Time bar (total: 2.4s)
| 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 |
| 75.1% | 0.1% | 24.8% | 13 |
| 75.2% | 0% | 24.8% | 14 |
Compiled 8 to 6 computations (25% saved)
| 881.0ms | 2729× | body | 1024 | valid |
| 305.0ms | 1398× | body | 512 | valid |
| 257.0ms | 3172× | body | 128 | valid |
| 105.0ms | 275× | body | 2048 | valid |
| 103.0ms | 682× | body | 256 | valid |
| 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 | 146 | 6 |
| 9 | 222 | 6 |
| 10 | 349 | 6 |
| 11 | 507 | 6 |
| 12 | 579 | 6 |
| 13 | 615 | 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 7 to 5 computations (28.6% 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 | 146 | 6 |
| 9 | 222 | 6 |
| 10 | 349 | 6 |
| 11 | 507 | 6 |
| 12 | 579 | 6 |
| 13 | 615 | 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 10 to 6 computations (40% saved)
Found 2 expressions with local error:
| New | Error | Program |
|---|---|---|
| ✓ | 0.0b | (expm1.f64 x) |
| ✓ | 0.0b | (/.f64 (expm1.f64 x) x) |
6 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) |
| 0.0ms | x | @ | 0 | (expm1.f64 x) |
| 0.0ms | x | @ | inf | (expm1.f64 x) |
| 1× | batch-egg-rewrite |
| 449× | pow1_binary64 |
| 417× | add-log-exp_binary64 |
| 417× | log1p-expm1-u_binary64 |
| 417× | expm1-log1p-u_binary64 |
| 407× | add-exp-log_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 9 |
| 1 | 83 | 9 |
| 2 | 1104 | 9 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 (expm1.f64 x) 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 (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 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 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 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 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 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.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 (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 cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)))))) (#(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 expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))))))) |
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (*.f64 (exp.f64 x) (exp.f64 x)) (+.f64 1 (*.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (exp.f64 x) (exp.f64 x)) 1) (+.f64 (exp.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (expm1.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (expm1.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (expm1.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (expm1.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (expm1.f64 x))))))) |
| 1× | egg-herbie |
| 803× | unswap-sqr_binary64 |
| 467× | distribute-lft-out_binary64 |
| 406× | fma-def_binary64 |
| 362× | *-commutative_binary64 |
| 227× | distribute-rgt-out_binary64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 157 |
| 1 | 90 | 155 |
| 2 | 198 | 155 |
| 3 | 573 | 143 |
| 4 | 1480 | 143 |
| 5 | 2562 | 143 |
| 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) |
x |
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x) |
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)) |
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x))) |
(-.f64 (exp.f64 x) 1) |
(-.f64 (exp.f64 x) 1) |
(-.f64 (exp.f64 x) 1) |
(-.f64 (exp.f64 x) 1) |
(-.f64 (exp.f64 x) 1) |
(-.f64 (exp.f64 x) 1) |
(-.f64 (exp.f64 x) 1) |
(-.f64 (exp.f64 x) 1) |
| 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 x (*.f64 x 1/6) (fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) 1))) |
(fma.f64 1/2 x (fma.f64 x (*.f64 x (fma.f64 x 1/24 1/6)) 1)) |
(fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) (fma.f64 1/2 x 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) |
x |
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x) |
(fma.f64 1/2 (*.f64 x x) x) |
(fma.f64 x (*.f64 1/2 x) x) |
(*.f64 x (fma.f64 1/2 x 1)) |
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)) |
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x)) |
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) x)) |
(*.f64 x (fma.f64 x (fma.f64 x 1/6 1/2) 1)) |
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x))) |
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) x))) |
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/24 (pow.f64 x 4) x))) |
(fma.f64 x (*.f64 x (fma.f64 x 1/6 1/2)) (fma.f64 1/24 (pow.f64 x 4) x)) |
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 4) x)) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) (fma.f64 1/2 x 1))) |
(-.f64 (exp.f64 x) 1) |
(expm1.f64 x) |
(-.f64 (exp.f64 x) 1) |
(expm1.f64 x) |
(-.f64 (exp.f64 x) 1) |
(expm1.f64 x) |
(-.f64 (exp.f64 x) 1) |
(expm1.f64 x) |
(-.f64 (exp.f64 x) 1) |
(expm1.f64 x) |
(-.f64 (exp.f64 x) 1) |
(expm1.f64 x) |
(-.f64 (exp.f64 x) 1) |
(expm1.f64 x) |
(-.f64 (exp.f64 x) 1) |
(expm1.f64 x) |
Compiled 593 to 294 computations (50.4% saved)
4 alts after pruning (4 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 63 | 4 | 67 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 64 | 4 | 68 |
| Status | Error | Program |
|---|---|---|
| ▶ | 0.0b | (pow.f64 (/.f64 x (expm1.f64 x)) -1) |
| 0.4b | (*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x))) | |
| 43.4b | (*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x)) | |
| 0.1b | (*.f64 (/.f64 1 x) (expm1.f64 x)) |
Compiled 86 to 58 computations (32.6% saved)
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.0b | (expm1.f64 x) | |
| ✓ | 0.0b | (pow.f64 (/.f64 x (expm1.f64 x)) -1) |
| ✓ | 0.0b | (/.f64 x (expm1.f64 x)) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | inf | (/.f64 x (expm1.f64 x)) |
| 1.0ms | x | @ | -inf | (pow.f64 (/.f64 x (expm1.f64 x)) -1) |
| 1.0ms | x | @ | -inf | (/.f64 x (expm1.f64 x)) |
| 1.0ms | x | @ | inf | (pow.f64 (/.f64 x (expm1.f64 x)) -1) |
| 1.0ms | x | @ | 0 | (/.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 |
| 61× | add-sqr-sqrt_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 (exp.f64 (log1p.f64 (/.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 log.f64 (+.f64 1 (expm1.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 cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (expm1.f64 x) 3)))))) (#(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 expm1.f64 (log1p.f64 (/.f64 x (expm1.f64 x)))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.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)) (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 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 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 /.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.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 log.f64 (+.f64 1 (expm1.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 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 expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))))))) |
| 1× | egg-herbie |
| 933× | fma-def_binary64 |
| 803× | unswap-sqr_binary64 |
| 306× | *-commutative_binary64 |
| 167× | associate-*l*_binary64 |
| 151× | distribute-lft-out_binary64 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 35 | 176 |
| 1 | 88 | 170 |
| 2 | 187 | 170 |
| 3 | 522 | 158 |
| 4 | 1422 | 155 |
| 5 | 2981 | 155 |
| 6 | 4954 | 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)) |
(/.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 (*.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 (-.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 1182 to 618 computations (47.7% saved)
4 alts after pruning (4 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 112 | 4 | 116 |
| Fresh | 3 | 0 | 3 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 116 | 4 | 120 |
| Status | Error | Program |
|---|---|---|
| 0.0b | (expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) | |
| 0.1b | (pow.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) | |
| ▶ | 0.0b | (/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x))) |
| 0.1b | (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 x (expm1.f64 x)))) |
Compiled 76 to 54 computations (28.9% saved)
Found 3 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.0b | (expm1.f64 x) | |
| ✓ | 0.0b | (/.f64 1 (expm1.f64 x)) |
| ✓ | 0.0b | (/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | 0 | (/.f64 1 (expm1.f64 x)) |
| 1.0ms | x | @ | -inf | (/.f64 1 (expm1.f64 x)) |
| 0.0ms | x | @ | inf | (/.f64 1 (expm1.f64 x)) |
| 0.0ms | x | @ | 0 | (/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x))) |
| 0.0ms | x | @ | inf | (/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x))) |
| 1× | batch-egg-rewrite |
| 712× | pow1_binary64 |
| 659× | add-log-exp_binary64 |
| 659× | log1p-expm1-u_binary64 |
| 659× | expm1-log1p-u_binary64 |
| 73× | add-sqr-sqrt_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 7 | 18 |
| 1 | 150 | 12 |
| 2 | 1965 | 12 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x))) |
(/.f64 1 (expm1.f64 x)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.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 (/.f64 1 x) (expm1.f64 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 (cbrt.f64 (pow.f64 x -2)) (*.f64 (/.f64 1 (cbrt.f64 x)) (expm1.f64 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 -1/2) (*.f64 (pow.f64 x -1/2) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 x) (/.f64 1 (/.f64 -1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) 1) (/.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x -1/2) 1) (/.f64 (pow.f64 x -1/2) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 (expm1.f64 x) -2))) (/.f64 (/.f64 1 x) (/.f64 1 (cbrt.f64 (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 (pow.f64 (expm1.f64 x) -2))) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x -1/2) (cbrt.f64 (pow.f64 (expm1.f64 x) -2))) (/.f64 (pow.f64 x -1/2) (/.f64 1 (cbrt.f64 (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (expm1.f64 x) -1/2)) (/.f64 (/.f64 1 x) (pow.f64 (expm1.f64 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) (pow.f64 (expm1.f64 x) -1/2)) (/.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 (expm1.f64 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 x) -1) (neg.f64 (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 (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 (/.f64 1 x) (/.f64 -1 (expm1.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 log.f64 (+.f64 1 (expm1.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 (/.f64 (pow.f64 x -2) x) (pow.f64 (/.f64 1 (expm1.f64 x)) 3)))))) (#(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 expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))))))) |
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (expm1.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (pow.f64 (expm1.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) -2)) (/.f64 1 (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (expm1.f64 x) -1/2) (pow.f64 (expm1.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 -1 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (expm1.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (expm1.f64 x)) -1) (pow.f64 (sqrt.f64 (expm1.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (expm1.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (expm1.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 x) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (expm1.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (expm1.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (expm1.f64 x)))))))) |
| 1× | egg-herbie |
| 892× | fma-def_binary64 |
| 753× | fma-neg_binary64 |
| 263× | distribute-rgt-neg-in_binary64 |
| 243× | unswap-sqr_binary64 |
| 229× | cancel-sign-sub-inv_binary64 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 33 | 175 |
| 1 | 85 | 173 |
| 2 | 186 | 173 |
| 3 | 528 | 167 |
| 4 | 1280 | 164 |
| 5 | 2646 | 164 |
| 6 | 4670 | 164 |
| 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) |
(/.f64 1 x) |
(-.f64 (/.f64 1 x) 1/2) |
(-.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1/2) |
(-.f64 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 1/2) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
| 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 (-.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 x) |
(-.f64 (/.f64 1 x) 1/2) |
(+.f64 (/.f64 1 x) -1/2) |
(-.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1/2) |
(+.f64 (fma.f64 1/12 x (/.f64 1 x)) -1/2) |
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) -1/2) |
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 -1/2)) |
(-.f64 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 1/2) |
(+.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))) -1/2) |
(+.f64 (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 (/.f64 1 x))) -1/2) |
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 (pow.f64 x 3) -1/720 -1/2)) |
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) -1/2)) |
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 -1/2))) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (expm1.f64 x)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (expm1.f64 x)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (expm1.f64 x)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (expm1.f64 x)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (expm1.f64 x)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (expm1.f64 x)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (expm1.f64 x)) |
(/.f64 1 (-.f64 (exp.f64 x) 1)) |
(/.f64 1 (expm1.f64 x)) |
Compiled 1102 to 698 computations (36.7% saved)
4 alts after pruning (3 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 100 | 0 | 100 |
| Fresh | 0 | 3 | 3 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 100 | 4 | 104 |
| Status | Error | Program |
|---|---|---|
| ▶ | 0.0b | (expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) |
| 0.1b | (pow.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) | |
| ✓ | 0.0b | (/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x))) |
| 0.1b | (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 x (expm1.f64 x)))) |
Compiled 67 to 47 computations (29.9% saved)
Found 4 expressions with local error:
| New | Error | Program |
|---|---|---|
| 0.0b | (expm1.f64 x) | |
| ✓ | 0.0b | (log1p.f64 (/.f64 (expm1.f64 x) x)) |
| 0.0b | (/.f64 (expm1.f64 x) x) | |
| ✓ | 0.0b | (expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | inf | (log1p.f64 (/.f64 (expm1.f64 x) x)) |
| 1.0ms | x | @ | -inf | (log1p.f64 (/.f64 (expm1.f64 x) x)) |
| 0.0ms | x | @ | 0 | (log1p.f64 (/.f64 (expm1.f64 x) x)) |
| 0.0ms | x | @ | 0 | (expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) |
| 0.0ms | x | @ | inf | (expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) |
| 1× | batch-egg-rewrite |
| 530× | pow1_binary64 |
| 492× | expm1-log1p-u_binary64 |
| 491× | add-log-exp_binary64 |
| 491× | log1p-expm1-u_binary64 |
| 479× | add-exp-log_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 14 |
| 1 | 104 | 14 |
| 2 | 1310 | 14 |
| 1× | node limit |
| Inputs |
|---|
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) |
(log1p.f64 (/.f64 (expm1.f64 x) x)) |
| Outputs |
|---|
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 (expm1.f64 x) x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 (expm1.f64 x) x) 1) 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 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 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 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 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 (/.f64 1 x) (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 (cbrt.f64 (*.f64 x x))) (/.f64 (expm1.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (*.f64 x x))) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (*.f64 x x))) (/.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 (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 (pow.f64 (+.f64 (/.f64 (expm1.f64 x) x) 1) 3) 1) (+.f64 (*.f64 (+.f64 (/.f64 (expm1.f64 x) x) 1) (+.f64 (/.f64 (expm1.f64 x) x) 1)) (+.f64 1 (*.f64 (+.f64 (/.f64 (expm1.f64 x) x) 1) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 (/.f64 (expm1.f64 x) x) 1) (+.f64 (/.f64 (expm1.f64 x) x) 1)) 1) (+.f64 (+.f64 (/.f64 (expm1.f64 x) x) 1) 1))))) (#(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) (cbrt.f64 (*.f64 x x))) (cbrt.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 cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)))))) (#(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 (log1p.f64 (/.f64 (expm1.f64 x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) (cbrt.f64 (pow.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 2)) (cbrt.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) (sqrt.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 (/.f64 (expm1.f64 x) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))))) |
| 1× | egg-herbie |
| 711× | associate-/l*_binary64 |
| 480× | associate-/r*_binary64 |
| 337× | distribute-rgt-in_binary64 |
| 333× | distribute-lft-in_binary64 |
| 206× | fma-def_binary64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 60 | 414 |
| 1 | 155 | 374 |
| 2 | 428 | 355 |
| 3 | 1813 | 342 |
| 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) |
(log.f64 2) |
(+.f64 (log.f64 2) (*.f64 1/4 x)) |
(+.f64 (log.f64 2) (+.f64 (*.f64 1/4 x) (*.f64 5/96 (pow.f64 x 2)))) |
(+.f64 (log.f64 2) (+.f64 (*.f64 1/4 x) (+.f64 (*.f64 1/192 (pow.f64 x 3)) (*.f64 5/96 (pow.f64 x 2))))) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) (pow.f64 x 2)))) (/.f64 1 x)) |
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) (+.f64 (*.f64 -1/2 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) (pow.f64 x 2))) (*.f64 1/3 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3) (pow.f64 x 3))))) (/.f64 1 x)) |
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) (+.f64 (*.f64 -1/2 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) (pow.f64 x 2))) (+.f64 (*.f64 -1/4 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 4) (pow.f64 x 4))) (*.f64 1/3 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3) (pow.f64 x 3)))))) (/.f64 1 x)) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) (pow.f64 x 2)))) (/.f64 1 x)) |
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) (+.f64 (*.f64 -1/2 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) (pow.f64 x 2))) (*.f64 1/3 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3) (pow.f64 x 3))))) (/.f64 1 x)) |
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) (+.f64 (*.f64 -1/2 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) (pow.f64 x 2))) (+.f64 (*.f64 -1/4 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 4) (pow.f64 x 4))) (*.f64 1/3 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3) (pow.f64 x 3)))))) (/.f64 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)) |
(+.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))) |
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 (*.f64 x 1/24) 1/6))))) |
(/.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) |
(log.f64 2) |
(+.f64 (log.f64 2) (*.f64 1/4 x)) |
(+.f64 (log.f64 2) (*.f64 x 1/4)) |
(fma.f64 x 1/4 (log.f64 2)) |
(+.f64 (log.f64 2) (+.f64 (*.f64 1/4 x) (*.f64 5/96 (pow.f64 x 2)))) |
(+.f64 (log.f64 2) (fma.f64 1/4 x (*.f64 (*.f64 x x) 5/96))) |
(+.f64 (log.f64 2) (fma.f64 x 1/4 (*.f64 x (*.f64 x 5/96)))) |
(fma.f64 x 1/4 (fma.f64 x (*.f64 x 5/96) (log.f64 2))) |
(fma.f64 x 1/4 (fma.f64 (*.f64 x x) 5/96 (log.f64 2))) |
(+.f64 (log.f64 2) (+.f64 (*.f64 1/4 x) (+.f64 (*.f64 1/192 (pow.f64 x 3)) (*.f64 5/96 (pow.f64 x 2))))) |
(+.f64 (log.f64 2) (fma.f64 1/4 x (fma.f64 1/192 (pow.f64 x 3) (*.f64 (*.f64 x x) 5/96)))) |
(+.f64 (log.f64 2) (fma.f64 x 1/4 (fma.f64 (*.f64 x x) 5/96 (*.f64 (pow.f64 x 3) 1/192)))) |
(+.f64 (fma.f64 x 1/4 (log.f64 2)) (*.f64 (*.f64 x x) (+.f64 5/96 (*.f64 x 1/192)))) |
(+.f64 (log.f64 2) (*.f64 x (+.f64 (*.f64 x (+.f64 5/96 (*.f64 x 1/192))) 1/4))) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) (pow.f64 x 2)))) (/.f64 1 x)) |
(+.f64 (/.f64 (exp.f64 x) x) (-.f64 (*.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x))) (/.f64 1 x))) |
(+.f64 (*.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x))) (/.f64 (expm1.f64 x) x)) |
(fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (/.f64 (expm1.f64 x) x)) |
(*.f64 (+.f64 (/.f64 (*.f64 (expm1.f64 x) -1/2) x) 1) (/.f64 (expm1.f64 x) x)) |
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) (+.f64 (*.f64 -1/2 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) (pow.f64 x 2))) (*.f64 1/3 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3) (pow.f64 x 3))))) (/.f64 1 x)) |
(+.f64 (/.f64 (exp.f64 x) x) (-.f64 (fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (*.f64 1/3 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)))) (/.f64 1 x))) |
(+.f64 (fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (/.f64 1/3 (/.f64 (pow.f64 x 3) (pow.f64 (expm1.f64 x) 3)))) (/.f64 (expm1.f64 x) x)) |
(+.f64 (*.f64 1/3 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (/.f64 (expm1.f64 x) x))) |
(+.f64 (*.f64 1/3 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (*.f64 (+.f64 (/.f64 (*.f64 (expm1.f64 x) -1/2) x) 1) (/.f64 (expm1.f64 x) x))) |
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) (+.f64 (*.f64 -1/2 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) (pow.f64 x 2))) (+.f64 (*.f64 -1/4 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 4) (pow.f64 x 4))) (*.f64 1/3 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3) (pow.f64 x 3)))))) (/.f64 1 x)) |
(+.f64 (/.f64 (exp.f64 x) x) (-.f64 (fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (fma.f64 -1/4 (/.f64 (pow.f64 (expm1.f64 x) 4) (pow.f64 x 4)) (*.f64 1/3 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3))))) (/.f64 1 x))) |
(+.f64 (fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (fma.f64 1/3 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)) (*.f64 -1/4 (/.f64 (pow.f64 (expm1.f64 x) 4) (pow.f64 x 4))))) (/.f64 (expm1.f64 x) x)) |
(+.f64 (fma.f64 1/3 (pow.f64 (/.f64 (expm1.f64 x) x) 3) (*.f64 -1/4 (/.f64 (pow.f64 (expm1.f64 x) 4) (pow.f64 x 4)))) (fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (/.f64 (expm1.f64 x) x))) |
(+.f64 (fma.f64 -1/4 (pow.f64 (/.f64 (expm1.f64 x) x) 4) (*.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (+.f64 -1/2 (/.f64 (expm1.f64 x) (/.f64 x 1/3))))) (/.f64 (expm1.f64 x) x)) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
(/.f64 (expm1.f64 x) x) |
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) (pow.f64 x 2)))) (/.f64 1 x)) |
(+.f64 (/.f64 (exp.f64 x) x) (-.f64 (*.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x))) (/.f64 1 x))) |
(+.f64 (*.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x))) (/.f64 (expm1.f64 x) x)) |
(fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (/.f64 (expm1.f64 x) x)) |
(*.f64 (+.f64 (/.f64 (*.f64 (expm1.f64 x) -1/2) x) 1) (/.f64 (expm1.f64 x) x)) |
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) (+.f64 (*.f64 -1/2 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) (pow.f64 x 2))) (*.f64 1/3 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3) (pow.f64 x 3))))) (/.f64 1 x)) |
(+.f64 (/.f64 (exp.f64 x) x) (-.f64 (fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (*.f64 1/3 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)))) (/.f64 1 x))) |
(+.f64 (fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (/.f64 1/3 (/.f64 (pow.f64 x 3) (pow.f64 (expm1.f64 x) 3)))) (/.f64 (expm1.f64 x) x)) |
(+.f64 (*.f64 1/3 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (/.f64 (expm1.f64 x) x))) |
(+.f64 (*.f64 1/3 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (*.f64 (+.f64 (/.f64 (*.f64 (expm1.f64 x) -1/2) x) 1) (/.f64 (expm1.f64 x) x))) |
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) (+.f64 (*.f64 -1/2 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) (pow.f64 x 2))) (+.f64 (*.f64 -1/4 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 4) (pow.f64 x 4))) (*.f64 1/3 (/.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3) (pow.f64 x 3)))))) (/.f64 1 x)) |
(+.f64 (/.f64 (exp.f64 x) x) (-.f64 (fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (fma.f64 -1/4 (/.f64 (pow.f64 (expm1.f64 x) 4) (pow.f64 x 4)) (*.f64 1/3 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3))))) (/.f64 1 x))) |
(+.f64 (fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (fma.f64 1/3 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)) (*.f64 -1/4 (/.f64 (pow.f64 (expm1.f64 x) 4) (pow.f64 x 4))))) (/.f64 (expm1.f64 x) x)) |
(+.f64 (fma.f64 1/3 (pow.f64 (/.f64 (expm1.f64 x) x) 3) (*.f64 -1/4 (/.f64 (pow.f64 (expm1.f64 x) 4) (pow.f64 x 4)))) (fma.f64 -1/2 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (/.f64 (expm1.f64 x) x))) |
(+.f64 (fma.f64 -1/4 (pow.f64 (/.f64 (expm1.f64 x) x) 4) (*.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) (*.f64 x x)) (+.f64 -1/2 (/.f64 (expm1.f64 x) (/.f64 x 1/3))))) (/.f64 (expm1.f64 x) x)) |
Compiled 1622 to 841 computations (48.2% saved)
4 alts after pruning (2 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 148 | 0 | 148 |
| Fresh | 0 | 2 | 2 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 1 | 1 |
| Total | 148 | 4 | 152 |
| Status | Error | Program |
|---|---|---|
| ✓ | 0.0b | (expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) |
| 0.1b | (pow.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) | |
| ✓ | 0.0b | (/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x))) |
| 0.1b | (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 x (expm1.f64 x)))) |
Compiled 38 to 27 computations (28.9% saved)
Total -62.1b remaining (-397295.4%)
Threshold costs -62.1b (-397295.4%)
| Inputs |
|---|
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) |
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) |
(/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x))) |
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 x (expm1.f64 x)))) |
(pow.f64 (/.f64 x (expm1.f64 x)) -1) |
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x))) |
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x)) |
(*.f64 (/.f64 1 x) (expm1.f64 x)) |
(/.f64 (expm1.f64 x) x) |
(/.f64 (-.f64 (exp.f64 x) 1) x) |
| Outputs |
|---|
(pow.f64 (/.f64 x (expm1.f64 x)) -1) |
| Time | Error | Segments | Branch |
| 6.0ms | 0.0b | 1 | x |
| 3.0ms | 0.0b | 1 | (/.f64 (-.f64 (exp.f64 x) 1) x) |
Compiled 93 to 47 computations (49.5% saved)
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 9 |
| 1× | saturated |
| Inputs |
|---|
(pow.f64 (/.f64 x (expm1.f64 x)) -1) |
| Outputs |
|---|
(pow.f64 (/.f64 x (expm1.f64 x)) -1) |
| 1× | fuel |
Compiled 14 to 10 computations (28.6% saved)
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