Details

analyze8.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 107 to 71 computations (33.6% saved)

sample3.1s (53.1%)

Results

3.0s	8256×	body	128	valid
34.0ms	114×	body	128	invalid

Compiler

Compiled 318 to 211 computations (33.6% saved)

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

847×	`unswap-sqr_binary64`
640×	`associate-*l/_binary64`
462×	`associate-*r/_binary64`
372×	`associate-/l*_binary64`
366×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	35	152
1	91	82
2	278	58
3	1167	52
4	3376	49
5	3967	47
6	4726	47
7	5673	47

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

2.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.8b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (fabs.f64 x) (fabs.f64 x)))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 2) (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 3 4) (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 15 8) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))
▶	2.7b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))

Status

Error

Program

2.8b

(*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))

▶

2.7b

(*.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))))

Compiler

Compiled 404 to 266 computations (34.2% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
✓	0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
✓	1.0b	(sqrt.f64 (PI.f64))
✓	2.6b	(exp.f64 (*.f64 x x))

series23.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

18.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
3.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 (PI.f64))

rewrite48.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

249×	`add-sqr-sqrt_binary64`
244×	`log1p-expm1-u_binary64`
244×	`expm1-log1p-u_binary64`
238×	`add-log-exp_binary64`
237×	`add-cbrt-cube_binary64`

Counts

4 → 78

Calls

4 calls:

46.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
46.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
46.0ms	(sqrt.f64 (PI.f64))
46.0ms	(exp.f64 (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	73
1	515	67
2	4787	67
0	0	0
1	0	0

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

691×	`associate-/l*_binary64`
629×	`associate-+l+_binary64`
514×	`distribute-rgt-out_binary64`
259×	`*-commutative_binary64`
258×	`associate-/r/_binary64`

Counts

114 → 108

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	66	998
1	166	910
2	467	752
3	1668	661
4	3171	651
5	3943	651
6	4358	651
7	5226	651

prune135.0ms (2.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	90	18	108
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	92	18	110

Error

0.7b

Counts

110 → 18

Alt Table

Status	Error	Program
	3.0b	(exp.f64 (+.f64 (log1p.f64 (fma.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2) (/.f64 15/8 (pow.f64 x 6)))) (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))))))
	2.7b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.8b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (pow.f64 (cbrt.f64 (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) 3))))
▶	1.2b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.7b	(/.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 1 (fma.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2) (/.f64 15/8 (pow.f64 x 6))))) (fabs.f64 x))
	2.7b	(+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (fabs.f64 x) (pow.f64 x 6))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (fabs.f64 x) (pow.f64 x 4))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
	2.9b	(-.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2) (/.f64 15/8 (pow.f64 x 6))))))) 1)
	2.8b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.7b	(+.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (.f64 (fma.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2) (/.f64 15/8 (pow.f64 x 6))) (/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x))))
	4.4b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	3.1b	(.f64 (/.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 x) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	4.6b	(.f64 (/.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	3.2b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	11.0b	(.f64 (/.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (.f64 x x)) 3) 1/3) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.8b	(.f64 (/.f64 (/.f64 (pow.f64 (E.f64) (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	3.0b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x x))) 2) (cbrt.f64 (exp.f64 (.f64 x x)))) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.9b	(.f64 (/.f64 (/.f64 (expm1.f64 (log1p.f64 (exp.f64 (.f64 x x)))) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 15/8 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 7))) (.f64 (/.f64 (exp.f64 (.f64 x x)) x) (+.f64 1 (+.f64 (/.f64 3/4 (pow.f64 x 4)) (/.f64 1/2 (.f64 x x)))))))

Compiler

Compiled 4833 to 2940 computations (39.2% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
	1.0b	(sqrt.f64 (PI.f64))
✓	1.0b	(pow.f64 (exp.f64 x) x)

series18.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

15.0ms

(*.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))))

2.0ms

(pow.f64 (exp.f64 x) x)

rewrite38.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

259×	`add-sqr-sqrt_binary64`
253×	`log1p-expm1-u_binary64`
253×	`expm1-log1p-u_binary64`
248×	`add-log-exp_binary64`
246×	`add-cbrt-cube_binary64`

Counts

2 → 37

Calls

2 calls:

36.0ms

(*.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))))

36.0ms

(pow.f64 (exp.f64 x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	53
1	534	49
2	4993	49
0	0	0
1	0	0

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

689×	`associate-/l*_binary64`
627×	`associate-+l+_binary64`
510×	`distribute-rgt-out_binary64`
257×	`*-commutative_binary64`
250×	`associate-/r/_binary64`

Counts

61 → 61

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	833
1	153	745
2	444	587
3	1642	496
4	3125	486
5	3887	486
6	4290	486
7	5152	486

prune157.0ms (2.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	88	14	102
Fresh	13	4	17
Picked	1	0	1
Done	0	0	0
Total	102	18	120

Error

0.3b

Counts

120 → 18

Alt Table

Status	Error	Program
	2.7b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.6b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.2b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (-.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))) 1))))
	1.4b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.6b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 3)
	2.7b	(expm1.f64 (log1p.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))))
	2.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 15/8 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 7))) (.f64 (/.f64 (exp.f64 (.f64 x x)) x) (+.f64 1 (+.f64 (/.f64 3/4 (pow.f64 x 4)) (/.f64 1/2 (.f64 x x)))))))
	1.2b	(fma.f64 (sqrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) (sqrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))))
	1.7b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	4.6b	(.f64 (/.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.9b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	11.0b	(.f64 (/.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (.f64 x x)) 3) 1/3) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.2b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 2)
	10.6b	(pow.f64 (pow.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))) 3) 1/3)
	1.4b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.2b	(/.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))) (fabs.f64 x))
▶	1.1b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.4b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) 2) (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))))

Compiler

Compiled 4643 to 2811 computations (39.5% saved)

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
✓	0.4b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
	1.0b	(pow.f64 (exp.f64 x) x)

series28.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

15.0ms

(*.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))))

12.0ms

(/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))

rewrite67.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

269×	`log1p-expm1-u_binary64`
269×	`expm1-log1p-u_binary64`
264×	`add-log-exp_binary64`
261×	`add-cbrt-cube_binary64`
260×	`add-exp-log_binary64`

Counts

2 → 37

Calls

2 calls:

66.0ms

(/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))

66.0ms

(*.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	61
1	569	55
2	4935	55
3	4990	55
0	0	0
1	0	0

simplify97.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

652×	`distribute-rgt-out_binary64`
318×	`*-commutative_binary64`
298×	`distribute-lft-in_binary64`
289×	`associate-/r/_binary64`
282×	`fma-def_binary64`

Counts

61 → 62

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	62	983
1	160	885
2	483	705
3	1883	607
4	2861	597
5	3771	597
6	4288	597
7	4553	597
8	4901	597

prune145.0ms (2.5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	102	23	125

Error

0.3b

Counts

125 → 23

Alt Table

Status	Error	Program
	1.2b	(.f64 (/.f64 (/.f64 (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.6b	(.f64 (/.f64 (.f64 (exp.f64 (pow.f64 x 2)) (sqrt.f64 (/.f64 1 (PI.f64)))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.7b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	4.6b	(.f64 (/.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.7b	(.f64 (/.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	11.0b	(.f64 (/.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (.f64 x x)) 3) 1/3) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.4b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.6b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 3)
▶	1.2b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))
	10.6b	(pow.f64 (pow.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))) 3) 1/3)
	1.6b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64)))) 3) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.4b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.7b	(expm1.f64 (log1p.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))))
	2.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 15/8 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 7))) (.f64 (/.f64 (exp.f64 (.f64 x x)) x) (+.f64 1 (+.f64 (/.f64 3/4 (pow.f64 x 4)) (/.f64 1/2 (.f64 x x)))))))
	1.2b	(fma.f64 (sqrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) (sqrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))))
	1.7b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.6b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.4b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) 2) (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))))
	1.6b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.9b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.2b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 2)
	1.2b	(/.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))) (fabs.f64 x))
	1.6b	(.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64)))) 2) (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))

Compiler

Compiled 5395 to 3388 computations (37.2% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
✓	0.4b	(*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))
✓	0.4b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))
	1.0b	(pow.f64 (exp.f64 x) x)

series22.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

18.0ms

(*.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))

4.0ms

(*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))

rewrite43.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

264×	`add-sqr-sqrt_binary64`
257×	`log1p-expm1-u_binary64`
257×	`expm1-log1p-u_binary64`
251×	`add-log-exp_binary64`
248×	`add-cbrt-cube_binary64`

Counts

2 → 34

Calls

2 calls:

42.0ms

(*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))

42.0ms

(*.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	60
1	550	57
2	4958	57
0	0	0
1	0	0

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

691×	`associate-/l*_binary64`
599×	`associate-+l+_binary64`
489×	`distribute-rgt-out_binary64`
258×	`associate-/r/_binary64`
254×	`associate-/l/_binary64`

Counts

58 → 55

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	907
1	143	823
2	408	667
3	1523	576
4	2991	566
5	3750	566
6	4165	566
7	5023	566

prune149.0ms (2.5%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	4	18	22
Picked	0	1	1
Done	0	0	0
Total	103	24	127

Error

0.3b

Counts

127 → 24

Alt Table

Status	Error	Program
	1.2b	(.f64 (/.f64 (/.f64 (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.6b	(.f64 (/.f64 (.f64 (exp.f64 (pow.f64 x 2)) (sqrt.f64 (/.f64 1 (PI.f64)))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.6b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))
	4.6b	(.f64 (/.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.6b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2) (/.f64 15/8 (pow.f64 x 6)))))) 3)
	1.6b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.7b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))
	1.9b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.2b	(/.f64 (*.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 1 (fma.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2) (/.f64 15/8 (pow.f64 x 6))))) (fabs.f64 x))
	2.7b	(.f64 (/.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	11.0b	(.f64 (/.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (.f64 x x)) 3) 1/3) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.2b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (log.f64 (pow.f64 (exp.f64 (pow.f64 x -2)) (fma.f64 3/4 (pow.f64 x -2) 1/2))))))
✓	1.2b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))
	10.6b	(pow.f64 (pow.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))) 3) 1/3)
	1.6b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64)))) 3) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.4b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.7b	(expm1.f64 (log1p.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))))
	2.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 15/8 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 7))) (.f64 (/.f64 (exp.f64 (.f64 x x)) x) (+.f64 1 (+.f64 (/.f64 3/4 (pow.f64 x 4)) (/.f64 1/2 (.f64 x x)))))))
	1.2b	(fma.f64 (sqrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) (sqrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))))
	1.7b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.2b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 2)
	1.4b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.6b	(.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64)))) 2) (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.4b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) 2) (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))))

Compiler

Compiled 4406 to 2893 computations (34.3% saved)

regimes774.0ms (13.3%)

Accuracy

Total 0.8b remaining (67.4%)

Threshold costs 0.8b (67.4%)

Counts

171 → 1

Compiler

Compiled 17945 to 13329 computations (25.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	48
1	31	48
2	30	48

end570.0ms (9.8%)

Compiler: Compiled 944 to 663 computations (29.8% saved)

Details

analyze8.0ms (0.1%)

sample3.1s (53.1%)

simplify70.0ms (1.2%)

prune7.0ms (0.1%)

localize19.0ms (0.3%)

series23.0ms (0.4%)

rewrite48.0ms (0.8%)

simplify84.0ms (1.4%)

prune135.0ms (2.3%)

localize19.0ms (0.3%)

series18.0ms (0.3%)

rewrite38.0ms (0.6%)

simplify85.0ms (1.5%)

prune157.0ms (2.7%)

localize28.0ms (0.5%)

series28.0ms (0.5%)

rewrite67.0ms (1.2%)

simplify97.0ms (1.7%)

prune145.0ms (2.5%)

localize25.0ms (0.4%)

series22.0ms (0.4%)

rewrite43.0ms (0.7%)

simplify75.0ms (1.3%)

prune149.0ms (2.5%)

regimes774.0ms (13.3%)

simplify2.0ms (0%)

end570.0ms (9.8%)

Profiling