Details

analyze8.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 107 to 71 computations (33.6% saved)

sample2.7s (46.6%)

Results

2.7s	8256×	body	128	valid
38.0ms	131×	body	128	invalid

Compiler

Compiled 214 to 142 computations (33.6% saved)

preprocess27.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

626×	`associate-*l/_binary64`
457×	`associate-*r/_binary64`
381×	`associate-/l*_binary64`
344×	`distribute-rgt-in_binary64`
324×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	152
1	91	82
2	305	58
3	1481	52
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 104 to 69 computations (33.7% saved)

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

626×	`associate-*l/_binary64`
457×	`associate-*r/_binary64`
381×	`associate-/l*_binary64`
344×	`distribute-rgt-in_binary64`
324×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	152
1	91	82
2	305	58
3	1481	52

Stop Event

1×	node limit

Counts

1 → 2

prune9.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

1.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.7b	(.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

▶

1.4b

(*.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (*.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))

2.7b

(*.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 413 to 278 computations (32.7% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
✓	1.0b	(sqrt.f64 (PI.f64))
✓	1.1b	(pow.f64 (/.f64 1 (fabs.f64 x)) 5)
✓	1.1b	(pow.f64 (exp.f64 x) x)

series90.0ms (1.6%)

Counts

4 → 36

Calls

9 calls:

33.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))	x	inf
27.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))	x	-inf
11.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))	x	0
7.0ms	(pow.f64 (/.f64 1 (fabs.f64 x)) 5)	x	-inf
6.0ms	(pow.f64 (/.f64 1 (fabs.f64 x)) 5)	x	inf

rewrite35.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

289×	`add-sqr-sqrt_binary64`
275×	`pow1_binary64`
274×	`*-un-lft-identity_binary64`
272×	`add-log-exp_binary64`
270×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	71
1	578	71
0	25	71

Stop Event

1×	saturated
1×	node limit

Counts

4 → 37

simplify50.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-def_binary64`
354×	`associate-/l/_binary64`
342×	`associate-+l+_binary64`
325×	`associate-+r+_binary64`
221×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	1346
1	286	1234
2	952	956
3	4476	833

Stop Event

1×	node limit

Counts

73 → 61

prune92.0ms (1.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	48	13	61
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	49	14	63

Error

0.5b

Counts

63 → 14

Alt Table

Status	Error	Program
	2.5b	(expm1.f64 (log1p.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))))
	2.5b	(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
	1.4b	(/.f64 (.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))))) (sqrt.f64 (PI.f64)))
	1.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (log.f64 (exp.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.7b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.5b	(exp.f64 (log.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))))
	2.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
▶	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))))
	8.4b	(cbrt.f64 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))))
	1.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (.f64 (sqrt.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5)) (sqrt.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.6b	(.f64 (/.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	9.4b	(.f64 (/.f64 (cbrt.f64 (.f64 (.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (exp.f64 x) x)) (pow.f64 (exp.f64 x) x))) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.7b	(.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 3897 to 2448 computations (37.2% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
✓	0.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))
✓	0.3b	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))
	1.1b	(pow.f64 (exp.f64 x) x)

series23.0ms (0.4%)

Counts

3 → 36

Calls

9 calls:

6.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))	x	-inf
4.0ms	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))	x	-inf
3.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))	x	inf
3.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))	x	-inf
2.0ms	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))	x	inf

rewrite38.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

216×	`add-sqr-sqrt_binary64`
205×	`add-log-exp_binary64`
203×	`add-exp-log_binary64`
203×	`pow1_binary64`
203×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	57
1	437	53
0	19	57

Stop Event

1×	saturated
1×	node limit

Counts

3 → 90

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

703×	`associate-l_binary64`
687×	`associate-*l/_binary64`
626×	`fma-def_binary64`
460×	`associate-*r/_binary64`
281×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	685
1	163	681
2	366	661
3	831	625
4	2300	625

Stop Event

1×	node limit

Counts

126 → 121

prune254.0ms (4.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	145	12	157
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	149	22	171

Error

0.4b

Counts

171 → 22

Alt Table

Status	Error	Program
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 (pow.f64 x -2) 3)) 1) (pow.f64 (exp.f64 x) x)) (.f64 (+.f64 (/.f64 1/4 (pow.f64 x 4)) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 x -2)) 1))) x))))
	2.5b	(expm1.f64 (log1p.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))))
	2.5b	(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (pow.f64 (exp.f64 x) (/.f64 x 2))) x))))
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (+.f64 (.f64 1/8 (pow.f64 (pow.f64 x -2) 3)) 1) (.f64 (/.f64 x (pow.f64 (exp.f64 x) x)) (+.f64 (/.f64 1/4 (pow.f64 x 4)) (-.f64 1 (.f64 (*.f64 1/2 (pow.f64 x -2)) 1)))))))
	1.4b	(/.f64 (.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))))) (sqrt.f64 (PI.f64)))
	1.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (log.f64 (exp.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) 1) (/.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) x))))
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 15/8 (pow.f64 x 7)))) (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))))
	1.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (.f64 (sqrt.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5)) (sqrt.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (exp.f64 (-.f64 (.f64 x x) (.f64 5 (log.f64 x)))) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))))
	8.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (cbrt.f64 (pow.f64 (.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 (pow.f64 (exp.f64 x) x) x)) 3))))
	1.3b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (pow.f64 (sqrt.f64 (.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))) 2)))
	9.4b	(.f64 (/.f64 (cbrt.f64 (.f64 (.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (exp.f64 x) x)) (pow.f64 (exp.f64 x) x))) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.7b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
▶	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (pow.f64 (exp.f64 x) x)) (*.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))
	2.5b	(exp.f64 (log.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))))
	2.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (.f64 (/.f64 x (pow.f64 (exp.f64 x) x)) (fma.f64 1/2 (pow.f64 x -2) -1)))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (pow.f64 (cbrt.f64 (.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))) 3)))
	9.8b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (pow.f64 (pow.f64 (.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 (pow.f64 (exp.f64 x) x) x)) 3) 1/3)))

Compiler

Compiled 8485 to 5176 computations (39% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))
✓	0.4b	(/.f64 (.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (pow.f64 (exp.f64 x) x)) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))
✓	0.4b	(*.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (pow.f64 (exp.f64 x) x))
	1.1b	(pow.f64 (exp.f64 x) x)

series16.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

5.0ms	(/.f64 (.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (pow.f64 (exp.f64 x) x)) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))	x	-inf
4.0ms	(/.f64 (.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (pow.f64 (exp.f64 x) x)) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))	x	inf
2.0ms	(*.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (pow.f64 (exp.f64 x) x))	x	-inf
2.0ms	(*.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (pow.f64 (exp.f64 x) x))	x	inf
1.0ms	(/.f64 (.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (pow.f64 (exp.f64 x) x)) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))	x	0

rewrite65.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

257×	`prod-diff_binary64`
183×	`add-sqr-sqrt_binary64`
177×	`pow1_binary64`
176×	`add-log-exp_binary64`
175×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	49
1	389	45
2	4909	45
0	18	49

Stop Event

1×	saturated
1×	node limit

Counts

2 → 76

simplify32.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-def_binary64`
319×	`associate-/r/_binary64`
294×	`fma-neg_binary64`
226×	`cancel-sign-sub-inv_binary64`
210×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	451
1	118	447
2	287	427
3	738	397
4	2594	397

Stop Event

1×	node limit

Counts

100 → 98

prune318.0ms (5.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	171	9	180
Fresh	9	12	21
Picked	1	0	1
Done	0	0	0
Total	181	21	202

Error

0.3b

Counts

202 → 21

Alt Table

Status	Error	Program
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (/.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (pow.f64 (cbrt.f64 (.f64 x (fma.f64 1/2 (pow.f64 x -2) -1))) 2)) (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.f64 (.f64 x (fma.f64 1/2 (pow.f64 x -2) -1)))))))
	2.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (-.f64 (.f64 1/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 4))) (exp.f64 (pow.f64 x 2))) (*.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))
	1.4b	(/.f64 (.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))))) (sqrt.f64 (PI.f64)))
	1.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (log.f64 (exp.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (pow.f64 (exp.f64 x) x))) 2) x) (/.f64 (cbrt.f64 (.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (pow.f64 (exp.f64 x) x))) (fma.f64 1/2 (pow.f64 x -2) -1)))))
	2.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) 1) (/.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) x))))
	1.3b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (pow.f64 (sqrt.f64 (.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))) 2)))
	9.4b	(.f64 (/.f64 (cbrt.f64 (.f64 (.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (exp.f64 x) x)) (pow.f64 (exp.f64 x) x))) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	9.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (pow.f64 (exp.f64 x) x)) 3)) (*.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 15/8 (pow.f64 x 7)))) (/.f64 (.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (pow.f64 (exp.f64 x) x)) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (pow.f64 (exp.f64 x) x))) 3) (*.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))
	9.8b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (pow.f64 (pow.f64 (.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 (pow.f64 (exp.f64 x) x) x)) 3) 1/3)))
	1.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.7b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
▶	1.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (/.f64 (.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 x -4) 3)) -1) (pow.f64 (exp.f64 x) x)) (+.f64 (/.f64 1/16 (pow.f64 x 8)) (fma.f64 1/4 (pow.f64 x -4) 1))) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))
	2.5b	(exp.f64 (log.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))))
	2.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.5b	(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (.f64 x (fma.f64 1/2 (pow.f64 x -2) -1))) 2)) (/.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (cbrt.f64 (.f64 x (fma.f64 1/2 (pow.f64 x -2) -1)))))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (cbrt.f64 (/.f64 (.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (/.f64 (pow.f64 (exp.f64 x) x) x)) (fma.f64 1/2 (pow.f64 x -2) -1))) (pow.f64 (cbrt.f64 (/.f64 (.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (/.f64 (pow.f64 (exp.f64 x) x) x)) (fma.f64 1/2 (pow.f64 x -2) -1))) 2))))
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (exp.f64 (-.f64 (.f64 x x) (.f64 5 (log.f64 x)))) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))))

Compiler

Compiled 10691 to 7147 computations (33.1% saved)

localize34.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (/.f64 (.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 x -4) 3)) -1) (pow.f64 (exp.f64 x) x)) (+.f64 (/.f64 1/16 (pow.f64 x 8)) (fma.f64 1/4 (pow.f64 x -4) 1))) (*.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))
✓	0.4b	(/.f64 (.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 x -4) 3)) -1) (pow.f64 (exp.f64 x) x)) (+.f64 (/.f64 1/16 (pow.f64 x 8)) (fma.f64 1/4 (pow.f64 x -4) 1)))
✓	0.7b	(pow.f64 (pow.f64 x -4) 3)
	1.1b	(pow.f64 (exp.f64 x) x)

series28.0ms (0.5%)

Counts

3 → 36

Calls

9 calls:

9.0ms	(/.f64 (/.f64 (.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 x -4) 3)) -1) (pow.f64 (exp.f64 x) x)) (+.f64 (/.f64 1/16 (pow.f64 x 8)) (fma.f64 1/4 (pow.f64 x -4) 1))) (*.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))	x	-inf
5.0ms	(/.f64 (/.f64 (.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 x -4) 3)) -1) (pow.f64 (exp.f64 x) x)) (+.f64 (/.f64 1/16 (pow.f64 x 8)) (fma.f64 1/4 (pow.f64 x -4) 1))) (*.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))	x	inf
4.0ms	(/.f64 (.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 x -4) 3)) -1) (pow.f64 (exp.f64 x) x)) (+.f64 (/.f64 1/16 (pow.f64 x 8)) (fma.f64 1/4 (pow.f64 x -4) 1)))	x	-inf
4.0ms	(/.f64 (.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 x -4) 3)) -1) (pow.f64 (exp.f64 x) x)) (+.f64 (/.f64 1/16 (pow.f64 x 8)) (fma.f64 1/4 (pow.f64 x -4) 1)))	x	inf
2.0ms	(/.f64 (/.f64 (.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 x -4) 3)) -1) (pow.f64 (exp.f64 x) x)) (+.f64 (/.f64 1/16 (pow.f64 x 8)) (fma.f64 1/4 (pow.f64 x -4) 1))) (*.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))	x	0

rewrite33.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

283×	`add-sqr-sqrt_binary64`
273×	`add-log-exp_binary64`
273×	`pow1_binary64`
272×	`log1p-expm1-u_binary64`
272×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	87
1	615	87
0	28	100

Stop Event

1×	saturated
1×	node limit

Counts

3 → 30

simplify37.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-def_binary64`
436×	`unswap-sqr_binary64`
294×	`fma-neg_binary64`
247×	`associate-/r*_binary64`
226×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	535
1	125	531
2	299	511
3	768	481
4	2887	481

Stop Event

1×	node limit

Counts

66 → 53

prune181.0ms (3.1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	2	18	20
Picked	1	0	1
Done	0	0	0
Total	88	22	110

Error

0.3b

Counts

110 → 22

Alt Table

Status	Error	Program
	9.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (/.f64 (.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 x -4) 3)) -1) (cbrt.f64 (.f64 (.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (exp.f64 x) x)) (pow.f64 (exp.f64 x) x)))) (+.f64 (/.f64 1/16 (pow.f64 x 8)) (fma.f64 1/4 (pow.f64 x -4) 1))) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))
	1.4b	(/.f64 (.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))))) (sqrt.f64 (PI.f64)))
	1.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (log.f64 (exp.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (pow.f64 (exp.f64 x) x))) 2) x) (/.f64 (cbrt.f64 (.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (pow.f64 (exp.f64 x) x))) (fma.f64 1/2 (pow.f64 x -2) -1)))))
	2.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) 1) (/.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) x))))
	1.3b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (pow.f64 (sqrt.f64 (.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))) 2)))
	9.4b	(.f64 (/.f64 (cbrt.f64 (.f64 (.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (exp.f64 x) x)) (pow.f64 (exp.f64 x) x))) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (/.f64 (.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 x -4) 3)) -1) (pow.f64 (exp.f64 x) x)) (+.f64 (/.f64 1/16 (pow.f64 x 8)) (fma.f64 1/4 (pow.f64 x -4) 1))) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (pow.f64 (exp.f64 x) x))) 3) (*.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))
	9.8b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (pow.f64 (pow.f64 (.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 (pow.f64 (exp.f64 x) x) x)) 3) 1/3)))
	1.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.7b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (/.f64 (.f64 (+.f64 (.f64 1/64 (pow.f64 (pow.f64 x -4) 3)) -1) (.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (cbrt.f64 (pow.f64 (exp.f64 x) x)))) (+.f64 (/.f64 1/16 (pow.f64 x 8)) (fma.f64 1/4 (pow.f64 x -4) 1))) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))
	2.5b	(exp.f64 (log.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))))
	2.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.5b	(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (.f64 x (fma.f64 1/2 (pow.f64 x -2) -1))) 2)) (/.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (cbrt.f64 (.f64 x (fma.f64 1/2 (pow.f64 x -2) -1)))))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (/.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (pow.f64 (cbrt.f64 (.f64 x (fma.f64 1/2 (pow.f64 x -2) -1))) 2)) (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.f64 (.f64 x (fma.f64 1/2 (pow.f64 x -2) -1)))))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (cbrt.f64 (/.f64 (.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (/.f64 (pow.f64 (exp.f64 x) x) x)) (fma.f64 1/2 (pow.f64 x -2) -1))) (pow.f64 (cbrt.f64 (/.f64 (.f64 (fma.f64 1/4 (pow.f64 x -4) -1) (/.f64 (pow.f64 (exp.f64 x) x) x)) (fma.f64 1/2 (pow.f64 x -2) -1))) 2))))
	2.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (.f64 (.f64 (fma.f64 1/64 (pow.f64 x -12) -1) (exp.f64 (.f64 x x))) (/.f64 1 (+.f64 (/.f64 1/16 (pow.f64 x 8)) (fma.f64 1/4 (pow.f64 x -4) 1)))) (*.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (exp.f64 (-.f64 (.f64 x x) (.f64 5 (log.f64 x)))) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))))
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 15/8 (pow.f64 x 7)))) (/.f64 (.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (pow.f64 (exp.f64 x) x)) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))

Compiler

Compiled 6309 to 4381 computations (30.6% saved)

regimes954.0ms (16.3%)

Accuracy

Total 0.9b remaining (68.3%)

Threshold costs 0.9b (68.3%)

Counts

180 → 1

Compiler

Compiled 25172 to 18219 computations (27.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	88
1	56	88

Stop Event

1×

saturated

end667.0ms (11.4%)

Stop Event

1×

fuel

Compiler

Compiled 1212 to 877 computations (27.6% saved)

Details

analyze8.0ms (0.1%)

sample2.7s (46.6%)

preprocess27.0ms (0.5%)

simplify18.0ms (0.3%)

prune9.0ms (0.2%)

localize22.0ms (0.4%)

series90.0ms (1.6%)

rewrite35.0ms (0.6%)

simplify50.0ms (0.9%)

prune92.0ms (1.6%)

localize19.0ms (0.3%)

series23.0ms (0.4%)

rewrite38.0ms (0.7%)

simplify33.0ms (0.6%)

prune254.0ms (4.4%)

localize27.0ms (0.5%)

series16.0ms (0.3%)

rewrite65.0ms (1.1%)

simplify32.0ms (0.6%)

prune318.0ms (5.5%)

localize34.0ms (0.6%)

series28.0ms (0.5%)

rewrite33.0ms (0.6%)

simplify37.0ms (0.6%)

prune181.0ms (3.1%)

regimes954.0ms (16.3%)

simplify3.0ms (0%)

end667.0ms (11.4%)

Profiling