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)

sample3.2s (50.6%)

Results

3.2s	8256×	body	128	valid
40.0ms	131×	body	128	invalid

Compiler

Compiled 214 to 142 computations (33.6% saved)

preprocess30.0ms (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

prune8.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

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)

localize23.0ms (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)

series96.0ms (1.5%)

Counts

4 → 36

Calls

9 calls:

35.0ms	(.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
26.0ms	(.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	(pow.f64 (/.f64 1 (fabs.f64 x)) 5)	x	-inf
10.0ms	(.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
6.0ms	(pow.f64 (/.f64 1 (fabs.f64 x)) 5)	x	inf

rewrite38.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

270×	`log1p-expm1-u_binary64`
270×	`expm1-log1p-u_binary64`
268×	`add-cbrt-cube_binary64`
266×	`add-log-exp_binary64`
263×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	71
1	579	61

Stop Event

1×	node limit

Counts

4 → 65

simplify50.0ms (0.8%)

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

101 → 89

prune127.0ms (2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	69	20	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	71	20	91

Error

0.3b

Counts

91 → 20

Alt Table

Status	Error	Program
	1.7b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))))) 3)
	1.5b	(.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 (exp.f64 (log1p.f64 (pow.f64 (fabs.f64 x) -5))) 1) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.3b	(/.f64 (.f64 (pow.f64 (exp.f64 x) x) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x)))) (sqrt.f64 (PI.f64)))
	2.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 2) (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)))))
	9.4b	(.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3)) (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	(fma.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.4b	(.f64 (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (pow.f64 (exp.f64 x) (/.f64 x 2))) (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)))))
	1.6b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (expm1.f64 (log1p.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 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (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	(expm1.f64 (log1p.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))))))
	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 (+.f64 1 (expm1.f64 (pow.f64 (fabs.f64 x) -5)))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (+.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)))))
	2.6b	(.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) 1) (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) (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2)) (+.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))))))))
	9.3b	(pow.f64 (pow.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x)))) 3) 1/3)
	1.7b	(.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.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)))))
	2.6b	(.f64 (/.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.f64 (exp.f64 x)) x)) (sqrt.f64 (PI.f64))) (+.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))))
	1.3b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))))) 2)

Compiler

Compiled 4893 to 3101 computations (36.6% saved)

localize21.0ms (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:

5.0ms	(.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 (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 (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

rewrite37.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

212×	`add-sqr-sqrt_binary64`
203×	`log1p-expm1-u_binary64`
203×	`expm1-log1p-u_binary64`
201×	`add-cbrt-cube_binary64`
201×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	57
1	437	53

Stop Event

1×	node limit

Counts

3 → 90

simplify38.0ms (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

prune266.0ms (4.2%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	160	9	169
Fresh	4	15	19
Picked	1	0	1
Done	0	0	0
Total	165	24	189

Error

0.2b

Counts

189 → 24

Alt Table

Status	Error	Program
	1.7b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))))) 3)
	1.5b	(.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 (exp.f64 (log1p.f64 (pow.f64 (fabs.f64 x) -5))) 1) (+.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) (fma.f64 15/8 (pow.f64 x -2) 3/4)) (pow.f64 x 5)) (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) 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 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) x))))
	1.3b	(/.f64 (.f64 (pow.f64 (exp.f64 x) x) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x)))) (sqrt.f64 (PI.f64)))
	2.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 2) (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)))))
	9.4b	(.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3)) (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 (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))))
	1.7b	(.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.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 (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)))
	2.6b	(.f64 (/.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.f64 (exp.f64 x)) x)) (sqrt.f64 (PI.f64))) (+.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)))) (pow.f64 (cbrt.f64 (.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))) 3)))
	1.6b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (expm1.f64 (log1p.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 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (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 1/8 (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))) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))))))
	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 (+.f64 1 (expm1.f64 (pow.f64 (fabs.f64 x) -5)))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.3b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))))) 2)
	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))))
	1.5b	(.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 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)) x))))
	1.4b	(.f64 (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (pow.f64 (exp.f64 x) (/.f64 x 2))) (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))))
	1.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (+.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) (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2)) (+.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)))))

Compiler

Compiled 8925 to 5448 computations (39% saved)

localize29.0ms (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 (0.2%)

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 1/4 (pow.f64 x 4)) 1) (pow.f64 (exp.f64 x) x))	x	0

rewrite71.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

257×	`prod-diff_binary64`
177×	`add-sqr-sqrt_binary64`
175×	`log1p-expm1-u_binary64`
175×	`expm1-log1p-u_binary64`
171×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	49
1	391	45
2	4891	45

Stop Event

1×	node limit

Counts

2 → 76

simplify31.0ms (0.5%)

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

prune344.0ms (5.4%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	185	7	192
Fresh	6	17	23
Picked	1	0	1
Done	0	0	0
Total	192	24	216

Error

0.2b

Counts

216 → 24

Alt Table

Status	Error	Program
	1.7b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))))) 3)
	1.5b	(.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 (exp.f64 (log1p.f64 (pow.f64 (fabs.f64 x) -5))) 1) (+.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) (fma.f64 15/8 (pow.f64 x -2) 3/4)) (pow.f64 x 5)) (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) 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 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) 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 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)) x))))
	5.1b	(.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 (cbrt.f64 (pow.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)))))
	1.3b	(/.f64 (.f64 (pow.f64 (exp.f64 x) x) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x)))) (sqrt.f64 (PI.f64)))
	2.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 2) (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)))))
	9.4b	(.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3)) (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 (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))))
	1.7b	(.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.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 (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)))
	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)))
▶	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (.f64 (-.f64 9/16 (/.f64 225/64 (pow.f64 x 4))) (pow.f64 (exp.f64 x) x)) (.f64 (-.f64 3/4 (.f64 15/8 (pow.f64 x -2))) (pow.f64 x 5))) (/.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	(expm1.f64 (log1p.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))))))
	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 (+.f64 1 (expm1.f64 (pow.f64 (fabs.f64 x) -5)))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (+.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 1/4 (pow.f64 x 4)) 1) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (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 (/.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 (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))))
	1.7b	(.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (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)))))
	1.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2)) (+.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 (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) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.f64 (exp.f64 x)) x))) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))
	1.6b	(.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) (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x))) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))

Compiler

Compiled 11287 to 7552 computations (33.1% saved)

localize35.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (.f64 (-.f64 9/16 (/.f64 225/64 (pow.f64 x 4))) (pow.f64 (exp.f64 x) x)) (.f64 (-.f64 3/4 (*.f64 15/8 (pow.f64 x -2))) (pow.f64 x 5)))
✓	0.4b	(.f64 (-.f64 3/4 (.f64 15/8 (pow.f64 x -2))) (pow.f64 x 5))
✓	0.4b	(*.f64 (-.f64 9/16 (/.f64 225/64 (pow.f64 x 4))) (pow.f64 (exp.f64 x) x))
	1.1b	(pow.f64 (exp.f64 x) x)

series22.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

5.0ms	(/.f64 (.f64 (-.f64 9/16 (/.f64 225/64 (pow.f64 x 4))) (pow.f64 (exp.f64 x) x)) (.f64 (-.f64 3/4 (*.f64 15/8 (pow.f64 x -2))) (pow.f64 x 5)))	x	-inf
4.0ms	(/.f64 (.f64 (-.f64 9/16 (/.f64 225/64 (pow.f64 x 4))) (pow.f64 (exp.f64 x) x)) (.f64 (-.f64 3/4 (*.f64 15/8 (pow.f64 x -2))) (pow.f64 x 5)))	x	inf
3.0ms	(.f64 (-.f64 3/4 (.f64 15/8 (pow.f64 x -2))) (pow.f64 x 5))	x	inf
2.0ms	(*.f64 (-.f64 9/16 (/.f64 225/64 (pow.f64 x 4))) (pow.f64 (exp.f64 x) x))	x	inf
2.0ms	(*.f64 (-.f64 9/16 (/.f64 225/64 (pow.f64 x 4))) (pow.f64 (exp.f64 x) x))	x	-inf

rewrite39.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

224×	`log1p-expm1-u_binary64`
224×	`expm1-log1p-u_binary64`
222×	`add-sqr-sqrt_binary64`
217×	`add-cbrt-cube_binary64`
216×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	70
1	484	70

Stop Event

1×	node limit

Counts

3 → 72

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Rules

960×	`fma-neg_binary64`
417×	`fma-def_binary64`
355×	`associate-/r*_binary64`
314×	`times-frac_binary64`
221×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	702
1	179	666
2	466	666
3	1293	594
4	4761	594

Stop Event

1×	node limit

Counts

108 → 98

prune269.0ms (4.2%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	23	23
Picked	0	1	1
Done	0	0	0
Total	146	24	170

Error

0.2b

Counts

170 → 24

Alt Table

Status	Error	Program
	1.7b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))))) 3)
	1.5b	(.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 (exp.f64 (log1p.f64 (pow.f64 (fabs.f64 x) -5))) 1) (+.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) (fma.f64 15/8 (pow.f64 x -2) 3/4)) (pow.f64 x 5)) (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) 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 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) 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 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)) x))))
	5.1b	(.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 (cbrt.f64 (pow.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)))))
	1.3b	(/.f64 (.f64 (pow.f64 (exp.f64 x) x) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x)))) (sqrt.f64 (PI.f64)))
	2.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 2) (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)))))
	9.4b	(.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3)) (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 (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))))
	1.7b	(.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.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 (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)))
	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)))
✓	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (.f64 (-.f64 9/16 (/.f64 225/64 (pow.f64 x 4))) (pow.f64 (exp.f64 x) x)) (.f64 (-.f64 3/4 (.f64 15/8 (pow.f64 x -2))) (pow.f64 x 5))) (/.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	(expm1.f64 (log1p.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))))))
	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 (+.f64 1 (expm1.f64 (pow.f64 (fabs.f64 x) -5)))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (+.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 1/4 (pow.f64 x 4)) 1) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (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 (/.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 (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))))
	1.7b	(.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (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)))))
	1.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) 2)) (+.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 (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) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.f64 (exp.f64 x)) x))) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))
	1.6b	(.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) (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x))) (.f64 (fma.f64 1/2 (pow.f64 x -2) -1) x))))

Compiler

Compiled 9064 to 6559 computations (27.6% saved)

regimes772.0ms (12.1%)

Accuracy

Total 1.0b remaining (75.1%)

Threshold costs 1.0b (75.1%)

Counts

148 → 1

Compiler

Compiled 19289 to 14106 computations (26.9% saved)

simplify2.0ms (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	42	88
1	53	88

Stop Event

1×

saturated

end675.0ms (10.6%)

Stop Event

1×

fuel

Compiler

Compiled 1127 to 815 computations (27.7% saved)

Details

analyze8.0ms (0.1%)

sample3.2s (50.6%)

preprocess30.0ms (0.5%)

simplify18.0ms (0.3%)

prune8.0ms (0.1%)

localize23.0ms (0.4%)

series96.0ms (1.5%)

rewrite38.0ms (0.6%)

simplify50.0ms (0.8%)

prune127.0ms (2%)

localize21.0ms (0.3%)

series23.0ms (0.4%)

rewrite37.0ms (0.6%)

simplify38.0ms (0.6%)

prune266.0ms (4.2%)

localize29.0ms (0.5%)

series16.0ms (0.2%)

rewrite71.0ms (1.1%)

simplify31.0ms (0.5%)

prune344.0ms (5.4%)

localize35.0ms (0.6%)

series22.0ms (0.3%)

rewrite39.0ms (0.6%)

simplify65.0ms (1%)

prune269.0ms (4.2%)

regimes772.0ms (12.1%)

simplify2.0ms (0%)

end675.0ms (10.6%)

Profiling