Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 71 to 33 computations (53.5% saved)

sample1.6s (38.6%)

Results

1.5s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify94.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1509×	`associate-/l*_binary64`
766×	`distribute-rgt-out_binary64`
744×	`distribute-lft-out_binary64`
549×	`unswap-sqr_binary64`
497×	`associate-/r*_binary64`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	32	75
1	74	59
2	239	41
3	928	37
4	1549	37
5	3195	37
6	3534	37
7	3698	33
8	2289	33
9	2775	33
10	2823	33
11	4807	33
12	5324	33

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
▶	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Status

Error

Program

0.5b

(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))

▶

0.1b

(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 272 to 147 computations (46% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
✓	0.1b	(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
✓	0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
✓	1.0b	(sqrt.f64 (PI.f64))

series79.0ms (1.9%)

Counts

4 → 36

Calls

4 calls:

58.0ms	(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
12.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
9.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 (PI.f64))

rewrite37.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

274×	`log1p-expm1-u_binary64`
274×	`expm1-log1p-u_binary64`
268×	`add-cbrt-cube_binary64`
267×	`add-log-exp_binary64`
266×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	89
1	612	66
2	4919	66

Stop Event

1×	node limit

Counts

4 → 60

Calls

4 calls:

36.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
36.0ms	(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
36.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
36.0ms	(sqrt.f64 (PI.f64))

simplify113.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

2001×	`fma-def_binary64`
777×	`*-commutative_binary64`
687×	`associate-l_binary64`
479×	`associate-r_binary64`
450×	`sqr-pow_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	720
1	63	720
2	156	720
3	399	696
4	927	696
5	2296	696
6	2662	696
7	2663	696
8	2777	696
9	2969	696
10	3254	696
11	4429	696
12	4853	696
13	4891	696

Stop Event

1×	node limit

Counts

96 → 64

prune91.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	62	4	66

Error

Counts

66 → 4

Alt Table

Status	Error	Program
	0.5b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	1.1b	(fabs.f64 (.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
▶	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))

Compiler

Compiled 3834 to 1644 computations (57.1% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))
✓	0.0b	(fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
✓	0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
✓	0.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))

series100.0ms (2.5%)

Counts

4 → 36

Calls

4 calls:

38.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))
26.0ms	(fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
23.0ms	(fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))
13.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))

rewrite58.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

332×	`log1p-udef_binary64`
204×	`add-sqr-sqrt_binary64`
195×	`log1p-expm1-u_binary64`
195×	`expm1-log1p-u_binary64`
193×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	98
1	436	77
2	4285	77
3	4880	77

Stop Event

1×	node limit

Counts

4 → 78

Calls

4 calls:

56.0ms	(fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))
56.0ms	(fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
56.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
56.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))

simplify134.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1269×	`fma-def_binary64`
748×	`sqr-pow_binary64`
467×	`cube-prod_binary64`
421×	`*-commutative_binary64`
344×	`pow-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	1311
1	119	1167
2	282	838
3	609	790
4	1267	790
5	1421	790
6	1693	790
7	1763	790
8	1908	790
9	2097	790
10	3031	790
11	3257	790
12	3587	790
13	4014	790
14	4664	790
15	4824	790

Stop Event

1×	node limit

Counts

114 → 94

prune115.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	94	4	98

Error

Counts

98 → 4

Alt Table

Status	Error	Program
	1.1b	(fabs.f64 (.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
▶	0.5b	(fabs.f64 (/.f64 (fma.f64 x (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5)))) (sqrt.f64 (PI.f64))))
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 3013 to 2112 computations (29.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5)))
✓	0.1b	(*.f64 1/5 (pow.f64 x 5))
✓	0.3b	(/.f64 (fma.f64 x (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5)))) (sqrt.f64 (PI.f64)))
	1.0b	(sqrt.f64 (PI.f64))

series16.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

7.0ms

(/.f64 (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5)))) (sqrt.f64 (PI.f64)))

6.0ms

(fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5)))

3.0ms

(*.f64 1/5 (pow.f64 x 5))

rewrite57.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

312×	`log1p-udef_binary64`
191×	`prod-diff_binary64`
181×	`add-sqr-sqrt_binary64`
174×	`log1p-expm1-u_binary64`
174×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	52
1	381	52
2	4063	52
3	4735	52

Stop Event

1×	node limit

Counts

3 → 69

Calls

3 calls:

55.0ms

(fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5)))

55.0ms

(*.f64 1/5 (pow.f64 x 5))

55.0ms

(/.f64 (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5)))) (sqrt.f64 (PI.f64)))

simplify122.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1067×	`fma-def_binary64`
750×	`cube-prod_binary64`
711×	`sqr-pow_binary64`
690×	`unswap-sqr_binary64`
582×	`fabs-mul_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	609
1	93	609
2	218	517
3	532	459
4	1151	447
5	1642	447
6	1841	447
7	2088	447
8	2526	447
9	2549	447
10	2716	447
11	2979	447
12	3197	447
13	3572	447
14	4095	447
15	4379	447
16	4925	447

Stop Event

1×	node limit

Counts

93 → 84

prune109.0ms (2.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	103	4	107

Error

Counts

107 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
▶	0.5b	(fabs.f64 (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (fma.f64 x (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5))))) -1))
✓	0.5b	(fabs.f64 (/.f64 (fma.f64 x (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5)))) (sqrt.f64 (PI.f64))))
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 2983 to 2060 computations (30.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/5 (pow.f64 x 5))
✓	0.3b	(pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (fma.f64 x (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5))))) -1)
✓	0.3b	(/.f64 (sqrt.f64 (PI.f64)) (fma.f64 x (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5)))))
	1.0b	(sqrt.f64 (PI.f64))

series15.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

8.0ms

(pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5))))) -1)

7.0ms

(/.f64 (sqrt.f64 (PI.f64)) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5)))))

rewrite61.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

338×	`log1p-udef_binary64`
199×	`add-sqr-sqrt_binary64`
191×	`log1p-expm1-u_binary64`
191×	`expm1-log1p-u_binary64`
191×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	65
1	422	62
2	4427	62
3	5113	62

Stop Event

1×	node limit

Counts

2 → 76

Calls

2 calls:

59.0ms

(pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5))))) -1)

59.0ms

(/.f64 (sqrt.f64 (PI.f64)) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5)))))

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-neg_binary64`
641×	`cancel-sign-sub-inv_binary64`
420×	`fma-def_binary64`
286×	`*-commutative_binary64`
257×	`associate-*l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	921
1	225	833
2	580	711
3	1764	629
4	3419	629
5	4954	629
6	4973	629
7	4956	629

Stop Event

1×	node limit

Counts

100 → 106

prune142.0ms (3.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	138	4	142

Error

Counts

142 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
✓	0.5b	(fabs.f64 (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (fma.f64 x (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5))))) -1))
✓	0.5b	(fabs.f64 (/.f64 (fma.f64 x (fma.f64 2/3 (.f64 x x) 2) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5)))) (sqrt.f64 (PI.f64))))
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 4152 to 2899 computations (30.2% saved)

regimes884.0ms (21.7%)

Accuracy

Total 0.1b remaining (72.8%)

Threshold costs 0.1b (72.8%)

Counts

126 → 1

Compiler

Compiled 24299 to 16701 computations (31.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	80
1	43	80
2	42	80

Stop Event

1×

saturated

end117.0ms (2.9%)

Compiler: Compiled 242 to 166 computations (31.4% saved)

Details

analyze5.0ms (0.1%)

sample1.6s (38.6%)

simplify94.0ms (2.3%)

prune5.0ms (0.1%)

localize21.0ms (0.5%)

series79.0ms (1.9%)

rewrite37.0ms (0.9%)

simplify113.0ms (2.8%)

prune91.0ms (2.2%)

localize14.0ms (0.4%)

series100.0ms (2.5%)

rewrite58.0ms (1.4%)

simplify134.0ms (3.3%)

prune115.0ms (2.8%)

localize13.0ms (0.3%)

series16.0ms (0.4%)

rewrite57.0ms (1.4%)

simplify122.0ms (3%)

prune109.0ms (2.7%)

localize14.0ms (0.3%)

series15.0ms (0.4%)

rewrite61.0ms (1.5%)

simplify76.0ms (1.9%)

prune142.0ms (3.5%)

regimes884.0ms (21.7%)

simplify3.0ms (0.1%)

end117.0ms (2.9%)

Profiling