Details

analyze9.0ms (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)

sample2.7s (41.8%)

Results

2.6s	8256×	body	128	valid
39.0ms	124×	body	128	invalid

Compiler

Compiled 318 to 211 computations (33.6% saved)

simplify67.0ms (1%)

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

2.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.1b	(.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))))))
▶	2.9b	(.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

3.1b

(*.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))))))

▶

2.9b

(*.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)

localize15.0ms (0.2%)

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)))))
✓	0.5b	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x))
✓	1.0b	(sqrt.f64 (PI.f64))
✓	2.6b	(exp.f64 (*.f64 x x))

series37.0ms (0.6%)

Counts

4 → 36

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x))
16.0ms	(.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)))))
2.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 (PI.f64))

rewrite44.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

79× egg-rr

Counts

4 → 79

Calls

2 calls:

41.0ms

((exp.f64 (*.f64 x x)) (sqrt.f64 (PI.f64)) (/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (*.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))))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	74
1	515	70
2	4787	70
0	0	0
1	0	0

simplify129.0ms (2%)

Algorithm

1×	egg-herbie

Rules

589×	`distribute-rgt-out_binary64`
388×	`associate-/l/_binary64`
370×	`associate-/r/_binary64`
338×	`*-commutative_binary64`
332×	`fma-def_binary64`

Counts

115 → 112

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	1163
1	199	1062
2	572	850
3	2038	725
4	3026	715
5	3895	715
6	4430	715
7	4857	715
8	4990	715
9	4911	715

prune149.0ms (2.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	94	18	112
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	95	19	114

Error

0.7b

Counts

114 → 19

Alt Table

Status	Error	Program
	11.1b	(.f64 (pow.f64 (pow.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) 3) 1/3) (+.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 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))))))
	3.1b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.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)
	11.1b	(.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)))))
	2.9b	(+.f64 (/.f64 (/.f64 (exp.f64 (.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 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x))))
	2.9b	(.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 (exp.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	3.4b	(.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)))))
	3.0b	(.f64 (expm1.f64 (log1p.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)))))
	2.9b	(+.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))))))))
	3.1b	(.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)))))
	3.2b	(expm1.f64 (log1p.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.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)))))))
	3.0b	(.f64 (pow.f64 (sqrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x))) 2) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	3.6b	(.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)))))
	3.3b	(.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)))))
▶	1.5b	(.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)))))
	3.2b	(.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)))))
	3.1b	(exp.f64 (+.f64 (log1p.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 x x) (log.f64 (*.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))))))
	10.9b	(cbrt.f64 (.f64 (pow.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) 3) (pow.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)))) 3)))

Compiler

Compiled 5309 to 3191 computations (39.9% saved)

localize18.0ms (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)))))
✓	0.5b	(/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))
	1.0b	(sqrt.f64 (PI.f64))
✓	1.1b	(pow.f64 (exp.f64 x) x)

series47.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

27.0ms

(/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))

17.0ms

(*.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)

rewrite65.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

55× egg-rr

Counts

3 → 55

Calls

2 calls:

63.0ms

((pow.f64 (exp.f64 x) x) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (*.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))))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	70
1	534	66
2	4993	66
0	0	0
1	0	0

simplify132.0ms (2%)

Algorithm

1×	egg-herbie

Rules

589×	`distribute-rgt-out_binary64`
388×	`associate-/l/_binary64`
370×	`associate-/r/_binary64`
338×	`*-commutative_binary64`
332×	`fma-def_binary64`

Counts

91 → 87

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	1163
1	199	1062
2	572	850
3	2038	725
4	3026	715
5	3895	715
6	4430	715
7	4857	715
8	4990	715
9	4911	715

prune209.0ms (3.2%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	90	16	106
Fresh	12	6	18
Picked	1	0	1
Done	0	0	0
Total	103	22	125

Error

0.3b

Counts

125 → 22

Alt Table

Status	Error	Program
	10.0b	(cbrt.f64 (.f64 (pow.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) 3) (pow.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)))) 3)))
	1.9b	(.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)))))
	2.2b	(.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)))))
	1.8b	(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)
	1.6b	(.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)))))
	1.9b	(.f64 (.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 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 (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)))))
	2.9b	(.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)))))
	1.5b	(.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (/.f64 1 (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)))))
▶	1.5b	(/.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))
	3.4b	(.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)))))
	2.8b	(.f64 (exp.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.5b	(.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)))))
	2.9b	(+.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))))))))
	1.5b	(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))))
	3.0b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.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)))))
	10.0b	(.f64 (cbrt.f64 (pow.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) 3)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	3.6b	(.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)))))
	3.0b	(.f64 (pow.f64 (sqrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x))) 2) (+.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 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) 3) (+.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	(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)))))))
	2.1b	(.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)))))

Compiler

Compiled 5259 to 3176 computations (39.6% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.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)))))
✓	0.5b	(/.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))
	1.0b	(sqrt.f64 (PI.f64))
	1.1b	(pow.f64 (exp.f64 x) x)

series32.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

19.0ms

(/.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))

13.0ms

(*.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)))))

rewrite75.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

68× egg-rr

Counts

2 → 68

Calls

2 calls:

72.0ms

((/.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)) (*.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))))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	81
1	478	77
2	4584	77
3	5144	77
0	0	0
1	0	0

simplify128.0ms (2%)

Algorithm

1×	egg-herbie

Rules

483×	`associate-/l/_binary64`
435×	`sqr-pow_binary64`
430×	`fma-def_binary64`
313×	`*-commutative_binary64`
280×	`distribute-rgt-out_binary64`

Counts

92 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	1331
1	208	1168
2	642	938
3	2227	807
4	3135	797
5	3565	797
6	3778	797
7	4070	797
8	4609	797
9	5202	797

prune314.0ms (4.9%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	7	14	21
Picked	0	1	1
Done	0	0	0
Total	141	23	164

Error

0.3b

Counts

164 → 23

Alt Table

Status	Error	Program
	1.9b	(.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)))))
	1.6b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (cbrt.f64 (.f64 x x))) (/.f64 (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2)))) (cbrt.f64 x)))
	2.2b	(.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)))))
	1.8b	(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)
	1.5b	(/.f64 (fma.f64 (sqrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64)))) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2))) (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))))) (fabs.f64 x))
	1.6b	(.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)))))
	1.9b	(.f64 (.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 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
✓	1.5b	(/.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))
	3.4b	(.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)))))
	2.8b	(.f64 (exp.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.2b	(/.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (+.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))
	3.0b	(/.f64 (.f64 (/.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.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))
	3.3b	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2)))))) (sqrt.f64 (PI.f64))) (sqrt.f64 x)))
	1.5b	(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))))
	2.0b	(/.f64 (.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.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))
	10.0b	(.f64 (cbrt.f64 (pow.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) 3)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	3.6b	(.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)))))
	3.0b	(.f64 (pow.f64 (sqrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x))) 2) (+.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) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (+.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))
	1.9b	(.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) 3) (+.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 (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)))))
	1.5b	(.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)))))
	1.6b	(.f64 (/.f64 (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2)))) (cbrt.f64 (*.f64 x x))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (cbrt.f64 x)))

Compiler

Compiled 6500 to 4342 computations (33.2% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
✓	0.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (+.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)))))
✓	0.5b	(/.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (+.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	(pow.f64 (exp.f64 x) x)

series42.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

18.0ms

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

12.0ms

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

12.0ms

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

rewrite71.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

61× egg-rr

Counts

3 → 61

Calls

2 calls:

69.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	96
1	513	91
2	4771	91
3	5426	91
0	0	0
1	0	0

simplify143.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

507×	`fma-def_binary64`
483×	`associate-/l/_binary64`
344×	`distribute-rgt-out_binary64`
308×	`distribute-lft-out_binary64`
266×	`times-frac_binary64`

Counts

97 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	88	1572
1	237	1395
2	726	1141
3	2555	1003
4	3570	993
5	4321	993
6	4414	993
7	4735	993
8	5113	993

prune177.0ms (2.7%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	1	20	21
Picked	0	1	1
Done	1	0	1
Total	122	24	146

Error

0.3b

Counts

146 → 24

Alt Table

Status	Error	Program
	1.9b	(.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)))))
	2.0b	(/.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))) (+.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 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (cbrt.f64 (.f64 x x))) (/.f64 (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2)))) (cbrt.f64 x)))
	2.2b	(.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)))))
	1.8b	(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)
	1.5b	(/.f64 (fma.f64 (sqrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64)))) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2))) (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))))) (fabs.f64 x))
	1.6b	(.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)))))
	1.9b	(.f64 (.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 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 (exp.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	3.4b	(.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)))))
	2.2b	(/.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (+.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))
	3.0b	(/.f64 (.f64 (/.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.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))
	3.3b	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2)))))) (sqrt.f64 (PI.f64))) (sqrt.f64 x)))
	1.5b	(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))))
	1.9b	(/.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))) (+.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))
	2.0b	(/.f64 (.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.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))
	10.0b	(.f64 (cbrt.f64 (pow.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) 3)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	3.6b	(.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)))))
	3.0b	(.f64 (pow.f64 (sqrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x))) 2) (+.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) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (+.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))
	2.9b	(.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)))))
	1.5b	(.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)))))
	1.6b	(.f64 (/.f64 (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2)))) (cbrt.f64 (*.f64 x x))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (cbrt.f64 x)))
	1.9b	(/.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))))) (+.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))

Compiler

Compiled 4864 to 3220 computations (33.8% saved)

regimes1.2s (19%)

Accuracy

Total 0.9b remaining (73.8%)

Threshold costs 0.9b (73.8%)

Counts

207 → 1

Compiler

Compiled 21536 to 15990 computations (25.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	44
1	29	44
2	28	44

end582.0ms (9%)

Compiler: Compiled 936 to 656 computations (29.9% saved)

Details

analyze9.0ms (0.1%)

sample2.7s (41.8%)

simplify67.0ms (1%)

prune7.0ms (0.1%)

localize15.0ms (0.2%)

series37.0ms (0.6%)

rewrite44.0ms (0.7%)

simplify129.0ms (2%)

prune149.0ms (2.3%)

localize18.0ms (0.3%)

series47.0ms (0.7%)

rewrite65.0ms (1%)

simplify132.0ms (2%)

prune209.0ms (3.2%)

localize17.0ms (0.3%)

series32.0ms (0.5%)

rewrite75.0ms (1.2%)

simplify128.0ms (2%)

prune314.0ms (4.9%)

localize22.0ms (0.3%)

series42.0ms (0.7%)

rewrite71.0ms (1.1%)

simplify143.0ms (2.2%)

prune177.0ms (2.7%)

regimes1.2s (19%)

simplify5.0ms (0.1%)

end582.0ms (9%)

Profiling