Details

analyze95.0ms (0.6%)

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)

sample73.0ms (0.4%)

Algorithm

1×

intervals

Results

57.0ms	256×	body	128	valid
3.0ms	260×	pre	128	true
1.0ms	4×	body	128	invalid

Compiler

Compiled 212 to 141 computations (33.5% saved)

simplify79.0ms (0.5%)

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 → 1

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	35	152
1	91	86
2	261	60
3	1006	52
4	3215	49
5	3806	47
6	4565	47
7	5512	47

prune9.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

2.3b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	2.5b	(.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)))))
	2.6b	(.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))))))

Status

Error

Program

▶

2.5b

(*.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)))))

2.6b

(*.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))))))

Compiler

Compiled 301 to 201 computations (33.2% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)
2.4b	(exp.f64 (*.f64 x x))

rewrite136.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

26×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64` `times-frac_binary64`
15×	`sqrt-prod_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 87

Calls

4 calls:

9.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
5.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 2952 to 1389 computations (52.9% saved)

series66.0ms (0.4%)

Error

2.2b

Counts

4 → 18

Calls

4 calls:

21.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
19.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
11.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1306 to 962 computations (26.3% saved)

simplify137.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

470×	`distribute-rgt-in_binary64`
437×	`distribute-lft-in_binary64`
303×	`associate-/r/_binary64`
184×	`associate-/l*_binary64`
177×	`associate-l_binary64`

Counts

105 → 48

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	1907
1	327	1726
2	821	1714
3	2290	1714
4	4880	1714
5	4993	1714
6	4931	1714

prune73.0ms (0.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	39	9	48
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	40	10	50

Error

2.0b

Counts

50 → 10

Alt Table

Status	Error	Program
	2.5b	(.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 (cbrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) (cbrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))))) (/.f64 x (/.f64 (cbrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) x))))))
	10.6b	(.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (exp.f64 (.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)))))
	10.7b	(.f64 (/.f64 (/.f64 (cbrt.f64 (pow.f64 (exp.f64 (.f64 x x)) 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 (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (/.f64 (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)))))
	2.6b	(.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))))))
▶	2.4b	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (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)))))
	2.5b	(.f64 (/.f64 (.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (/.f64 (sqrt.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)))))
	2.5b	(.f64 (/.f64 (.f64 (/.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (fabs.f64 (cbrt.f64 PI.f64))) (/.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (sqrt.f64 (cbrt.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 (/.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (fabs.f64 (cbrt.f64 PI.f64))) (/.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (sqrt.f64 (cbrt.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)))))
	2.4b	(.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 (pow.f64 1/2 3) (pow.f64 (/.f64 3/4 (.f64 x x)) 3)) (.f64 (.f64 x x) (+.f64 1/4 (-.f64 (/.f64 9/16 (pow.f64 x 4)) (/.f64 3/8 (.f64 x x)))))))))

Compiler

Compiled 2068 to 1203 computations (41.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64)))
0.3b	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (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)))))
0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.4b	(exp.f64 (*.f64 x x))

rewrite246.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

31×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
21×	`associate-r_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 109

Calls

4 calls:

37.0ms	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (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)))))
13.0ms	(.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64)))
10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 4437 to 2570 computations (42.1% saved)

series129.0ms (0.8%)

Error

2.0b

Counts

4 → 30

Calls

4 calls:

51.0ms	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (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)))))
21.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
18.0ms	(.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64)))
12.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 2126 to 1612 computations (24.2% saved)

simplify221.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

275×	`associate-+l+_binary64`
249×	`associate-l_binary64`
219×	`associate-/l/_binary64`
215×	`associate-+r+_binary64`
199×	`associate-r_binary64` `+-commutative_binary64`

Counts

139 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	270	4918
1	756	4176
2	2746	3941
3	4354	3923
4	4979	3923
5	4995	3923
6	4929	3923

prune152.0ms (0.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	84	11	95
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	89	16	105

Error

1.6b

Counts

105 → 16

Alt Table

Status	Error	Program
▶	2.4b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))
	2.7b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x)) (.f64 (cbrt.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))) (cbrt.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))) (cbrt.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))))
	2.4b	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) (/.f64 x (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x)))) x))))))
	10.6b	(.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (exp.f64 (.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)))))
	2.7b	(.f64 (/.f64 (exp.f64 (.f64 x x)) (.f64 (cbrt.f64 (fabs.f64 x)) (cbrt.f64 (fabs.f64 x)))) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) (cbrt.f64 x))))
	2.8b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (/.f64 (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)))))
	2.6b	(.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 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))
	2.5b	(.f64 (/.f64 (.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (/.f64 (sqrt.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 (.f64 (cbrt.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x))) (cbrt.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)))) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (cbrt.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (*.f64 x x)) x)))))
	2.5b	(.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x))) (sqrt.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 (sqrt.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x))) (sqrt.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))
	2.8b	(.f64 (/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (fabs.f64 (cbrt.f64 PI.f64))) (/.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (sqrt.f64 (cbrt.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 (exp.f64 (.f64 x x)) (fabs.f64 (cbrt.f64 (/.f64 1 PI.f64)))) (sqrt.f64 (cbrt.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)))))
	2.7b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (cbrt.f64 (exp.f64 (.f64 x x))))) (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)))))
	2.4b	(/.f64 (.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (+.f64 1 (pow.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) 3))) (.f64 x (+.f64 1 (.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) (+.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) -1)))))
	2.7b	(exp.f64 (-.f64 (.f64 x x) (log.f64 (/.f64 x (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))))

Compiler

Compiled 4377 to 2687 computations (38.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))
0.4b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))
0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.4b	(exp.f64 (*.f64 x x))

rewrite406.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

94×	`times-frac_binary64`
70×	`add-sqr-sqrt_binary64`
65×	`-un-lft-identity_binary64` `associate-l*_binary64`
55×	`add-cube-cbrt_binary64`
42×	`sqrt-prod_binary64`

Counts

4 → 171

Calls

4 calls:

44.0ms	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))
41.0ms	(.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))
12.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 7829 to 4834 computations (38.3% saved)

series148.0ms (0.9%)

Error

1.6b

Counts

4 → 36

Calls

4 calls:

47.0ms	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))
35.0ms	(.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))
22.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
11.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 2229 to 1788 computations (19.8% saved)

simplify321.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

386×	`distribute-rgt-in_binary64`
374×	`distribute-lft-in_binary64`
291×	`associate-l_binary64`
287×	`associate-r_binary64`
229×	`associate-l/_binary64` `-commutative_binary64`

Counts

207 → 163

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	343	9655
1	1006	8341
2	3984	8341
3	4554	8341
4	4976	8341
5	4882	8341

prune241.0ms (1.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	155	8	163
Fresh	5	10	15
Picked	0	1	1
Done	0	0	0
Total	160	19	179

Error

1.5b

Counts

179 → 19

Alt Table

Status	Error	Program
	3.1b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (sqrt.f64 (.f64 (cbrt.f64 (/.f64 1 PI.f64)) (cbrt.f64 (/.f64 1 PI.f64)))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (sqrt.f64 (cbrt.f64 (/.f64 1 PI.f64))) (cbrt.f64 x)))))
	3.0b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (sqrt.f64 (.f64 (cbrt.f64 (/.f64 1 PI.f64)) (cbrt.f64 (/.f64 1 PI.f64)))) (sqrt.f64 x)) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (sqrt.f64 (cbrt.f64 (/.f64 1 PI.f64))) (sqrt.f64 x)))))
	2.7b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64)))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (cbrt.f64 x)))))
	2.5b	(.f64 (sqrt.f64 (/.f64 (exp.f64 (.f64 x x)) 1)) (.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))
	2.8b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x)) (cbrt.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x))) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (cbrt.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x)))))
✓	2.4b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))
	2.7b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x)) (.f64 (cbrt.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))) (cbrt.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))) (cbrt.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))))
▶	2.4b	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) (/.f64 x (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x)))) x))))))
	2.8b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (/.f64 (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)))))
	2.7b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))
	2.7b	(.f64 (.f64 (cbrt.f64 (.f64 (exp.f64 (.f64 x x)) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))) (cbrt.f64 (.f64 (exp.f64 (.f64 x x)) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))) (cbrt.f64 (.f64 (exp.f64 (.f64 x x)) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))))
	2.7b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64)))) 1) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) x))))
	2.8b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64)))) (sqrt.f64 x)) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (sqrt.f64 x)))))
	2.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x))) (cbrt.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)))) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (cbrt.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (*.f64 x x)) x)))))
	2.5b	(.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x))) (sqrt.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 (sqrt.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x))) (sqrt.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))
	2.8b	(.f64 (/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (fabs.f64 (cbrt.f64 PI.f64))) (/.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (sqrt.f64 (cbrt.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 (exp.f64 (.f64 x x)) (fabs.f64 (cbrt.f64 (/.f64 1 PI.f64)))) (sqrt.f64 (cbrt.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)))))
	2.7b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (cbrt.f64 (exp.f64 (.f64 x x))))) (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	(exp.f64 (-.f64 (.f64 x x) (log.f64 (/.f64 x (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))))

Compiler

Compiled 6865 to 4317 computations (37.1% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64)))
0.3b	(/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) (/.f64 x (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) x)))
0.3b	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) (/.f64 x (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x)))) x))))))
2.4b	(exp.f64 (*.f64 x x))

rewrite2.1s (12.5%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

1682×	`times-frac_binary64`
1035×	`*-un-lft-identity_binary64`
735×	`add-sqr-sqrt_binary64`
723×	`add-cube-cbrt_binary64`
628×	`sqrt-prod_binary64`

Counts

4 → 750

Calls

4 calls:

595.0ms	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) (/.f64 x (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x)))) x))))))
40.0ms	(/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) (/.f64 x (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) x)))
10.0ms	(.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64)))
2.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 31758 to 19757 computations (37.8% saved)

series138.0ms (0.8%)

Error

1.5b

Counts

4 → 30

Calls

4 calls:

49.0ms	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) (/.f64 x (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x)))) x))))))
22.0ms	(.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64)))
20.0ms	(/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) (/.f64 x (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) x)))
18.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 2376 to 1812 computations (23.7% saved)

simplify744.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

763×	`associate-/r/_binary64`
714×	`associate-/l/_binary64`
525×	`associate-/l*_binary64`
472×	`times-frac_binary64`
160×	`distribute-rgt-in_binary64`

Counts

780 → 733

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	824	46911
1	1919	43307
2	4976	43307

prune846.0ms (5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	732	1	733
Fresh	0	17	17
Picked	1	0	1
Done	0	1	1
Total	733	19	752

Error

1.5b

Counts

752 → 19

Alt Table

Status	Error	Program
	3.1b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (sqrt.f64 (.f64 (cbrt.f64 (/.f64 1 PI.f64)) (cbrt.f64 (/.f64 1 PI.f64)))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (sqrt.f64 (cbrt.f64 (/.f64 1 PI.f64))) (cbrt.f64 x)))))
	3.0b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (sqrt.f64 (.f64 (cbrt.f64 (/.f64 1 PI.f64)) (cbrt.f64 (/.f64 1 PI.f64)))) (sqrt.f64 x)) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (sqrt.f64 (cbrt.f64 (/.f64 1 PI.f64))) (sqrt.f64 x)))))
	2.7b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64)))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (cbrt.f64 x)))))
	2.5b	(.f64 (sqrt.f64 (/.f64 (exp.f64 (.f64 x x)) 1)) (.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))
	2.8b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x)) (cbrt.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x))) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (cbrt.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x)))))
	2.4b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))
	2.7b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x)) (.f64 (cbrt.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))) (cbrt.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))) (cbrt.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))))
	2.8b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (/.f64 (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)))))
	2.7b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))
	2.5b	(.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64)))) (.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) (/.f64 x (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x)))) x))))))
	2.7b	(.f64 (.f64 (cbrt.f64 (.f64 (exp.f64 (.f64 x x)) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))) (cbrt.f64 (.f64 (exp.f64 (.f64 x x)) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))) (cbrt.f64 (.f64 (exp.f64 (.f64 x x)) (.f64 (/.f64 (sqrt.f64 (/.f64 1 PI.f64)) x) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))))))
	2.7b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64)))) 1) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) x))))
	2.8b	(.f64 (/.f64 (exp.f64 (.f64 x x)) 1) (.f64 (/.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64)))) (sqrt.f64 x)) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 PI.f64))) (sqrt.f64 x)))))
	2.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x))) (cbrt.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)))) (.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (cbrt.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (*.f64 x x)) x)))))
	2.5b	(.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x))) (sqrt.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 (sqrt.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (exp.f64 (.f64 x x)) x))) (sqrt.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))
	2.8b	(.f64 (/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (fabs.f64 (cbrt.f64 PI.f64))) (/.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (sqrt.f64 (cbrt.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 (exp.f64 (.f64 x x)) (fabs.f64 (cbrt.f64 (/.f64 1 PI.f64)))) (sqrt.f64 (cbrt.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)))))
	2.7b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (cbrt.f64 (exp.f64 (.f64 x x))))) (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	(exp.f64 (-.f64 (.f64 x x) (log.f64 (/.f64 x (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))))

Compiler

Compiled 19614 to 11983 computations (38.9% saved)

regimes7.6s (44.8%)

Accuracy

Total -0.6b remaining (-45.9%)

Threshold costs -0.6b (-45.9%)

Compiler

Compiled 122330 to 85179 computations (30.4% saved)

simplify3.0ms (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	27	66
1	34	66
2	33	66

end1.0ms (0%)

Compiler: Compiled 43 to 32 computations (25.6% saved)

sample2.8s (16.8%)

Algorithm

1×

intervals

Results

1.7s	8000×	body	128	valid
97.0ms	8131×	pre	128	true
26.0ms	131×	body	128	invalid

Compiler

Compiled 1205 to 801 computations (33.5% saved)

Details

analyze95.0ms (0.6%)

sample73.0ms (0.4%)

simplify79.0ms (0.5%)

prune9.0ms (0.1%)

localize22.0ms (0.1%)

rewrite136.0ms (0.8%)

series66.0ms (0.4%)

simplify137.0ms (0.8%)

prune73.0ms (0.4%)

localize20.0ms (0.1%)

rewrite246.0ms (1.5%)

series129.0ms (0.8%)

simplify221.0ms (1.3%)

prune152.0ms (0.9%)

localize20.0ms (0.1%)

rewrite406.0ms (2.4%)

series148.0ms (0.9%)

simplify321.0ms (1.9%)

prune241.0ms (1.4%)

localize28.0ms (0.2%)

rewrite2.1s (12.5%)

series138.0ms (0.8%)

simplify744.0ms (4.4%)

prune846.0ms (5%)

regimes7.6s (44.8%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.8s (16.8%)

Profiling