Details

analyze98.0ms (1.3%)

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)

sample72.0ms (1%)

Algorithm

1×

intervals

Results

52.0ms	256×	body	128	valid
7.0ms	261×	pre	128	true
1.0ms	5×	body	128	invalid

Compiler

Compiled 212 to 141 computations (33.5% saved)

simplify79.0ms (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 → 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

2.6b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	2.7b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.9b	(.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

▶

2.7b

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

2.9b

(*.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)

localize19.0ms (0.3%)

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)
2.6b	(exp.f64 (*.f64 x x))

rewrite139.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.9b

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))
8.0ms	(/.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)

series67.0ms (0.9%)

Error

2.5b

Counts

4 → 18

Calls

4 calls:

19.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
18.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
13.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1306 to 962 computations (26.3% saved)

simplify137.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

468×	`distribute-rgt-in_binary64`
432×	`distribute-lft-in_binary64`
301×	`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	2282	1714
4	4808	1714
5	4968	1714
6	4883	1714

prune74.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	37	11	48
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	38	12	50

Error

2.4b

Counts

50 → 12

Alt Table

Status	Error	Program
	3.1b	(.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)))))
	3.1b	(.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)))))
	2.8b	(.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)))))
	9.4b	(.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)))))
	2.8b	(.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 (/.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))))))
▶	2.7b	(.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)))))
	2.9b	(.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))))))
	2.8b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.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)))))))))
	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 1 (/.f64 x (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) x))))))
	2.7b	(.f64 (/.f64 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 PI.f64))) (/.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)))))
	9.4b	(.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)))))

Compiler

Compiled 2210 to 1303 computations (41% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64)))
0.4b	(.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)))))
0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.6b	(exp.f64 (*.f64 x x))

rewrite240.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

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:

36.0ms	(.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)))))
10.0ms	(.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64)))
9.0ms	(/.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)

series124.0ms (1.7%)

Error

2.3b

Counts

4 → 30

Calls

4 calls:

47.0ms	(.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))
20.0ms	(.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64)))
11.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 2126 to 1612 computations (24.2% saved)

simplify161.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

271×	`associate-+l+_binary64`
243×	`associate-l_binary64`
211×	`associate-+r+_binary64`
210×	`associate-/l/_binary64`
198×	`+-commutative_binary64`

Counts

139 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	260	4892
1	733	4166
2	2676	3931
3	4262	3913
4	4946	3913

prune143.0ms (1.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	86	10	96
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	93	15	108

Error

2.0b

Counts

108 → 15

Alt Table

Status	Error	Program
	3.0b	(.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 (exp.f64 (.f64 x x)) (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 (/.f64 1 PI.f64)) (sqrt.f64 x))))
	3.1b	(.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)))))
	3.1b	(.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 (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)))))
	3.1b	(.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)))))))
	2.8b	(.f64 (/.f64 (.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))) (sqrt.f64 (/.f64 (cbrt.f64 1) (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	(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)))))))))
	2.8b	(.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)))))
	3.2b	(.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)))))
	3.0b	(.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))))))
	2.9b	(.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 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) x))
	2.9b	(.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)))))
	9.4b	(.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)))))

Compiler

Compiled 4201 to 2559 computations (39.1% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) x)
0.3b	(.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) x))
0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.6b	(exp.f64 (*.f64 x x))

rewrite256.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

64×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
23×	`add-cbrt-cube_binary64` `distribute-lft-out_binary64`
21×	`add-exp-log_binary64`

Counts

4 → 113

Calls

4 calls:

36.0ms	(.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) x))
31.0ms	(/.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) x)
9.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 4496 to 2696 computations (40% saved)

series124.0ms (1.6%)

Error

2.0b

Counts

4 → 36

Calls

4 calls:

44.0ms	(.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) x))
25.0ms	(/.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) x)
19.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
11.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 2002 to 1588 computations (20.7% saved)

simplify139.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

665×	`associate-/r*_binary64`
527×	`distribute-rgt-in_binary64`
502×	`distribute-lft-in_binary64`
236×	`associate-l_binary64`
162×	`associate-r_binary64`

Counts

149 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	5671
1	641	4875
2	2221	4818
3	5364	4818

prune112.0ms (1.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	3	11	14
Picked	0	1	1
Done	0	0	0
Total	85	17	102

Error

1.9b

Counts

102 → 17

Alt Table

Status	Error	Program
	3.0b	(.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 (exp.f64 (.f64 x x)) (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 (/.f64 1 PI.f64)) (sqrt.f64 x))))
	3.0b	(exp.f64 (+.f64 (.f64 x x) (log.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) x)))))
	3.1b	(.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)))))
	3.1b	(.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 (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)))))
	3.1b	(.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)))))))
	2.8b	(.f64 (.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (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 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))) x))
	2.8b	(.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)))))
	3.2b	(.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)))))
	3.0b	(.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))))))
▶	2.7b	(.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 (+.f64 (pow.f64 1 3) (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	(.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) x))
	2.9b	(.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)))))
	3.0b	(.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (.f64 (.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)))))) (/.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))))) x)))
	3.0b	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (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)))) (cbrt.f64 x)))
	9.4b	(.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)))))

Compiler

Compiled 3478 to 2196 computations (36.9% saved)

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(/.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))
0.7b	(pow.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) 3)
2.6b	(exp.f64 (*.f64 x x))

rewrite262.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

23×	`*-un-lft-identity_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`times-frac_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out_binary64`

Counts

4 → 88

Calls

4 calls:

23.0ms	(pow.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) 3)
13.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 6470 to 4150 computations (35.9% saved)

series151.0ms (2%)

Error

1.9b

Counts

4 → 30

Calls

4 calls:

37.0ms	(pow.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) 3)
28.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
26.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
18.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 4336 to 3137 computations (27.7% saved)

simplify116.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

405×	`associate-/r*_binary64`
342×	`distribute-rgt-in_binary64`
313×	`distribute-lft-in_binary64`
272×	`times-frac_binary64`
270×	`associate-*l/_binary64`

Counts

118 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2703
1	476	2520
2	1378	2477
3	4709	2477
4	4900	2477

prune126.0ms (1.7%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	69	20	89

Error

1.9b

Counts

89 → 20

Alt Table

Status	Error	Program
	3.0b	(.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 (exp.f64 (.f64 x x)) (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 (/.f64 1 PI.f64)) (sqrt.f64 x))))
	3.0b	(exp.f64 (+.f64 (.f64 x x) (log.f64 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (/.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) x)))))
	3.1b	(.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)))))
	3.1b	(.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 (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)))))
	3.1b	(.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)))))))
	27.6b	(.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 (+.f64 (pow.f64 1 3) (+.f64 (/.f64 1/8 (pow.f64 x 6)) (+.f64 (/.f64 297/64 (pow.f64 x 12)) (+.f64 (/.f64 9/16 (pow.f64 x 8)) (/.f64 9/4 (pow.f64 x 10)))))) (.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))))))
	30.2b	(.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 (+.f64 (pow.f64 1 3) (+.f64 (/.f64 1/8 (pow.f64 x 6)) (+.f64 (/.f64 9/16 (pow.f64 x 8)) (/.f64 9/4 (pow.f64 x 10))))) (.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))))))
	33.3b	(.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 (+.f64 (pow.f64 1 3) (+.f64 (/.f64 1/8 (pow.f64 x 6)) (/.f64 9/16 (pow.f64 x 8)))) (.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))))))
	2.8b	(.f64 (.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (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 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))))) x))
	2.8b	(.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)))))
	3.2b	(.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)))))
	3.0b	(.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))))))
	2.7b	(.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 (+.f64 (pow.f64 1 3) (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	(.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (/.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) x))
	2.9b	(.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)))))
	3.0b	(.f64 (.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (/.f64 1 PI.f64))) (.f64 (.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)))))) (/.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))))) x)))
	3.0b	(.f64 (/.f64 (.f64 (exp.f64 (.f64 x x)) (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)))) (cbrt.f64 x)))
	9.4b	(.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)))))

Compiler

Compiled 4192 to 2774 computations (33.8% saved)

regimes2.0s (26.1%)

Accuracy

Total -0.5b remaining (-35.7%)

Threshold costs -0.5b (-35.7%)

Compiler

Compiled 41642 to 28047 computations (32.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	47
1	29	47
2	28	47

end1.0ms (0%)

Compiler: Compiled 31 to 22 computations (29% saved)

sample2.8s (37.7%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
99.0ms	8124×	pre	128	true
24.0ms	124×	body	128	invalid

Compiler

Compiled 1233 to 820 computations (33.5% saved)

Details

analyze98.0ms (1.3%)

sample72.0ms (1%)

simplify79.0ms (1%)

prune9.0ms (0.1%)

localize19.0ms (0.3%)

rewrite139.0ms (1.8%)

series67.0ms (0.9%)

simplify137.0ms (1.8%)

prune74.0ms (1%)

localize19.0ms (0.3%)

rewrite240.0ms (3.2%)

series124.0ms (1.7%)

simplify161.0ms (2.1%)

prune143.0ms (1.9%)

localize22.0ms (0.3%)

rewrite256.0ms (3.4%)

series124.0ms (1.6%)

simplify139.0ms (1.9%)

prune112.0ms (1.5%)

localize31.0ms (0.4%)

rewrite262.0ms (3.5%)

series151.0ms (2%)

simplify116.0ms (1.5%)

prune126.0ms (1.7%)

regimes2.0s (26.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample2.8s (37.7%)

Profiling