Details

analyze9.0ms (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 (48%)

Results

2.7s	8256×	body	128	valid
36.0ms	111×	body	128	invalid

Compiler

Compiled 318 to 211 computations (33.6% 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

1.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.9b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (fabs.f64 x) (fabs.f64 x)))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 2) (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 3 4) (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 15 8) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))
▶	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 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))

Status

Error

Program

2.9b

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

▶

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 (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)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.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 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
✓	1.0b	(sqrt.f64 (PI.f64))
✓	1.0b	(pow.f64 (exp.f64 x) x)
✓	1.1b	(pow.f64 (/.f64 1 (fabs.f64 x)) 5)

series86.0ms (1.5%)

Counts

4 → 36

Calls

4 calls:

65.0ms	(.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)))))
18.0ms	(pow.f64 (/.f64 1 (fabs.f64 x)) 5)
2.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 (PI.f64))

rewrite37.0ms (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

Calls

4 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)))))
35.0ms	(sqrt.f64 (PI.f64))
35.0ms	(pow.f64 (exp.f64 x) x)
35.0ms	(pow.f64 (/.f64 1 (fabs.f64 x)) 5)

simplify43.0ms (0.8%)

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

prune131.0ms (2.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	71	18	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	73	18	91

Error

0.3b

Counts

91 → 18

Alt Table

Status	Error	Program
	1.6b	(.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)))))
	9.1b	(.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)))))
	1.7b	(.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)))))
	2.0b	(.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)))))
	1.6b	(.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)))))
	2.9b	(.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)))))
	2.8b	(+.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))))))))
	2.2b	(.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)))))
	9.0b	(cbrt.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))
	1.9b	(.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)))))
	1.6b	(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)
	2.4b	(.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)))))
▶	1.4b	(/.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)))
	2.8b	(-.f64 (exp.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)
	1.7b	(.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)))))
	2.9b	(exp.f64 (+.f64 (log.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)))) (-.f64 (.f64 x x) (log.f64 (sqrt.f64 (PI.f64))))))
	1.9b	(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)
	10.0b	(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)

Compiler

Compiled 4711 to 2988 computations (36.6% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.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)))
✓	0.6b	(.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))))
	1.0b	(sqrt.f64 (PI.f64))
	1.0b	(pow.f64 (exp.f64 x) x)

series76.0ms (1.3%)

Counts

2 → 24

Calls

2 calls:

44.0ms

(/.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)))

31.0ms

(*.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))))

rewrite31.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

240×	`add-sqr-sqrt_binary64`
229×	`log1p-expm1-u_binary64`
229×	`expm1-log1p-u_binary64`
227×	`add-log-exp_binary64`
226×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	84
1	500	72

Stop Event

1×	node limit

Counts

2 → 34

Calls

2 calls:

30.0ms

(/.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)))

30.0ms

(*.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))))

simplify37.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-def_binary64`
643×	`associate-+l+_binary64`
624×	`associate-+r+_binary64`
276×	`times-frac_binary64`
251×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	1885
1	375	1775
2	1253	1214

Stop Event

1×	node limit

Counts

58 → 59

prune144.0ms (2.5%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	94	8	102
Fresh	6	11	17
Picked	0	1	1
Done	0	0	0
Total	100	20	120

Error

0.3b

Counts

120 → 20

Alt Table

Status	Error	Program
	1.6b	(.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)))))
	9.1b	(.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)))))
	1.6b	(/.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)))) (cbrt.f64 (pow.f64 (PI.f64) 3/2)))
	2.7b	(/.f64 (exp.f64 (+.f64 (*.f64 x x) (log.f64 (fma.f64 (pow.f64 x -5) (fma.f64 15/8 (pow.f64 x -2) 3/4) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) x))))) (sqrt.f64 (PI.f64)))
	1.7b	(.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)))))
	2.0b	(.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)))))
	1.6b	(.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)))))
	1.6b	(/.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)))) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64)))))
	2.9b	(.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)))))
▶	1.4b	(/.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)))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
	2.9b	(exp.f64 (+.f64 (log.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)))) (-.f64 (.f64 x x) (log.f64 (sqrt.f64 (PI.f64))))))
	1.9b	(/.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.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)))
	1.9b	(.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)))))
	2.8b	(/.f64 (.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.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)))
	1.9b	(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)
✓	1.4b	(/.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)))
	2.4b	(/.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)))) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 2) (cbrt.f64 (sqrt.f64 (PI.f64)))))
	2.2b	(.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)))))
	10.0b	(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)
	9.0b	(/.f64 (.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3)) (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)))

Compiler

Compiled 4962 to 3282 computations (33.9% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))
✓	0.4b	(/.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)))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
	0.6b	(.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))))
	1.0b	(pow.f64 (exp.f64 x) x)

series52.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

44.0ms

(/.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)))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))

8.0ms

(/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))

rewrite31.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`add-sqr-sqrt_binary64`
245×	`log1p-expm1-u_binary64`
245×	`expm1-log1p-u_binary64`
243×	`add-log-exp_binary64`
241×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	59
1	536	56

Stop Event

1×	node limit

Counts

2 → 36

Calls

2 calls:

28.0ms

(/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))

28.0ms

(/.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)))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

555×	`fma-def_binary64`
362×	`associate-/l/_binary64`
317×	`associate-+l+_binary64`
308×	`associate-+r+_binary64`
227×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	1351
1	265	1243
2	886	919
3	4283	796

Stop Event

1×	node limit

Counts

60 → 56

prune167.0ms (2.9%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	97	10	107
Fresh	5	13	18
Picked	1	0	1
Done	0	1	1
Total	103	24	127

Error

0.2b

Counts

127 → 24

Alt Table

Status	Error	Program
	2.4b	(/.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)))) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 2) (cbrt.f64 (sqrt.f64 (PI.f64)))))
	2.8b	(/.f64 (.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.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)))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2)))
	1.8b	(/.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 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))) 2) (cbrt.f64 (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x)))))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2)))
▶	1.4b	(/.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 (/.f64 1 x) (/.f64 1/2 (pow.f64 x 3))))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
	1.7b	(.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)))))
	2.0b	(.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)))))
	1.6b	(.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)))))
	1.6b	(/.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)))) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64)))))
	1.7b	(/.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 (exp.f64 (log1p.f64 (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x)))) 1))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
	2.9b	(.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)))))
	2.8b	(/.f64 (.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.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)))
	1.6b	(/.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))) (log.f64 (exp.f64 (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x)))))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
	1.9b	(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)
	2.7b	(/.f64 (exp.f64 (+.f64 (.f64 x x) (log.f64 (fma.f64 (pow.f64 x -5) (fma.f64 15/8 (pow.f64 x -2) 3/4) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) x))))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2)))
	10.0b	(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)
	9.0b	(/.f64 (.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3)) (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)))
	1.8b	(/.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))) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))) 3))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
✓	1.4b	(/.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)))
	1.6b	(.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)))))
	2.0b	(/.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.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)))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2)))
	2.8b	(exp.f64 (-.f64 (*.f64 x x) (log.f64 (/.f64 (sqrt.f64 (PI.f64)) (fma.f64 (pow.f64 (fabs.f64 x) -5) (fma.f64 15/8 (pow.f64 x -2) 3/4) (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x)))))))
	2.2b	(.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)))))
	1.9b	(.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 (.f64 (pow.f64 (exp.f64 x) x) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (cbrt.f64 (/.f64 (pow.f64 (fma.f64 1/2 (pow.f64 x -2) 1) 3) (pow.f64 (fabs.f64 x) 3))))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))

Compiler

Compiled 5699 to 3847 computations (32.5% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1/2 (pow.f64 x 3))
✓	0.4b	(/.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 (/.f64 1 x) (/.f64 1/2 (pow.f64 x 3))))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
✓	0.6b	(.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 (/.f64 1 x) (/.f64 1/2 (pow.f64 x 3)))))
	1.0b	(pow.f64 (exp.f64 x) x)

series26.0ms (0.5%)

Counts

3 → 24

Calls

3 calls:

14.0ms

(/.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 (/.f64 1 x) (/.f64 1/2 (pow.f64 x 3))))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))

9.0ms

(*.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 (/.f64 1 x) (/.f64 1/2 (pow.f64 x 3)))))

3.0ms

(/.f64 1/2 (pow.f64 x 3))

rewrite33.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

262×	`log1p-expm1-u_binary64`
262×	`expm1-log1p-u_binary64`
258×	`add-cbrt-cube_binary64`
255×	`add-log-exp_binary64`
252×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	92
1	573	83

Stop Event

1×	node limit

Counts

3 → 49

Calls

3 calls:

32.0ms

(/.f64 1/2 (pow.f64 x 3))

32.0ms

(/.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 (/.f64 1 x) (/.f64 1/2 (pow.f64 x 3))))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))

32.0ms

(*.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 (/.f64 1 x) (/.f64 1/2 (pow.f64 x 3)))))

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

365×	`distribute-rgt-out_binary64`
320×	`fma-def_binary64`
312×	`associate-/r/_binary64`
311×	`associate-/l/_binary64`
247×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	70	1124
1	197	1022
2	586	796
3	2309	754
4	3634	732
5	4554	732

Stop Event

1×	node limit

Counts

73 → 80

prune139.0ms (2.4%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	3	19	22
Picked	0	1	1
Done	0	1	1
Total	103	25	128

Error

0.2b

Counts

128 → 25

Alt Table

Status	Error	Program
	2.4b	(/.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)))) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 2) (cbrt.f64 (sqrt.f64 (PI.f64)))))
	2.8b	(/.f64 (.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.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)))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2)))
	1.8b	(/.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 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))) 2) (cbrt.f64 (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x)))))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2)))
	2.0b	(/.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.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)))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2)))
	1.6b	(/.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 (/.f64 1 x) (log.f64 (pow.f64 (exp.f64 1/2) (pow.f64 x -3)))))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
✓	1.4b	(/.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 (/.f64 1 x) (/.f64 1/2 (pow.f64 x 3))))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
	1.6b	(/.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 (/.f64 1 x) (-.f64 (exp.f64 (log1p.f64 (.f64 1/2 (pow.f64 x -3)))) 1)))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2)))
	2.7b	(/.f64 (exp.f64 (+.f64 (.f64 x x) (log.f64 (fma.f64 (pow.f64 (fabs.f64 x) -5) (fma.f64 15/8 (pow.f64 x -2) 3/4) (fma.f64 1/2 (pow.f64 x -3) (/.f64 1 x)))))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2)))
	1.7b	(.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)))))
	2.0b	(.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)))))
	1.6b	(.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)))))
	1.6b	(/.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)))) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64)))))
	1.7b	(/.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 (exp.f64 (log1p.f64 (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x)))) 1))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
	2.8b	(exp.f64 (-.f64 (*.f64 x x) (log.f64 (/.f64 (sqrt.f64 (PI.f64)) (fma.f64 (pow.f64 (fabs.f64 x) -5) (fma.f64 15/8 (pow.f64 x -2) 3/4) (fma.f64 1/2 (pow.f64 x -3) (/.f64 1 x)))))))
	2.9b	(.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)))))
	2.8b	(/.f64 (.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.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)))
	1.6b	(/.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))) (log.f64 (exp.f64 (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x)))))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
	1.9b	(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)
✓	1.4b	(/.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)))
	1.6b	(.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)))))
	2.2b	(.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)))))
	1.9b	(.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 (.f64 (pow.f64 (exp.f64 x) x) (fma.f64 (pow.f64 (fabs.f64 x) -5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))) (cbrt.f64 (/.f64 (pow.f64 (fma.f64 1/2 (pow.f64 x -2) 1) 3) (pow.f64 (fabs.f64 x) 3))))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
	10.0b	(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)
	1.8b	(/.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))) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (fabs.f64 x))) 3))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))

Compiler

Compiled 4308 to 2922 computations (32.2% saved)

regimes1.1s (18.7%)

Accuracy

Total 1.0b remaining (84.6%)

Threshold costs 0b (0%)

Counts

198 → 1

Compiler

Compiled 20891 to 15927 computations (23.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	53
1	32	53

Stop Event

1×

saturated

end646.0ms (11.3%)

Compiler: Compiled 986 to 737 computations (25.3% saved)

Details

analyze9.0ms (0.1%)

sample2.7s (48%)

simplify18.0ms (0.3%)

prune9.0ms (0.2%)

localize21.0ms (0.4%)

series86.0ms (1.5%)

rewrite37.0ms (0.6%)

simplify43.0ms (0.8%)

prune131.0ms (2.3%)

localize20.0ms (0.4%)

series76.0ms (1.3%)

rewrite31.0ms (0.5%)

simplify37.0ms (0.7%)

prune144.0ms (2.5%)

localize22.0ms (0.4%)

series52.0ms (0.9%)

rewrite31.0ms (0.5%)

simplify42.0ms (0.7%)

prune167.0ms (2.9%)

localize24.0ms (0.4%)

series26.0ms (0.5%)

rewrite33.0ms (0.6%)

simplify54.0ms (0.9%)

prune139.0ms (2.4%)

regimes1.1s (18.7%)

simplify2.0ms (0%)

end646.0ms (11.3%)

Profiling