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 (45.9%)

Results

2.5s	8256×	body	128	valid
33.0ms	113×	body	128	invalid

Compiler

Compiled 318 to 211 computations (33.6% saved)

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

847×	`unswap-sqr_binary64`
640×	`associate-*l/_binary64`
462×	`associate-*r/_binary64`
372×	`associate-/l*_binary64`
366×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	35	152
1	91	82
2	278	58
3	1167	52
4	3376	49
5	3967	47
6	4726	47
7	5673	47

prune7.0ms (0.1%)

Pruning

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

2.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.6b	(.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))))))
▶	2.5b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))

Status

Error

Program

2.6b

(*.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))))))

▶

2.5b

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

Compiler

Compiled 404 to 266 computations (34.2% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
✓	0.4b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
✓	1.0b	(sqrt.f64 (PI.f64))
✓	2.3b	(exp.f64 (*.f64 x x))

series22.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

16.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
3.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 (PI.f64))

rewrite44.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

249×	`add-sqr-sqrt_binary64`
244×	`log1p-expm1-u_binary64`
244×	`expm1-log1p-u_binary64`
238×	`add-log-exp_binary64`
237×	`add-cbrt-cube_binary64`

Counts

4 → 81

Calls

4 calls:

42.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
42.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
42.0ms	(sqrt.f64 (PI.f64))
42.0ms	(exp.f64 (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	73
1	515	67
2	4787	67
0	0	0
1	0	0

simplify87.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

691×	`associate-/l*_binary64`
629×	`associate-+l+_binary64`
514×	`distribute-rgt-out_binary64`
259×	`*-commutative_binary64`
258×	`associate-/r/_binary64`

Counts

117 → 110

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	66	998
1	166	910
2	467	752
3	1668	661
4	3171	651
5	3943	651
6	4358	651
7	5226	651

prune149.0ms (2.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	94	16	110
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	95	17	112

Error

0.7b

Counts

112 → 17

Alt Table

Status	Error	Program
	2.8b	(exp.f64 (+.f64 (log1p.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))) (-.f64 (.f64 x x) (log.f64 (*.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))))))
	2.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 15/8 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 7))) (.f64 (/.f64 (exp.f64 (.f64 x x)) x) (+.f64 1 (+.f64 (/.f64 3/4 (pow.f64 x 4)) (/.f64 1/2 (.f64 x x)))))))
	2.7b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.5b	(+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (fabs.f64 x) (pow.f64 x 6))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (fabs.f64 x) (pow.f64 x 4))) (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))))))))
	2.6b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x))) 2) (cbrt.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x))) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) (/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x))))
	2.6b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.8b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 3)
	2.8b	(.f64 (/.f64 (/.f64 (pow.f64 (E.f64) (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	10.6b	(pow.f64 (pow.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))) 3) 1/3)
▶	1.2b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.6b	(.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))))))
	2.5b	(/.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))) (fabs.f64 x))
	2.8b	(-.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))))) 1)
	2.8b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x x))) 2) (cbrt.f64 (exp.f64 (.f64 x x)))) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	4.1b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.6b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 2)
	2.6b	(.f64 (/.f64 (/.f64 (expm1.f64 (log1p.f64 (exp.f64 (.f64 x x)))) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))

Compiler

Compiled 4971 to 3016 computations (39.3% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series17.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

15.0ms

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

2.0ms

(pow.f64 (exp.f64 x) x)

rewrite55.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

259×	`add-sqr-sqrt_binary64`
253×	`log1p-expm1-u_binary64`
253×	`expm1-log1p-u_binary64`
248×	`add-log-exp_binary64`
246×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

54.0ms

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

54.0ms

(pow.f64 (exp.f64 x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	53
1	534	49
2	4993	49
0	0	0
1	0	0

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

689×	`associate-/l*_binary64`
627×	`associate-+l+_binary64`
510×	`distribute-rgt-out_binary64`
257×	`*-commutative_binary64`
250×	`associate-/r/_binary64`

Counts

63 → 63

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	833
1	153	745
2	444	587
3	1642	496
4	3125	486
5	3887	486
6	4290	486
7	5152	486

prune147.0ms (2.5%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	89	16	105
Fresh	10	6	16
Picked	1	0	1
Done	0	0	0
Total	100	22	122

Error

0.3b

Counts

122 → 22

Alt Table

Status	Error	Program
	1.2b	(*.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (log.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2))))))
	1.3b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 2)
	2.5b	(+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (fabs.f64 x) (pow.f64 x 6))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (fabs.f64 x) (pow.f64 x 4))) (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))))))))
	1.6b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 3)
	4.1b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.0b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	10.6b	(pow.f64 (pow.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))) 3) 1/3)
	1.7b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.6b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.3b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.6b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 2)
▶	1.2b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.8b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 3)
	2.8b	(.f64 (/.f64 (/.f64 (pow.f64 (E.f64) (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.6b	(expm1.f64 (log1p.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))))
	1.2b	(+.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))))
	1.6b	(.f64 (/.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))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.4b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) 2) (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))))
	1.2b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (pow.f64 (cbrt.f64 (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) 3))))
	2.6b	(.f64 (/.f64 (/.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.5b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	9.8b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))) 3))

Compiler

Compiled 5027 to 3110 computations (38.1% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
	0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
✓	0.4b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.0b	(pow.f64 (exp.f64 x) x)

series26.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

17.0ms

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

9.0ms

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

rewrite100.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

269×	`log1p-expm1-u_binary64`
269×	`expm1-log1p-u_binary64`
264×	`add-log-exp_binary64`
261×	`add-cbrt-cube_binary64`
260×	`add-exp-log_binary64`

Counts

2 → 39

Calls

2 calls:

99.0ms

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

99.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	61
1	569	55
2	4935	55
3	4990	55
0	0	0
1	0	0

simplify97.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

652×	`distribute-rgt-out_binary64`
318×	`*-commutative_binary64`
298×	`distribute-lft-in_binary64`
289×	`associate-/r/_binary64`
282×	`fma-def_binary64`

Counts

63 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	62	983
1	160	885
2	483	705
3	1883	607
4	2861	597
5	3771	597
6	4288	597
7	4553	597
8	4901	597

prune177.0ms (3.1%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	5	16	21
Picked	1	0	1
Done	0	0	0
Total	109	23	132

Error

0.3b

Counts

132 → 23

Alt Table

Status	Error	Program
	1.7b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64)))) 3) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.3b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 2)
	2.5b	(+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (fabs.f64 x) (pow.f64 x 6))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (fabs.f64 x) (pow.f64 x 4))) (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))))))))
	1.6b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 3)
	1.7b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.6b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.3b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.5b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.f64 (exp.f64 x)) x)) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.6b	(.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))))) 1) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.5b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.5b	(.f64 (/.f64 (/.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.6b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 2)
	2.8b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 3)
	2.8b	(.f64 (/.f64 (/.f64 (pow.f64 (E.f64) (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	2.6b	(expm1.f64 (log1p.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))))
	1.2b	(+.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))))
	2.0b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.5b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.6b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.4b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) 2) (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))))
	9.8b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))))) 3))
	1.2b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (pow.f64 (cbrt.f64 (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) 3))))
▶	1.2b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (log.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2))))))

Compiler

Compiled 5500 to 3500 computations (36.4% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
✓	0.4b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (log.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2))))))
	1.0b	(pow.f64 (exp.f64 x) x)
✓	3.2b	(log.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2)))

series297.0ms (5.1%)

Counts

2 → 24

Calls

2 calls:

278.0ms

(log.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2)))

19.0ms

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

rewrite36.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

274×	`log1p-expm1-u_binary64`
274×	`expm1-log1p-u_binary64`
269×	`add-log-exp_binary64`
265×	`add-exp-log_binary64`
264×	`add-cbrt-cube_binary64`

Counts

2 → 41

Calls

2 calls:

35.0ms

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

35.0ms

(log.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	60
1	587	57
2	4802	57
0	0	0
1	0	0

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

689×	`distribute-rgt-out_binary64`
391×	`associate-+l+_binary64`
306×	`distribute-lft-in_binary64`
283×	`fma-def_binary64`
276×	`associate-/r/_binary64`

Counts

65 → 62

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	65	933
1	172	842
2	497	689
3	1803	584
4	2865	574
5	3849	568
6	4955	568

prune172.0ms (3%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	4	18	22
Picked	0	1	1
Done	0	0	0
Total	111	25	136

Error

0.2b

Counts

136 → 25

Alt Table

Status	Error	Program
	1.7b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64)))) 3) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.3b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 2)
	2.5b	(+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (fabs.f64 x) (pow.f64 x 6))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (fabs.f64 x) (pow.f64 x 4))) (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))))))))
	1.6b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 3)
	2.6b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.6b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (log.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2))))))
	1.7b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x) (pow.f64 (sqrt.f64 (exp.f64 x)) x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	1.3b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.5b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.5b	(.f64 (/.f64 (/.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (log.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2))))))
	2.5b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) x) (pow.f64 (cbrt.f64 (exp.f64 x)) x)) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.6b	(.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))))) 1) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.2b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2))))))))
	1.5b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	2.8b	(pow.f64 (cbrt.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 3)
	2.8b	(.f64 (/.f64 (/.f64 (pow.f64 (E.f64) (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
	9.8b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2) (/.f64 15/8 (pow.f64 x 6))))) 3))
	1.4b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) 2) (cbrt.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))) (.f64 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))))
	2.0b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
	1.3b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2))))))))
	2.6b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (*.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))) 2)
	2.6b	(expm1.f64 (log1p.f64 (.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (fma.f64 15/8 (pow.f64 x -6) (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2)))))))
	1.2b	(fma.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (/.f64 1 (fabs.f64 x)) (*.f64 (fma.f64 (pow.f64 x -2) (fma.f64 3/4 (pow.f64 x -2) 1/2) (/.f64 15/8 (pow.f64 x 6))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x))))
	1.2b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (pow.f64 (cbrt.f64 (.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2) (pow.f64 x -2))) 3))))
✓	1.2b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (log.f64 (pow.f64 (exp.f64 (fma.f64 3/4 (pow.f64 x -2) 1/2)) (pow.f64 x -2))))))

Compiler

Compiled 4984 to 3378 computations (32.2% saved)

regimes702.0ms (12.1%)

Accuracy

Total 0.9b remaining (69.8%)

Threshold costs 0.9b (69.8%)

Counts

157 → 1

Compiler

Compiled 16781 to 12450 computations (25.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	4294967295
1	35	4294967295
2	34	4294967295

end675.0ms (11.7%)

Compiler: Compiled 1033 to 775 computations (25% saved)

Details

analyze8.0ms (0.1%)

sample2.7s (45.9%)

simplify69.0ms (1.2%)

prune7.0ms (0.1%)

localize20.0ms (0.3%)

series22.0ms (0.4%)

rewrite44.0ms (0.8%)

simplify87.0ms (1.5%)

prune149.0ms (2.6%)

localize20.0ms (0.3%)

series17.0ms (0.3%)

rewrite55.0ms (0.9%)

simplify80.0ms (1.4%)

prune147.0ms (2.5%)

localize21.0ms (0.4%)

series26.0ms (0.5%)

rewrite100.0ms (1.7%)

simplify97.0ms (1.7%)

prune177.0ms (3.1%)

localize27.0ms (0.5%)

series297.0ms (5.1%)

rewrite36.0ms (0.6%)

simplify72.0ms (1.2%)

prune172.0ms (3%)

regimes702.0ms (12.1%)

simplify2.0ms (0%)

end675.0ms (11.7%)

Profiling