |
| Inputs |
|---|
1 |
(-.f64 1 (*.f64 1/2 (pow.f64 x 2))) |
(-.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 4)) (*.f64 1/2 (pow.f64 x 2)))) |
(-.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 4)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))) |
(*.f64 (sqrt.f64 -1) x) |
(+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)) |
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) |
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (+.f64 (*.f64 (sqrt.f64 -1) x) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) |
(*.f64 -1 (*.f64 (sqrt.f64 -1) x)) |
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) |
(-.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) |
(-.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (+.f64 (*.f64 (sqrt.f64 -1) x) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))))) |
| Outputs |
|---|
1 |
(-.f64 1 (*.f64 1/2 (pow.f64 x 2))) |
(+.f64 1 (*.f64 -1/2 (*.f64 x x))) |
(-.f64 1 (*.f64 x (*.f64 x 1/2))) |
(fma.f64 (*.f64 x x) -1/2 1) |
(-.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 4)) (*.f64 1/2 (pow.f64 x 2)))) |
(-.f64 1 (fma.f64 1/8 (pow.f64 x 4) (*.f64 1/2 (*.f64 x x)))) |
(-.f64 1 (fma.f64 1/2 (*.f64 x x) (*.f64 1/8 (pow.f64 x 4)))) |
(+.f64 (*.f64 (pow.f64 x 4) -1/8) (fma.f64 (*.f64 x x) -1/2 1)) |
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) -1/8 1)) |
(-.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 4)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))) |
(-.f64 1 (fma.f64 1/8 (pow.f64 x 4) (fma.f64 1/16 (pow.f64 x 6) (*.f64 1/2 (*.f64 x x))))) |
(-.f64 1 (fma.f64 1/8 (pow.f64 x 4) (fma.f64 1/2 (*.f64 x x) (*.f64 1/16 (pow.f64 x 6))))) |
(-.f64 1 (fma.f64 1/2 (*.f64 x x) (fma.f64 1/8 (pow.f64 x 4) (*.f64 1/16 (pow.f64 x 6))))) |
(+.f64 (fma.f64 (*.f64 x x) -1/2 1) (fma.f64 (pow.f64 x 4) -1/8 (*.f64 (pow.f64 x 6) -1/16))) |
(*.f64 (sqrt.f64 -1) x) |
(*.f64 x (sqrt.f64 -1)) |
(+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)) |
(+.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) |
(fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) |
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) |
(+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (-.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) |
(+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (fma.f64 x (sqrt.f64 -1) (/.f64 -1/8 (*.f64 (neg.f64 (sqrt.f64 -1)) (pow.f64 x 3))))) |
(+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))))) |
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))) |
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (+.f64 (*.f64 (sqrt.f64 -1) x) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) |
(+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (-.f64 (fma.f64 (sqrt.f64 -1) x (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) |
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) (-.f64 (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))) (/.f64 1/8 (*.f64 (neg.f64 (sqrt.f64 -1)) (pow.f64 x 3))))) |
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) (+.f64 (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))))) |
(-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (*.f64 (/.f64 -1 (*.f64 x (sqrt.f64 -1))) (+.f64 (/.f64 1/8 (*.f64 x x)) 1/2))) |
(*.f64 -1 (*.f64 (sqrt.f64 -1) x)) |
(neg.f64 (*.f64 x (sqrt.f64 -1))) |
(*.f64 x (neg.f64 (sqrt.f64 -1))) |
(*.f64 (sqrt.f64 -1) (neg.f64 x)) |
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) |
(neg.f64 (+.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))) |
(-.f64 (/.f64 -1/2 (*.f64 x (sqrt.f64 -1))) (*.f64 x (sqrt.f64 -1))) |
(-.f64 (/.f64 (/.f64 -1/2 x) (sqrt.f64 -1)) (*.f64 x (sqrt.f64 -1))) |
(-.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) |
(-.f64 (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (+.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))) |
(-.f64 (/.f64 1/8 (*.f64 (neg.f64 (sqrt.f64 -1)) (pow.f64 x 3))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))) |
(-.f64 (/.f64 -1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))) |
(-.f64 (*.f64 (/.f64 -1 (*.f64 x (sqrt.f64 -1))) (+.f64 (/.f64 1/8 (*.f64 x x)) 1/2)) (*.f64 x (sqrt.f64 -1))) |
(-.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (+.f64 (*.f64 (sqrt.f64 -1) x) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))))) |
(-.f64 (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (fma.f64 (sqrt.f64 -1) x (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))) |
(-.f64 (fma.f64 1/8 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (/.f64 -1/2 (*.f64 x (sqrt.f64 -1)))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))) |
(+.f64 (/.f64 -1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))) (-.f64 (/.f64 (/.f64 -1/2 x) (sqrt.f64 -1)) (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))) |
(-.f64 (*.f64 (/.f64 -1 (*.f64 x (sqrt.f64 -1))) (+.f64 (/.f64 1/8 (*.f64 x x)) 1/2)) (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))) |
3 alts after pruning (2 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 43 | 2 | 45 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 43 | 3 | 46 |
| Status | Error | Program |
|---|---|---|
| 0.3b | (fma.f64 (*.f64 x x) -1/2 1) | |
| ✓ | 0.0b | (sqrt.f64 (-.f64 1 (*.f64 x x))) |
| ▶ | 0.0b | (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))) |
Compiled 641 to 485 computations (24.3% saved)
Found 2 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.0b | (sqrt.f64 (-.f64 1 (*.f64 x x))) | |
| ✓ | 0.0b | (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))) |
| 1.0ms | x | @ | inf | (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))) |
| 1.0ms | x | @ | 0 | (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))) |
| 1× | batch-egg-rewrite |
| 661× | pow1_binary64 |
| 618× | add-log-exp_binary64 |
| 618× | expm1-log1p-u_binary64 |
| 617× | log1p-expm1-u_binary64 |
| 71× | add-sqr-sqrt_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 9 |
| 1 | 147 | 9 |
| 2 | 1748 | 9 |
| 1× | node limit |
| Inputs |
|---|
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3) 1) (+.f64 (*.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (+.f64 1 (*.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) 1) (+.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (-.f64 1 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (*.f64 x (neg.f64 x))) 1/2)))))) |
| 1× | egg-herbie |
| 591× | fma-def_binary64 |
| 439× | cancel-sign-sub-inv_binary64 |
| 315× | fma-neg_binary64 |
| 217× | associate-/l/_binary64 |
| 193× | associate-*r/_binary64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 47 | 268 |
| 1 | 152 | 255 |
| 2 | 451 | 246 |
| 3 | 1698 | 240 |
| 1× | node limit |
| Inputs |
|---|
1 |
(-.f64 1 (*.f64 1/2 (pow.f64 x 2))) |
(-.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 4)) (*.f64 1/2 (pow.f64 x 2)))) |
(-.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 4)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))) |
(*.f64 (sqrt.f64 -1) x) |
(+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)) |
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) |
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (+.f64 (*.f64 (sqrt.f64 -1) x) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) |
(*.f64 -1 (*.f64 (sqrt.f64 -1) x)) |
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) |
(-.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) |
(-.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (+.f64 (*.f64 (sqrt.f64 -1) x) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))))) |
| Outputs |
|---|
1 |
(-.f64 1 (*.f64 1/2 (pow.f64 x 2))) |
(+.f64 1 (*.f64 -1/2 (*.f64 x x))) |
(-.f64 1 (*.f64 x (*.f64 x 1/2))) |
(fma.f64 (*.f64 x x) -1/2 1) |
(-.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 4)) (*.f64 1/2 (pow.f64 x 2)))) |
(-.f64 1 (fma.f64 1/8 (pow.f64 x 4) (*.f64 1/2 (*.f64 x x)))) |
(-.f64 1 (fma.f64 1/2 (*.f64 x x) (*.f64 1/8 (pow.f64 x 4)))) |
(+.f64 (*.f64 (pow.f64 x 4) -1/8) (fma.f64 (*.f64 x x) -1/2 1)) |
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) -1/8 1)) |
(-.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 4)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))) |
(-.f64 1 (fma.f64 1/8 (pow.f64 x 4) (fma.f64 1/16 (pow.f64 x 6) (*.f64 1/2 (*.f64 x x))))) |
(-.f64 1 (fma.f64 1/8 (pow.f64 x 4) (fma.f64 1/2 (*.f64 x x) (*.f64 1/16 (pow.f64 x 6))))) |
(-.f64 1 (fma.f64 1/2 (*.f64 x x) (fma.f64 1/8 (pow.f64 x 4) (*.f64 1/16 (pow.f64 x 6))))) |
(+.f64 (fma.f64 (*.f64 x x) -1/2 1) (fma.f64 (pow.f64 x 4) -1/8 (*.f64 (pow.f64 x 6) -1/16))) |
(*.f64 (sqrt.f64 -1) x) |
(*.f64 x (sqrt.f64 -1)) |
(+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)) |
(+.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) |
(fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) |
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) |
(+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (-.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) |
(+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (fma.f64 x (sqrt.f64 -1) (/.f64 -1/8 (*.f64 (neg.f64 (sqrt.f64 -1)) (pow.f64 x 3))))) |
(+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))))) |
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))) |
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (+.f64 (*.f64 (sqrt.f64 -1) x) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) |
(+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (-.f64 (fma.f64 (sqrt.f64 -1) x (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) |
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) (-.f64 (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))) (/.f64 1/8 (*.f64 (neg.f64 (sqrt.f64 -1)) (pow.f64 x 3))))) |
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) (+.f64 (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))))) |
(-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (*.f64 (/.f64 -1 (*.f64 x (sqrt.f64 -1))) (+.f64 (/.f64 1/8 (*.f64 x x)) 1/2))) |
(*.f64 -1 (*.f64 (sqrt.f64 -1) x)) |
(neg.f64 (*.f64 x (sqrt.f64 -1))) |
(*.f64 x (neg.f64 (sqrt.f64 -1))) |
(*.f64 (sqrt.f64 -1) (neg.f64 x)) |
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) |
(neg.f64 (+.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))) |
(-.f64 (/.f64 -1/2 (*.f64 x (sqrt.f64 -1))) (*.f64 x (sqrt.f64 -1))) |
(-.f64 (/.f64 (/.f64 -1/2 x) (sqrt.f64 -1)) (*.f64 x (sqrt.f64 -1))) |
(-.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) |
(-.f64 (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (+.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))) |
(-.f64 (/.f64 1/8 (*.f64 (neg.f64 (sqrt.f64 -1)) (pow.f64 x 3))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))) |
(-.f64 (/.f64 -1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))) |
(-.f64 (*.f64 (/.f64 -1 (*.f64 x (sqrt.f64 -1))) (+.f64 (/.f64 1/8 (*.f64 x x)) 1/2)) (*.f64 x (sqrt.f64 -1))) |
(-.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (+.f64 (*.f64 (sqrt.f64 -1) x) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))))) |
(-.f64 (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (fma.f64 (sqrt.f64 -1) x (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))) |
(-.f64 (fma.f64 1/8 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (/.f64 -1/2 (*.f64 x (sqrt.f64 -1)))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))) |
(+.f64 (/.f64 -1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))) (-.f64 (/.f64 (/.f64 -1/2 x) (sqrt.f64 -1)) (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))) |
(-.f64 (*.f64 (/.f64 -1 (*.f64 x (sqrt.f64 -1))) (+.f64 (/.f64 1/8 (*.f64 x x)) 1/2)) (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))) |
3 alts after pruning (1 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 94 | 0 | 94 |
| Fresh | 0 | 1 | 1 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 1 | 1 |
| Total | 94 | 3 | 97 |
| Status | Error | Program |
|---|---|---|
| ▶ | 0.3b | (fma.f64 (*.f64 x x) -1/2 1) |
| ✓ | 0.0b | (sqrt.f64 (-.f64 1 (*.f64 x x))) |
| ✓ | 0.0b | (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))) |
Compiled 1414 to 1083 computations (23.4% saved)
3 alts after pruning (0 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 0 | 0 | 0 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 2 | 2 |
| Total | 0 | 3 | 3 |
| Status | Error | Program |
|---|---|---|
| ✓ | 0.3b | (fma.f64 (*.f64 x x) -1/2 1) |
| ✓ | 0.0b | (sqrt.f64 (-.f64 1 (*.f64 x x))) |
| ✓ | 0.0b | (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))) |
Compiled 23 to 17 computations (26.1% saved)
Total 0.0b remaining (91.3%)
Threshold costs 0.0b (91.3%)
Compiled 246 to 184 computations (25.2% saved)
| 1× | egg-herbie |
| 3× | +-commutative_binary64 |
| 3× | sub-neg_binary64 |
| 2× | *-commutative_binary64 |
| 2× | neg-sub0_binary64 |
| 2× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 13 |
| 1 | 15 | 13 |
| 2 | 22 | 13 |
| 3 | 26 | 13 |
| 4 | 28 | 13 |
| 1× | saturated |
| Inputs |
|---|
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))) |
| Outputs |
|---|
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))) |
| 1× | done |
Compiled 41 to 31 computations (24.4% saved)
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