Details

analyze91.0ms (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)

sample81.0ms (1.2%)

Algorithm

1×

intervals

Results

66.0ms	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)

simplify74.0ms (1.1%)

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	82
2	278	58
3	1167	52
4	3376	49
5	3967	47
6	4726	47
7	5673	47

prune7.0ms (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

2.9b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	3.0b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	3.2b	(.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

▶

3.0b

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

3.2b

(*.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)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
1.0b	(sqrt.f64 PI.f64)
2.8b	(exp.f64 (*.f64 x x))

rewrite227.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

26×	`add-cube-cbrt_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`pow1_binary64`
19×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`

Counts

4 → 165

Calls

4 calls:

21.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
18.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
12.0ms	(exp.f64 (*.f64 x x))
10.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 5707 to 2817 computations (50.6% saved)

series73.0ms (1%)

Error

2.8b

Counts

4 → 24

Calls

4 calls:

37.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
15.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
8.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1604 to 1203 computations (25% saved)

simplify149.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

623×	`associate-/l*_binary64`
249×	`fma-neg_binary64`
163×	`associate-l_binary64`
153×	`associate-/l/_binary64`
142×	`associate-r_binary64`

Counts

189 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	4909
1	677	4305
2	2536	4026
3	4913	4026
4	4987	4026

prune97.0ms (1.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	71	16	87
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	73	16	89

Error

1.1b

Counts

89 → 16

Alt Table

Status	Error	Program
	7.3b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))) (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)))))
	7.6b	(sqrt.f64 (.f64 (pow.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 PI.f64)) 2) (pow.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)))
	3.1b	(exp.f64 (-.f64 (.f64 x x) (-.f64 (log.f64 (.f64 x (sqrt.f64 PI.f64))) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))
	3.0b	(/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (.f64 (/.f64 x (+.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))) (fma.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) 1)))
	3.1b	(.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 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 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 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)))))))
	3.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64)))) (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64))))) (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64)))))
	6.6b	(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.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)))))
	3.3b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64)))))
	3.2b	(.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 PI.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))))))) (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))))))
	3.2b	(pow.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64))) 1)
	7.8b	(.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 PI.f64)) 2) (pow.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))) (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (*.f64 x (sqrt.f64 PI.f64)))))
▶	2.9b	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (+.f64 (/.f64 (exp.f64 (.f64 x x)) x) (.f64 1/2 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 3)))) (+.f64 (.f64 3/4 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 5))) (.f64 15/8 (/.f64 (exp.f64 (.f64 x x)) (*.f64 x (pow.f64 x 6)))))))
	3.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))) (cbrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 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 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 PI.f64)))))
	3.2b	(/.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (sqrt.f64 PI.f64)) (fabs.f64 x))
	11.6b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64))) 3))
	3.0b	(.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)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3)))))

Compiler

Compiled 4048 to 2341 computations (42.2% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

2.8b	(exp.f64 (*.f64 x x))
2.8b	(exp.f64 (*.f64 x x))
2.8b	(exp.f64 (*.f64 x x))
2.8b	(exp.f64 (*.f64 x x))

rewrite164.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

28×	`add-log-exp_binary64`
20×	`add-cube-cbrt_binary64`
16×	`exp-to-pow_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`add-cbrt-cube_binary64`

Counts

4 → 124

Calls

4 calls:

15.0ms	(exp.f64 (*.f64 x x))
13.0ms	(exp.f64 (*.f64 x x))
12.0ms	(exp.f64 (*.f64 x x))
12.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 4171 to 2002 computations (52% saved)

series98.0ms (1.4%)

Error

1.1b

Counts

4 → 24

Calls

4 calls:

12.0ms	(exp.f64 (*.f64 x x))
10.0ms	(exp.f64 (*.f64 x x))
9.0ms	(exp.f64 (*.f64 x x))
9.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 2569 to 1650 computations (35.8% saved)

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

900×	`fma-def_binary64`
414×	`unswap-sqr_binary64`
267×	`distribute-rgt-in_binary64`
263×	`distribute-lft-in_binary64`
223×	`associate-l_binary64`

Counts

148 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	980
1	70	896
2	137	888
3	345	888
4	1152	888
5	4737	888
6	4929	888

prune63.0ms (0.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	44	16	60

Error

1.1b

Counts

60 → 16

Alt Table

Status	Error	Program
	7.3b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))) (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)))))
	7.6b	(sqrt.f64 (.f64 (pow.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 PI.f64)) 2) (pow.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)))
	3.1b	(exp.f64 (-.f64 (.f64 x x) (-.f64 (log.f64 (.f64 x (sqrt.f64 PI.f64))) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))
	3.0b	(/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (.f64 (/.f64 x (+.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))) (fma.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) 1)))
	3.1b	(.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 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 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 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)))))))
	3.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64)))) (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64))))) (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64)))))
	6.6b	(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.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)))))
	3.3b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64)))))
	3.2b	(.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 PI.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))))))) (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))))))
	3.2b	(pow.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64))) 1)
	7.8b	(.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 PI.f64)) 2) (pow.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))) (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (*.f64 x (sqrt.f64 PI.f64)))))
✓	2.9b	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (+.f64 (/.f64 (exp.f64 (.f64 x x)) x) (.f64 1/2 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 3)))) (+.f64 (.f64 3/4 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 5))) (.f64 15/8 (/.f64 (exp.f64 (.f64 x x)) (*.f64 x (pow.f64 x 6)))))))
	3.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))) (cbrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 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 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 PI.f64)))))
	3.2b	(/.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (sqrt.f64 PI.f64)) (fabs.f64 x))
	11.6b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64))) 3))
▶	3.0b	(.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)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3)))))

Compiler

Compiled 2960 to 1738 computations (41.3% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3))
0.7b	(pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3)
1.0b	(sqrt.f64 PI.f64)
2.8b	(exp.f64 (*.f64 x x))

rewrite205.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

25×	`add-cube-cbrt_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`add-log-exp_binary64`
12×	`log1p-expm1-u_binary64`
12×	`expm1-log1p-u_binary64`

Counts

4 → 153

Calls

4 calls:

17.0ms	(pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3)
14.0ms	(exp.f64 (*.f64 x x))
11.0ms	(sqrt.f64 PI.f64)
10.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3))

Compiler

Compiled 4216 to 2253 computations (46.6% saved)

series55.0ms (0.8%)

Error

1.1b

Counts

4 → 24

Calls

4 calls:

19.0ms	(pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3)
14.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3))
9.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1572 to 1192 computations (24.2% saved)

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Rules

706×	`associate-l_binary64`
621×	`associate-r_binary64`
242×	`associate-*l/_binary64`
228×	`associate-*r/_binary64`
218×	`associate-/r*_binary64`

Counts

177 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	2092
1	313	1875
2	936	1831
3	5029	1831

prune76.0ms (1.1%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	13	14
Picked	0	1	1
Done	0	1	1
Total	80	16	96

Error

1.1b

Counts

96 → 16

Alt Table

Status	Error	Program
	7.3b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))) (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)))))
	6.6b	(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) 3)))))
	7.6b	(sqrt.f64 (.f64 (pow.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 PI.f64)) 2) (pow.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)))
	3.1b	(exp.f64 (-.f64 (.f64 x x) (-.f64 (log.f64 (.f64 x (sqrt.f64 PI.f64))) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))
▶	3.0b	(/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (.f64 (/.f64 x (+.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))) (fma.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) 1)))
	3.1b	(.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 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 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 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)))))))
	3.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64)))) (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64))))) (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64)))))
	6.6b	(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.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)))))
	3.3b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64)))))
	3.2b	(.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 PI.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))))))) (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))))))
	3.2b	(pow.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64))) 1)
✓	2.9b	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (+.f64 (/.f64 (exp.f64 (.f64 x x)) x) (.f64 1/2 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 3)))) (+.f64 (.f64 3/4 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 5))) (.f64 15/8 (/.f64 (exp.f64 (.f64 x x)) (*.f64 x (pow.f64 x 6)))))))
	3.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))) (cbrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 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 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 PI.f64)))))
	3.2b	(/.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (sqrt.f64 PI.f64)) (fabs.f64 x))
	11.6b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64))) 3))
✓	3.0b	(.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)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3)))))

Compiler

Compiled 3147 to 1842 computations (41.5% saved)

localize30.0ms (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))
0.7b	(pow.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) 3)
1.0b	(sqrt.f64 PI.f64)
2.8b	(exp.f64 (*.f64 x x))

rewrite249.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

28×	`add-cube-cbrt_binary64`
18×	`add-sqr-sqrt_binary64`
17×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
13×	`pow1_binary64`

Counts

4 → 162

Calls

4 calls:

18.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
15.0ms	(pow.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) 3)
12.0ms	(exp.f64 (*.f64 x x))
11.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 9254 to 5533 computations (40.2% saved)

series77.0ms (1.1%)

Error

1.1b

Counts

4 → 24

Calls

4 calls:

24.0ms	(pow.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) 3)
19.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
12.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 3204 to 2224 computations (30.6% saved)

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-/l*_binary64`
482×	`associate-/r*_binary64`
337×	`fma-def_binary64`
308×	`distribute-rgt-in_binary64`
294×	`distribute-lft-in_binary64`

Counts

186 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	2909
1	480	2512
2	1554	2487
3	5087	2487

prune89.0ms (1.3%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	2	11	13
Picked	1	0	1
Done	0	2	2
Total	73	17	90

Error

1.0b

Counts

90 → 17

Alt Table

Status	Error	Program
	7.6b	(sqrt.f64 (.f64 (pow.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 PI.f64)) 2) (pow.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)))
	3.1b	(exp.f64 (-.f64 (.f64 x x) (-.f64 (log.f64 (.f64 x (sqrt.f64 PI.f64))) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))))
	3.1b	(.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 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 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 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)))))))
	3.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64)))) (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64))))) (cbrt.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64)))))
	6.7b	(/.f64 (/.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))) (sqrt.f64 PI.f64)) (.f64 (/.f64 x (+.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))) (fma.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) 1)))
	11.6b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64))) 3))
	7.3b	(/.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (sqrt.f64 PI.f64)) (.f64 (/.f64 x (+.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))) (fma.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) 1)))
	30.4b	(/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (.f64 (/.f64 x (+.f64 1 (+.f64 (/.f64 1/8 (pow.f64 x 6)) (+.f64 (/.f64 9/16 (pow.f64 x 8)) (/.f64 9/4 (pow.f64 x 10)))))) (fma.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) 1)))
	3.3b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64)))))
	6.6b	(.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.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)) x) (sqrt.f64 PI.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))))))) (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))))))
	3.2b	(pow.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (.f64 x (sqrt.f64 PI.f64))) 1)
	2.9b	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (+.f64 (+.f64 (/.f64 (exp.f64 (.f64 x x)) x) (.f64 1/2 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 3)))) (+.f64 (.f64 3/4 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 5))) (.f64 15/8 (/.f64 (exp.f64 (.f64 x x)) (*.f64 x (pow.f64 x 6)))))))
	3.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))) (cbrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 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 (/.f64 (exp.f64 (.f64 x x)) x) (sqrt.f64 PI.f64)))))
	3.2b	(/.f64 (/.f64 (exp.f64 (+.f64 (.f64 x x) (log1p.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))) (sqrt.f64 PI.f64)) (fabs.f64 x))
	33.2b	(/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (.f64 (/.f64 x (+.f64 1 (+.f64 (/.f64 1/8 (pow.f64 x 6)) (/.f64 9/16 (pow.f64 x 8))))) (fma.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) 1)))
	3.0b	(.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)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3)))))

Compiler

Compiled 4074 to 2531 computations (37.9% saved)

regimes1.4s (19.7%)

Accuracy

Total 0.3b remaining (20.8%)

Threshold costs 0.3b (20.8%)

Compiler

Compiled 35129 to 23187 computations (34% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	72
1	41	72
2	40	72

end3.0ms (0%)

Compiler: Compiled 47 to 30 computations (36.2% saved)

sample3.4s (48.6%)

Algorithm

1×

intervals

Results

2.3s	8000×	body	128	valid
105.0ms	8119×	pre	128	true
32.0ms	119×	body	128	invalid

Compiler

Compiled 1027 to 668 computations (35% saved)

Details

analyze91.0ms (1.3%)

sample81.0ms (1.2%)

simplify74.0ms (1.1%)

prune7.0ms (0.1%)

localize20.0ms (0.3%)

rewrite227.0ms (3.2%)

series73.0ms (1%)

simplify149.0ms (2.1%)

prune97.0ms (1.4%)

localize27.0ms (0.4%)

rewrite164.0ms (2.4%)

series98.0ms (1.4%)

simplify86.0ms (1.2%)

prune63.0ms (0.9%)

localize22.0ms (0.3%)

rewrite205.0ms (2.9%)

series55.0ms (0.8%)

simplify69.0ms (1%)

prune76.0ms (1.1%)

localize30.0ms (0.4%)

rewrite249.0ms (3.6%)

series77.0ms (1.1%)

simplify82.0ms (1.2%)

prune89.0ms (1.3%)

regimes1.4s (19.7%)

simplify4.0ms (0.1%)

end3.0ms (0%)

sample3.4s (48.6%)

Profiling