Time bar (total: 6.8s)
| 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)
| 571.0ms | 4996× | body | 256 | valid |
| 539.0ms | 2031× | body | 1024 | valid |
| 158.0ms | 1003× | body | 512 | valid |
| 66.0ms | 226× | body | 2048 | valid |
| 1.0ms | 9× | 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 |
|---|---|---|
| ▶ | 30.3b | (-.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 |
|---|---|---|
| ✓ | 5.1b | (-.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 | @ | 0 | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 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× | 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)
10 alts after pruning (9 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 27 | 9 | 36 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 27 | 10 | 37 |
| Status | Error | Program |
|---|---|---|
| ▶ | 30.2b | (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) |
| ▶ | 29.2b | (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 30.3b | (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) | |
| ✓ | 30.3b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 29.8b | (/.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)))) | |
| 30.3b | (+.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))) | |
| ▶ | 30.7b | (+.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))) |
| ▶ | 30.5b | (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) |
| 32.4b | 1 | |
| ▶ | 30.3b | (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) |
Compiled 254 to 180 computations (29.1% 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))) |
| ✓ | 3.9b | (+.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 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| ✓ | 0.0b | (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) |
| 5.1b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
Compiled 36 to 23 computations (36.1% saved)
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | inf | (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 2.0ms | x | @ | 0 | (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 2.0ms | x | @ | -inf | (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 1.0ms | x | @ | inf | (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) |
| 0.0ms | x | @ | 0 | (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) |
| 1× | batch-egg-rewrite |
| 875× | pow1_binary64 |
| 817× | expm1-log1p-u_binary64 |
| 816× | log1p-expm1-u_binary64 |
| 815× | add-log-exp_binary64 |
| 795× | add-exp-log_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 24 |
| 1 | 174 | 24 |
| 2 | 2319 | 24 |
| 1× | node limit |
| Inputs |
|---|
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) |
(log1p.f64 (-.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 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) -1)))) (#(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 (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 (pow.f64 (+.f64 x 1) 3/2) (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x))))) (/.f64 (pow.f64 x 3/2) (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) (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 1 (+.f64 (+.f64 x 1) (+.f64 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 x 1) (+.f64 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 x 1) (+.f64 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 x 1) (+.f64 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 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3) 1) (+.f64 (*.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (+.f64 1 (*.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1))))))) (#(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 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1) (+.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1))))) (#(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 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))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (pow.f64 (cbrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2) (cbrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (sqrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))) |
| 1× | egg-herbie |
| 1× | 1-exp_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 4 |
| 1 | 6 | 4 |
| 1× | saturated |
| Inputs |
|---|
1 |
(log.f64 2) |
| Outputs |
|---|
1 |
(log.f64 2) |
Found 1 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 30.4b | (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)
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | 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 | (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) |
| 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× | 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 | 21 |
| 1 | 192 | 11 |
| 2 | 2283 | 11 |
| 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))) |
| 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))))))))) |
| 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 |
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.3b | (cbrt.f64 (sqrt.f64 (+.f64 x 1))) |
| ✓ | 0.3b | (cbrt.f64 (+.f64 x 1)) |
| ✓ | 30.4b | (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 | |
|---|---|---|---|---|
| 5.0ms | x | @ | -inf | (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) |
| 3.0ms | 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 | (cbrt.f64 (sqrt.f64 (+.f64 x 1))) |
| 1.0ms | x | @ | -inf | (cbrt.f64 (sqrt.f64 (+.f64 x 1))) |
| 1.0ms | x | @ | 0 | (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) |
| 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 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.6b | (cbrt.f64 (sqrt.f64 x)) |
| ✓ | 0.7b | (cbrt.f64 x) |
| 5.1b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) | |
| ✓ | 61.5b | (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)) |
Compiled 54 to 21 computations (61.1% saved)
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 22.0ms | x | @ | 0 | (cbrt.f64 (sqrt.f64 x)) |
| 6.0ms | x | @ | inf | (cbrt.f64 (sqrt.f64 x)) |
| 2.0ms | x | @ | -inf | (cbrt.f64 (sqrt.f64 x)) |
| 2.0ms | x | @ | -inf | (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)) |
| 1.0ms | x | @ | 0 | (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)) |
| 1× | batch-egg-rewrite |
| 494× | pow1_binary64 |
| 475× | add-sqr-sqrt_binary64 |
| 460× | add-log-exp_binary64 |
| 459× | log1p-expm1-u_binary64 |
| 459× | expm1-log1p-u_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 7 | 23 |
| 1 | 138 | 15 |
| 2 | 1648 | 15 |
| 1× | node limit |
| Inputs |
|---|
(fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)) |
(cbrt.f64 x) |
(cbrt.f64 (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)))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/6) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 x)) (*.f64 (cbrt.f64 (pow.f64 x 1/6)) (pow.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 x x))) (cbrt.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/4) (pow.f64 (sqrt.f64 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 x) 1/6) (*.f64 (pow.f64 (sqrt.f64 x) 1/6) (pow.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x x)) 1/3) (cbrt.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x 1/6) (cbrt.f64 (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 x))))))) |
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 x 1/6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/6) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 x)) (neg.f64 (cbrt.f64 (pow.f64 x 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x 1/6)) (cbrt.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 x) 1/6) (pow.f64 (sqrt.f64 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 x) 1/6) (neg.f64 (pow.f64 (sqrt.f64 x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (cbrt.f64 (*.f64 x x)))) (sqrt.f64 (cbrt.f64 (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 x 1/4) 1/3) (pow.f64 (pow.f64 x 1/4) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (sqrt.f64 x) 1/6)) (pow.f64 (sqrt.f64 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (cbrt.f64 (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (pow.f64 (sqrt.f64 x) 1/6)) (pow.f64 (sqrt.f64 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (sqrt.f64 x)) (+.f64 0 (+.f64 (cbrt.f64 x) (*.f64 0 (pow.f64 x 1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (cbrt.f64 x)) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 x 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 x) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 x 1/6))))))) |
| 1× | egg-herbie |
| 1004× | sqr-pow_binary64 |
| 806× | associate-*l*_binary64 |
| 562× | cube-prod_binary64 |
| 555× | associate-*r*_binary64 |
| 515× | *-commutative_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 84 |
| 1 | 31 | 84 |
| 2 | 55 | 84 |
| 3 | 125 | 84 |
| 4 | 483 | 84 |
| 5 | 2646 | 84 |
| 6 | 2722 | 84 |
| 7 | 2889 | 84 |
| 8 | 3085 | 84 |
| 9 | 3327 | 84 |
| 10 | 3659 | 84 |
| 11 | 4386 | 84 |
| 12 | 4928 | 84 |
| 13 | 5656 | 84 |
| 14 | 6103 | 84 |
| 15 | 6501 | 84 |
| 16 | 6829 | 84 |
| 17 | 7153 | 84 |
| 18 | 7341 | 84 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) 1) 1/3)) |
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) 1) 1/3)) |
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) 1) 1/3)) |
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) 1) 1/3)) |
| Outputs |
|---|
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(pow.f64 x 1/6) |
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) 1) 1/3)) |
(*.f64 (pow.f64 (neg.f64 x) 1/6) (cbrt.f64 (sqrt.f64 -1))) |
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) 1) 1/3)) |
(*.f64 (pow.f64 (neg.f64 x) 1/6) (cbrt.f64 (sqrt.f64 -1))) |
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) 1) 1/3)) |
(*.f64 (pow.f64 (neg.f64 x) 1/6) (cbrt.f64 (sqrt.f64 -1))) |
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) 1) 1/3)) |
(*.f64 (pow.f64 (neg.f64 x) 1/6) (cbrt.f64 (sqrt.f64 -1))) |
Compiled 12356 to 7594 computations (38.5% saved)
7 alts after pruning (6 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 626 | 5 | 631 |
| Fresh | 3 | 1 | 4 |
| Picked | 1 | 0 | 1 |
| Done | 4 | 1 | 5 |
| Total | 634 | 7 | 641 |
| Status | Error | Program |
|---|---|---|
| ▶ | 29.3b | (/.f64 (+.f64 x (-.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3)) |
| 32.4b | 1 | |
| ▶ | 30.3b | (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) |
| ✓ | 30.3b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| ▶ | 29.2b | (/.f64 (+.f64 x (-.f64 1 x)) (expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) |
| ▶ | 30.3b | (-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1) |
| ▶ | 0.2b | (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
Compiled 142 to 112 computations (21.1% saved)
Found 2 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.0b | (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) | |
| ✓ | 0.2b | (/.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 |
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| ✓ | 3.8b | (-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1) |
| 5.1b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
Compiled 39 to 26 computations (33.3% saved)
6 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))) |
| 1.0ms | x | @ | inf | (-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1) |
| 0.0ms | x | @ | -inf | (-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1) |
| 0.0ms | x | @ | 0 | (-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1) |
| 1× | batch-egg-rewrite |
| 716× | fma-def_binary64 |
| 411× | log-prod_binary64 |
| 390× | fma-neg_binary64 |
| 306× | pow-prod-down_binary64 |
| 248× | pow2_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 31 |
| 1 | 216 | 25 |
| 2 | 3299 | 25 |
| 1× | node limit |
| Inputs |
|---|
(-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1) |
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1 x)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1 x)) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (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 1 x)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/6)) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (neg.f64 (sqrt.f64 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 0 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(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 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))))) (#(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 *.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (*.f64 3 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (/.f64 1 (+.f64 1 (+.f64 x (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (*.f64 2 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (-.f64 x x)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1) (expm1.f64 (*.f64 1/2 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) (-.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2)) (expm1.f64 (*.f64 3 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2) (expm1.f64 (*.f64 2 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 x (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))) (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 1 (-.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (*.f64 3 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (+.f64 (pow.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (*.f64 3 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (+.f64 (pow.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (-.f64 1 (*.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 1 (+.f64 x (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (*.f64 2 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 (*.f64 3 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 (*.f64 2 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (neg.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (neg.f64 (+.f64 1 (+.f64 x (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (-.f64 x x))) (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1) 3)) (+.f64 1 (-.f64 (pow.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1) 2) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 1 x) (-.f64 (pow.f64 (neg.f64 (sqrt.f64 x)) 2) (*.f64 (sqrt.f64 (+.f64 1 x)) (neg.f64 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1) 2)) (-.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1)))))) (#(struct:change #<rule egg-rr> (2) 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| 1× | egg-herbie |
| 1× | 1-exp_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 2 | 3 |
| 1 | 5 | 3 |
| 1× | saturated |
| Inputs |
|---|
1 |
2 |
1 |
| Outputs |
|---|
1 |
2 |
1 |
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| ✓ | 0.1b | (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) |
| 5.1b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
Compiled 38 to 25 computations (34.2% saved)
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 12.0ms | x | @ | inf | (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) |
| 2.0ms | x | @ | -inf | (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) |
| 2.0ms | x | @ | inf | (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 1.0ms | x | @ | -inf | (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 1.0ms | x | @ | 0 | (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) |
| 1× | batch-egg-rewrite |
| 923× | pow1_binary64 |
| 862× | add-log-exp_binary64 |
| 862× | log1p-expm1-u_binary64 |
| 862× | expm1-log1p-u_binary64 |
| 840× | add-exp-log_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 24 |
| 1 | 217 | 24 |
| 2 | 2520 | 24 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) |
(sqrt.f64 (-.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 (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 (pow.f64 (+.f64 x 1) 3/2) (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x))))) (/.f64 (pow.f64 x 3/2) (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) (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 (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 (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 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (*.f64 (cbrt.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 (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 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1/4) (*.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1/4) (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 x 1) (+.f64 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 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1/4)) (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1/4))))) (#(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 (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (cbrt.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 x 1) (+.f64 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 x 1) (+.f64 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 x 1) (+.f64 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 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))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.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))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (cbrt.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1/4) (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (sqrt.f64 (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.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)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.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)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))) |
| 1× | egg-herbie |
| 1× | 1-exp_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1 | 2 |
| 1 | 4 | 2 |
| 1× | saturated |
| Inputs |
|---|
1 |
1 |
| Outputs |
|---|
1 |
1 |
Found 4 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)) (expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) |
| ✓ | 2.4b | (expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) |
| 3.9b | (+.f64 x (-.f64 1 x)) |
Compiled 59 to 38 computations (35.6% saved)
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (/.f64 (+.f64 x (-.f64 1 x)) (expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) |
| 1.0ms | x | @ | inf | (/.f64 (+.f64 x (-.f64 1 x)) (expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) |
| 1.0ms | x | @ | -inf | (expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) |
| 0.0ms | x | @ | inf | (expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) |
| 0.0ms | x | @ | 0 | (expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) |
| 1× | batch-egg-rewrite |
| 703× | fma-def_binary64 |
| 583× | log-prod_binary64 |
| 358× | fma-neg_binary64 |
| 320× | pow2_binary64 |
| 220× | pow1/3_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 12 | 31 |
| 1 | 257 | 22 |
| 2 | 3839 | 22 |
| 1× | node limit |
| Inputs |
|---|
(expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) |
(/.f64 (+.f64 x (-.f64 1 x)) (expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) |
| 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 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (+.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 (+.f64 x 1) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) (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 (+.f64 x (-.f64 1 x)) (/.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.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 (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4)) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (/.f64 1 (-.f64 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(#(struct:change #<rule egg-rr> (2) ((x fma.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 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))))))) |
| 1× | egg-herbie |
| 1× | 1-exp_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1 | 2 |
| 1 | 4 | 2 |
| 1× | saturated |
| Inputs |
|---|
1 |
1 |
| Outputs |
|---|
1 |
1 |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.1b | (/.f64 (+.f64 x (-.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3)) |
| ✓ | 0.3b | (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| ✓ | 0.4b | (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3) |
| 3.9b | (+.f64 x (-.f64 1 x)) |
Compiled 62 to 41 computations (33.9% saved)
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 19.0ms | x | @ | -inf | (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3) |
| 17.0ms | x | @ | inf | (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3) |
| 5.0ms | x | @ | -inf | (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 4.0ms | x | @ | 0 | (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3) |
| 3.0ms | x | @ | -inf | (/.f64 (+.f64 x (-.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3)) |
| 1× | batch-egg-rewrite |
| 708× | fma-def_binary64 |
| 622× | log-prod_binary64 |
| 355× | fma-neg_binary64 |
| 228× | expm1-udef_binary64 |
| 228× | log1p-udef_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 44 |
| 1 | 304 | 35 |
| 2 | 4134 | 35 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3) |
(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
(/.f64 (+.f64 x (-.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3)) |
| 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 0 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (cbrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (log.f64 (cbrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 x 1) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (/.f64 x (-.f64 (sqrt.f64 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(sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (/.f64 (+.f64 1 (-.f64 x x)) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (/.f64 (+.f64 1 (-.f64 x x)) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1 (-.f64 x x)) 2)) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (/.f64 (cbrt.f64 (+.f64 1 (-.f64 x x))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1 (-.f64 x x)) 2)) 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x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))) (/.f64 (+.f64 1 (-.f64 x x)) (cbrt.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 fma.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1 (-.f64 x x)) 2)) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))) (cbrt.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 fma.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1 (-.f64 x x)) 2)) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))) (cbrt.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 fma.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1 (-.f64 x x)) 2)) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))) (cbrt.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 fma.f64 (/.f64 1 (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (/.f64 (+.f64 1 (-.f64 x x)) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (/.f64 (+.f64 1 (-.f64 x x)) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (/.f64 (+.f64 1 (-.f64 x x)) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1 (-.f64 x x)) 2)) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (/.f64 (cbrt.f64 (+.f64 1 (-.f64 x x))) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1 (-.f64 x x)) 2)) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (/.f64 (cbrt.f64 (+.f64 1 (-.f64 x x))) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 1 (-.f64 x x)) 2)) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (/.f64 (cbrt.f64 (+.f64 1 (-.f64 x x))) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 1 (-.f64 x x))) (-.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 fma.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 1 (-.f64 x x))) (-.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 fma.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 1 (-.f64 x x))) (-.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 fma.f64 (/.f64 (+.f64 1 (-.f64 x 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 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (+.f64 1 (-.f64 x 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 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (+.f64 1 (-.f64 x 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 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 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 |
Compiled 24274 to 16078 computations (33.8% saved)
11 alts after pruning (8 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1158 | 8 | 1166 |
| Fresh | 1 | 0 | 1 |
| Picked | 1 | 0 | 1 |
| Done | 2 | 3 | 5 |
| Total | 1162 | 11 | 1173 |
| Status | Error | Program |
|---|---|---|
| ✓ | 30.3b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 0.4b | (/.f64 1 (pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x 1) 1/4)) 2)) | |
| ▶ | 15.4b | (*.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)))))) |
| ✓ | 30.3b | (-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1) |
| ▶ | 30.9b | (-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)) 1) |
| 0.6b | (*.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))) | |
| ▶ | 8.6b | (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3)) |
| ▶ | 0.2b | (sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) |
| ▶ | 0.3b | (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2) |
| 32.4b | 1 | |
| ✓ | 0.2b | (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
Compiled 250 to 202 computations (19.2% saved)
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) |
| ✓ | 0.1b | (sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) |
| ✓ | 0.3b | (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2) |
Compiled 39 to 26 computations (33.3% saved)
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | x | @ | -inf | (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2) |
| 2.0ms | x | @ | -inf | (sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) |
| 2.0ms | x | @ | inf | (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2) |
| 1.0ms | x | @ | 0 | (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2) |
| 1.0ms | x | @ | inf | (sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) |
| 1× | batch-egg-rewrite |
| 439× | fma-def_binary64 |
| 435× | prod-exp_binary64 |
| 414× | log-prod_binary64 |
| 298× | exp-prod_binary64 |
| 297× | pow-prod-down_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 10 | 39 |
| 1 | 216 | 39 |
| 2 | 2745 | 39 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2) |
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) |
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) |
| Outputs |
|---|
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3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 x (+.f64 1 x)))) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (-.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 2)) (cbrt.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (log.f64 (+.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 (sqrt.f64 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(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.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 (*.f64 3 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4))) 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 fma.f64 1 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 x)) 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) 1 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/6) (cbrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/6) (cbrt.f64 x) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (pow.f64 x 1/6) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 x)) (pow.f64 (+.f64 1 x) 1/6) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4) (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 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 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (+.f64 1 (sqrt.f64 (+.f64 1 x))) |
| ✓ | 3.8b | (-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)) 1) |
| ✓ | 6.6b | (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)) |
Compiled 38 to 27 computations (28.9% saved)
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | inf | (-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)) 1) |
| 1.0ms | x | @ | -inf | (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)) |
| 0.0ms | x | @ | inf | (+.f64 1 (sqrt.f64 (+.f64 1 x))) |
| 0.0ms | x | @ | -inf | (+.f64 1 (sqrt.f64 (+.f64 1 x))) |
| 0.0ms | x | @ | inf | (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)) |
| 1× | batch-egg-rewrite |
| 776× | fma-def_binary64 |
| 445× | log-prod_binary64 |
| 397× | fma-neg_binary64 |
| 337× | pow-prod-down_binary64 |
| 265× | pow2_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 40 |
| 1 | 215 | 34 |
| 2 | 3293 | 34 |
| 1× | node limit |
| Inputs |
|---|
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)) |
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)) 1) |
(+.f64 1 (sqrt.f64 (+.f64 1 x))) |
| Outputs |
|---|
((#(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 +.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 1 (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 x 1/6)) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 1)))) (#(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 (neg.f64 (sqrt.f64 x)) (+.f64 1 (sqrt.f64 (+.f64 1 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 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 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| 1× | egg-herbie |
| 660× | distribute-rgt-in_binary64 |
| 606× | distribute-lft-in_binary64 |
| 536× | unswap-sqr_binary64 |
| 494× | associate-*l*_binary64 |
| 442× | fma-def_binary64 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 42 |
| 1 | 47 | 40 |
| 2 | 105 | 40 |
| 3 | 296 | 34 |
| 4 | 743 | 33 |
| 5 | 2349 | 33 |
| 6 | 3987 | 33 |
| 7 | 4215 | 33 |
| 8 | 4515 | 33 |
| 9 | 5054 | 33 |
| 10 | 6051 | 33 |
| 1× | node limit |
| Inputs |
|---|
2 |
1 |
1 |
2 |
(+.f64 (*.f64 1/2 x) 2) |
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2)) |
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3))))) |
| Outputs |
|---|
2 |
1 |
1 |
2 |
(+.f64 (*.f64 1/2 x) 2) |
(fma.f64 1/2 x 2) |
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2)) |
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 2)) |
(fma.f64 x (*.f64 x -1/8) (fma.f64 1/2 x 2)) |
(fma.f64 x (fma.f64 x -1/8 1/2) 2) |
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3))))) |
(fma.f64 -1/8 (*.f64 x x) (+.f64 (fma.f64 1/2 x 2) (*.f64 1/16 (pow.f64 x 3)))) |
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 2))) |
(fma.f64 x (*.f64 x -1/8) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 2))) |
(fma.f64 1/2 x (fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) 2)) |
(fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))) 2) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.3b | (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) |
| ✓ | 4.5b | (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))) |
| ✓ | 8.4b | (*.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)))))) |
| ✓ | 14.2b | (sqrt.f64 (*.f64 (+.f64 1 x) x)) |
Compiled 100 to 71 computations (29% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | x | @ | -inf | (*.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)))))) |
| 2.0ms | x | @ | 0 | (*.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)))))) |
| 2.0ms | x | @ | inf | (*.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)))))) |
| 1.0ms | x | @ | -inf | (sqrt.f64 (*.f64 (+.f64 1 x) x)) |
| 1.0ms | x | @ | 0 | (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) |
| 1× | batch-egg-rewrite |
| 521× | fma-neg_binary64 |
| 302× | expm1-udef_binary64 |
| 302× | log1p-udef_binary64 |
| 256× | log-pow_binary64 |
| 189× | add-sqr-sqrt_binary64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 15 | 70 |
| 1 | 365 | 70 |
| 2 | 5724 | 61 |
| 1× | node limit |
| Inputs |
|---|
(sqrt.f64 (*.f64 (+.f64 1 x) 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)))))) |
(-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))) |
(/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 x))) (cbrt.f64 (+.f64 x (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (*.f64 x x))) (cbrt.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 x))) (sqrt.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 2)) 1/2) (pow.f64 (cbrt.f64 (+.f64 x (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 x (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x (cbrt.f64 (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (cbrt.f64 (pow.f64 x 3/2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 (log.f64 x) (log1p.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 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 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (*.f64 (/.f64 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 1 x) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))) (*.f64 (-.f64 x (hypot.f64 x (sqrt.f64 x))) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 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| 1× | egg-herbie |
| 776× | fma-def_binary64 |
| 425× | associate-+l+_binary64 |
| 332× | associate-+r+_binary64 |
| 307× | associate-/r*_binary64 |
| 241× | associate--r+_binary64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 219 | 1886 |
| 1 | 675 | 1579 |
| 2 | 2266 | 1297 |
| 1× | node limit |
| Inputs |
|---|
x |
(+.f64 1/2 x) |
(-.f64 (+.f64 1/2 x) (*.f64 1/8 (/.f64 1 x))) |
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) x)) (*.f64 1/8 (/.f64 1 x))) |
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) |
(+.f64 1/2 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) |
(+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))) |
(+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 x 2)))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))))) |
(/.f64 1 (+.f64 1 (pow.f64 x 3/2))) |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
(-.f64 (+.f64 (*.f64 1/4 (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 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) x)) (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))) |
(-.f64 (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) (+.f64 (*.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) x)) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/4 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))) (pow.f64 x 2))) (*.f64 3/16 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))))))))) |
(*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) |
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) |
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 -1 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 -3/4 (-.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) (*.f64 -3/32 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) x)))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) |
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 3/16 (-.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) (+.f64 (*.f64 -1/64 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 -3/4 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 -3/4 (-.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) (*.f64 -3/32 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))))))) (pow.f64 x 2))) (*.f64 -1 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 -3/4 (-.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) (*.f64 -3/32 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) x))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) |
-1/2 |
(-.f64 (*.f64 1/8 (/.f64 1 x)) 1/2) |
(-.f64 (*.f64 1/8 (/.f64 1 x)) (+.f64 1/2 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))) |
(-.f64 (+.f64 (*.f64 5/128 (/.f64 1 (pow.f64 x 3))) (*.f64 1/8 (/.f64 1 x))) (+.f64 1/2 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))) |
(*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) |
(-.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) 1/2) |
(-.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) (+.f64 1/2 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))))) |
(-.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 x 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))))) |
(/.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)))))) |
| Outputs |
|---|
x |
(+.f64 1/2 x) |
(+.f64 x 1/2) |
(-.f64 (+.f64 1/2 x) (*.f64 1/8 (/.f64 1 x))) |
(-.f64 (+.f64 x 1/2) (/.f64 1/8 x)) |
(+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)) |
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) x)) (*.f64 1/8 (/.f64 1 x))) |
(-.f64 (+.f64 1/2 (+.f64 x (/.f64 1/16 (*.f64 x x)))) (/.f64 1/8 x)) |
(+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 x x))) (+.f64 x (/.f64 -1/8 x))) |
(+.f64 x (+.f64 (/.f64 -1/8 x) (+.f64 1/2 (/.f64 1/16 (*.f64 x x))))) |
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) |
x |
(+.f64 1/2 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) |
(+.f64 x 1/2) |
(+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))) |
(-.f64 (+.f64 x 1/2) (/.f64 1/8 x)) |
(+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)) |
(+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 x 2)))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))))) |
(-.f64 (+.f64 1/2 (+.f64 x (/.f64 1/16 (*.f64 x x)))) (/.f64 1/8 x)) |
(+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 x x))) (+.f64 x (/.f64 -1/8 x))) |
(+.f64 x (+.f64 (/.f64 -1/8 x) (+.f64 1/2 (/.f64 1/16 (*.f64 x x))))) |
(/.f64 1 (+.f64 1 (pow.f64 x 3/2))) |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
(-.f64 (+.f64 (*.f64 1/4 (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 (fma.f64 1/4 (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 (sqrt.f64 (/.f64 1 x))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)) |
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)) |
(-.f64 (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) x)) (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))) |
(-.f64 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (fma.f64 3/4 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8) x) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/32)))) |
(-.f64 (-.f64 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 3/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/32))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/32) x)) |
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/32 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 x -3/32))))) |
(-.f64 (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) (+.f64 (*.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) x)) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/4 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))) (pow.f64 x 2))) (*.f64 3/16 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))))))))) |
(-.f64 (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) (fma.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 3/4 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8) x) (fma.f64 3/4 (/.f64 (-.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (fma.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 3/4 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)))) (*.f64 x x)) (*.f64 3/16 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8) (*.f64 x x))))))))) |
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-1/2 |
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(+.f64 (/.f64 5/128 (pow.f64 x 3)) (-.f64 (/.f64 1/8 x) (+.f64 1/2 (/.f64 1/16 (*.f64 x x))))) |
(+.f64 (/.f64 1/8 x) (-.f64 (/.f64 5/128 (pow.f64 x 3)) (+.f64 1/2 (/.f64 1/16 (*.f64 x x))))) |
(+.f64 (+.f64 (/.f64 1/8 x) (+.f64 (/.f64 5/128 (pow.f64 x 3)) -1/2)) (/.f64 -1/16 (*.f64 x x))) |
(*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) |
(*.f64 x (+.f64 1 (pow.f64 (sqrt.f64 -1) 2))) |
(*.f64 x 0) |
0 |
(-.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) 1/2) |
-1/2 |
(-.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) (+.f64 1/2 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))))) |
(+.f64 (/.f64 1/8 x) -1/2) |
(-.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 x 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))))) |
(-.f64 (/.f64 1/8 x) (+.f64 1/2 (/.f64 1/16 (*.f64 x x)))) |
(+.f64 (/.f64 1/8 x) (+.f64 -1/2 (/.f64 -1/16 (*.f64 x x)))) |
(/.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)))) |
(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 x x) (-.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 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (fma.f64 (*.f64 x x) (+.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 (*.f64 x -3/2) (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) |
(fma.f64 x (*.f64 x (+.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)))) (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 (+.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 9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (-.f64 (/.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 x x) (-.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 (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)))) (fma.f64 (pow.f64 x 3) (+.f64 (/.f64 9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (+.f64 (/.f64 1/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (*.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 x (*.f64 x (+.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 (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 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 (+.f64 (/.f64 9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (-.f64 (/.f64 1/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (/.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))))) x)))) |
(*.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 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)) |
(+.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 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8))) |
(-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)) (*.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 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 3/16) (*.f64 x 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 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)))) |
(-.f64 (-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)) (/.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 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)) (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)))) |
(/.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 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) |
(-.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 x (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))) |
(+.f64 (/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) (/.f64 (/.f64 -3/8 x) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)))) |
(-.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 (*.f64 x x) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (-.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 x (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))) |
(+.f64 (+.f64 (/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) (/.f64 (/.f64 -3/8 x) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)))) (/.f64 3/16 (*.f64 (*.f64 x x) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))))) |
(-.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 (/.f64 1/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (/.f64 3/16 (*.f64 (*.f64 x x) (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 (/.f64 3/16 (*.f64 x x)) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (fma.f64 7/128 (/.f64 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (pow.f64 x 3)) (/.f64 3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))) |
(+.f64 (+.f64 (/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) (/.f64 (/.f64 -3/8 x) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)))) (-.f64 (/.f64 3/16 (*.f64 (*.f64 x x) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)))) (/.f64 7/128 (*.f64 (pow.f64 x 3) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)))))) |
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) |
| ✓ | 0.3b | (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2) |
Compiled 41 to 28 computations (31.7% saved)
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 14.0ms | x | @ | inf | (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2) |
| 6.0ms | 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 | 28 |
| 1 | 244 | 28 |
| 2 | 2988 | 28 |
| 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) |
| 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)))))) |
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/6) (/.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)))) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/6))))) (#(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)) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))) (sqrt.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -3/2 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 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)))) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/4 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1) -1/2))))) (#(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) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1) 1/2))))) (#(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) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1/4) 2)))))) |
| 1× | egg-herbie |
| 1× | 1-exp_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1 | 2 |
| 1 | 4 | 2 |
| 1× | saturated |
| Inputs |
|---|
1 |
1 |
| Outputs |
|---|
1 |
1 |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.0b | (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) | |
| ✓ | 0.2b | (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) |
| ✓ | 0.3b | (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3) |
| ✓ | 8.6b | (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3)) |
Compiled 52 to 36 computations (30.8% saved)
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 7.0ms | x | @ | -inf | (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3) |
| 4.0ms | x | @ | inf | (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3) |
| 2.0ms | x | @ | 0 | (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3) |
| 1.0ms | x | @ | -inf | (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3)) |
| 1.0ms | x | @ | -inf | (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) |
| 1× | batch-egg-rewrite |
| 439× | fma-def_binary64 |
| 437× | log-prod_binary64 |
| 314× | exp-prod_binary64 |
| 313× | pow-prod-down_binary64 |
| 255× | pow2_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 11 | 45 |
| 1 | 246 | 42 |
| 2 | 2995 | 42 |
| 1× | node limit |
| Inputs |
|---|
(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3)) |
(pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3) |
(/.f64 1 (+.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 (/.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 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 x (+.f64 1 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 *.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 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (neg.f64 (neg.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) (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2) (cbrt.f64 (+.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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -6) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -9) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2) -1/2)))) (#(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 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x 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| 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 |
Compiled 20710 to 15085 computations (27.2% saved)
13 alts after pruning (8 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 936 | 7 | 943 |
| Fresh | 2 | 1 | 3 |
| Picked | 1 | 0 | 1 |
| Done | 2 | 5 | 7 |
| Total | 941 | 13 | 954 |
| Status | Error | Program |
|---|---|---|
| 50.8b | (*.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))))) | |
| ✓ | 30.3b | (-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1) |
| ✓ | 30.9b | (-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)) 1) |
| ✓ | 0.2b | (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
| 32.2b | (-.f64 (-.f64 (+.f64 (*.f64 1/2 x) 2) (sqrt.f64 x)) 1) | |
| 29.7b | (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) | |
| 32.8b | (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) | |
| 0.4b | (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) -2) | |
| ✓ | 30.3b | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| ✓ | 0.2b | (sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) |
| 11.4b | (*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x 0))) | |
| 32.4b | 1 | |
| 31.1b | (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)) |
Compiled 148 to 122 computations (17.6% saved)
| Inputs |
|---|
1 |
1 |
1 |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
(/.f64 1 (+.f64 1 (pow.f64 x 3/2))) |
(-.f64 (-.f64 (+.f64 (*.f64 1/2 x) 2) (sqrt.f64 x)) 1) |
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)) 1) |
(-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1) |
(/.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 0))) |
(*.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) 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)))))) |
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) |
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) |
(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) |
(pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) -2) |
(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)) |
(/.f64 1 (pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x 1) 1/4)) 2)) |
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)) |
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) |
(/.f64 (+.f64 x (-.f64 1 x)) (expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) |
(/.f64 (+.f64 x (-.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3)) |
(/.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)))) |
(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 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 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))) |
| Outputs |
|---|
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
3 calls:
| 29.0ms | x |
| 14.0ms | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 8.0ms | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| Error | Segments | Branch |
|---|---|---|
| 0.2b | 1 | x |
| 0.2b | 1 | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 0.2b | 1 | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
Compiled 382 to 270 computations (29.3% saved)
| Inputs |
|---|
1 |
1 |
1 |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
(/.f64 1 (+.f64 1 (pow.f64 x 3/2))) |
(-.f64 (-.f64 (+.f64 (*.f64 1/2 x) 2) (sqrt.f64 x)) 1) |
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| Outputs |
|---|
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
3 calls:
| 20.0ms | x |
| 11.0ms | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 9.0ms | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| Error | Segments | Branch |
|---|---|---|
| 0.7b | 2 | x |
| 0.7b | 2 | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
| 0.7b | 2 | (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) |
Compiled 52 to 40 computations (23.1% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 3.223814019293059e-5 | 6.4739818299131e-5 |
Compiled 12 to 9 computations (25% saved)
| Inputs |
|---|
1 |
1 |
1 |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
(/.f64 1 (+.f64 1 (pow.f64 x 3/2))) |
(-.f64 (-.f64 (+.f64 (*.f64 1/2 x) 2) (sqrt.f64 x)) 1) |
| Outputs |
|---|
(-.f64 (-.f64 (+.f64 (*.f64 1/2 x) 2) (sqrt.f64 x)) 1) |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
1 calls:
| 61.0ms | x |
| Error | Segments | Branch |
|---|---|---|
| 1.8b | 2 | x |
Compiled 29 to 24 computations (17.2% saved)
| 1× | binary-search |
| Time | Left | Right |
|---|---|---|
| 35.0ms | 0.021398597363671983 | 1.370840529417722 |
Compiled 12 to 9 computations (25% saved)
| Inputs |
|---|
1 |
1 |
1 |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
(/.f64 1 (+.f64 1 (pow.f64 x 3/2))) |
| Outputs |
|---|
(/.f64 1 (+.f64 1 (pow.f64 x 3/2))) |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
1 calls:
| 40.0ms | x |
| Error | Segments | Branch |
|---|---|---|
| 2.7b | 2 | x |
Compiled 19 to 16 computations (15.8% saved)
| 1× | binary-search |
| Time | Left | Right |
|---|---|---|
| 35.0ms | 1.370840529417722 | 49.65230930963503 |
Compiled 12 to 9 computations (25% saved)
| Inputs |
|---|
1 |
1 |
1 |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
| Outputs |
|---|
1 |
(*.f64 1/2 (sqrt.f64 (/.f64 1 x))) |
1 calls:
| 16.0ms | x |
| Error | Segments | Branch |
|---|---|---|
| 2.7b | 2 | x |
Compiled 12 to 10 computations (16.7% saved)
| 1× | binary-search |
| Time | Left | Right |
|---|---|---|
| 46.0ms | 0.021398597363671983 | 1.370840529417722 |
Compiled 12 to 9 computations (25% saved)
Total 0.0b remaining (0%)
Threshold costs 0.0b (0%)
| Inputs |
|---|
1 |
1 |
1 |
| Outputs |
|---|
1 |
1 calls:
| 7.0ms | x |
| Error | Segments | Branch |
|---|---|---|
| 32.4b | 1 | x |
Compiled 6 to 5 computations (16.7% saved)
| 1× | egg-herbie |
| 8× | +-commutative_binary64 |
| 4× | sub-neg_binary64 |
| 3× | *-commutative_binary64 |
| 1× | neg-sub0_binary64 |
| 1× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 33 | 122 |
| 1 | 47 | 122 |
| 2 | 52 | 122 |
| 3 | 54 | 122 |
| 4 | 55 | 122 |
| 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)) 7378697629483821/147573952589676412928) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
(if (<=.f64 x 394734449104012992/18446744073709551616) (-.f64 (-.f64 (+.f64 (*.f64 1/2 x) 2) (sqrt.f64 x)) 1) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) |
(if (<=.f64 x 3086858448735013/2251799813685248) (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) |
(if (<=.f64 x 394734449104012992/18446744073709551616) 1 (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) |
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)) 7378697629483821/147573952589676412928) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) |
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 7378697629483821/147573952589676412928) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) |
(if (<=.f64 x 394734449104012992/18446744073709551616) (-.f64 (-.f64 (+.f64 (*.f64 1/2 x) 2) (sqrt.f64 x)) 1) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) |
(if (<=.f64 x 6167725767250203/288230376151711744) (+.f64 (-.f64 (+.f64 (*.f64 x 1/2) 2) (sqrt.f64 x)) -1) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) |
(if (<=.f64 x 3086858448735013/2251799813685248) (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) |
(if (<=.f64 x 394734449104012992/18446744073709551616) 1 (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) |
(if (<=.f64 x 6167725767250203/288230376151711744) 1 (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) |
1 |
Compiled 87 to 70 computations (19.5% saved)
Compiled 82 to 63 computations (23.2% saved)
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