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 (44.9%)

Results

2.6s	8256×	body	128	valid
46.0ms	158×	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

prune10.0ms (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
	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))))))
▶	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 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))

Status

Error

Program

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))))))

▶

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 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) 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 (exp.f64 x) x)
✓	1.1b	(pow.f64 (/.f64 1 (fabs.f64 x)) 5)

series83.0ms (1.4%)

Counts

4 → 36

Calls

9 calls:

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
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
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
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

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-def_binary64`
355×	`associate-/l/_binary64`
340×	`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	4474	833

Stop Event

1×	node limit

Counts

101 → 89

prune119.0ms (2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	74	15	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	76	15	91

Error

0.3b

Counts

91 → 15

Alt Table

Status	Error	Program
	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)))))
	1.7b	(.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)))))
	2.0b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (+.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 (/.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)))))
	1.7b	(.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 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	11.4b	(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)
	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)))))
	1.2b	(/.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)))
	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 (log.f64 (exp.f64 (pow.f64 (fabs.f64 x) -5))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.5b	(.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)))))
	2.7b	(.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)))))
	1.3b	(.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))))))))
	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)

Compiler

Compiled 4521 to 2838 computations (37.2% saved)

localize20.0ms (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))
✓	0.4b	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))
✓	0.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))
	1.1b	(pow.f64 (exp.f64 x) x)

series24.0ms (0.4%)

Counts

3 → 36

Calls

9 calls:

6.0ms	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) 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
3.0ms	(.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

rewrite36.0ms (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

simplify39.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

688×	`associate-l_binary64`
685×	`associate-*l/_binary64`
626×	`fma-def_binary64`
472×	`associate-*r/_binary64`
282×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	685
1	163	681
2	366	661
3	835	625
4	2301	625

Stop Event

1×	node limit

Counts

126 → 120

prune207.0ms (3.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	160	8	168
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	162	21	183

Error

0.3b

Counts

183 → 21

Alt Table

Status	Error	Program
	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)))))
	1.7b	(.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)))))
	2.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (.f64 (/.f64 x (exp.f64 (.f64 x x))) (fma.f64 1/2 (pow.f64 x -2) -1))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 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)))))
	2.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 (exp.f64 (.f64 x x)) x)))) 1) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	2.0b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (+.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 (/.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)))))
	1.7b	(.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)))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
▶	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (pow.f64 (exp.f64 x) x)) x) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	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)
	1.6b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.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)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	11.4b	(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)
	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)))))
	1.2b	(/.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)))
	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 (log.f64 (exp.f64 (pow.f64 (fabs.f64 x) -5))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.5b	(.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)))))
	2.7b	(.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)))))
	1.3b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x)) (.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 15/8 (pow.f64 x 7))))))
	2.6b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))

Compiler

Compiled 8650 to 5207 computations (39.8% 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))
	0.4b	(.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 1 (/.f64 1/2 (.f64 x x))) (pow.f64 (exp.f64 x) x))
	1.1b	(pow.f64 (exp.f64 x) x)

series6.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

3.0ms	(.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (pow.f64 (exp.f64 x) x))	x	-inf
2.0ms	(.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (pow.f64 (exp.f64 x) x))	x	inf
1.0ms	(.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (pow.f64 (exp.f64 x) x))	x	0

rewrite40.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

440×	`log-prod_binary64`
229×	`fma-def_binary64`
175×	`prod-diff_binary64`
172×	`expm1-udef_binary64`
172×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	211	16
2	2617	15

Stop Event

1×	node limit

Counts

1 → 44

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

924×	`fma-def_binary64`
434×	`associate-l_binary64`
401×	`unswap-sqr_binary64`
272×	`associate-r_binary64`
233×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	208
1	50	196
2	113	196
3	270	178
4	798	178
5	3314	178

Stop Event

1×	node limit

Counts

56 → 56

prune258.0ms (4.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	177	7	184
Fresh	5	15	20
Picked	1	0	1
Done	0	0	0
Total	183	22	205

Error

0.3b

Counts

205 → 22

Alt Table

Status	Error	Program
	1.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (pow.f64 (exp.f64 x) (/.f64 x 2)))) x) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	1.2b	(/.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)))
	10.6b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3))) x) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.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 (log.f64 (exp.f64 (pow.f64 (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 (+.f64 1 (/.f64 1/2 (.f64 x x))) (pow.f64 (exp.f64 x) x)) x) (.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 15/8 (pow.f64 x 7))))))
	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)))))
	1.7b	(.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)))))
	2.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (.f64 (/.f64 x (exp.f64 (.f64 x x))) (fma.f64 1/2 (pow.f64 x -2) -1))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (fma.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x) (.f64 (/.f64 (/.f64 1/2 x) x) (pow.f64 (exp.f64 x) x))) x) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	2.7b	(.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)))))
	2.0b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (+.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 (/.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 (fma.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)) (.f64 (/.f64 (/.f64 1/2 x) x) (pow.f64 (exp.f64 x) x))) x) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 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)))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	11.4b	(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)
	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)))))
	1.5b	(.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)))))
	2.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 (exp.f64 (.f64 x x)) x)))) 1) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	7.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (fma.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))) (.f64 (/.f64 (/.f64 1/2 x) x) (pow.f64 (exp.f64 x) x))) x) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	2.6b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (exp.f64 (fma.f64 x x (log1p.f64 (/.f64 (/.f64 1/2 x) x)))) x) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	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)

Compiler

Compiled 9401 to 5629 computations (40.1% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (pow.f64 (exp.f64 x) x)) x) (.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 15/8 (pow.f64 x 7))))))
✓	0.3b	(*.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 15/8 (pow.f64 x 7))))
	0.4b	(.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (pow.f64 (exp.f64 x) x))
	1.1b	(pow.f64 (exp.f64 x) x)

series23.0ms (0.4%)

Counts

2 → 24

Calls

6 calls:

6.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (pow.f64 (exp.f64 x) x)) x) (.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 15/8 (pow.f64 x 7))))))	x	-inf
6.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (pow.f64 (exp.f64 x) x)) x) (.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 15/8 (pow.f64 x 7))))))	x	inf
3.0ms	(*.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 15/8 (pow.f64 x 7))))	x	-inf
3.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (pow.f64 (exp.f64 x) x)) x) (.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 15/8 (pow.f64 x 7))))))	x	0
3.0ms	(*.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 15/8 (pow.f64 x 7))))	x	inf

rewrite32.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

287×	`log1p-expm1-u_binary64`
287×	`expm1-log1p-u_binary64`
284×	`add-cbrt-cube_binary64`
281×	`add-log-exp_binary64`
278×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	80
1	609	70

Stop Event

1×	node limit

Counts

2 → 32

simplify31.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

495×	`associate-*l/_binary64`
470×	`associate-/r*_binary64`
448×	`associate-/l*_binary64`
396×	`associate-*r/_binary64`
374×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	907
1	189	822
2	532	752
3	1773	670

Stop Event

1×	node limit

Counts

56 → 59

prune771.0ms (12.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	159	4	163
Fresh	5	16	21
Picked	1	0	1
Done	0	0	0
Total	165	20	185

Error

0.3b

Counts

185 → 20

Alt Table

Status	Error	Program
	1.2b	(/.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)))
	1.3b	(pow.f64 (sqrt.f64 (.f64 (pow.f64 (PI.f64) -1/2) (fma.f64 (pow.f64 (exp.f64 x) x) (fma.f64 15/8 (pow.f64 x -7) (.f64 3/4 (pow.f64 x -5))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 x (pow.f64 (exp.f64 x) x)))))) 2)
	10.6b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3))) x) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.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 (log.f64 (exp.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)))))
	1.7b	(.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)))))
	2.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (-.f64 (/.f64 1/4 (pow.f64 x 4)) 1) (.f64 (/.f64 x (exp.f64 (.f64 x x))) (fma.f64 1/2 (pow.f64 x -2) -1))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (fma.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x) (.f64 (/.f64 (/.f64 1/2 x) x) (pow.f64 (exp.f64 x) x))) x) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	2.7b	(.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)))))
	2.0b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (+.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 (/.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)))))
	1.7b	(.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	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (+.f64 (exp.f64 (pow.f64 x 2)) (.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 2)))) x) (*.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 15/8 (pow.f64 x 7))))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	1.6b	(pow.f64 (cbrt.f64 (.f64 (pow.f64 (PI.f64) -1/2) (fma.f64 (pow.f64 (exp.f64 x) x) (fma.f64 15/8 (pow.f64 x -7) (.f64 3/4 (pow.f64 x -5))) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 x (pow.f64 (exp.f64 x) x)))))) 3)
	1.5b	(.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)))))
	1.1b	(+.f64 (.f64 (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 x (pow.f64 (exp.f64 x) x))) (pow.f64 (PI.f64) -1/2)) (.f64 (.f64 (pow.f64 (exp.f64 x) x) (fma.f64 15/8 (pow.f64 x -7) (.f64 3/4 (pow.f64 x -5)))) (pow.f64 (PI.f64) -1/2)))
	2.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 (exp.f64 (.f64 x x)) x)))) 1) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	7.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (fma.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 x x))) (.f64 (/.f64 (/.f64 1/2 x) x) (pow.f64 (exp.f64 x) x))) x) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	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)))))

Compiler

Compiled 6979 to 4386 computations (37.2% saved)

regimes855.0ms (14.3%)

Accuracy

Total 0.9b remaining (73.2%)

Threshold costs 0.9b (73.2%)

Counts

169 → 1

Compiler

Compiled 19775 to 14112 computations (28.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	57
1	33	57

Stop Event

1×

saturated

end504.0ms (8.4%)

Stop Event

1×

fuel

Compiler

Compiled 867 to 608 computations (29.9% saved)

Details

analyze8.0ms (0.1%)

sample2.7s (44.9%)

preprocess27.0ms (0.5%)

simplify18.0ms (0.3%)

prune10.0ms (0.2%)

localize23.0ms (0.4%)

series83.0ms (1.4%)

rewrite38.0ms (0.6%)

simplify44.0ms (0.7%)

prune119.0ms (2%)

localize20.0ms (0.3%)

series24.0ms (0.4%)

rewrite36.0ms (0.6%)

simplify39.0ms (0.7%)

prune207.0ms (3.5%)

localize19.0ms (0.3%)

series6.0ms (0.1%)

rewrite40.0ms (0.7%)

simplify33.0ms (0.6%)

prune258.0ms (4.3%)

localize21.0ms (0.4%)

series23.0ms (0.4%)

rewrite32.0ms (0.5%)

simplify31.0ms (0.5%)

prune771.0ms (12.9%)

regimes855.0ms (14.3%)

simplify2.0ms (0%)

end504.0ms (8.4%)

Profiling