Time bar (total: 4.8s)
| 1× | search |
| True | Other | False | Iter |
|---|---|---|---|
| 0% | 100% | 0% | 0 |
| 0% | 100% | 0% | 1 |
| 0% | 100% | 0% | 2 |
| 25% | 50% | 25% | 3 |
| 37.5% | 25% | 37.5% | 4 |
| 43.7% | 12.5% | 43.8% | 5 |
| 46.9% | 6.2% | 46.9% | 6 |
| 48.4% | 3.1% | 48.5% | 7 |
| 49.2% | 1.6% | 49.2% | 8 |
| 49.6% | 0.8% | 49.6% | 9 |
| 49.8% | 0.4% | 49.8% | 10 |
| 49.9% | 0.2% | 49.9% | 11 |
| 49.9% | 0.1% | 50% | 12 |
Compiled 9 to 7 computations (22.2% saved)
| 501.0ms | 2066× | body | 1024 | valid |
| 474.0ms | 4982× | body | 256 | valid |
| 167.0ms | 1001× | body | 512 | valid |
| 61.0ms | 207× | body | 2048 | valid |
| 1.0ms | 7× | body | 256 | invalid |
| 2× | egg-herbie |
| 39× | fma-def_binary64 |
| 32× | fma-neg_binary64 |
| 15× | cancel-sign-sub-inv_binary64 |
| 12× | sub-neg_binary64 |
| 10× | distribute-rgt-in_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 7 | 11 |
| 1 | 12 | 11 |
| 2 | 16 | 11 |
| 3 | 23 | 11 |
| 4 | 32 | 11 |
| 5 | 49 | 11 |
| 6 | 86 | 11 |
| 7 | 122 | 11 |
| 8 | 168 | 11 |
| 9 | 204 | 11 |
| 10 | 230 | 11 |
| 11 | 232 | 11 |
| 0 | 1 | 1 |
| 1× | saturated |
| 1× | saturated |
| Inputs |
|---|
0 |
| Outputs |
|---|
0 |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| Outputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
Compiled 9 to 7 computations (22.2% saved)
| 1× | egg-herbie |
| 39× | fma-def_binary64 |
| 32× | fma-neg_binary64 |
| 15× | cancel-sign-sub-inv_binary64 |
| 12× | sub-neg_binary64 |
| 10× | distribute-rgt-in_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 7 | 11 |
| 1 | 12 | 11 |
| 2 | 16 | 11 |
| 3 | 23 | 11 |
| 4 | 32 | 11 |
| 5 | 49 | 11 |
| 6 | 86 | 11 |
| 7 | 122 | 11 |
| 8 | 168 | 11 |
| 9 | 204 | 11 |
| 10 | 230 | 11 |
| 11 | 232 | 11 |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| Outputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
Compiled 8 to 6 computations (25% 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 |
|---|---|---|
| ▶ | 29.8b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
Compiled 8 to 6 computations (25% saved)
Found 1 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 3.3b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
Compiled 19 to 12 computations (36.8% saved)
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | inf | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 1.0ms | x | @ | -inf | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 1.0ms | x | @ | 0 | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 1× | batch-egg-rewrite |
| 794× | pow1_binary64 |
| 742× | log1p-expm1-u_binary64 |
| 742× | expm1-log1p-u_binary64 |
| 741× | add-log-exp_binary64 |
| 723× | add-exp-log_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 7 | 11 |
| 1 | 153 | 11 |
| 2 | 2111 | 11 |
| 1× | node limit |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (/.f64 1 (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (-.f64 1 x)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4)) (-.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x))) (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (neg.f64 (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 x (-.f64 1 x))) (neg.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 x 1) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))))))) |
| 1× | egg-herbie |
| 1× | 1-exp_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 4 | 1 |
| 1× | saturated |
| Inputs |
|---|
1 |
| Outputs |
|---|
1 |
Compiled 506 to 330 computations (34.8% saved)
8 alts after pruning (7 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 29 | 7 | 36 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 29 | 8 | 37 |
| Status | Error | Program |
|---|---|---|
| 30.2b | (/.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 x 1) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))) | |
| ▶ | 29.8b | (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))) |
| ▶ | 28.9b | (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| ▶ | 29.8b | (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) |
| ✓ | 29.8b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| ▶ | 29.4b | (/.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))) |
| ▶ | 30.0b | (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) |
| 31.1b | 1 |
Compiled 242 to 164 computations (32.2% saved)
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| ✓ | 0.1b | (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| ✓ | 2.4b | (+.f64 x (-.f64 1 x)) |
Compiled 40 to 25 computations (37.5% saved)
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | -inf | (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 2.0ms | x | @ | inf | (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 1.0ms | x | @ | -inf | (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 1.0ms | x | @ | 0 | (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 1.0ms | x | @ | inf | (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 1× | batch-egg-rewrite |
| 689× | fma-def_binary64 |
| 545× | log-prod_binary64 |
| 347× | fma-neg_binary64 |
| 300× | pow2_binary64 |
| 206× | pow1/3_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 38 |
| 1 | 236 | 29 |
| 2 | 3628 | 29 |
| 1× | node limit |
| Inputs |
|---|
(+.f64 x (-.f64 1 x)) |
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 x (-.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (+.f64 (+.f64 x -1) x)) (/.f64 (pow.f64 (-.f64 1 x) 2) (+.f64 (+.f64 x -1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (-.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) (cbrt.f64 (pow.f64 (+.f64 x (-.f64 1 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x (-.f64 1 x)) 2)) (cbrt.f64 (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (sqrt.f64 (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (-.f64 1 x) 3)) (/.f64 1 (fma.f64 (-.f64 1 x) (-.f64 (-.f64 1 x) x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 (-.f64 1 x) 2)) (/.f64 1 (+.f64 (+.f64 x -1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (-.f64 1 x) (-.f64 (-.f64 1 x) x) (*.f64 x x)) (+.f64 (pow.f64 x 3) (pow.f64 (-.f64 1 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 x -1) x) (-.f64 (*.f64 x x) (pow.f64 (-.f64 1 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (-.f64 1 x) 3)) (fma.f64 (-.f64 1 x) (-.f64 (-.f64 1 x) x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (-.f64 1 x) 3)) (+.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (*.f64 x x) (*.f64 x (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (-.f64 1 x) 2)) (+.f64 (+.f64 x -1) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (-.f64 1 x) 3))) (neg.f64 (fma.f64 (-.f64 1 x) (-.f64 (-.f64 1 x) x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (-.f64 1 x) 2))) (neg.f64 (+.f64 (+.f64 x -1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 x 3)) (+.f64 (pow.f64 (+.f64 x 1) 2) (fma.f64 x x (fma.f64 x x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x x)) (+.f64 (+.f64 x 1) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x x)) (-.f64 (-.f64 1 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (-.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (-.f64 1 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (-.f64 1 x)) 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fma.f64 (sqrt.f64 x) 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (*.f64 x x))) (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))) |
| 1× | egg-herbie |
| 1× | 1-exp_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1 | 14 |
| 1 | 4 | 14 |
| 1× | saturated |
| Inputs |
|---|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
| Outputs |
|---|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
Found 2 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (pow.f64 (+.f64 x 1) 1/4) |
| ✓ | 29.8b | (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) |
Compiled 31 to 20 computations (35.5% saved)
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | inf | (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) |
| 2.0ms | x | @ | -inf | (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) |
| 1.0ms | x | @ | inf | (pow.f64 (+.f64 x 1) 1/4) |
| 1.0ms | x | @ | 0 | (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) |
| 1.0ms | x | @ | -inf | (pow.f64 (+.f64 x 1) 1/4) |
| 1× | batch-egg-rewrite |
| 745× | pow1_binary64 |
| 696× | add-log-exp_binary64 |
| 696× | log1p-expm1-u_binary64 |
| 696× | expm1-log1p-u_binary64 |
| 680× | add-exp-log_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 28 |
| 1 | 192 | 18 |
| 2 | 2283 | 18 |
| 1× | node limit |
| Inputs |
|---|
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) |
(pow.f64 (+.f64 x 1) 1/4) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (+.f64 x 1)) 1) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) 0) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) 2) (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3) (pow.f64 x 3/2)) (+.f64 (+.f64 x 1) (-.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 x 1) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/4)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/4) (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/4) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/4) (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/4 (log1p.f64 x))))))) |
| 1× | egg-herbie |
| 583× | fma-def_binary64 |
| 309× | times-frac_binary64 |
| 286× | distribute-rgt-out_binary64 |
| 236× | associate-/l*_binary64 |
| 234× | associate-*l*_binary64 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 55 | 352 |
| 1 | 150 | 337 |
| 2 | 382 | 266 |
| 3 | 1139 | 214 |
| 4 | 4236 | 194 |
| 5 | 6673 | 194 |
| 1× | node limit |
| Inputs |
|---|
1 |
1 |
(+.f64 1 (*.f64 1/4 x)) |
(+.f64 1 (+.f64 (*.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x))) |
(+.f64 1 (+.f64 (*.f64 7/128 (pow.f64 x 3)) (+.f64 (*.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x)))) |
(pow.f64 x 1/4) |
(+.f64 (pow.f64 x 1/4) (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4))) |
(+.f64 (pow.f64 x 1/4) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))) |
(+.f64 (*.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)) (+.f64 (pow.f64 x 1/4) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))) |
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) |
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) |
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))) |
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 7/128 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))) |
| Outputs |
|---|
1 |
1 |
(+.f64 1 (*.f64 1/4 x)) |
(fma.f64 1/4 x 1) |
(+.f64 1 (+.f64 (*.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x))) |
(+.f64 1 (fma.f64 -3/32 (*.f64 x x) (*.f64 1/4 x))) |
(+.f64 (fma.f64 1/4 x 1) (*.f64 x (*.f64 x -3/32))) |
(fma.f64 1/4 x (fma.f64 x (*.f64 x -3/32) 1)) |
(fma.f64 x (fma.f64 x -3/32 1/4) 1) |
(+.f64 1 (+.f64 (*.f64 7/128 (pow.f64 x 3)) (+.f64 (*.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x)))) |
(+.f64 1 (fma.f64 7/128 (pow.f64 x 3) (fma.f64 -3/32 (*.f64 x x) (*.f64 1/4 x)))) |
(+.f64 (fma.f64 7/128 (pow.f64 x 3) (*.f64 x (*.f64 x -3/32))) (fma.f64 1/4 x 1)) |
(fma.f64 7/128 (pow.f64 x 3) (fma.f64 1/4 x (fma.f64 x (*.f64 x -3/32) 1))) |
(fma.f64 1/4 x (fma.f64 (*.f64 x x) (fma.f64 x 7/128 -3/32) 1)) |
(pow.f64 x 1/4) |
(+.f64 (pow.f64 x 1/4) (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4))) |
(fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (pow.f64 x 1/4)) |
(+.f64 (pow.f64 x 1/4) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))) |
(+.f64 (pow.f64 x 1/4) (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))) |
(+.f64 (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (pow.f64 x 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))) |
(fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (fma.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (pow.f64 x 1/4))) |
(+.f64 (*.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)) (+.f64 (pow.f64 x 1/4) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))) |
(fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (+.f64 (pow.f64 x 1/4) (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))) |
(+.f64 (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))) (fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (pow.f64 x 1/4))) |
(fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (fma.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (pow.f64 x 1/4)))) |
(fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (fma.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (pow.f64 x 1/4)))) |
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) |
(pow.f64 x 1/4) |
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) |
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))) |
(fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) |
(fma.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4) (*.f64 1/4 (/.f64 (pow.f64 (/.f64 -1 x) -1/4) (/.f64 x (pow.f64 -1 1/4))))) |
(*.f64 (+.f64 (/.f64 1/4 x) 1) (pow.f64 (exp.f64 1/4) (log.f64 x))) |
(*.f64 (+.f64 1 (/.f64 1/4 x)) (pow.f64 x 1/4)) |
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))) |
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (*.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x))))) |
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (/.f64 (*.f64 1/4 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x))) |
(fma.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) -1/4) (/.f64 x (pow.f64 -1 1/4))) (+.f64 1/4 (/.f64 -3/32 x)))) |
(fma.f64 (/.f64 (pow.f64 (exp.f64 1/4) (log.f64 x)) x) (+.f64 1/4 (/.f64 -3/32 x)) (pow.f64 (exp.f64 1/4) (log.f64 x))) |
(fma.f64 (/.f64 (pow.f64 x 1/4) x) (+.f64 1/4 (/.f64 -3/32 x)) (pow.f64 x 1/4)) |
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 7/128 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))) |
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 7/128 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (*.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)))))) |
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 7/128 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (/.f64 (*.f64 1/4 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)))) |
(fma.f64 7/128 (/.f64 (pow.f64 (/.f64 -1 x) -1/4) (/.f64 (pow.f64 x 3) (pow.f64 -1 1/4))) (fma.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) -1/4) (/.f64 x (pow.f64 -1 1/4))) (+.f64 1/4 (/.f64 -3/32 x))))) |
(+.f64 (pow.f64 (exp.f64 1/4) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 1/4) (log.f64 x)) x) (+.f64 1/4 (+.f64 (/.f64 -3/32 x) (/.f64 7/128 (*.f64 x x)))))) |
(+.f64 (pow.f64 x 1/4) (*.f64 (/.f64 (pow.f64 x 1/4) x) (+.f64 (/.f64 7/128 (*.f64 x x)) (+.f64 1/4 (/.f64 -3/32 x))))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))) |
| ✓ | 0.1b | (/.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))) |
| ✓ | 0.5b | (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) |
| ✓ | 15.4b | (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) |
Compiled 61 to 25 computations (59% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | -inf | (/.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))) |
| 2.0ms | x | @ | -inf | (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) |
| 1.0ms | x | @ | inf | (/.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))) |
| 0.0ms | x | @ | -inf | (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) |
| 0.0ms | x | @ | inf | (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))) |
| 1× | batch-egg-rewrite |
| 466× | fma-def_binary64 |
| 456× | log-prod_binary64 |
| 295× | fma-neg_binary64 |
| 231× | pow2_binary64 |
| 185× | pow-unpow_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 11 | 52 |
| 1 | 268 | 26 |
| 2 | 4088 | 26 |
| 1× | node limit |
| Inputs |
|---|
(-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) |
(*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) |
(/.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))) |
(-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (+.f64 x 1)) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (+.f64 x 1)) (fma.f64 (neg.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 x (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x (+.f64 x 1)))) (fma.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))) (sqrt.f64 (+.f64 x 1))) (*.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x (+.f64 x 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (+.f64 x (+.f64 x 1))))))))) (#(struct:change 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(+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (sqrt.f64 (+.f64 x (+.f64 x 1)))) (+.f64 x (+.f64 1 (fma.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 x (+.f64 x 1)) (sqrt.f64 (+.f64 x (+.f64 x 1)))) (neg.f64 (sqrt.f64 (+.f64 x (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (+.f64 x (+.f64 1 (fma.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))) (-.f64 x (+.f64 x 1))) (neg.f64 (sqrt.f64 (+.f64 x (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 1/6) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 x 1)) -1/2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (+.f64 x (+.f64 x 1)) -1/2) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 x (+.f64 x (+.f64 x 1)) (pow.f64 (+.f64 x 1) 2)) (+.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 x 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 x (+.f64 x 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 x (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (+.f64 x 1))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (exp.f64 (+.f64 x 1)) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (+.f64 x 1))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (exp.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 x) (+.f64 1 (expm1.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (+.f64 1 (expm1.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 x 1))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 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| 1× | egg-herbie |
| 828× | fma-def_binary64 |
| 617× | fma-neg_binary64 |
| 388× | cube-prod_binary64 |
| 361× | associate-*r*_binary64 |
| 328× | distribute-rgt-neg-in_binary64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 12 | 37 |
| 1 | 27 | 29 |
| 2 | 57 | 26 |
| 3 | 129 | 26 |
| 4 | 381 | 26 |
| 5 | 1416 | 26 |
| 6 | 3270 | 26 |
| 7 | 4638 | 26 |
| 8 | 6057 | 26 |
| 1× | unsound |
| Inputs |
|---|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
(*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) |
(+.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) 1) |
(+.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) 1) |
(+.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) 1) |
x |
x |
x |
x |
x |
x |
x |
x |
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) |
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) |
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) |
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) |
1 |
1 |
| Outputs |
|---|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
(*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) |
(*.f64 0 x) |
0 |
(+.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) 1) |
1 |
(+.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) 1) |
1 |
(+.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) 1) |
1 |
x |
x |
x |
x |
x |
x |
x |
x |
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) |
x |
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) |
x |
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) |
x |
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) |
x |
1 |
1 |
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.2b | (cbrt.f64 (sqrt.f64 (+.f64 x 1))) |
| ✓ | 0.3b | (cbrt.f64 (+.f64 x 1)) |
| ✓ | 29.8b | (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) |
Compiled 37 to 24 computations (35.1% saved)
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (cbrt.f64 (sqrt.f64 (+.f64 x 1))) |
| 1.0ms | x | @ | -inf | (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) |
| 1.0ms | x | @ | inf | (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) |
| 1.0ms | x | @ | 0 | (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) |
| 1.0ms | x | @ | inf | (cbrt.f64 (sqrt.f64 (+.f64 x 1))) |
| 1× | batch-egg-rewrite |
| 767× | pow1_binary64 |
| 714× | log1p-expm1-u_binary64 |
| 714× | expm1-log1p-u_binary64 |
| 713× | add-log-exp_binary64 |
| 693× | add-exp-log_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 35 |
| 1 | 200 | 24 |
| 2 | 2397 | 24 |
| 1× | node limit |
| Inputs |
|---|
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) |
(cbrt.f64 (+.f64 x 1)) |
(cbrt.f64 (sqrt.f64 (+.f64 x 1))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) 0) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 x 1) (-.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 x 1) x) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (*.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)) (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 2) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) (*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 1 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/3)))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 1/6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 2)) (sqrt.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 1/3) (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1/2) 1/3)))))) |
| 1× | egg-herbie |
| 717× | fma-def_binary64 |
| 327× | distribute-rgt-out_binary64 |
| 309× | times-frac_binary64 |
| 296× | associate-*l*_binary64 |
| 260× | associate-*r*_binary64 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 66 | 395 |
| 1 | 179 | 372 |
| 2 | 462 | 303 |
| 3 | 1336 | 245 |
| 4 | 4746 | 225 |
| 5 | 7024 | 225 |
| 1× | node limit |
| Inputs |
|---|
1 |
1 |
(+.f64 1 (*.f64 1/3 x)) |
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (*.f64 1/3 x))) |
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 5/81 (pow.f64 x 3)) (*.f64 1/3 x)))) |
1 |
(+.f64 1 (*.f64 1/6 x)) |
(+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 -5/72 (pow.f64 x 2)))) |
(+.f64 (*.f64 55/1296 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 -5/72 (pow.f64 x 2))))) |
(pow.f64 x 1/6) |
(+.f64 (pow.f64 x 1/6) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) |
(+.f64 (pow.f64 x 1/6) (+.f64 (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))) |
(+.f64 (*.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) (+.f64 (pow.f64 x 1/6) (+.f64 (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))))) |
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) |
(+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) |
(+.f64 (*.f64 -5/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))) |
(+.f64 (*.f64 -5/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 55/1296 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))) |
| Outputs |
|---|
1 |
1 |
(+.f64 1 (*.f64 1/3 x)) |
(fma.f64 1/3 x 1) |
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (*.f64 1/3 x))) |
(fma.f64 -1/9 (*.f64 x x) (+.f64 1 (*.f64 1/3 x))) |
(fma.f64 -1/9 (*.f64 x x) (fma.f64 1/3 x 1)) |
(fma.f64 1/3 x (fma.f64 -1/9 (*.f64 x x) 1)) |
(fma.f64 x (fma.f64 x -1/9 1/3) 1) |
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 5/81 (pow.f64 x 3)) (*.f64 1/3 x)))) |
(fma.f64 -1/9 (*.f64 x x) (+.f64 1 (fma.f64 5/81 (pow.f64 x 3) (*.f64 1/3 x)))) |
(+.f64 (fma.f64 5/81 (pow.f64 x 3) (*.f64 1/3 x)) (fma.f64 -1/9 (*.f64 x x) 1)) |
(fma.f64 x (*.f64 x -1/9) (fma.f64 1/3 x (fma.f64 5/81 (pow.f64 x 3) 1))) |
(fma.f64 x (fma.f64 x -1/9 1/3) (fma.f64 5/81 (pow.f64 x 3) 1)) |
1 |
(+.f64 1 (*.f64 1/6 x)) |
(+.f64 1 (*.f64 x 1/6)) |
(fma.f64 x 1/6 1) |
(+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 -5/72 (pow.f64 x 2)))) |
(+.f64 1 (fma.f64 1/6 x (*.f64 (*.f64 x x) -5/72))) |
(+.f64 (fma.f64 x 1/6 1) (*.f64 x (*.f64 x -5/72))) |
(fma.f64 x 1/6 (fma.f64 x (*.f64 x -5/72) 1)) |
(fma.f64 x (fma.f64 x -5/72 1/6) 1) |
(+.f64 (*.f64 55/1296 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 -5/72 (pow.f64 x 2))))) |
(fma.f64 55/1296 (pow.f64 x 3) (+.f64 1 (fma.f64 1/6 x (*.f64 (*.f64 x x) -5/72)))) |
(+.f64 (fma.f64 x 1/6 (*.f64 x (*.f64 x -5/72))) (fma.f64 (pow.f64 x 3) 55/1296 1)) |
(fma.f64 (pow.f64 x 3) 55/1296 (fma.f64 x 1/6 (fma.f64 x (*.f64 x -5/72) 1))) |
(fma.f64 x (fma.f64 x -5/72 1/6) (fma.f64 (pow.f64 x 3) 55/1296 1)) |
(pow.f64 x 1/6) |
(+.f64 (pow.f64 x 1/6) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) |
(fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (pow.f64 x 1/6)) |
(+.f64 (pow.f64 x 1/6) (+.f64 (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))) |
(+.f64 (pow.f64 x 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))) |
(+.f64 (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (pow.f64 x 1/6)) (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))) |
(fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (pow.f64 x 1/6))) |
(+.f64 (*.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) (+.f64 (pow.f64 x 1/6) (+.f64 (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))))) |
(fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (+.f64 (pow.f64 x 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))))) |
(+.f64 (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))) (fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (pow.f64 x 1/6))) |
(fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (pow.f64 x 1/6)))) |
(fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (pow.f64 x 1/6)))) |
(fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (pow.f64 x 1/6)))) |
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) |
(pow.f64 x 1/6) |
(+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) |
(+.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))) |
(fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) |
(fma.f64 1/6 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 -1 1/6)) x) (*.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 -1 1/6))) |
(*.f64 (+.f64 (/.f64 1/6 x) 1) (pow.f64 (exp.f64 1/6) (log.f64 x))) |
(*.f64 (+.f64 1 (/.f64 1/6 x)) (pow.f64 x 1/6)) |
(+.f64 (*.f64 -5/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))) |
(fma.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (+.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))) |
(fma.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) |
(fma.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 -1 1/6) (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 -1 1/6)) x) (+.f64 1/6 (/.f64 -5/72 x)))) |
(fma.f64 (/.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) x) (+.f64 1/6 (/.f64 -5/72 x)) (pow.f64 (exp.f64 1/6) (log.f64 x))) |
(fma.f64 (/.f64 (pow.f64 x 1/6) x) (+.f64 1/6 (/.f64 -5/72 x)) (pow.f64 x 1/6)) |
(+.f64 (*.f64 -5/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 55/1296 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))) |
(fma.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (fma.f64 55/1296 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (+.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))))) |
(fma.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (fma.f64 55/1296 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))) |
(fma.f64 55/1296 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 -1 1/6)) (pow.f64 x 3)) (fma.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 -1 1/6) (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 -1 1/6)) x) (+.f64 1/6 (/.f64 -5/72 x))))) |
(+.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) x) (+.f64 (+.f64 1/6 (/.f64 55/1296 (*.f64 x x))) (/.f64 -5/72 x)))) |
(+.f64 (pow.f64 x 1/6) (*.f64 (/.f64 (pow.f64 x 1/6) x) (+.f64 1/6 (+.f64 (/.f64 55/1296 (*.f64 x x)) (/.f64 -5/72 x))))) |
Found 2 expressions with local error:
| New | Error | Program |
|---|---|---|
| 3.3b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) | |
| ✓ | 61.2b | (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)) |
Compiled 55 to 35 computations (36.4% saved)
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)) |
| 1.0ms | x | @ | 0 | (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)) |
| 1.0ms | x | @ | inf | (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)) |
| 1× | batch-egg-rewrite |
| 522× | pow1_binary64 |
| 507× | add-sqr-sqrt_binary64 |
| 488× | add-log-exp_binary64 |
| 487× | log1p-expm1-u_binary64 |
| 487× | expm1-log1p-u_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 7 | 15 |
| 1 | 150 | 8 |
| 2 | 1755 | 8 |
| 1× | node limit |
| Inputs |
|---|
(fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 x) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) 2) (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)) (+.f64 x (-.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 x x) (-.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))))) |
| 1× | egg-herbie |
| 3× | sub-neg_binary64 |
| 2× | +-commutative_binary64 |
| 2× | fma-def_binary64 |
| 1× | *-commutative_binary64 |
| 1× | associate-+l-_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 5 |
| 1 | 7 | 5 |
| 2 | 9 | 5 |
| 3 | 10 | 5 |
| 4 | 12 | 5 |
| 5 | 16 | 5 |
| 6 | 20 | 5 |
| 7 | 25 | 5 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 -1 (sqrt.f64 x)) |
| Outputs |
|---|
(*.f64 -1 (sqrt.f64 x)) |
(neg.f64 (sqrt.f64 x)) |
Compiled 18593 to 12037 computations (35.3% saved)
5 alts after pruning (4 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 879 | 4 | 883 |
| Fresh | 2 | 0 | 2 |
| Picked | 1 | 0 | 1 |
| Done | 4 | 1 | 5 |
| Total | 886 | 5 | 891 |
| Status | Error | Program |
|---|---|---|
| ✓ | 29.8b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| ▶ | 28.9b | (*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x)))) |
| ▶ | 31.7b | (*.f64 (-.f64 x (+.f64 x 1)) (/.f64 1 (neg.f64 (sqrt.f64 (+.f64 x (+.f64 x 1)))))) |
| 31.1b | 1 | |
| ▶ | 0.1b | (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
Compiled 63 to 47 computations (25.4% saved)
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (sqrt.f64 (+.f64 x (+.f64 x 1))) |
| ✓ | 0.0b | (+.f64 x (+.f64 x 1)) |
| ✓ | 0.2b | (/.f64 1 (neg.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))))) |
| ✓ | 2.4b | (-.f64 x (+.f64 x 1)) |
Compiled 53 to 37 computations (30.2% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | -inf | (/.f64 1 (neg.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))))) |
| 1.0ms | x | @ | inf | (/.f64 1 (neg.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))))) |
| 0.0ms | x | @ | inf | (sqrt.f64 (+.f64 x (+.f64 x 1))) |
| 0.0ms | x | @ | -inf | (sqrt.f64 (+.f64 x (+.f64 x 1))) |
| 0.0ms | x | @ | 0 | (/.f64 1 (neg.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))))) |
| 4× | egg-rewrite |
| 1× | egg-rewrite-iter-limit |
| 1× | batch-egg-rewrite |
| 865× | pow1_binary64 |
| 810× | log1p-expm1-u_binary64 |
| 810× | expm1-log1p-u_binary64 |
| 809× | add-log-exp_binary64 |
| 792× | add-exp-log_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 28 |
| 1 | 208 | 28 |
| 2 | 3365 | 28 |
| 0 | 5 | 7 |
| 1 | 115 | 7 |
| 2 | 1889 | 7 |
| 0 | 5 | 7 |
| 0 | 8 | 14 |
| 1 | 181 | 12 |
| 2 | 2581 | 12 |
| 0 | 5 | 7 |
| 1 | 114 | 7 |
| 2 | 1672 | 7 |
| 0 | 6 | 9 |
| 1 | 134 | 9 |
| 2 | 1893 | 9 |
| 1× | node limit |
| 1× | node limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | unsound |
| 1× | unsound |
| Inputs |
|---|
(-.f64 x (+.f64 x 1)) |
(/.f64 1 (neg.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))))) |
(+.f64 x (+.f64 x 1)) |
(sqrt.f64 (+.f64 x (+.f64 x 1))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (neg.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 x (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (-.f64 x (+.f64 x 1))) (cbrt.f64 (-.f64 x (+.f64 x 1)))) (cbrt.f64 (-.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 x (+.f64 x 1))) (sqrt.f64 (-.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3)) (+.f64 (*.f64 x x) (+.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) (*.f64 x (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (*.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 x (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 x (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (-.f64 x (+.f64 x 1)) (-.f64 x (+.f64 x 1))) (-.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 x (+.f64 x 1)))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (+.f64 x x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (+.f64 x x)))))))) (#(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 (cbrt.f64 (sqrt.f64 (+.f64 1 (+.f64 x x))))) (cbrt.f64 (/.f64 1 (+.f64 1 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (+.f64 1 (+.f64 x x)))) (/.f64 1 (cbrt.f64 (sqrt.f64 (+.f64 1 (+.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 1 (+.f64 x x))) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 (+.f64 x x))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (sqrt.f64 (+.f64 1 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (+.f64 x x))) -1) (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (+.f64 x x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 1 (+.f64 x x)) 1/4) -1) (pow.f64 (pow.f64 (+.f64 1 (+.f64 x x)) 1/4) -1))))) (#(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 (/.f64 1 (sqrt.f64 (+.f64 1 (+.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (+.f64 x x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (+.f64 1 (+.f64 x x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 (+.f64 x x))) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (+.f64 1 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (+.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (+.f64 x x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (+.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (+.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (sqrt.f64 (+.f64 1 (+.f64 x x)))))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (-.f64 (+.f64 x -1) x)) (/.f64 (pow.f64 (+.f64 x 1) 2) (-.f64 (+.f64 x -1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (+.f64 x 1))) (pow.f64 (cbrt.f64 (+.f64 x (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (+.f64 x 1))) 2) (cbrt.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))) (sqrt.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3)) (/.f64 1 (fma.f64 x x (*.f64 (+.f64 x 1) (-.f64 (+.f64 x 1) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x 1) 2)) (/.f64 1 (-.f64 (+.f64 x -1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (*.f64 (+.f64 x 1) (-.f64 (+.f64 x 1) x))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 x -1) x) (-.f64 (*.f64 x x) (pow.f64 (+.f64 x 1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3)) (fma.f64 x x (*.f64 (+.f64 x 1) (-.f64 (+.f64 x 1) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3)) (+.f64 (pow.f64 (+.f64 x 1) 2) (-.f64 (*.f64 x x) (*.f64 x (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x 1) 2)) (-.f64 (+.f64 x -1) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3))) (neg.f64 (fma.f64 x x (*.f64 (+.f64 x 1) (-.f64 (+.f64 x 1) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x 1) 2))) (neg.f64 (-.f64 (+.f64 x -1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x x) 3) 1) (+.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (-.f64 1 (*.f64 (+.f64 x x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x x)) (-.f64 (+.f64 x 1) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 x x) (+.f64 x x)) 1) (-.f64 (+.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (cbrt.f64 (+.f64 x 1)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)) x))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 x 1)))) (cbrt.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 1/4) (pow.f64 (+.f64 x (+.f64 x 1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x (+.f64 x 1))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x (+.f64 x 1))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x (+.f64 x 1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x 1) 2))) (sqrt.f64 (-.f64 (+.f64 x -1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3))) (sqrt.f64 (fma.f64 x x (*.f64 (+.f64 x 1) (-.f64 (+.f64 x 1) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (+.f64 x 1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))))))))) |
| 1× | egg-herbie |
| 826× | fma-def_binary64 |
| 734× | distribute-rgt-neg-in_binary64 |
| 538× | distribute-lft-neg-in_binary64 |
| 469× | unsub-neg_binary64 |
| 296× | neg-sub0_binary64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 29 | 134 |
| 1 | 73 | 134 |
| 2 | 173 | 134 |
| 3 | 551 | 124 |
| 4 | 1381 | 124 |
| 5 | 3050 | 124 |
| 6 | 4808 | 124 |
| 7 | 7460 | 124 |
| 1× | node limit |
| Inputs |
|---|
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
(-.f64 x 1) |
(-.f64 (+.f64 (*.f64 -3/2 (pow.f64 x 2)) x) 1) |
(-.f64 (+.f64 (*.f64 5/2 (pow.f64 x 3)) (+.f64 (*.f64 -3/2 (pow.f64 x 2)) x)) 1) |
1 |
(+.f64 (*.f64 2 x) 1) |
(+.f64 (*.f64 2 x) 1) |
(+.f64 (*.f64 2 x) 1) |
(*.f64 2 x) |
(+.f64 1 (*.f64 2 x)) |
(+.f64 1 (*.f64 2 x)) |
(+.f64 1 (*.f64 2 x)) |
(*.f64 2 x) |
(+.f64 1 (*.f64 2 x)) |
(+.f64 1 (*.f64 2 x)) |
(+.f64 1 (*.f64 2 x)) |
1 |
(+.f64 1 x) |
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)) |
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x))) |
| Outputs |
|---|
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
(-.f64 x 1) |
(+.f64 x -1) |
(-.f64 (+.f64 (*.f64 -3/2 (pow.f64 x 2)) x) 1) |
(+.f64 (fma.f64 -3/2 (*.f64 x x) x) -1) |
(fma.f64 (fma.f64 x -3/2 1) x -1) |
(fma.f64 x (fma.f64 x -3/2 1) -1) |
(-.f64 (+.f64 (*.f64 5/2 (pow.f64 x 3)) (+.f64 (*.f64 -3/2 (pow.f64 x 2)) x)) 1) |
(+.f64 (fma.f64 5/2 (pow.f64 x 3) (fma.f64 -3/2 (*.f64 x x) x)) -1) |
(+.f64 (fma.f64 x (*.f64 x -3/2) (fma.f64 5/2 (pow.f64 x 3) x)) -1) |
(+.f64 x (fma.f64 (*.f64 x x) (fma.f64 x 5/2 -3/2) -1)) |
(+.f64 (fma.f64 (*.f64 x x) (fma.f64 x 5/2 -3/2) x) -1) |
(fma.f64 (*.f64 x x) (fma.f64 x 5/2 -3/2) (+.f64 x -1)) |
1 |
(+.f64 (*.f64 2 x) 1) |
(fma.f64 2 x 1) |
(fma.f64 x 2 1) |
(+.f64 (*.f64 2 x) 1) |
(fma.f64 2 x 1) |
(fma.f64 x 2 1) |
(+.f64 (*.f64 2 x) 1) |
(fma.f64 2 x 1) |
(fma.f64 x 2 1) |
(*.f64 2 x) |
(*.f64 x 2) |
(+.f64 1 (*.f64 2 x)) |
(fma.f64 2 x 1) |
(fma.f64 x 2 1) |
(+.f64 1 (*.f64 2 x)) |
(fma.f64 2 x 1) |
(fma.f64 x 2 1) |
(+.f64 1 (*.f64 2 x)) |
(fma.f64 2 x 1) |
(fma.f64 x 2 1) |
(*.f64 2 x) |
(*.f64 x 2) |
(+.f64 1 (*.f64 2 x)) |
(fma.f64 2 x 1) |
(fma.f64 x 2 1) |
(+.f64 1 (*.f64 2 x)) |
(fma.f64 2 x 1) |
(fma.f64 x 2 1) |
(+.f64 1 (*.f64 2 x)) |
(fma.f64 2 x 1) |
(fma.f64 x 2 1) |
1 |
(+.f64 1 x) |
(+.f64 x 1) |
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)) |
(+.f64 1 (fma.f64 -1/2 (*.f64 x x) x)) |
(+.f64 1 (fma.f64 (*.f64 x x) -1/2 x)) |
(+.f64 x (fma.f64 x (*.f64 x -1/2) 1)) |
(fma.f64 (fma.f64 x -1/2 1) x 1) |
(fma.f64 x (fma.f64 x -1/2 1) 1) |
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x))) |
(+.f64 1 (fma.f64 1/2 (pow.f64 x 3) (fma.f64 -1/2 (*.f64 x x) x))) |
(+.f64 1 (fma.f64 (pow.f64 x 3) 1/2 (fma.f64 (*.f64 x x) -1/2 x))) |
(+.f64 1 (fma.f64 (pow.f64 x 3) 1/2 (fma.f64 x (*.f64 x -1/2) x))) |
(fma.f64 (*.f64 x x) (fma.f64 x 1/2 -1/2) (+.f64 x 1)) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))) |
| ✓ | 0.0b | (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) |
| ✓ | 0.0b | (*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x)))) |
| 2.4b | (+.f64 x (-.f64 1 x)) |
Compiled 94 to 59 computations (37.2% saved)
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 5.0ms | x | @ | 0 | (*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x)))) |
| 2.0ms | x | @ | -inf | (*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x)))) |
| 2.0ms | x | @ | inf | (*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x)))) |
| 1.0ms | x | @ | 0 | (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) |
| 1.0ms | x | @ | inf | (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) |
| 1× | batch-egg-rewrite |
| 527× | fma-neg_binary64 |
| 326× | expm1-udef_binary64 |
| 326× | log1p-udef_binary64 |
| 205× | add-sqr-sqrt_binary64 |
| 200× | pow1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 76 |
| 1 | 392 | 76 |
| 2 | 6131 | 76 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x)))) |
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) |
(-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 768× | times-frac_binary64 |
| 403× | associate-/l*_binary64 |
| 343× | distribute-rgt-in_binary64 |
| 329× | fma-def_binary64 |
| 325× | distribute-lft-in_binary64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 111 | 775 |
| 1 | 318 | 740 |
| 2 | 902 | 678 |
| 3 | 3215 | 571 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 1 (+.f64 1 (pow.f64 x 3/2))) |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) |
(*.f64 3/2 (/.f64 x (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) |
(-.f64 (*.f64 3/2 (/.f64 x (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 5/8 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) |
(/.f64 1 (+.f64 1 (pow.f64 x 3/2))) |
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) |
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (pow.f64 x 2)))) |
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 (*.f64 (-.f64 (+.f64 (*.f64 9/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 1/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (+.f64 1 (pow.f64 x 3/2))))) (pow.f64 x 3)) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (pow.f64 x 2))))) |
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) |
(+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) |
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))) |
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -3/4 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (*.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -9/128 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))) |
(/.f64 1/2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) |
(-.f64 (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))) |
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))) |
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) (*.f64 7/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))) |
1 |
x |
(+.f64 1 x) |
(*.f64 3 x) |
(+.f64 (*.f64 3 x) 1) |
| Outputs |
|---|
(/.f64 1 (+.f64 1 (pow.f64 x 3/2))) |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) |
(+.f64 (*.f64 1/2 (+.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) |
(fma.f64 1/2 (+.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/8)) |
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 1/8)) |
(*.f64 3/2 (/.f64 x (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) |
(/.f64 (*.f64 3/2 x) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) |
(*.f64 3/2 (/.f64 x (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) |
(*.f64 3/2 (/.f64 x (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)))) |
(/.f64 x (/.f64 (exp.f64 (*.f64 3/2 (log.f64 x))) 3/2)) |
(-.f64 (*.f64 3/2 (/.f64 x (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 5/8 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) |
(-.f64 (/.f64 (*.f64 3/2 x) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (/.f64 5/8 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) |
(fma.f64 3/2 (/.f64 x (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (/.f64 -5/8 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) |
(fma.f64 3/2 (/.f64 x (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2))) (/.f64 -5/8 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)))) |
(fma.f64 3/2 (/.f64 x (exp.f64 (*.f64 3/2 (log.f64 x)))) (*.f64 (pow.f64 (exp.f64 -3/2) (log.f64 x)) -5/8)) |
(/.f64 1 (+.f64 1 (pow.f64 x 3/2))) |
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) |
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (/.f64 (*.f64 -3/2 x) (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) |
(fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x 3/2)))) |
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (pow.f64 x 2)))) |
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (*.f64 (-.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 x x)))) |
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (*.f64 (+.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 x x)))) |
(fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (fma.f64 (+.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 x x) (/.f64 1 (+.f64 1 (pow.f64 x 3/2))))) |
(fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (fma.f64 (+.f64 (/.f64 9/4 (pow.f64 (hypot.f64 1 (pow.f64 x 3/4)) 6)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 x x) (/.f64 1 (+.f64 1 (pow.f64 x 3/2))))) |
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 (*.f64 (-.f64 (+.f64 (*.f64 9/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 1/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (+.f64 1 (pow.f64 x 3/2))))) (pow.f64 x 3)) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (pow.f64 x 2))))) |
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (fma.f64 (+.f64 (+.f64 (/.f64 9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 1/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 -3/2 (/.f64 (-.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 1 (pow.f64 x 3/2))))) (pow.f64 x 3) (*.f64 (-.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 x x))))) |
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (fma.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (-.f64 (/.f64 9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (*.f64 3/2 (-.f64 (/.f64 9/4 (*.f64 (+.f64 1 (pow.f64 x 3/2)) (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)))))) (*.f64 (+.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 x x))))) |
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (*.f64 (*.f64 x x) (+.f64 (+.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 x (-.f64 (/.f64 1/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (-.f64 (/.f64 (+.f64 (/.f64 27/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 1 (pow.f64 x 3/2))) (/.f64 9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))))))))) |
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (fma.f64 (pow.f64 x 3) (fma.f64 3/2 (+.f64 (/.f64 3/8 (pow.f64 (hypot.f64 1 (pow.f64 x 3/4)) 6)) (/.f64 -9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 4))) (+.f64 (/.f64 9/16 (pow.f64 (hypot.f64 1 (pow.f64 x 3/4)) 6)) (/.f64 1/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (*.f64 x (+.f64 (/.f64 -3/2 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (*.f64 x (+.f64 (/.f64 9/4 (pow.f64 (hypot.f64 1 (pow.f64 x 3/4)) 6)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))))))) |
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) |
(+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) |
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) |
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))) |
(fma.f64 -1 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16) (*.f64 x x)) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))) |
(-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) x) (/.f64 -3/16 x))) |
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 3/16) (*.f64 x x)))) |
(fma.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 x (/.f64 3/16 x))))) |
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -3/4 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (*.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -9/128 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))) |
(fma.f64 -1 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16) (*.f64 x x)) (fma.f64 -1 (/.f64 (fma.f64 -3/4 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -11/128)) (pow.f64 x 3)) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))) |
(-.f64 (-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -11/128 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 9/64)) (pow.f64 x 3))) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) x) (/.f64 -3/16 x))) |
(-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (fma.f64 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) x) (/.f64 -3/16 x) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 7/128) (pow.f64 x 3)))) |
(fma.f64 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) x) (/.f64 3/16 x) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -7/128) (pow.f64 x 3))))) |
(/.f64 1/2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) |
(/.f64 1/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) |
(/.f64 1/2 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) |
(/.f64 1/2 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2))) |
(*.f64 1/2 (pow.f64 (exp.f64 -3/2) (log.f64 x))) |
(-.f64 (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))) |
(-.f64 (/.f64 1/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (/.f64 3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))) |
(fma.f64 1/2 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (*.f64 -3/8 (/.f64 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) x))) |
(+.f64 (/.f64 1/2 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2))) (/.f64 (/.f64 -3/8 x) (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)))) |
(fma.f64 1/2 (pow.f64 (exp.f64 -3/2) (log.f64 x)) (*.f64 -3/8 (/.f64 (pow.f64 (exp.f64 -3/2) (log.f64 x)) x))) |
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))) |
(+.f64 (/.f64 3/16 (*.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x))) (-.f64 (/.f64 1/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (/.f64 3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))) |
(fma.f64 3/16 (/.f64 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (*.f64 x x)) (fma.f64 1/2 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (*.f64 -3/8 (/.f64 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) x)))) |
(+.f64 (/.f64 1/2 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2))) (+.f64 (/.f64 3/16 (*.f64 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)) (*.f64 x x))) (/.f64 (/.f64 -3/8 x) (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2))))) |
(fma.f64 1/2 (pow.f64 (exp.f64 -3/2) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 -3/2) (log.f64 x)) x) (-.f64 (/.f64 3/16 x) 3/8))) |
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) (*.f64 7/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))) |
(+.f64 (/.f64 3/16 (*.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x))) (-.f64 (/.f64 1/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (+.f64 (/.f64 3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 7/128 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))))) |
(-.f64 (fma.f64 1/2 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (/.f64 3/16 (*.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)))) (fma.f64 3/8 (/.f64 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) x) (/.f64 7/128 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))) |
(+.f64 (/.f64 1/2 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2))) (+.f64 (/.f64 3/16 (*.f64 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)) (*.f64 x x))) (-.f64 (/.f64 (/.f64 -3/8 x) (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2))) (/.f64 (/.f64 7/128 (pow.f64 x 3)) (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)))))) |
(+.f64 (fma.f64 1/2 (pow.f64 (exp.f64 -3/2) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 -3/2) (log.f64 x)) x) (-.f64 (/.f64 3/16 x) 3/8))) (*.f64 (/.f64 (pow.f64 (exp.f64 -3/2) (log.f64 x)) (pow.f64 x 3)) -7/128)) |
1 |
x |
(+.f64 1 x) |
(*.f64 3 x) |
(*.f64 x 3) |
(+.f64 (*.f64 3 x) 1) |
(fma.f64 3 x 1) |
(fma.f64 x 3 1) |
Found 2 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.0b | (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) | |
| ✓ | 0.1b | (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
Compiled 28 to 18 computations (35.7% saved)
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 1.0ms | x | @ | inf | (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 0.0ms | x | @ | 0 | (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 1× | batch-egg-rewrite |
| 905× | pow1_binary64 |
| 845× | log1p-expm1-u_binary64 |
| 845× | expm1-log1p-u_binary64 |
| 844× | add-log-exp_binary64 |
| 823× | add-exp-log_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 14 |
| 1 | 178 | 14 |
| 2 | 2466 | 14 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1) (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (-.f64 x x))) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))))) |
| 1× | egg-herbie |
| 1× | 1-exp_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 4 | 1 |
| 1× | saturated |
| Inputs |
|---|
1 |
| Outputs |
|---|
1 |
Compiled 13303 to 8672 computations (34.8% saved)
10 alts after pruning (8 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 461 | 8 | 469 |
| Fresh | 1 | 0 | 1 |
| Picked | 0 | 1 | 1 |
| Done | 2 | 1 | 3 |
| Total | 464 | 10 | 474 |
| Status | Error | Program |
|---|---|---|
| ▶ | 31.7b | (*.f64 (-.f64 x (+.f64 x 1)) (/.f64 1 (neg.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1)))) |
| ✓ | 29.8b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 14.4b | (*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))))) | |
| ▶ | 30.5b | (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
| 9.3b | (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3)) | |
| ▶ | 0.3b | (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2) |
| 31.1b | 1 | |
| ▶ | 32.1b | (*.f64 (-.f64 x (+.f64 x 1)) (-.f64 x 1)) |
| ▶ | 31.9b | (*.f64 (-.f64 x (+.f64 x 1)) (/.f64 1 (neg.f64 (+.f64 x 1)))) |
| ✓ | 0.1b | (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
Compiled 220 to 174 computations (20.9% saved)
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) |
| ✓ | 0.1b | (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) |
| ✓ | 0.2b | (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2) |
Compiled 41 to 28 computations (31.7% saved)
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 10.0ms | x | @ | -inf | (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2) |
| 4.0ms | x | @ | inf | (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2) |
| 2.0ms | x | @ | 0 | (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2) |
| 2.0ms | x | @ | -inf | (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) |
| 1.0ms | x | @ | inf | (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) |
| 1× | batch-egg-rewrite |
| 441× | fma-def_binary64 |
| 436× | log-prod_binary64 |
| 321× | exp-prod_binary64 |
| 301× | pow-prod-down_binary64 |
| 271× | pow2_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 11 | 39 |
| 1 | 244 | 39 |
| 2 | 2988 | 39 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2) |
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) |
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/4) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -3/4) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/6) 5) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2)) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1) 1)))))) |
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(sqrt.f64 (+.f64 1 x))))))) |
| 1× | egg-herbie |
| 1× | 1-exp_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1 | 3 |
| 1 | 4 | 3 |
| 1× | saturated |
| Inputs |
|---|
1 |
1 |
1 |
| Outputs |
|---|
1 |
1 |
1 |
Found 1 expressions with local error:
| New | Error | Program |
|---|---|---|
| 2.4b | (-.f64 x (+.f64 x 1)) |
Compiled 23 to 15 computations (34.8% saved)
Found 2 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (/.f64 1 (neg.f64 (+.f64 x 1))) |
| 2.4b | (-.f64 x (+.f64 x 1)) |
Compiled 33 to 24 computations (27.3% saved)
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | 0 | (/.f64 1 (neg.f64 (+.f64 x 1))) |
| 0.0ms | x | @ | inf | (/.f64 1 (neg.f64 (+.f64 x 1))) |
| 0.0ms | x | @ | -inf | (/.f64 1 (neg.f64 (+.f64 x 1))) |
| 1× | batch-egg-rewrite |
| 549× | pow1_binary64 |
| 514× | log1p-expm1-u_binary64 |
| 514× | expm1-log1p-u_binary64 |
| 513× | add-log-exp_binary64 |
| 503× | add-exp-log_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 9 |
| 1 | 132 | 7 |
| 2 | 1790 | 7 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 1 (neg.f64 (+.f64 x 1))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (+.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (pow.f64 (+.f64 1 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -2)) (/.f64 1 (cbrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 x))))))) |
| 1× | egg-herbie |
| 599× | fma-def_binary64 |
| 513× | associate-*l*_binary64 |
| 426× | associate-*r*_binary64 |
| 401× | fma-neg_binary64 |
| 377× | difference-of-squares_binary64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 27 | 173 |
| 1 | 70 | 171 |
| 2 | 161 | 164 |
| 3 | 466 | 164 |
| 4 | 1541 | 164 |
| 5 | 6787 | 164 |
| 1× | node limit |
| Inputs |
|---|
-1 |
(-.f64 x 1) |
(-.f64 (+.f64 (*.f64 -1 (pow.f64 x 2)) x) 1) |
(-.f64 (+.f64 (*.f64 -1 (pow.f64 x 2)) (+.f64 (pow.f64 x 3) x)) 1) |
(/.f64 -1 x) |
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 x)) |
(-.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x))) |
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x))) |
(/.f64 -1 x) |
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 x)) |
(-.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x))) |
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x))) |
| Outputs |
|---|
-1 |
(-.f64 x 1) |
(+.f64 x -1) |
(+.f64 -1 x) |
(-.f64 (+.f64 (*.f64 -1 (pow.f64 x 2)) x) 1) |
(+.f64 (fma.f64 -1 (*.f64 x x) x) -1) |
(+.f64 -1 (-.f64 x (*.f64 x x))) |
(-.f64 x (fma.f64 x x 1)) |
(-.f64 (+.f64 (*.f64 -1 (pow.f64 x 2)) (+.f64 (pow.f64 x 3) x)) 1) |
(+.f64 (fma.f64 -1 (*.f64 x x) (+.f64 x (pow.f64 x 3))) -1) |
(+.f64 -1 (-.f64 (+.f64 x (pow.f64 x 3)) (*.f64 x x))) |
(*.f64 (fma.f64 x x 1) (+.f64 -1 x)) |
(*.f64 (+.f64 -1 x) (fma.f64 x x 1)) |
(/.f64 -1 x) |
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 x)) |
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 x)) |
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 x)) |
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 1 x)) |
(-.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x))) |
(-.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))) |
(+.f64 (-.f64 (/.f64 (/.f64 1 x) x) (/.f64 1 x)) (/.f64 -1 (pow.f64 x 3))) |
(+.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 -1 x) (/.f64 1 (pow.f64 x 3)))) |
(+.f64 (/.f64 -1 x) (*.f64 (+.f64 (/.f64 -1 x) 1) (/.f64 1 (*.f64 x x)))) |
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x))) |
(+.f64 (/.f64 1 (pow.f64 x 4)) (-.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))) |
(+.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))) |
(+.f64 (/.f64 (/.f64 1 x) x) (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 -1 x) (/.f64 -1 (pow.f64 x 3))))) |
(+.f64 (+.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 -1 x) (/.f64 1 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4))) |
(+.f64 (+.f64 (/.f64 -1 x) (*.f64 (+.f64 (/.f64 -1 x) 1) (/.f64 1 (*.f64 x x)))) (/.f64 1 (pow.f64 x 4))) |
(/.f64 -1 x) |
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 x)) |
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 x)) |
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 x)) |
(-.f64 (/.f64 (/.f64 1 x) x) (/.f64 1 x)) |
(-.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x))) |
(-.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))) |
(+.f64 (-.f64 (/.f64 (/.f64 1 x) x) (/.f64 1 x)) (/.f64 -1 (pow.f64 x 3))) |
(+.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 -1 x) (/.f64 1 (pow.f64 x 3)))) |
(+.f64 (/.f64 -1 x) (*.f64 (+.f64 (/.f64 -1 x) 1) (/.f64 1 (*.f64 x x)))) |
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x))) |
(+.f64 (/.f64 1 (pow.f64 x 4)) (-.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))) |
(+.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))) |
(+.f64 (/.f64 (/.f64 1 x) x) (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 -1 x) (/.f64 -1 (pow.f64 x 3))))) |
(+.f64 (+.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 -1 x) (/.f64 1 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4))) |
(+.f64 (+.f64 (/.f64 -1 x) (*.f64 (+.f64 (/.f64 -1 x) 1) (/.f64 1 (*.f64 x x)))) (/.f64 1 (pow.f64 x 4))) |
Found 1 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.1b | (sqrt.f64 (/.f64 1 x)) |
Compiled 17 to 13 computations (23.5% saved)
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (sqrt.f64 (/.f64 1 x)) |
| 0.0ms | x | @ | 0 | (sqrt.f64 (/.f64 1 x)) |
| 0.0ms | x | @ | inf | (sqrt.f64 (/.f64 1 x)) |
| 1× | batch-egg-rewrite |
| 399× | pow1_binary64 |
| 386× | add-sqr-sqrt_binary64 |
| 376× | *-un-lft-identity_binary64 |
| 371× | add-log-exp_binary64 |
| 371× | log1p-expm1-u_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 6 |
| 1 | 99 | 4 |
| 2 | 1101 | 4 |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 (/.f64 1 x)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (pow.f64 1 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (pow.f64 1 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 x -1/2)) (sqrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x -2))) (pow.f64 (*.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 -1) (pow.f64 (/.f64 1 (neg.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -1/2)) (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -1/2)) (pow.f64 (*.f64 (cbrt.f64 (pow.f64 x -1/2)) (pow.f64 x -1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (pow.f64 x -1/2))) (pow.f64 (*.f64 (sqrt.f64 (pow.f64 x -1/2)) (pow.f64 x -1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -1/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1/2) (pow.f64 (cbrt.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (sqrt.f64 (pow.f64 x -1/2)) 3) 1/2) (sqrt.f64 (sqrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 x -1/2) (/.f64 1 (cbrt.f64 x))) 1/2) (sqrt.f64 (cbrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (/.f64 1 x) 3/2)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (/.f64 1 x) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 1 x) (/.f64 1 (cbrt.f64 x))) 1/3) (cbrt.f64 (cbrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (pow.f64 x -1/2))) 1/3) (sqrt.f64 (cbrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x -1/2))) 2) 3) (cbrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) -1) (pow.f64 (sqrt.f64 (cbrt.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 x -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 x -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 x))))))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 0 | 0 |
| 1× | saturated |
| Inputs |
|---|
| Outputs |
|---|
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.0b | (+.f64 x (+.f64 x 1)) | |
| ✓ | 0.0b | (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1) |
| ✓ | 0.2b | (/.f64 1 (neg.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1))) |
| 2.4b | (-.f64 x (+.f64 x 1)) |
Compiled 83 to 63 computations (24.1% saved)
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | inf | (/.f64 1 (neg.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1))) |
| 0.0ms | x | @ | -inf | (/.f64 1 (neg.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1))) |
| 0.0ms | x | @ | 0 | (/.f64 1 (neg.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1))) |
| 0.0ms | x | @ | -inf | (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1) |
| 0.0ms | x | @ | inf | (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1) |
| 1× | batch-egg-rewrite |
| 647× | fma-def_binary64 |
| 431× | log-prod_binary64 |
| 365× | fma-neg_binary64 |
| 253× | pow2_binary64 |
| 172× | log-div_binary64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 35 |
| 1 | 240 | 21 |
| 2 | 3830 | 15 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 1 (neg.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1))) |
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (fma.f64 x 2 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 x 2 1) -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 x 2 1) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 x 2 1) -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 x 2 1) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (fma.f64 x 2 1) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (fma.f64 x 2 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x 2 1) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 x 2 1) -1/2)) (cbrt.f64 (/.f64 1 (fma.f64 x 2 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (fma.f64 x 2 1))) (cbrt.f64 (pow.f64 (fma.f64 x 2 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x 2 1) -1/4) (pow.f64 (fma.f64 x 2 1) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (pow.f64 (fma.f64 x 2 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (fma.f64 x 2 1))) (cbrt.f64 (pow.f64 (fma.f64 x 2 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 2 1) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 2 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 2 1) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 x 2 1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 2 1) -3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 2 1) 1/6) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (fma.f64 x 2 1) -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 2 1) 1/4) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 2 1) -1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 2 1) 3/2) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (fma.f64 x 2 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (fma.f64 x 2 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (fma.f64 x 2 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 2 1) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (fma.f64 x 2 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (fma.f64 x 2 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (fma.f64 x 2 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (+.f64 x x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x 2 1) -1/2)) 1)))))) |
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exp.f64 (*.f64 1/2 (log1p.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (+.f64 x x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (+.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (fma.f64 x 2 1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (sqrt.f64 (fma.f64 x 2 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (sqrt.f64 (fma.f64 x 2 1)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x 2 1)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x 2 1)) -1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (sqrt.f64 (fma.f64 x 2 1))) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (sqrt.f64 (fma.f64 x 2 1))) -1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 x 2 1)) (pow.f64 (fma.f64 x 2 1) 1/6) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 x 2 1)) (neg.f64 (pow.f64 (fma.f64 x 2 1) 1/6)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 x 2 1) 1/6) (cbrt.f64 (fma.f64 x 2 1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (fma.f64 x 2 1)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (fma.f64 x 2 1)))) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (fma.f64 x 2 1)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (fma.f64 x 2 1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (fma.f64 x 2 1)))) 2) (*.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (fma.f64 x 2 1)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 x 2 1) 1/4) (pow.f64 (fma.f64 x 2 1) 1/4) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 x 2 1) 1/4) (neg.f64 (pow.f64 (fma.f64 x 2 1) 1/4)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (fma.f64 x 2 1) 1/4)) (hypot.f64 1 (pow.f64 (fma.f64 x 2 1) 1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (fma.f64 x 2 1) 1/4)) (*.f64 (hypot.f64 1 (pow.f64 (fma.f64 x 2 1) 1/4)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (sqrt.f64 (fma.f64 x 2 1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (+.f64 1 (sqrt.f64 (fma.f64 x 2 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 (log1p.f64 (sqrt.f64 (fma.f64 x 2 1))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (fma.f64 x 2 1))) 2) (+.f64 (sqrt.f64 (fma.f64 x 2 1)) 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (fma.f64 x 2 1) 3/2)) (/.f64 1 (-.f64 (+.f64 1 (fma.f64 x 2 1)) (sqrt.f64 (fma.f64 x 2 1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 2 (log1p.f64 (sqrt.f64 (fma.f64 x 2 1))))) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 x 2 1)) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (fma.f64 x 2 1)) (/.f64 1 (+.f64 1 (sqrt.f64 (fma.f64 x 2 1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 x 2 1)) -1)) 2) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 x 2 1)) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 x 2 1)) -1)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 x 2 1)) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (fma.f64 x 2 1) 1/4)) (pow.f64 (fma.f64 x 2 1) 1/4) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 x 2 1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (hypot.f64 1 (pow.f64 (fma.f64 x 2 1) 1/4)) 1) (-.f64 (hypot.f64 1 (pow.f64 (fma.f64 x 2 1) 1/4)) 1) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 (fma.f64 x 2 1) 1/4) 1) (-.f64 (pow.f64 (fma.f64 x 2 1) 1/4) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (fma.f64 x 2 1))) (pow.f64 (fma.f64 x 2 1) 1/6) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1 (cbrt.f64 (fma.f64 x 2 1))) (pow.f64 (fma.f64 x 2 1) 1/6) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1 (pow.f64 (fma.f64 x 2 1) 1/4)) (pow.f64 (fma.f64 x 2 1) 1/4) 0))))) |
| 1× | egg-herbie |
| 819× | fma-def_binary64 |
| 734× | distribute-rgt-neg-in_binary64 |
| 538× | distribute-lft-neg-in_binary64 |
| 469× | unsub-neg_binary64 |
| 296× | neg-sub0_binary64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 26 | 68 |
| 1 | 68 | 68 |
| 2 | 167 | 68 |
| 3 | 530 | 58 |
| 4 | 1383 | 58 |
| 5 | 3048 | 58 |
| 6 | 4811 | 58 |
| 7 | 7446 | 58 |
| 1× | node limit |
| Inputs |
|---|
-1 |
(-.f64 x 1) |
(-.f64 (+.f64 (*.f64 -3/2 (pow.f64 x 2)) x) 1) |
(-.f64 (+.f64 (*.f64 5/2 (pow.f64 x 3)) (+.f64 (*.f64 -3/2 (pow.f64 x 2)) x)) 1) |
1 |
(+.f64 1 x) |
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)) |
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x))) |
| Outputs |
|---|
-1 |
(-.f64 x 1) |
(+.f64 x -1) |
(-.f64 (+.f64 (*.f64 -3/2 (pow.f64 x 2)) x) 1) |
(+.f64 (fma.f64 -3/2 (*.f64 x x) x) -1) |
(+.f64 x (fma.f64 x (*.f64 x -3/2) -1)) |
(fma.f64 (fma.f64 x -3/2 1) x -1) |
(fma.f64 x (fma.f64 x -3/2 1) -1) |
(-.f64 (+.f64 (*.f64 5/2 (pow.f64 x 3)) (+.f64 (*.f64 -3/2 (pow.f64 x 2)) x)) 1) |
(+.f64 (fma.f64 5/2 (pow.f64 x 3) (fma.f64 -3/2 (*.f64 x x) x)) -1) |
(+.f64 (fma.f64 -3/2 (*.f64 x x) x) (fma.f64 5/2 (pow.f64 x 3) -1)) |
(+.f64 x (fma.f64 x (*.f64 x (fma.f64 x 5/2 -3/2)) -1)) |
(+.f64 x (fma.f64 (*.f64 x x) (fma.f64 x 5/2 -3/2) -1)) |
1 |
(+.f64 1 x) |
(+.f64 x 1) |
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)) |
(+.f64 1 (fma.f64 -1/2 (*.f64 x x) x)) |
(+.f64 1 (fma.f64 (*.f64 x x) -1/2 x)) |
(+.f64 x (fma.f64 (*.f64 x x) -1/2 1)) |
(fma.f64 (fma.f64 x -1/2 1) x 1) |
(fma.f64 x (fma.f64 x -1/2 1) 1) |
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x))) |
(+.f64 1 (fma.f64 1/2 (pow.f64 x 3) (fma.f64 -1/2 (*.f64 x x) x))) |
(+.f64 1 (fma.f64 (pow.f64 x 3) 1/2 (fma.f64 (*.f64 x x) -1/2 x))) |
(+.f64 1 (fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 3) 1/2 x))) |
(fma.f64 x (*.f64 x (fma.f64 x 1/2 -1/2)) (+.f64 x 1)) |
(+.f64 x (fma.f64 (*.f64 x x) (fma.f64 x 1/2 -1/2) 1)) |
Compiled 8067 to 6366 computations (21.1% saved)
14 alts after pruning (10 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 432 | 8 | 440 |
| Fresh | 1 | 2 | 3 |
| Picked | 1 | 0 | 1 |
| Done | 2 | 4 | 6 |
| Total | 436 | 14 | 450 |
| Status | Error | Program |
|---|---|---|
| ✓ | 29.8b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 14.4b | (*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))))) | |
| 30.4b | (*.f64 1/2 (pow.f64 x -1/2)) | |
| 32.8b | (*.f64 -1 (-.f64 x 1)) | |
| 31.0b | (*.f64 -1 (/.f64 1 (neg.f64 (+.f64 x 1)))) | |
| ✓ | 32.1b | (*.f64 (-.f64 x (+.f64 x 1)) (-.f64 x 1)) |
| 60.9b | (*.f64 (-.f64 x (+.f64 x 1)) (/.f64 -1 x)) | |
| 31.1b | 1 | |
| 32.5b | (*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 x (+.f64 x 1))) (/.f64 1 (neg.f64 (+.f64 x 1)))) | |
| 26.8b | (*.f64 -1 (/.f64 1 (neg.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1)))) | |
| 32.7b | (*.f64 1/2 (exp.f64 (*.f64 -1/2 (log.f64 x)))) | |
| ✓ | 30.5b | (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
| 40.2b | (*.f64 1/2 (cbrt.f64 (pow.f64 (/.f64 1 x) 3/2))) | |
| ✓ | 0.1b | (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
Compiled 151 to 120 computations (20.5% saved)
| Inputs |
|---|
1 |
1 |
1 |
(*.f64 -1 (-.f64 x 1)) |
(*.f64 -1 (/.f64 1 (neg.f64 (+.f64 x 1)))) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 -1 x)) |
(*.f64 (-.f64 x (+.f64 x 1)) (-.f64 x 1)) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 1 (neg.f64 (+.f64 x 1)))) |
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 x (+.f64 x 1))) (/.f64 1 (neg.f64 (+.f64 x 1)))) |
(*.f64 1/2 (pow.f64 x -1/2)) |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
(*.f64 -1 (/.f64 1 (neg.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1)))) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 1 (neg.f64 (sqrt.f64 (+.f64 x (+.f64 x 1)))))) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 1 (neg.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1)))) |
(*.f64 1/2 (exp.f64 (*.f64 -1/2 (log.f64 x)))) |
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
(*.f64 1/2 (cbrt.f64 (pow.f64 (/.f64 1 x) 3/2))) |
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))))) |
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2) |
(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3)) |
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) |
(/.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))) |
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x)))) |
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) |
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))) |
(/.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 x 1) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))) |
| Outputs |
|---|
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
3 calls:
| 13.0ms | x |
| 8.0ms | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 5.0ms | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| Error | Segments | Branch |
|---|---|---|
| 0.1b | 1 | x |
| 0.1b | 1 | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 0.1b | 1 | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
Compiled 363 to 252 computations (30.6% saved)
| Inputs |
|---|
1 |
1 |
1 |
(*.f64 -1 (-.f64 x 1)) |
(*.f64 -1 (/.f64 1 (neg.f64 (+.f64 x 1)))) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 -1 x)) |
(*.f64 (-.f64 x (+.f64 x 1)) (-.f64 x 1)) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 1 (neg.f64 (+.f64 x 1)))) |
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 x (+.f64 x 1))) (/.f64 1 (neg.f64 (+.f64 x 1)))) |
(*.f64 1/2 (pow.f64 x -1/2)) |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
(*.f64 -1 (/.f64 1 (neg.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1)))) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 1 (neg.f64 (sqrt.f64 (+.f64 x (+.f64 x 1)))))) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 1 (neg.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1)))) |
(*.f64 1/2 (exp.f64 (*.f64 -1/2 (log.f64 x)))) |
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
(*.f64 1/2 (cbrt.f64 (pow.f64 (/.f64 1 x) 3/2))) |
| Outputs |
|---|
(*.f64 1/2 (pow.f64 x -1/2)) |
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
3 calls:
| 15.0ms | x |
| 6.0ms | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 6.0ms | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| Error | Segments | Branch |
|---|---|---|
| 0.3b | 2 | x |
| 0.3b | 2 | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 0.3b | 2 | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
Compiled 171 to 132 computations (22.8% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 3.8251891965046525e-6 | 0.03332064105008392 |
Compiled 12 to 9 computations (25% saved)
| Inputs |
|---|
1 |
1 |
1 |
(*.f64 -1 (-.f64 x 1)) |
(*.f64 -1 (/.f64 1 (neg.f64 (+.f64 x 1)))) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 -1 x)) |
(*.f64 (-.f64 x (+.f64 x 1)) (-.f64 x 1)) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 1 (neg.f64 (+.f64 x 1)))) |
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 x (+.f64 x 1))) (/.f64 1 (neg.f64 (+.f64 x 1)))) |
(*.f64 1/2 (pow.f64 x -1/2)) |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
(*.f64 -1 (/.f64 1 (neg.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1)))) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 1 (neg.f64 (sqrt.f64 (+.f64 x (+.f64 x 1)))))) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 1 (neg.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x (+.f64 x 1)))) 1)))) |
(*.f64 1/2 (exp.f64 (*.f64 -1/2 (log.f64 x)))) |
| Outputs |
|---|
(*.f64 (-.f64 x (+.f64 x 1)) (-.f64 x 1)) |
(*.f64 1/2 (pow.f64 x -1/2)) |
1 calls:
| 50.0ms | x |
| Error | Segments | Branch |
|---|---|---|
| 1.9b | 2 | x |
Compiled 140 to 108 computations (22.9% saved)
| 1× | binary-search |
| Time | Left | Right |
|---|---|---|
| 35.0ms | 0.07676580519094359 | 224.67172130447653 |
Compiled 12 to 9 computations (25% saved)
| Inputs |
|---|
1 |
1 |
1 |
(*.f64 -1 (-.f64 x 1)) |
(*.f64 -1 (/.f64 1 (neg.f64 (+.f64 x 1)))) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 -1 x)) |
(*.f64 (-.f64 x (+.f64 x 1)) (-.f64 x 1)) |
(*.f64 (-.f64 x (+.f64 x 1)) (/.f64 1 (neg.f64 (+.f64 x 1)))) |
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 x (+.f64 x 1))) (/.f64 1 (neg.f64 (+.f64 x 1)))) |
| Outputs |
|---|
(*.f64 -1 (/.f64 1 (neg.f64 (+.f64 x 1)))) |
1 calls:
| 12.0ms | x |
| Error | Segments | Branch |
|---|---|---|
| 31.0b | 1 | x |
Compiled 73 to 54 computations (26% saved)
Total -1.8b remaining (-5.8%)
Threshold costs -1.8b (-5.8%)
| Inputs |
|---|
1 |
1 |
1 |
(*.f64 -1 (-.f64 x 1)) |
| Outputs |
|---|
1 |
1 calls:
| 8.0ms | x |
| Error | Segments | Branch |
|---|---|---|
| 31.1b | 1 | x |
Compiled 11 to 9 computations (18.2% saved)
| 1× | egg-herbie |
| 9× | +-commutative_binary64 |
| 7× | sub-neg_binary64 |
| 6× | *-commutative_binary64 |
| 4× | neg-sub0_binary64 |
| 3× | neg-mul-1_binary64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 27 | 86 |
| 1 | 44 | 84 |
| 2 | 56 | 82 |
| 3 | 63 | 82 |
| 4 | 66 | 82 |
| 1× | fuel |
| 1× | saturated |
| Inputs |
|---|
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 5902958103587057/1180591620717411303424) (*.f64 1/2 (pow.f64 x -1/2)) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
(if (<=.f64 x 1416079161969580544/18446744073709551616) (*.f64 (-.f64 x (+.f64 x 1)) (-.f64 x 1)) (*.f64 1/2 (pow.f64 x -1/2))) |
(*.f64 -1 (/.f64 1 (neg.f64 (+.f64 x 1)))) |
1 |
| Outputs |
|---|
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) |
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 5902958103587057/1180591620717411303424) (*.f64 1/2 (pow.f64 x -1/2)) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 5902958103587057/1180591620717411303424) (*.f64 1/2 (pow.f64 x -1/2)) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) |
(if (<=.f64 x 1416079161969580544/18446744073709551616) (*.f64 (-.f64 x (+.f64 x 1)) (-.f64 x 1)) (*.f64 1/2 (pow.f64 x -1/2))) |
(if (<=.f64 x 2765779613221837/36028797018963968) (*.f64 (-.f64 x (+.f64 1 x)) (+.f64 x -1)) (*.f64 1/2 (pow.f64 x -1/2))) |
(if (<=.f64 x 2765779613221837/36028797018963968) (*.f64 (+.f64 x (-.f64 -1 x)) (+.f64 x -1)) (*.f64 1/2 (pow.f64 x -1/2))) |
(*.f64 -1 (/.f64 1 (neg.f64 (+.f64 x 1)))) |
(neg.f64 (/.f64 1 (+.f64 (neg.f64 x) -1))) |
(/.f64 -1 (+.f64 -1 (neg.f64 x))) |
(/.f64 -1 (-.f64 -1 x)) |
1 |
Compiled 60 to 46 computations (23.3% saved)
Compiled 56 to 41 computations (26.8% saved)
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