Time bar (total: 6.0s)
| 1× | search |
| True | Other | False | Iter |
|---|---|---|---|
| 0% | 100% | 0% | 0 |
| 0% | 100% | 0% | 1 |
| 0% | 100% | 0% | 2 |
| 25% | 75% | 0% | 3 |
| 62.5% | 37.5% | 0% | 4 |
| 68.7% | 18.7% | 12.5% | 5 |
| 71.8% | 9.4% | 18.8% | 6 |
| 73.4% | 4.7% | 21.9% | 7 |
| 74.2% | 2.3% | 23.5% | 8 |
| 74.6% | 1.2% | 24.3% | 9 |
| 75% | 0.6% | 24.5% | 10 |
| 75.1% | 0.3% | 24.6% | 11 |
| 75.1% | 0.1% | 24.7% | 12 |
Compiled 8 to 6 computations (25% saved)
| 1.7s | 2805× | body | 1024 | valid |
| 580.0ms | 3826× | body | 256 | valid |
| 283.0ms | 1348× | body | 512 | valid |
| 113.0ms | 277× | body | 2048 | valid |
| 1.0ms | 11× | body | 256 | invalid |
| 2× | egg-herbie |
| 95× | fma-def_binary64 |
| 80× | fma-neg_binary64 |
| 32× | distribute-rgt-in_binary64 |
| 28× | cancel-sign-sub-inv_binary64 |
| 26× | distribute-lft-in_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 6 |
| 1 | 15 | 6 |
| 2 | 18 | 6 |
| 3 | 22 | 6 |
| 4 | 30 | 6 |
| 5 | 40 | 6 |
| 6 | 59 | 6 |
| 7 | 100 | 6 |
| 8 | 145 | 6 |
| 9 | 223 | 6 |
| 10 | 352 | 6 |
| 11 | 511 | 6 |
| 12 | 583 | 6 |
| 13 | 619 | 6 |
| 0 | 1 | 1 |
| 1× | saturated |
| 1× | saturated |
| Inputs |
|---|
0 |
| Outputs |
|---|
0 |
| Inputs |
|---|
(/.f64 (-.f64 (exp.f64 x) 1) x) |
| Outputs |
|---|
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
Compiled 8 to 6 computations (25% saved)
| 1× | egg-herbie |
| 95× | fma-def_binary64 |
| 80× | fma-neg_binary64 |
| 32× | distribute-rgt-in_binary64 |
| 28× | cancel-sign-sub-inv_binary64 |
| 26× | distribute-lft-in_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 6 |
| 1 | 15 | 6 |
| 2 | 18 | 6 |
| 3 | 22 | 6 |
| 4 | 30 | 6 |
| 5 | 40 | 6 |
| 6 | 59 | 6 |
| 7 | 100 | 6 |
| 8 | 145 | 6 |
| 9 | 223 | 6 |
| 10 | 352 | 6 |
| 11 | 511 | 6 |
| 12 | 583 | 6 |
| 13 | 619 | 6 |
| 1× | saturated |
| Inputs |
|---|
(/.f64 (-.f64 (exp.f64 x) 1) x) |
| Outputs |
|---|
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
Compiled 11 to 7 computations (36.4% saved)
1 alts after pruning (1 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 | 1 | 2 |
| Fresh | 1 | 0 | 1 |
| Picked | 0 | 0 | 0 |
| Done | 0 | 0 | 0 |
| Total | 2 | 1 | 3 |
| Status | Error | Program |
|---|---|---|
| ▶ | 0.0b | (/.f64 (expm1.f64 x) x) |
Compiled 5 to 3 computations (40% saved)
Found 1 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (/.f64 (expm1.f64 x) x) |
Compiled 8 to 3 computations (62.5% saved)
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (/.f64 (expm1.f64 x) x) |
| 1.0ms | x | @ | inf | (/.f64 (expm1.f64 x) x) |
| 1.0ms | x | @ | 0 | (/.f64 (expm1.f64 x) x) |
| 1× | batch-egg-rewrite |
| 449× | pow1_binary64 |
| 430× | add-sqr-sqrt_binary64 |
| 424× | *-un-lft-identity_binary64 |
| 417× | add-log-exp_binary64 |
| 417× | log1p-expm1-u_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 6 |
| 1 | 83 | 6 |
| 2 | 1104 | 6 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 (expm1.f64 x) x) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) x) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (expm1.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 x) x))))))) |
| 1× | egg-herbie |
| 688× | times-frac_binary64 |
| 636× | associate-/l/_binary64 |
| 536× | unswap-sqr_binary64 |
| 495× | associate-*l*_binary64 |
| 448× | fma-def_binary64 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 22 | 87 |
| 1 | 60 | 85 |
| 2 | 120 | 85 |
| 3 | 325 | 79 |
| 4 | 816 | 76 |
| 5 | 2522 | 76 |
| 6 | 4510 | 76 |
| 1× | node limit |
| Inputs |
|---|
1 |
(+.f64 (*.f64 1/2 x) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
| Outputs |
|---|
1 |
(+.f64 (*.f64 1/2 x) 1) |
(fma.f64 1/2 x 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1)) |
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1)) |
(fma.f64 x (fma.f64 x 1/6 1/2) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 1)) |
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
Compiled 345 to 161 computations (53.3% saved)
8 alts after pruning (7 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 33 | 7 | 40 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 33 | 8 | 41 |
| Status | Error | Program |
|---|---|---|
| ▶ | 0.5b | (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3) |
| ▶ | 0.1b | (*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x))) |
| ▶ | 0.0b | (pow.f64 (/.f64 x (expm1.f64 x)) -1) |
| ▶ | 20.4b | (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
| ▶ | 20.5b | (+.f64 (*.f64 1/2 x) 1) |
| 42.4b | (*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x))) | |
| 20.6b | 1 | |
| ✓ | 0.0b | (/.f64 (expm1.f64 x) x) |
Compiled 125 to 95 computations (24% saved)
Found 2 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (pow.f64 (/.f64 x (expm1.f64 x)) -1) |
| ✓ | 0.0b | (/.f64 x (expm1.f64 x)) |
Compiled 15 to 6 computations (60% saved)
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | inf | (/.f64 x (expm1.f64 x)) |
| 1.0ms | x | @ | 0 | (/.f64 x (expm1.f64 x)) |
| 1.0ms | x | @ | -inf | (pow.f64 (/.f64 x (expm1.f64 x)) -1) |
| 1.0ms | x | @ | inf | (pow.f64 (/.f64 x (expm1.f64 x)) -1) |
| 1.0ms | x | @ | -inf | (/.f64 x (expm1.f64 x)) |
| 1× | batch-egg-rewrite |
| 605× | pow1_binary64 |
| 565× | add-log-exp_binary64 |
| 565× | log1p-expm1-u_binary64 |
| 565× | expm1-log1p-u_binary64 |
| 551× | add-exp-log_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 15 |
| 1 | 125 | 12 |
| 2 | 1558 | 12 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 x (expm1.f64 x)) |
(pow.f64 (/.f64 x (expm1.f64 x)) -1) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 x (expm1.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) (cbrt.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) (sqrt.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (expm1.f64 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 x (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 x (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (expm1.f64 x)))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 x (expm1.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2)) (cbrt.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 x) x))))))) |
| 1× | egg-herbie |
| 933× | fma-def_binary64 |
| 803× | unswap-sqr_binary64 |
| 585× | associate-/l/_binary64 |
| 562× | times-frac_binary64 |
| 385× | associate-/r*_binary64 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 35 | 176 |
| 1 | 88 | 170 |
| 2 | 187 | 170 |
| 3 | 521 | 158 |
| 4 | 1475 | 155 |
| 5 | 3045 | 155 |
| 6 | 5017 | 155 |
| 1× | node limit |
| Inputs |
|---|
1 |
(+.f64 (*.f64 -1/2 x) 1) |
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2))))) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
1 |
(+.f64 (*.f64 1/2 x) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
| Outputs |
|---|
1 |
(+.f64 (*.f64 -1/2 x) 1) |
(fma.f64 -1/2 x 1) |
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))) |
(+.f64 (fma.f64 -1/2 x 1) (*.f64 1/12 (*.f64 x x))) |
(fma.f64 -1/2 x (fma.f64 1/12 (*.f64 x x) 1)) |
(fma.f64 -1/2 x (fma.f64 x (*.f64 x 1/12) 1)) |
(fma.f64 x (fma.f64 x 1/12 -1/2) 1) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2))))) |
(fma.f64 -1/720 (pow.f64 x 4) (+.f64 (fma.f64 -1/2 x 1) (*.f64 1/12 (*.f64 x x)))) |
(fma.f64 -1/720 (pow.f64 x 4) (fma.f64 -1/2 x (fma.f64 1/12 (*.f64 x x) 1))) |
(fma.f64 -1/2 x (fma.f64 -1/720 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/12) 1))) |
(fma.f64 x (fma.f64 x 1/12 -1/2) (fma.f64 -1/720 (pow.f64 x 4) 1)) |
(fma.f64 x (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 -1/2)) 1) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (expm1.f64 x)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (expm1.f64 x)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (expm1.f64 x)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (expm1.f64 x)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (expm1.f64 x)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (expm1.f64 x)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (expm1.f64 x)) |
(/.f64 x (-.f64 (exp.f64 x) 1)) |
(/.f64 x (expm1.f64 x)) |
1 |
(+.f64 (*.f64 1/2 x) 1) |
(fma.f64 1/2 x 1) |
(fma.f64 x 1/2 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1)) |
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) 1/6 1)) |
(fma.f64 x (*.f64 x 1/6) (fma.f64 x 1/2 1)) |
(fma.f64 x (fma.f64 x 1/6 1/2) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) 1/6 (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 x (*.f64 x (fma.f64 x 1/24 1/6)) (fma.f64 x 1/2 1)) |
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
Compiled 12 to 9 computations (25% saved)
Found 1 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.1b | (*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x))) |
Compiled 22 to 10 computations (54.5% saved)
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | 0 | (*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x))) |
| 0.0ms | x | @ | inf | (*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x))) |
| 0.0ms | x | @ | -inf | (*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x))) |
| 1× | batch-egg-rewrite |
| 555× | pow1_binary64 |
| 514× | add-log-exp_binary64 |
| 514× | log1p-expm1-u_binary64 |
| 514× | expm1-log1p-u_binary64 |
| 503× | add-exp-log_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 10 |
| 1 | 163 | 6 |
| 2 | 2149 | 6 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 0 x) (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (/.f64 x (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) -1) x)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 x) x))))))) |
| 1× | egg-herbie |
| 688× | times-frac_binary64 |
| 636× | associate-/l/_binary64 |
| 536× | unswap-sqr_binary64 |
| 495× | associate-*l*_binary64 |
| 448× | fma-def_binary64 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 22 | 87 |
| 1 | 60 | 85 |
| 2 | 120 | 85 |
| 3 | 325 | 79 |
| 4 | 816 | 76 |
| 5 | 2522 | 76 |
| 6 | 4510 | 76 |
| 1× | node limit |
| Inputs |
|---|
1 |
(+.f64 (*.f64 1/2 x) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
| Outputs |
|---|
1 |
(+.f64 (*.f64 1/2 x) 1) |
(fma.f64 1/2 x 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1)) |
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1)) |
(fma.f64 x (fma.f64 x 1/6 1/2) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 1)) |
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
| ✓ | 0.1b | (*.f64 1/24 (pow.f64 x 3)) |
| ✓ | 0.2b | (*.f64 1/6 (pow.f64 x 2)) |
| ✓ | 9.0b | (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
Compiled 64 to 52 computations (18.8% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | 0 | (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
| 1.0ms | x | @ | inf | (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
| 1.0ms | x | @ | 0 | (*.f64 1/24 (pow.f64 x 3)) |
| 1.0ms | x | @ | 0 | (*.f64 1/6 (pow.f64 x 2)) |
| 1.0ms | x | @ | -inf | (*.f64 1/24 (pow.f64 x 3)) |
| 1× | batch-egg-rewrite |
| 904× | fma-def_binary64 |
| 686× | log-prod_binary64 |
| 439× | fma-neg_binary64 |
| 280× | expm1-udef_binary64 |
| 280× | log1p-udef_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 52 |
| 1 | 362 | 48 |
| 2 | 4552 | 48 |
| 1× | node limit |
| Inputs |
|---|
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 4) 1/36) (-.f64 (*.f64 1/6 (*.f64 x x)) (fma.f64 1/24 (pow.f64 x 3) 1))) (/.f64 (pow.f64 (fma.f64 1/24 (pow.f64 x 3) 1) 2) (-.f64 (*.f64 1/6 (*.f64 x x)) (fma.f64 1/24 (pow.f64 x 3) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) (cbrt.f64 (pow.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)) 2)) (cbrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) (sqrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 6) 1/216 (pow.f64 (fma.f64 1/24 (pow.f64 x 3) 1) 3)) (/.f64 1 (fma.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (-.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 1/6 (*.f64 x x))) (*.f64 (pow.f64 x 4) 1/36))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/36) (pow.f64 (fma.f64 1/24 (pow.f64 x 3) 1) 2)) (/.f64 1 (-.f64 (*.f64 1/6 (*.f64 x x)) (fma.f64 1/24 (pow.f64 x 3) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (-.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 1/6 (*.f64 x x))) (*.f64 (pow.f64 x 4) 1/36)) (fma.f64 (pow.f64 x 6) 1/216 (pow.f64 (fma.f64 1/24 (pow.f64 x 3) 1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 1/6 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(*.f64 x x) 1/24) (fma.f64 1/6 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1/6 (fma.f64 1/24 (pow.f64 x 3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (*.f64 x 1/24) (fma.f64 1/6 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/6 (*.f64 x x)) 1 (fma.f64 1/24 (pow.f64 x 3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/6 (*.f64 x x)) (fma.f64 1/24 (pow.f64 x 3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/24 (pow.f64 x 3)) (fma.f64 1/6 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 1/6 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/6 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3) 1/24 (fma.f64 1/6 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/24 (pow.f64 x 3)) 1 (fma.f64 1/6 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/24 (pow.f64 x 3) 1) 1 (*.f64 1/6 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 1/24 (pow.f64 x 3) 1)) (pow.f64 (cbrt.f64 (fma.f64 1/24 (pow.f64 x 3) 1)) 2) (*.f64 1/6 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/24 (pow.f64 x 3) 1)) 2) (cbrt.f64 (fma.f64 1/24 (pow.f64 x 3) 1)) (*.f64 1/6 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/6 (*.f64 x x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/36)) (fma.f64 1/24 (pow.f64 x 3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 1/36)) (cbrt.f64 (*.f64 1/6 (*.f64 x x))) (fma.f64 1/24 (pow.f64 x 3) 1))))) (#(struct:change #<rule 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#<rule egg-rr> (2) ((x fma.f64 x (*.f64 x 1/6) (+.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1/6 (+.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/6 (*.f64 x x)) 1 (+.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/6 (*.f64 x x)) (+.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/24 (pow.f64 x 3) 1) (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/2) (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2)) (fma.f64 1/24 (pow.f64 x 3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/6 (*.f64 x x) 1) (fma.f64 1/24 (pow.f64 x 3) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/24 (pow.f64 x 3) 1) 1 (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)) 1 (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/2) 1 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x 1/2)) (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (cbrt.f64 (*.f64 x 1/2)) (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 1/24 (pow.f64 x 3) 1)) (pow.f64 (cbrt.f64 (fma.f64 1/24 (pow.f64 x 3) 1)) 2) (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/24 (pow.f64 x 3) 1)) 2) (cbrt.f64 (fma.f64 1/24 (pow.f64 x 3) 1)) (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/6 (*.f64 x x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/36)) (+.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 1/36)) (cbrt.f64 (*.f64 1/6 (*.f64 x x))) (+.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/2) (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (*.f64 (pow.f64 (cbrt.f64 x) 2) 1/6) (+.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) (cbrt.f64 (pow.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)) 2)) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)) 2)) (cbrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)) (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/24 (pow.f64 x 3) 1)) (sqrt.f64 (fma.f64 1/24 (pow.f64 x 3) 1)) (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 1/6)) (*.f64 x (sqrt.f64 1/6)) (+.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/2) (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) (sqrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 x 6) 1/216 (pow.f64 (fma.f64 1/24 (pow.f64 x 3) 1) 3)) (/.f64 1 (fma.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (-.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 1/6 (*.f64 x x))) (*.f64 (pow.f64 x 4) 1/36))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/13824 (pow.f64 (pow.f64 x 3) 3) 1) (/.f64 1 (+.f64 1 (fma.f64 1/576 (pow.f64 x 6) (*.f64 -1/24 (pow.f64 x 3))))) (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/36) (pow.f64 (fma.f64 1/24 (pow.f64 x 3) 1) 2)) (/.f64 1 (-.f64 (*.f64 1/6 (*.f64 x x)) (fma.f64 1/24 (pow.f64 x 3) 1))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (*.f64 1/576 (pow.f64 x 6))) (/.f64 1 (+.f64 1 (*.f64 -1/24 (pow.f64 x 3)))) (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2)) 1 (fma.f64 1/24 (pow.f64 x 3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2))) (cbrt.f64 (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2)))) (cbrt.f64 (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2))) (fma.f64 1/24 (pow.f64 x 3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (fma.f64 1/6 (*.f64 x x) 1)) (cbrt.f64 (fma.f64 1/6 (*.f64 x x) 1))) (cbrt.f64 (fma.f64 1/6 (*.f64 x x) 1)) (fma.f64 1/24 (pow.f64 x 3) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2))) (sqrt.f64 (fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2))) (fma.f64 1/24 (pow.f64 x 3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 1/6))) (hypot.f64 1 (*.f64 x (sqrt.f64 1/6))) (fma.f64 1/24 (pow.f64 x 3) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/6 x) x (+.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/6 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2) (+.f64 (fma.f64 1/24 (pow.f64 x 3) 1) (*.f64 x 1/2))))))) |
| 1× | egg-herbie |
| 660× | distribute-rgt-in_binary64 |
| 606× | distribute-lft-in_binary64 |
| 536× | unswap-sqr_binary64 |
| 494× | associate-*l*_binary64 |
| 460× | fma-def_binary64 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 189 |
| 1 | 58 | 189 |
| 2 | 120 | 179 |
| 3 | 320 | 156 |
| 4 | 792 | 146 |
| 5 | 2390 | 146 |
| 6 | 4026 | 146 |
| 7 | 4254 | 146 |
| 8 | 4554 | 146 |
| 9 | 5093 | 146 |
| 10 | 6090 | 146 |
| 1× | node limit |
| Inputs |
|---|
1 |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 1) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
1 |
(+.f64 (*.f64 1/2 x) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3))))) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3))))) |
| Outputs |
|---|
1 |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 1) |
(fma.f64 1/6 (*.f64 x x) 1) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(fma.f64 1/6 (*.f64 x x) (*.f64 1/24 (pow.f64 x 3))) |
(*.f64 (*.f64 x x) (+.f64 1/6 (*.f64 x 1/24))) |
(*.f64 (*.f64 x x) (fma.f64 x 1/24 1/6)) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(fma.f64 1/6 (*.f64 x x) (*.f64 1/24 (pow.f64 x 3))) |
(*.f64 (*.f64 x x) (+.f64 1/6 (*.f64 x 1/24))) |
(*.f64 (*.f64 x x) (fma.f64 x 1/24 1/6)) |
1 |
(+.f64 (*.f64 1/2 x) 1) |
(fma.f64 1/2 x 1) |
(fma.f64 x 1/2 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1)) |
(fma.f64 x 1/2 (fma.f64 1/6 (*.f64 x x) 1)) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 1)) |
(fma.f64 x (fma.f64 1/6 x 1/2) 1) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(fma.f64 1/6 (*.f64 x x) (*.f64 1/24 (pow.f64 x 3))) |
(*.f64 (*.f64 x x) (+.f64 1/6 (*.f64 x 1/24))) |
(*.f64 (*.f64 x x) (fma.f64 x 1/24 1/6)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/24 (pow.f64 x 3) (*.f64 x (+.f64 (*.f64 1/6 x) 1/2))) |
(*.f64 x (+.f64 (*.f64 x (fma.f64 x 1/24 1/6)) 1/2)) |
(*.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 1/6 (*.f64 x x) (+.f64 (fma.f64 1/2 x 1) (*.f64 1/24 (pow.f64 x 3)))) |
(+.f64 (fma.f64 x 1/2 1) (fma.f64 1/6 (*.f64 x x) (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) (fma.f64 x 1/2 1)) |
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(fma.f64 1/6 (*.f64 x x) (*.f64 1/24 (pow.f64 x 3))) |
(*.f64 (*.f64 x x) (+.f64 1/6 (*.f64 x 1/24))) |
(*.f64 (*.f64 x x) (fma.f64 x 1/24 1/6)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/24 (pow.f64 x 3) (*.f64 x (+.f64 (*.f64 1/6 x) 1/2))) |
(*.f64 x (+.f64 (*.f64 x (fma.f64 x 1/24 1/6)) 1/2)) |
(*.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 1/6 (*.f64 x x) (+.f64 (fma.f64 1/2 x 1) (*.f64 1/24 (pow.f64 x 3)))) |
(+.f64 (fma.f64 x 1/2 1) (fma.f64 1/6 (*.f64 x x) (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) (fma.f64 x 1/2 1)) |
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1) |
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.0b | (/.f64 (expm1.f64 x) x) | |
| ✓ | 0.2b | (cbrt.f64 (/.f64 (expm1.f64 x) x)) |
| ✓ | 0.3b | (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3) |
Compiled 21 to 7 computations (66.7% saved)
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | -inf | (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3) |
| 2.0ms | x | @ | inf | (cbrt.f64 (/.f64 (expm1.f64 x) x)) |
| 1.0ms | x | @ | inf | (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3) |
| 1.0ms | x | @ | -inf | (cbrt.f64 (/.f64 (expm1.f64 x) x)) |
| 1.0ms | x | @ | 0 | (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3) |
| 1× | batch-egg-rewrite |
| 624× | pow1_binary64 |
| 590× | add-log-exp_binary64 |
| 590× | log1p-expm1-u_binary64 |
| 590× | expm1-log1p-u_binary64 |
| 575× | add-exp-log_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 7 | 14 |
| 1 | 152 | 14 |
| 2 | 1626 | 14 |
| 1× | node limit |
| Inputs |
|---|
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3) |
(cbrt.f64 (/.f64 (expm1.f64 x) x)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) x) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) (*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2) 3) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) 3) (pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) 1) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2)) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 x (expm1.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (expm1.f64 x))) (neg.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (expm1.f64 x))) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 x) x))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (pow.f64 x -1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1/3) (pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (cbrt.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (cbrt.f64 x) (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (neg.f64 (expm1.f64 x))) (cbrt.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (cbrt.f64 (expm1.f64 x))) (neg.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)))))))) |
| 1× | egg-herbie |
| 1218× | fma-def_binary64 |
| 750× | sqr-pow_binary64 |
| 605× | cube-prod_binary64 |
| 477× | fabs-mul_binary64 |
| 370× | pow-sqr_binary64 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 30 | 82 |
| 1 | 77 | 78 |
| 2 | 182 | 75 |
| 3 | 519 | 62 |
| 4 | 1386 | 56 |
| 5 | 2414 | 56 |
| 6 | 2936 | 56 |
| 7 | 3069 | 56 |
| 8 | 3223 | 56 |
| 9 | 3413 | 56 |
| 10 | 3666 | 56 |
| 11 | 4316 | 56 |
| 12 | 4723 | 56 |
| 13 | 5252 | 56 |
| 14 | 5914 | 56 |
| 15 | 6738 | 56 |
| 16 | 7139 | 56 |
| 17 | 7507 | 56 |
| 18 | 7845 | 56 |
| 1× | node limit |
| Inputs |
|---|
1 |
(+.f64 (*.f64 1/2 x) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
1 |
(+.f64 1 (*.f64 1/6 x)) |
(+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 1/36 (pow.f64 x 2)))) |
(+.f64 1 (+.f64 (*.f64 1/6 x) (+.f64 (*.f64 1/324 (pow.f64 x 3)) (*.f64 1/36 (pow.f64 x 2))))) |
| Outputs |
|---|
1 |
(+.f64 (*.f64 1/2 x) 1) |
(fma.f64 1/2 x 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1)) |
(fma.f64 x (*.f64 x 1/6) (fma.f64 1/2 x 1)) |
(fma.f64 x (fma.f64 x 1/6 1/2) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) 1)) |
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 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 1/36 (pow.f64 x 2)))) |
(+.f64 1 (fma.f64 1/6 x (*.f64 (*.f64 x x) 1/36))) |
(+.f64 1 (fma.f64 x 1/6 (*.f64 x (*.f64 x 1/36)))) |
(fma.f64 x (*.f64 x 1/36) (fma.f64 x 1/6 1)) |
(fma.f64 x (fma.f64 x 1/36 1/6) 1) |
(+.f64 1 (+.f64 (*.f64 1/6 x) (+.f64 (*.f64 1/324 (pow.f64 x 3)) (*.f64 1/36 (pow.f64 x 2))))) |
(+.f64 1 (fma.f64 1/6 x (fma.f64 1/324 (pow.f64 x 3) (*.f64 (*.f64 x x) 1/36)))) |
(+.f64 1 (fma.f64 x 1/6 (fma.f64 (*.f64 x x) 1/36 (*.f64 (pow.f64 x 3) 1/324)))) |
(+.f64 (fma.f64 x 1/6 1) (*.f64 (*.f64 x x) (+.f64 1/36 (*.f64 x 1/324)))) |
(fma.f64 (pow.f64 x 3) 1/324 (fma.f64 x (fma.f64 x 1/36 1/6) 1)) |
(fma.f64 x (fma.f64 x (fma.f64 x 1/324 1/36) 1/6) 1) |
Compiled 7435 to 4804 computations (35.4% saved)
7 alts after pruning (4 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 457 | 4 | 461 |
| Fresh | 2 | 0 | 2 |
| Picked | 0 | 1 | 1 |
| Done | 3 | 2 | 5 |
| Total | 462 | 7 | 469 |
| Status | Error | Program |
|---|---|---|
| ▶ | 20.4b | (+.f64 (*.f64 1/2 x) (+.f64 (+.f64 0 (*.f64 1/6 (*.f64 x x))) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
| ✓ | 0.5b | (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3) |
| ▶ | 0.0b | (/.f64 1 (/.f64 x (expm1.f64 x))) |
| 20.6b | 1 | |
| ✓ | 20.5b | (+.f64 (*.f64 1/2 x) 1) |
| ▶ | 42.4b | (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x)) |
| ✓ | 0.0b | (/.f64 (expm1.f64 x) x) |
Compiled 57 to 42 computations (26.3% saved)
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (+.f64 (*.f64 1/2 x) (+.f64 (+.f64 0 (*.f64 1/6 (*.f64 x x))) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
| 0.1b | (*.f64 1/24 (pow.f64 x 3)) | |
| ✓ | 0.2b | (*.f64 1/6 (*.f64 x x)) |
| ✓ | 9.0b | (+.f64 (+.f64 0 (*.f64 1/6 (*.f64 x x))) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
Compiled 75 to 53 computations (29.3% saved)
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | 0 | (+.f64 (+.f64 0 (*.f64 1/6 (*.f64 x x))) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
| 0.0ms | x | @ | inf | (+.f64 (+.f64 0 (*.f64 1/6 (*.f64 x x))) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
| 0.0ms | x | @ | -inf | (+.f64 (+.f64 0 (*.f64 1/6 (*.f64 x x))) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
| 0.0ms | x | @ | -inf | (+.f64 (*.f64 1/2 x) (+.f64 (+.f64 0 (*.f64 1/6 (*.f64 x x))) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
| 0.0ms | x | @ | inf | (+.f64 (*.f64 1/2 x) (+.f64 (+.f64 0 (*.f64 1/6 (*.f64 x x))) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
| 1× | batch-egg-rewrite |
| 699× | log-prod_binary64 |
| 532× | fma-neg_binary64 |
| 278× | expm1-udef_binary64 |
| 278× | log1p-udef_binary64 |
| 212× | log-pow_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 49 |
| 1 | 390 | 41 |
| 2 | 4995 | 41 |
| 1× | node limit |
| Inputs |
|---|
(+.f64 (+.f64 0 (*.f64 1/6 (*.f64 x x))) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(*.f64 1/6 (*.f64 x x)) |
(+.f64 (*.f64 1/2 x) (+.f64 (+.f64 0 (*.f64 1/6 (*.f64 x x))) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
| Outputs |
|---|
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(+.f64 1 (expm1.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 x 1/2))) (exp.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 1/2) x) (+.f64 1 (expm1.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 x 1/2))) (+.f64 1 (expm1.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (*.f64 (pow.f64 (exp.f64 1/2) x) (pow.f64 (exp.f64 1/6) (*.f64 x x))) (exp.f64 (fma.f64 1/24 (pow.f64 x 3) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 x (+.f64 1/2 (*.f64 1/6 x)))) (+.f64 1 (expm1.f64 (fma.f64 1/24 (pow.f64 x 3) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (*.f64 (pow.f64 (exp.f64 1/2) x) (pow.f64 (exp.f64 1/6) (*.f64 x x))) 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/2) (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) 2) (cbrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 x x) 1/4)) (cbrt.f64 (*.f64 x 1/2)) (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) (sqrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)) (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))))))) |
| 1× | egg-herbie |
| 660× | distribute-rgt-in_binary64 |
| 606× | distribute-lft-in_binary64 |
| 536× | unswap-sqr_binary64 |
| 500× | associate-*l*_binary64 |
| 450× | fma-def_binary64 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 396 |
| 1 | 68 | 378 |
| 2 | 136 | 372 |
| 3 | 328 | 328 |
| 4 | 778 | 315 |
| 5 | 2379 | 315 |
| 6 | 4014 | 315 |
| 7 | 4242 | 315 |
| 8 | 4541 | 315 |
| 9 | 5080 | 315 |
| 10 | 6077 | 315 |
| 1× | node limit |
| Inputs |
|---|
1 |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 1) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (pow.f64 x 2)) |
1 |
(+.f64 (*.f64 1/2 x) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3))))) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3))))) |
| Outputs |
|---|
1 |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 1) |
(fma.f64 1/6 (*.f64 x x) 1) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)) |
(fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) 1) |
(fma.f64 x (*.f64 x (fma.f64 x 1/24 1/6)) 1) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)) |
(fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) 1) |
(fma.f64 x (*.f64 x (fma.f64 x 1/24 1/6)) 1) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(fma.f64 1/6 (*.f64 x x) (*.f64 1/24 (pow.f64 x 3))) |
(*.f64 (*.f64 x x) (+.f64 1/6 (*.f64 x 1/24))) |
(*.f64 x (*.f64 x (fma.f64 x 1/24 1/6))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)) |
(fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) 1) |
(fma.f64 x (*.f64 x (fma.f64 x 1/24 1/6)) 1) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)) |
(fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) 1) |
(fma.f64 x (*.f64 x (fma.f64 x 1/24 1/6)) 1) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(fma.f64 1/6 (*.f64 x x) (*.f64 1/24 (pow.f64 x 3))) |
(*.f64 (*.f64 x x) (+.f64 1/6 (*.f64 x 1/24))) |
(*.f64 x (*.f64 x (fma.f64 x 1/24 1/6))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)) |
(fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) 1) |
(fma.f64 x (*.f64 x (fma.f64 x 1/24 1/6)) 1) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)) |
(fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) 1) |
(fma.f64 x (*.f64 x (fma.f64 x 1/24 1/6)) 1) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (*.f64 x x)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (*.f64 x x)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (*.f64 x x)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (*.f64 x x)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (*.f64 x x)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (*.f64 x x)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (*.f64 x x)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (*.f64 x x)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (*.f64 x x)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (*.f64 x x)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (*.f64 x x)) |
(*.f64 1/6 (pow.f64 x 2)) |
(*.f64 1/6 (*.f64 x x)) |
1 |
(+.f64 (*.f64 1/2 x) 1) |
(fma.f64 1/2 x 1) |
(fma.f64 x 1/2 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1)) |
(fma.f64 x 1/2 (fma.f64 1/6 (*.f64 x x) 1)) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 1)) |
(fma.f64 x (fma.f64 1/6 x 1/2) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 x 1/2 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 x (fma.f64 1/6 x 1/2) (fma.f64 1/24 (pow.f64 x 3) 1)) |
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(fma.f64 1/6 (*.f64 x x) (*.f64 1/24 (pow.f64 x 3))) |
(*.f64 (*.f64 x x) (+.f64 1/6 (*.f64 x 1/24))) |
(*.f64 x (*.f64 x (fma.f64 x 1/24 1/6))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) (*.f64 x 1/2))) |
(fma.f64 1/24 (pow.f64 x 3) (*.f64 x (+.f64 (*.f64 1/6 x) 1/2))) |
(*.f64 x (+.f64 (*.f64 x (fma.f64 x 1/24 1/6)) 1/2)) |
(*.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 x 1/2 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 x (fma.f64 1/6 x 1/2) (fma.f64 1/24 (pow.f64 x 3) 1)) |
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1) |
(*.f64 1/24 (pow.f64 x 3)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (*.f64 1/24 (pow.f64 x 3))) |
(fma.f64 1/6 (*.f64 x x) (*.f64 1/24 (pow.f64 x 3))) |
(*.f64 (*.f64 x x) (+.f64 1/6 (*.f64 x 1/24))) |
(*.f64 x (*.f64 x (fma.f64 x 1/24 1/6))) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) (*.f64 x 1/2))) |
(fma.f64 1/24 (pow.f64 x 3) (*.f64 x (+.f64 (*.f64 1/6 x) 1/2))) |
(*.f64 x (+.f64 (*.f64 x (fma.f64 x 1/24 1/6)) 1/2)) |
(*.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2)) |
(+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 x 1/2 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 x (fma.f64 1/6 x 1/2) (fma.f64 1/24 (pow.f64 x 3) 1)) |
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1) |
Found 2 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.0b | (/.f64 x (expm1.f64 x)) | |
| ✓ | 0.0b | (/.f64 1 (/.f64 x (expm1.f64 x))) |
Compiled 15 to 6 computations (60% saved)
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | 0 | (/.f64 1 (/.f64 x (expm1.f64 x))) |
| 0.0ms | x | @ | -inf | (/.f64 1 (/.f64 x (expm1.f64 x))) |
| 0.0ms | x | @ | inf | (/.f64 1 (/.f64 x (expm1.f64 x))) |
| 1× | batch-egg-rewrite |
| 606× | pow1_binary64 |
| 562× | add-log-exp_binary64 |
| 562× | log1p-expm1-u_binary64 |
| 562× | expm1-log1p-u_binary64 |
| 548× | add-exp-log_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 9 |
| 1 | 124 | 6 |
| 2 | 1584 | 6 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 1 (/.f64 x (expm1.f64 x))) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (/.f64 (neg.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 x) 1) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (expm1.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 x) x))))))) |
| 1× | egg-herbie |
| 688× | times-frac_binary64 |
| 636× | associate-/l/_binary64 |
| 536× | unswap-sqr_binary64 |
| 495× | associate-*l*_binary64 |
| 448× | fma-def_binary64 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 22 | 87 |
| 1 | 60 | 85 |
| 2 | 120 | 85 |
| 3 | 325 | 79 |
| 4 | 816 | 76 |
| 5 | 2522 | 76 |
| 6 | 4510 | 76 |
| 1× | node limit |
| Inputs |
|---|
1 |
(+.f64 (*.f64 1/2 x) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
| Outputs |
|---|
1 |
(+.f64 (*.f64 1/2 x) 1) |
(fma.f64 1/2 x 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1)) |
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1)) |
(fma.f64 x (fma.f64 x 1/6 1/2) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 1)) |
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
Found 2 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x)) |
| ✓ | 0.2b | (/.f64 (expm1.f64 x) (sqrt.f64 x)) |
Compiled 19 to 5 computations (73.7% saved)
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 36.0ms | x | @ | inf | (/.f64 (expm1.f64 x) (sqrt.f64 x)) |
| 1.0ms | x | @ | -inf | (/.f64 (expm1.f64 x) (sqrt.f64 x)) |
| 1.0ms | x | @ | 0 | (/.f64 (expm1.f64 x) (sqrt.f64 x)) |
| 1.0ms | x | @ | -inf | (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x)) |
| 0.0ms | x | @ | 0 | (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x)) |
| 1× | batch-egg-rewrite |
| 710× | pow1_binary64 |
| 664× | add-log-exp_binary64 |
| 664× | log1p-expm1-u_binary64 |
| 664× | expm1-log1p-u_binary64 |
| 648× | add-exp-log_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 14 |
| 1 | 128 | 14 |
| 2 | 1800 | 14 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 (expm1.f64 x) (sqrt.f64 x)) |
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)) (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 (expm1.f64 x) (cbrt.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 x 1/4)) (/.f64 (expm1.f64 x) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 x)) (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 x 1/4)) (/.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (expm1.f64 x) (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (*.f64 (pow.f64 x -1/2) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)) (*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (neg.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 1 (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (expm1.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) (cbrt.f64 x)) (/.f64 (pow.f64 x -1/2) (cbrt.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) 1) (/.f64 (pow.f64 x -1/2) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)) 1) (/.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 1) (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)) (cbrt.f64 x)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (cbrt.f64 x)) (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (cbrt.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) (pow.f64 x 1/4)) (/.f64 (pow.f64 x -1/2) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 x 1/4)) (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)) (pow.f64 x 1/4)) (/.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (/.f64 (expm1.f64 x) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 x) x))))))) |
| 1× | egg-herbie |
| 716× | associate-/l*_binary64 |
| 546× | fma-def_binary64 |
| 525× | unswap-sqr_binary64 |
| 467× | associate-/r/_binary64 |
| 286× | div-sub_binary64 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 28 | 87 |
| 1 | 78 | 85 |
| 2 | 195 | 85 |
| 3 | 553 | 79 |
| 4 | 2096 | 76 |
| 5 | 6468 | 76 |
| 1× | node limit |
| Inputs |
|---|
1 |
(+.f64 (*.f64 1/2 x) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(*.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) |
(*.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) |
(*.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) |
(*.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) |
| Outputs |
|---|
1 |
(+.f64 (*.f64 1/2 x) 1) |
(fma.f64 1/2 x 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1)) |
(fma.f64 x (*.f64 x 1/6) (fma.f64 1/2 x 1)) |
(fma.f64 x (fma.f64 x 1/6 1/2) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3)))) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 1)) |
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(*.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) |
(/.f64 (expm1.f64 x) x) |
(*.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) |
(/.f64 (expm1.f64 x) x) |
(*.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) |
(/.f64 (expm1.f64 x) x) |
(*.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) |
(/.f64 (expm1.f64 x) x) |
Compiled 6868 to 4627 computations (32.6% saved)
8 alts after pruning (3 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 366 | 3 | 369 |
| Fresh | 1 | 0 | 1 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 5 | 5 |
| Total | 368 | 8 | 376 |
| Status | Error | Program |
|---|---|---|
| ✓ | 0.0b | (/.f64 1 (/.f64 x (expm1.f64 x))) |
| ▶ | 17.0b | (/.f64 1 (+.f64 (*.f64 -1/2 x) 1)) |
| ✓ | 20.4b | (+.f64 (*.f64 1/2 x) (+.f64 (+.f64 0 (*.f64 1/6 (*.f64 x x))) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
| ✓ | 0.5b | (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3) |
| 20.6b | 1 | |
| ✓ | 0.0b | (/.f64 (expm1.f64 x) x) |
| ▶ | 20.0b | (/.f64 1 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))))) |
| ✓ | 20.5b | (+.f64 (*.f64 1/2 x) 1) |
Compiled 76 to 61 computations (19.7% saved)
Found 1 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (/.f64 1 (+.f64 (*.f64 -1/2 x) 1)) |
Compiled 19 to 15 computations (21.1% saved)
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | 0 | (/.f64 1 (+.f64 (*.f64 -1/2 x) 1)) |
| 0.0ms | x | @ | inf | (/.f64 1 (+.f64 (*.f64 -1/2 x) 1)) |
| 0.0ms | x | @ | -inf | (/.f64 1 (+.f64 (*.f64 -1/2 x) 1)) |
| 1× | batch-egg-rewrite |
| 688× | pow1_binary64 |
| 641× | log1p-expm1-u_binary64 |
| 641× | expm1-log1p-u_binary64 |
| 640× | add-log-exp_binary64 |
| 628× | add-exp-log_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 7 | 8 |
| 1 | 151 | 8 |
| 2 | 1827 | 8 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (fma.f64 -1/2 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (fma.f64 -1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))) (cbrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2)) (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 -1/2 x 1) -1/2) (pow.f64 (fma.f64 -1/2 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (fma.f64 -1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/2 x 1)) 2) -1) (pow.f64 (cbrt.f64 (fma.f64 -1/2 x 1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (fma.f64 -1/2 x 1)) -1) (pow.f64 (sqrt.f64 (fma.f64 -1/2 x 1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (*.f64 -1/8 (pow.f64 x 3)))) (+.f64 (pow.f64 (*.f64 -1/2 x) 2) (-.f64 1 (*.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (pow.f64 (*.f64 -1/2 x) 2) -1)) (fma.f64 -1/2 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -1/2 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -1/2 x 1) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (fma.f64 -1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 -1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 -1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (*.f64 -1/2 x)))))))) |
| 1× | egg-herbie |
| 724× | fma-neg_binary64 |
| 686× | times-frac_binary64 |
| 450× | fma-def_binary64 |
| 417× | cancel-sign-sub-inv_binary64 |
| 398× | associate-*l/_binary64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 41 | 193 |
| 1 | 112 | 179 |
| 2 | 306 | 177 |
| 3 | 985 | 171 |
| 4 | 3002 | 171 |
| 1× | node limit |
| Inputs |
|---|
1 |
(+.f64 (*.f64 1/2 x) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/4 (pow.f64 x 2)))) |
(+.f64 (*.f64 1/2 x) (+.f64 1 (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 1/8 (pow.f64 x 3))))) |
(/.f64 -2 x) |
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x)))) |
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))) |
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 16 (/.f64 1 (pow.f64 x 4))))))) |
(/.f64 -2 x) |
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x)))) |
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))) |
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 16 (/.f64 1 (pow.f64 x 4))))))) |
| Outputs |
|---|
1 |
(+.f64 (*.f64 1/2 x) 1) |
(fma.f64 1/2 x 1) |
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/4 (pow.f64 x 2)))) |
(+.f64 (fma.f64 1/2 x 1) (*.f64 1/4 (*.f64 x x))) |
(fma.f64 1/2 x (fma.f64 1/4 (*.f64 x x) 1)) |
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/4) 1)) |
(fma.f64 x (fma.f64 x 1/4 1/2) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 1 (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 1/8 (pow.f64 x 3))))) |
(+.f64 (fma.f64 1/2 x 1) (fma.f64 1/4 (*.f64 x x) (*.f64 1/8 (pow.f64 x 3)))) |
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/4) (fma.f64 1/8 (pow.f64 x 3) 1))) |
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/8 1/4) 1)) |
(fma.f64 1/8 (pow.f64 x 3) (fma.f64 x (fma.f64 x 1/4 1/2) 1)) |
(/.f64 -2 x) |
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x)))) |
(neg.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 2 x))) |
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x)) |
(-.f64 (/.f64 -2 x) (/.f64 4 (*.f64 x x))) |
(-.f64 (/.f64 (/.f64 -4 x) x) (/.f64 2 x)) |
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))) |
(neg.f64 (+.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 2 x)) (/.f64 8 (pow.f64 x 3)))) |
(+.f64 (+.f64 (/.f64 -8 (pow.f64 x 3)) (/.f64 -4 (*.f64 x x))) (/.f64 -2 x)) |
(+.f64 (-.f64 (/.f64 -2 x) (/.f64 4 (*.f64 x x))) (/.f64 -8 (pow.f64 x 3))) |
(+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x)) (/.f64 -8 (pow.f64 x 3))) |
(+.f64 (-.f64 (/.f64 (/.f64 -4 x) x) (/.f64 2 x)) (/.f64 -8 (pow.f64 x 3))) |
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 16 (/.f64 1 (pow.f64 x 4))))))) |
(neg.f64 (+.f64 (/.f64 8 (pow.f64 x 3)) (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 16 (pow.f64 x 4)))))) |
(-.f64 (/.f64 -8 (pow.f64 x 3)) (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 16 (pow.f64 x 4))))) |
(+.f64 (+.f64 (-.f64 (/.f64 -2 x) (/.f64 4 (*.f64 x x))) (/.f64 -8 (pow.f64 x 3))) (/.f64 -16 (pow.f64 x 4))) |
(+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x)) (+.f64 (/.f64 -8 (pow.f64 x 3)) (/.f64 -16 (pow.f64 x 4)))) |
(-.f64 (-.f64 (/.f64 (/.f64 -4 x) x) (/.f64 2 x)) (+.f64 (/.f64 8 (pow.f64 x 3)) (/.f64 16 (pow.f64 x 4)))) |
(/.f64 -2 x) |
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x)))) |
(neg.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 2 x))) |
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x)) |
(-.f64 (/.f64 -2 x) (/.f64 4 (*.f64 x x))) |
(-.f64 (/.f64 (/.f64 -4 x) x) (/.f64 2 x)) |
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))) |
(neg.f64 (+.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 2 x)) (/.f64 8 (pow.f64 x 3)))) |
(+.f64 (+.f64 (/.f64 -8 (pow.f64 x 3)) (/.f64 -4 (*.f64 x x))) (/.f64 -2 x)) |
(+.f64 (-.f64 (/.f64 -2 x) (/.f64 4 (*.f64 x x))) (/.f64 -8 (pow.f64 x 3))) |
(+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x)) (/.f64 -8 (pow.f64 x 3))) |
(+.f64 (-.f64 (/.f64 (/.f64 -4 x) x) (/.f64 2 x)) (/.f64 -8 (pow.f64 x 3))) |
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 16 (/.f64 1 (pow.f64 x 4))))))) |
(neg.f64 (+.f64 (/.f64 8 (pow.f64 x 3)) (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 16 (pow.f64 x 4)))))) |
(-.f64 (/.f64 -8 (pow.f64 x 3)) (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 16 (pow.f64 x 4))))) |
(+.f64 (+.f64 (-.f64 (/.f64 -2 x) (/.f64 4 (*.f64 x x))) (/.f64 -8 (pow.f64 x 3))) (/.f64 -16 (pow.f64 x 4))) |
(+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x)) (+.f64 (/.f64 -8 (pow.f64 x 3)) (/.f64 -16 (pow.f64 x 4)))) |
(-.f64 (-.f64 (/.f64 (/.f64 -4 x) x) (/.f64 2 x)) (+.f64 (/.f64 8 (pow.f64 x 3)) (/.f64 16 (pow.f64 x 4)))) |
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.1b | (*.f64 -1/720 (pow.f64 x 4)) |
| ✓ | 0.2b | (*.f64 1/12 (pow.f64 x 2)) |
| ✓ | 0.4b | (/.f64 1 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))))) |
| ✓ | 9.0b | (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2))))) |
Compiled 81 to 66 computations (18.5% saved)
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | 0 | (*.f64 -1/720 (pow.f64 x 4)) |
| 1.0ms | x | @ | inf | (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2))))) |
| 0.0ms | x | @ | inf | (*.f64 -1/720 (pow.f64 x 4)) |
| 0.0ms | x | @ | inf | (/.f64 1 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))))) |
| 0.0ms | x | @ | inf | (*.f64 1/12 (pow.f64 x 2)) |
| 1× | batch-egg-rewrite |
| 900× | fma-def_binary64 |
| 438× | fma-neg_binary64 |
| 300× | expm1-udef_binary64 |
| 300× | log1p-udef_binary64 |
| 237× | log-pow_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 59 |
| 1 | 383 | 55 |
| 2 | 4877 | 55 |
| 1× | node limit |
| Inputs |
|---|
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2))))) |
(/.f64 1 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))))) |
(*.f64 1/12 (pow.f64 x 2)) |
(*.f64 -1/720 (pow.f64 x 4)) |
| Outputs |
|---|
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| 1× | egg-herbie |
| 829× | fma-neg_binary64 |
| 762× | unswap-sqr_binary64 |
| 559× | cancel-sign-sub-inv_binary64 |
| 543× | associate-/r*_binary64 |
| 500× | distribute-neg-frac_binary64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 61 | 347 |
| 1 | 159 | 335 |
| 2 | 380 | 333 |
| 3 | 1078 | 314 |
| 4 | 4507 | 314 |
| 1× | node limit |
| Inputs |
|---|
1 |
(+.f64 (*.f64 -1/2 x) 1) |
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))) |
(*.f64 -1/720 (pow.f64 x 4)) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (*.f64 1/12 (pow.f64 x 2))) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (*.f64 1/12 (pow.f64 x 2)))) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 1 (+.f64 (*.f64 -1/2 x) (*.f64 1/12 (pow.f64 x 2))))) |
(*.f64 -1/720 (pow.f64 x 4)) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (*.f64 1/12 (pow.f64 x 2))) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (*.f64 1/12 (pow.f64 x 2)))) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 1 (+.f64 (*.f64 -1/2 x) (*.f64 1/12 (pow.f64 x 2))))) |
1 |
(+.f64 (*.f64 1/2 x) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(/.f64 -720 (pow.f64 x 4)) |
(neg.f64 (+.f64 (*.f64 720 (/.f64 1 (pow.f64 x 4))) (*.f64 43200 (/.f64 1 (pow.f64 x 6))))) |
(-.f64 (*.f64 259200 (/.f64 1 (pow.f64 x 7))) (+.f64 (*.f64 720 (/.f64 1 (pow.f64 x 4))) (*.f64 43200 (/.f64 1 (pow.f64 x 6))))) |
(-.f64 (*.f64 259200 (/.f64 1 (pow.f64 x 7))) (+.f64 (*.f64 720 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 3110400 (/.f64 1 (pow.f64 x 8))) (*.f64 43200 (/.f64 1 (pow.f64 x 6)))))) |
(/.f64 -720 (pow.f64 x 4)) |
(neg.f64 (+.f64 (*.f64 720 (/.f64 1 (pow.f64 x 4))) (*.f64 43200 (/.f64 1 (pow.f64 x 6))))) |
(-.f64 (*.f64 259200 (/.f64 1 (pow.f64 x 7))) (+.f64 (*.f64 720 (/.f64 1 (pow.f64 x 4))) (*.f64 43200 (/.f64 1 (pow.f64 x 6))))) |
(-.f64 (*.f64 259200 (/.f64 1 (pow.f64 x 7))) (+.f64 (*.f64 720 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 3110400 (/.f64 1 (pow.f64 x 8))) (*.f64 43200 (/.f64 1 (pow.f64 x 6)))))) |
| Outputs |
|---|
1 |
(+.f64 (*.f64 -1/2 x) 1) |
(fma.f64 -1/2 x 1) |
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))) |
(+.f64 1 (fma.f64 -1/2 x (*.f64 1/12 (*.f64 x x)))) |
(fma.f64 -1/2 x (fma.f64 1/12 (*.f64 x x) 1)) |
(fma.f64 x (*.f64 x 1/12) (fma.f64 -1/2 x 1)) |
(fma.f64 x (fma.f64 x 1/12 -1/2) 1) |
(*.f64 -1/720 (pow.f64 x 4)) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (*.f64 1/12 (pow.f64 x 2))) |
(fma.f64 -1/720 (pow.f64 x 4) (*.f64 1/12 (*.f64 x x))) |
(fma.f64 -1/720 (pow.f64 x 4) (*.f64 (*.f64 1/12 x) x)) |
(fma.f64 x (*.f64 x 1/12) (*.f64 -1/720 (pow.f64 x 4))) |
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -1/720 1/12))) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (*.f64 1/12 (pow.f64 x 2)))) |
(fma.f64 -1/720 (pow.f64 x 4) (fma.f64 -1/2 x (*.f64 1/12 (*.f64 x x)))) |
(fma.f64 -1/720 (pow.f64 x 4) (fma.f64 -1/2 x (*.f64 (*.f64 1/12 x) x))) |
(fma.f64 -1/720 (pow.f64 x 4) (*.f64 x (+.f64 -1/2 (*.f64 x 1/12)))) |
(fma.f64 -1/720 (pow.f64 x 4) (*.f64 x (fma.f64 x 1/12 -1/2))) |
(fma.f64 x (fma.f64 x 1/12 -1/2) (*.f64 -1/720 (pow.f64 x 4))) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 1 (+.f64 (*.f64 -1/2 x) (*.f64 1/12 (pow.f64 x 2))))) |
(fma.f64 -1/720 (pow.f64 x 4) (+.f64 1 (fma.f64 -1/2 x (*.f64 1/12 (*.f64 x x))))) |
(fma.f64 -1/720 (pow.f64 x 4) (fma.f64 -1/2 x (fma.f64 1/12 (*.f64 x x) 1))) |
(fma.f64 -1/720 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/12) (fma.f64 -1/2 x 1))) |
(fma.f64 x (fma.f64 x 1/12 -1/2) (fma.f64 -1/720 (pow.f64 x 4) 1)) |
(*.f64 -1/720 (pow.f64 x 4)) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (*.f64 1/12 (pow.f64 x 2))) |
(fma.f64 -1/720 (pow.f64 x 4) (*.f64 1/12 (*.f64 x x))) |
(fma.f64 -1/720 (pow.f64 x 4) (*.f64 (*.f64 1/12 x) x)) |
(fma.f64 x (*.f64 x 1/12) (*.f64 -1/720 (pow.f64 x 4))) |
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -1/720 1/12))) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (*.f64 1/12 (pow.f64 x 2)))) |
(fma.f64 -1/720 (pow.f64 x 4) (fma.f64 -1/2 x (*.f64 1/12 (*.f64 x x)))) |
(fma.f64 -1/720 (pow.f64 x 4) (fma.f64 -1/2 x (*.f64 (*.f64 1/12 x) x))) |
(fma.f64 -1/720 (pow.f64 x 4) (*.f64 x (+.f64 -1/2 (*.f64 x 1/12)))) |
(fma.f64 -1/720 (pow.f64 x 4) (*.f64 x (fma.f64 x 1/12 -1/2))) |
(fma.f64 x (fma.f64 x 1/12 -1/2) (*.f64 -1/720 (pow.f64 x 4))) |
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 1 (+.f64 (*.f64 -1/2 x) (*.f64 1/12 (pow.f64 x 2))))) |
(fma.f64 -1/720 (pow.f64 x 4) (+.f64 1 (fma.f64 -1/2 x (*.f64 1/12 (*.f64 x x))))) |
(fma.f64 -1/720 (pow.f64 x 4) (fma.f64 -1/2 x (fma.f64 1/12 (*.f64 x x) 1))) |
(fma.f64 -1/720 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/12) (fma.f64 -1/2 x 1))) |
(fma.f64 x (fma.f64 x 1/12 -1/2) (fma.f64 -1/720 (pow.f64 x 4) 1)) |
1 |
(+.f64 (*.f64 1/2 x) 1) |
(fma.f64 1/2 x 1) |
(fma.f64 x 1/2 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1)) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1)) |
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) 1/6 1)) |
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/6) 1)) |
(fma.f64 x (fma.f64 x 1/6 1/2) 1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) 1/6 (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) 1)) |
(/.f64 -720 (pow.f64 x 4)) |
(neg.f64 (+.f64 (*.f64 720 (/.f64 1 (pow.f64 x 4))) (*.f64 43200 (/.f64 1 (pow.f64 x 6))))) |
(neg.f64 (+.f64 (/.f64 720 (pow.f64 x 4)) (/.f64 43200 (pow.f64 x 6)))) |
(+.f64 (/.f64 -720 (pow.f64 x 4)) (/.f64 -43200 (pow.f64 x 6))) |
(-.f64 (*.f64 259200 (/.f64 1 (pow.f64 x 7))) (+.f64 (*.f64 720 (/.f64 1 (pow.f64 x 4))) (*.f64 43200 (/.f64 1 (pow.f64 x 6))))) |
(-.f64 (-.f64 (/.f64 259200 (pow.f64 x 7)) (/.f64 720 (pow.f64 x 4))) (/.f64 43200 (pow.f64 x 6))) |
(-.f64 (/.f64 259200 (pow.f64 x 7)) (+.f64 (/.f64 720 (pow.f64 x 4)) (/.f64 43200 (pow.f64 x 6)))) |
(+.f64 (/.f64 -720 (pow.f64 x 4)) (+.f64 (/.f64 259200 (pow.f64 x 7)) (/.f64 -43200 (pow.f64 x 6)))) |
(-.f64 (*.f64 259200 (/.f64 1 (pow.f64 x 7))) (+.f64 (*.f64 720 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 3110400 (/.f64 1 (pow.f64 x 8))) (*.f64 43200 (/.f64 1 (pow.f64 x 6)))))) |
(-.f64 (/.f64 259200 (pow.f64 x 7)) (+.f64 (/.f64 720 (pow.f64 x 4)) (+.f64 (/.f64 43200 (pow.f64 x 6)) (/.f64 3110400 (pow.f64 x 8))))) |
(+.f64 (+.f64 (/.f64 -720 (pow.f64 x 4)) (/.f64 -43200 (pow.f64 x 6))) (-.f64 (/.f64 259200 (pow.f64 x 7)) (/.f64 3110400 (pow.f64 x 8)))) |
(+.f64 (+.f64 (/.f64 -720 (pow.f64 x 4)) (/.f64 -43200 (pow.f64 x 6))) (+.f64 (/.f64 259200 (pow.f64 x 7)) (/.f64 -3110400 (pow.f64 x 8)))) |
(/.f64 -720 (pow.f64 x 4)) |
(neg.f64 (+.f64 (*.f64 720 (/.f64 1 (pow.f64 x 4))) (*.f64 43200 (/.f64 1 (pow.f64 x 6))))) |
(neg.f64 (+.f64 (/.f64 720 (pow.f64 x 4)) (/.f64 43200 (pow.f64 x 6)))) |
(+.f64 (/.f64 -720 (pow.f64 x 4)) (/.f64 -43200 (pow.f64 x 6))) |
(-.f64 (*.f64 259200 (/.f64 1 (pow.f64 x 7))) (+.f64 (*.f64 720 (/.f64 1 (pow.f64 x 4))) (*.f64 43200 (/.f64 1 (pow.f64 x 6))))) |
(-.f64 (-.f64 (/.f64 259200 (pow.f64 x 7)) (/.f64 720 (pow.f64 x 4))) (/.f64 43200 (pow.f64 x 6))) |
(-.f64 (/.f64 259200 (pow.f64 x 7)) (+.f64 (/.f64 720 (pow.f64 x 4)) (/.f64 43200 (pow.f64 x 6)))) |
(+.f64 (/.f64 -720 (pow.f64 x 4)) (+.f64 (/.f64 259200 (pow.f64 x 7)) (/.f64 -43200 (pow.f64 x 6)))) |
(-.f64 (*.f64 259200 (/.f64 1 (pow.f64 x 7))) (+.f64 (*.f64 720 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 3110400 (/.f64 1 (pow.f64 x 8))) (*.f64 43200 (/.f64 1 (pow.f64 x 6)))))) |
(-.f64 (/.f64 259200 (pow.f64 x 7)) (+.f64 (/.f64 720 (pow.f64 x 4)) (+.f64 (/.f64 43200 (pow.f64 x 6)) (/.f64 3110400 (pow.f64 x 8))))) |
(+.f64 (+.f64 (/.f64 -720 (pow.f64 x 4)) (/.f64 -43200 (pow.f64 x 6))) (-.f64 (/.f64 259200 (pow.f64 x 7)) (/.f64 3110400 (pow.f64 x 8)))) |
(+.f64 (+.f64 (/.f64 -720 (pow.f64 x 4)) (/.f64 -43200 (pow.f64 x 6))) (+.f64 (/.f64 259200 (pow.f64 x 7)) (/.f64 -3110400 (pow.f64 x 8)))) |
Compiled 4507 to 3415 computations (24.2% saved)
10 alts after pruning (3 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 209 | 3 | 212 |
| Fresh | 1 | 0 | 1 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 6 | 6 |
| Total | 210 | 10 | 220 |
| Status | Error | Program |
|---|---|---|
| ✓ | 0.0b | (/.f64 1 (/.f64 x (expm1.f64 x))) |
| ✓ | 17.0b | (/.f64 1 (+.f64 (*.f64 -1/2 x) 1)) |
| ✓ | 20.4b | (+.f64 (*.f64 1/2 x) (+.f64 (+.f64 0 (*.f64 1/6 (*.f64 x x))) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
| ✓ | 0.5b | (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3) |
| 20.6b | 1 | |
| ✓ | 20.5b | (+.f64 (*.f64 1/2 x) 1) |
| 58.7b | (/.f64 -2 x) | |
| ✓ | 20.0b | (/.f64 1 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))))) |
| 60.0b | (-.f64 (/.f64 (/.f64 -4 x) x) (/.f64 2 x)) | |
| ✓ | 0.0b | (/.f64 (expm1.f64 x) x) |
Compiled 90 to 71 computations (21.1% saved)
| Inputs |
|---|
1 |
1 |
1 |
1 |
(/.f64 -2 x) |
(+.f64 (*.f64 1/2 x) 1) |
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1)) |
(-.f64 (/.f64 (/.f64 -4 x) x) (/.f64 2 x)) |
(/.f64 (expm1.f64 x) x) |
(/.f64 1 (/.f64 x (expm1.f64 x))) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x))) |
(+.f64 (*.f64 1/2 x) (+.f64 (+.f64 0 (*.f64 1/6 (*.f64 x x))) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(pow.f64 (/.f64 x (expm1.f64 x)) -1) |
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3))))) |
(/.f64 1 (+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))))) |
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3) |
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x)) |
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x))) |
| Outputs |
|---|
(/.f64 (expm1.f64 x) x) |
3 calls:
| 46.0ms | x |
| 5.0ms | (/.f64 (-.f64 (exp.f64 x) 1) x) |
| 4.0ms | (/.f64 (-.f64 (exp.f64 x) 1) x) |
| Error | Segments | Branch |
|---|---|---|
| 0.0b | 1 | x |
| 0.0b | 1 | (/.f64 (-.f64 (exp.f64 x) 1) x) |
| 0.0b | 1 | (/.f64 (-.f64 (exp.f64 x) 1) x) |
Compiled 155 to 104 computations (32.9% saved)
| Inputs |
|---|
1 |
1 |
1 |
1 |
(/.f64 -2 x) |
(+.f64 (*.f64 1/2 x) 1) |
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1)) |
(-.f64 (/.f64 (/.f64 -4 x) x) (/.f64 2 x)) |
| Outputs |
|---|
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1)) |
1 calls:
| 6.0ms | x |
| Error | Segments | Branch |
|---|---|---|
| 17.0b | 1 | x |
Compiled 31 to 24 computations (22.6% saved)
| Inputs |
|---|
1 |
1 |
1 |
1 |
(/.f64 -2 x) |
(+.f64 (*.f64 1/2 x) 1) |
| Outputs |
|---|
(/.f64 -2 x) |
(+.f64 (*.f64 1/2 x) 1) |
1 calls:
| 9.0ms | x |
| Error | Segments | Branch |
|---|---|---|
| 17.0b | 2 | x |
Compiled 15 to 12 computations (20% saved)
| 1× | binary-search |
| Time | Left | Right |
|---|---|---|
| 44.0ms | -21.71853681906379 | -0.8676585674290122 |
Compiled 11 to 8 computations (27.3% saved)
| Inputs |
|---|
1 |
1 |
1 |
1 |
(/.f64 -2 x) |
| Outputs |
|---|
(/.f64 -2 x) |
1 |
1 calls:
| 9.0ms | x |
| Error | Segments | Branch |
|---|---|---|
| 18.0b | 2 | x |
Compiled 10 to 8 computations (20% saved)
| 1× | binary-search |
| Time | Left | Right |
|---|---|---|
| 42.0ms | -21.71853681906379 | -0.8676585674290122 |
Compiled 11 to 8 computations (27.3% saved)
Total 0.0b remaining (0%)
Threshold costs 0.0b (0%)
| Inputs |
|---|
1 |
1 |
1 |
1 |
| Outputs |
|---|
1 |
1 calls:
| 4.0ms | x |
| Error | Segments | Branch |
|---|---|---|
| 20.6b | 1 | x |
Compiled 7 to 6 computations (14.3% saved)
| 1× | egg-herbie |
| 2× | +-commutative_binary64 |
| 2× | *-commutative_binary64 |
| 1× | 1-exp_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 19 | 45 |
| 1 | 25 | 45 |
| 1× | fuel |
| 1× | saturated |
| Inputs |
|---|
(/.f64 (expm1.f64 x) x) |
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1)) |
(if (<=.f64 x -6113224645335505/281474976710656) (/.f64 -2 x) (+.f64 (*.f64 1/2 x) 1)) |
(if (<=.f64 x -6113224645335505/281474976710656) (/.f64 -2 x) 1) |
1 |
| Outputs |
|---|
(/.f64 (expm1.f64 x) x) |
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1)) |
(/.f64 1 (+.f64 1 (*.f64 x -1/2))) |
(if (<=.f64 x -6113224645335505/281474976710656) (/.f64 -2 x) (+.f64 (*.f64 1/2 x) 1)) |
(if (<=.f64 x -6113224645335505/281474976710656) (/.f64 -2 x) (+.f64 1 (*.f64 x 1/2))) |
(if (<=.f64 x -6113224645335505/281474976710656) (/.f64 -2 x) 1) |
1 |
Compiled 37 to 29 computations (21.6% saved)
| 1× | egg-herbie |
| 95× | fma-def_binary64 |
| 80× | fma-neg_binary64 |
| 32× | distribute-rgt-in_binary64 |
| 28× | cancel-sign-sub-inv_binary64 |
| 26× | distribute-lft-in_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 6 |
| 1 | 15 | 6 |
| 2 | 18 | 6 |
| 3 | 22 | 6 |
| 4 | 30 | 6 |
| 5 | 40 | 6 |
| 6 | 59 | 6 |
| 7 | 100 | 6 |
| 8 | 145 | 6 |
| 9 | 223 | 6 |
| 10 | 352 | 6 |
| 11 | 511 | 6 |
| 12 | 583 | 6 |
| 13 | 619 | 6 |
| 1× | saturated |
Compiled 12 to 8 computations (33.3% saved)
Compiled 33 to 25 computations (24.2% saved)
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