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)

sample2.8s (40.8%)

Results

2.7s	8256×	body	128	valid
33.0ms	106×	body	128	invalid

Compiler

Compiled 318 to 211 computations (33.6% saved)

simplify68.0ms (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

2.5b

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))))))
▶	2.6b	(.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))))))

▶

2.6b

(*.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 (exp.f64 (*.f64 x x)) (sqrt.f64 (PI.f64)))
✓	0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
✓	1.0b	(sqrt.f64 (PI.f64))
✓	2.5b	(exp.f64 (*.f64 x x))

series17.0ms (0.2%)

Counts

4 → 36

Calls

4 calls:

10.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 (PI.f64)))
5.0ms	(/.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))

rewrite69.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

232×	`expm1-udef_binary64`
232×	`log1p-udef_binary64`
212×	`log-pow_binary64`
200×	`prod-diff_binary64`
137×	`fma-def_binary64`

Counts

4 → 114

Calls

4 calls:

67.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 (PI.f64)))
67.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
67.0ms	(sqrt.f64 (PI.f64))
67.0ms	(exp.f64 (*.f64 x x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	38
1	267	36
2	3449	36
3	4883	36

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

666×	`associate-*l/_binary64`
544×	`associate-/l*_binary64`
535×	`*-commutative_binary64`
486×	`fma-def_binary64`
442×	`distribute-rgt-out_binary64`

Counts

150 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	497
1	93	473
2	208	449
3	530	440
4	1735	440
5	3370	440
6	5331	440

prune196.0ms (2.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	122	14	136
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	123	15	138

Error

0.7b

Counts

138 → 15

Alt Table

Status	Error	Program
	2.6b	(.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)) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))))))
	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))))))
	3.1b	(.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)))))
	4.1b	(.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)))))
	2.6b	(.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 (sqrt.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (cbrt.f64 (pow.f64 x 4))) (/.f64 (sqrt.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 (cbrt.f64 x) 2))))))
	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)))))
	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 (pow.f64 (cbrt.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) 2) (.f64 (cbrt.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2))))))
	4.5b	(.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)))))
	2.5b	(.f64 (/.f64 (exp.f64 (fma.f64 x x (.f64 -1/2 (log.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 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x x))) 2) (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (pow.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)))))
	11.3b	(.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 (exp.f64 1) (.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)))))
▶	1.1b	(.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)) (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)))))
	2.6b	(.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (exp.f64 (.f64 x x))) -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)))))

Compiler

Compiled 5866 to 3460 computations (41% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series13.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64)))
2.0ms	(pow.f64 (exp.f64 x) x)

rewrite49.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

665×	`log1p-expm1-u_binary64`
665×	`expm1-log1p-u_binary64`
353×	`log-prod_binary64`
132×	`log-pow_binary64`
127×	`expm1-udef_binary64`

Counts

2 → 58

Calls

2 calls:

47.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64)))
47.0ms	(pow.f64 (exp.f64 x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	143	18
2	1738	18
3	5419	18

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

533×	`*-commutative_binary64`
498×	`distribute-rgt-out_binary64`
482×	`fma-def_binary64`
435×	`associate-l_binary64`
346×	`distribute-lft-out_binary64`

Counts

82 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	332
1	79	308
2	182	284
3	477	275
4	1574	275
5	2582	275
6	2857	275
7	3812	275
8	4974	275
9	4963	275

prune211.0ms (3%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	121	17	138
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	129	24	153

Error

0.3b

Counts

153 → 24

Alt Table

Status	Error	Program
	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)))))
	4.1b	(.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)))))
	1.1b	(.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)) (exp.f64 (log.f64 (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))))
	1.5b	(.f64 (/.f64 (.f64 (/.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (cbrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (cbrt.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)))))
	2.6b	(.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 (sqrt.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (cbrt.f64 (pow.f64 x 4))) (/.f64 (sqrt.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 (cbrt.f64 x) 2))))))
	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)))))
	1.5b	(.f64 (/.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (pow.f64 (PI.f64) 1/4)) (/.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.f64 (PI.f64) 1/4))) (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)) (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 (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)))))
	1.6b	(.f64 (/.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) 1) (/.f64 (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)))))
	2.7b	(.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)))))
	1.5b	(.f64 (/.f64 (.f64 (/.f64 1 (cbrt.f64 (PI.f64))) (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.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)))))
	2.5b	(.f64 (/.f64 (exp.f64 (fma.f64 x x (.f64 -1/2 (log.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 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x x))) 2) (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (pow.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)))))
	1.3b	(.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)))))
	1.2b	(.f64 (/.f64 (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (pow.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)))))
	1.2b	(.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))))
▶	1.1b	(.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)))))
	1.2b	(*.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)) (log.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2))))))
	1.1b	(.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (exp.f64 x) x)) -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)))))
	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 (pow.f64 (cbrt.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) 2) (.f64 (cbrt.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2))))))
	1.6b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 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)))))
	1.5b	(.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.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)))))

Compiler

Compiled 6709 to 3986 computations (40.6% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series30.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

17.0ms

(*.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)))))

13.0ms

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

rewrite66.0ms (1%)

Algorithm

1×	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 → 39

Calls

2 calls:

65.0ms

(*.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)))))

65.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

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

simplify94.0ms (1.4%)

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

63 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	62	983
1	160	885
2	483	705
3	1884	607
4	2861	597
5	3771	597
6	4288	597
7	4553	597
8	4901	597

prune189.0ms (2.7%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	123	9	132
Fresh	8	15	23
Picked	1	0	1
Done	0	0	0
Total	132	24	156

Error

0.3b

Counts

156 → 24

Alt Table

Status	Error	Program
	4.1b	(.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)))))
	1.1b	(/.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))
	1.5b	(.f64 (/.f64 (.f64 (/.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (cbrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (cbrt.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)))))
	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)))))
	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 (exp.f64 (log1p.f64 (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))) 1))))
	1.5b	(.f64 (/.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (pow.f64 (PI.f64) 1/4)) (/.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.f64 (PI.f64) 1/4))) (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)) (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 (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)))))
	1.6b	(.f64 (/.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) 1) (/.f64 (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)))))
	1.4b	(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))))
	1.5b	(.f64 (/.f64 (.f64 (/.f64 1 (cbrt.f64 (PI.f64))) (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.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)))))
	2.5b	(.f64 (/.f64 (exp.f64 (fma.f64 x x (.f64 -1/2 (log.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 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x x))) 2) (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (pow.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)))))
	1.3b	(.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)))))
	1.2b	(.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)))))
	2.5b	(+.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))))))))
	1.6b	(.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)))))
	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)
▶	1.1b	(.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)) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))))))
	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 (pow.f64 (cbrt.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) 2) (.f64 (cbrt.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2))))))
	1.6b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 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)))))
	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))))
	1.6b	(.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)))))
	1.5b	(.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.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)))))

Compiler

Compiled 6568 to 4160 computations (36.7% saved)

localize25.0ms (0.4%)

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	(expm1.f64 (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))
	1.0b	(pow.f64 (exp.f64 x) x)
✓	3.2b	(log.f64 (+.f64 1 (expm1.f64 (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))

series169.0ms (2.4%)

Counts

2 → 24

Calls

2 calls:

165.0ms	(log.f64 (+.f64 1 (expm1.f64 (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))
3.0ms	(expm1.f64 (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))

rewrite60.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

419×	`log-prod_binary64`
264×	`pow2_binary64`
194×	`fma-def_binary64`
185×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`

Counts

2 → 94

Calls

2 calls:

58.0ms	(expm1.f64 (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))
58.0ms	(log.f64 (+.f64 1 (expm1.f64 (*.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	12	30
1	227	30
2	2436	30
3	4852	30

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

724×	`associate-/l*_binary64`
563×	`fma-def_binary64`
540×	`associate-*l/_binary64`
455×	`associate-*r/_binary64`
434×	`unswap-sqr_binary64`

Counts

118 → 107

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	39	394
1	95	394
2	184	394
3	396	370
4	1225	370
5	4133	368
6	4347	362
7	4869	362
8	4914	362

prune272.0ms (3.9%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	156	7	163
Fresh	6	17	23
Picked	1	0	1
Done	0	0	0
Total	163	24	187

Error

0.2b

Counts

187 → 24

Alt Table

Status	Error	Program
	4.1b	(.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)))))
	1.1b	(/.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))
	30.0b	(.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 (+.f64 1 (+.f64 (fma.f64 (pow.f64 x -2) (fma.f64 (pow.f64 x -2) 7/8 1/2) (/.f64 19/48 (pow.f64 x 6))) (/.f64 145/384 (pow.f64 x 8))))))))
	1.5b	(.f64 (/.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (pow.f64 (PI.f64) 1/4)) (/.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.f64 (PI.f64) 1/4))) (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)) (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 (+.f64 1 (fma.f64 (+.f64 1 (pow.f64 (expm1.f64 (.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2))) 3)) (/.f64 1 (fma.f64 (expm1.f64 (.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2))) (-.f64 (expm1.f64 (*.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2))) 1) 1)) -1))))))
	2.0b	(.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)))))
	1.6b	(.f64 (/.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) 1) (/.f64 (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)))))
	1.4b	(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))))
	1.1b	(.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)) (log.f64 (+.f64 1 (fma.f64 (sqrt.f64 (exp.f64 (.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2)))) (sqrt.f64 (exp.f64 (.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2)))) -1))))))
	1.5b	(.f64 (/.f64 (.f64 (/.f64 1 (cbrt.f64 (PI.f64))) (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.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)))))
	2.5b	(.f64 (/.f64 (exp.f64 (fma.f64 x x (.f64 -1/2 (log.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)))))
	1.3b	(.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 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 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)))))
	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)) (log.f64 (+.f64 1 (expm1.f64 (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))))))
	1.4b	(.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)) (log.f64 (+.f64 1 (fma.f64 (cbrt.f64 (exp.f64 (.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2)))) (pow.f64 (cbrt.f64 (exp.f64 (.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2)))) 2) -1))))))
	1.5b	(.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.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 (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)) (log.f64 (+.f64 1 (expm1.f64 (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))))))
	1.6b	(.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)))))
	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)
	4.6b	(.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 (+.f64 1 (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 (.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 (.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) (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))))
	1.6b	(.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)))))
	2.5b	(+.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))))))))

Compiler

Compiled 7864 to 5661 computations (28% saved)

regimes1.4s (20.9%)

Accuracy

Total 0.9b remaining (70.9%)

Threshold costs 0.9b (70.9%)

Counts

272 → 1

Compiler

Compiled 30848 to 23610 computations (23.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	53
1	35	53
2	34	53

end837.0ms (12.1%)

Compiler: Compiled 1112 to 831 computations (25.3% saved)

Details

analyze9.0ms (0.1%)

sample2.8s (40.8%)

simplify68.0ms (1%)

prune7.0ms (0.1%)

localize15.0ms (0.2%)

series17.0ms (0.2%)

rewrite69.0ms (1%)

simplify55.0ms (0.8%)

prune196.0ms (2.8%)

localize20.0ms (0.3%)

series13.0ms (0.2%)

rewrite49.0ms (0.7%)

simplify89.0ms (1.3%)

prune211.0ms (3%)

localize24.0ms (0.4%)

series30.0ms (0.4%)

rewrite66.0ms (1%)

simplify94.0ms (1.4%)

prune189.0ms (2.7%)

localize25.0ms (0.4%)

series169.0ms (2.4%)

rewrite60.0ms (0.9%)

simplify75.0ms (1.1%)

prune272.0ms (3.9%)

regimes1.4s (20.9%)

simplify2.0ms (0%)

end837.0ms (12.1%)

Profiling