Details

analyze1.2s (15.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample3.9s (49.4%)

Results

2.5s	4158×	body	2048	valid
891.0ms	2064×	body	1024	valid
312.0ms	1008×	body	512	valid
105.0ms	479×	body	256	valid
69.0ms	547×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

529×	`rules-6-rev_binary64`
366×	`fma-neg_binary64`
350×	`rules-1_binary64`
342×	`rules-6_binary64`
273×	`rules-5-rev_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	25	19
2	47	19
3	144	19
4	664	19
5	3092	17
6	4650	17
7	4932	17

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.7b	(acos.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))

Compiler

Compiled 53 to 35 computations (34% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1))
✓	0.7b	(acos.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1))
2.0ms	(acos.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))

rewrite60.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

813×	`log1p-expm1-u_binary64`
813×	`expm1-log1p-u_binary64`
169×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`
86×	`add-cbrt-cube_binary64`

Counts

2 → 69

Calls

2 calls:

59.0ms	(/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1))
58.0ms	(acos.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	223	32
2	2402	32
3	5576	32
0	0	0
1	0	0

simplify36.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

949×	`fma-def_binary64`
702×	`rules-13_binary64`
545×	`rules-14-rev_binary64`
429×	`rules-20_binary64`
334×	`rules-21_binary64`

Counts

93 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	380
1	123	363
2	458	359
3	1756	359
4	5373	359

prune88.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	5	86

Error

0.7b

Counts

86 → 5

Alt Table

Status	Error	Program
	0.8b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
	2.6b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1))))))))
✓	0.7b	(acos.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))
▶	0.7b	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) 2) 3) (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 3)) (+.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))))))
	2.2b	(.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))) 2))

Compiler

Compiled 2629 to 1770 computations (32.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) 2) 3) (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 3)) (+.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))))))
✓	1.0b	(pow.f64 (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1))) 3)
✓	1.0b	(pow.f64 (/.f64 (PI.f64) 2) 3)
✓	1.8b	(+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))))

series254.0ms (3.2%)

Counts

4 → 36

Calls

4 calls:

217.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) 2) 3) (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 3)) (+.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))))))
20.0ms	(+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))))
17.0ms	(pow.f64 (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1))) 3)
0.0ms	(pow.f64 (/.f64 (PI.f64) 2) 3)

rewrite101.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

220×	`add-sqr-sqrt_binary64`
219×	`log1p-expm1-u_binary64`
219×	`expm1-log1p-u_binary64`
208×	`add-cbrt-cube_binary64`
206×	`add-log-exp_binary64`

Counts

4 → 129

Calls

4 calls:

97.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) 2) 3) (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 3)) (+.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))))))
97.0ms	(pow.f64 (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1))) 3)
97.0ms	(pow.f64 (/.f64 (PI.f64) 2) 3)
97.0ms	(+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	162
1	554	89
2	4761	89
3	4935	89
0	0	0
1	0	0

simplify116.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

716×	`rules-20_binary64`
354×	`rules-10-rev_binary64`
340×	`rules-4_binary64`
336×	`rules-33_binary64`
329×	`rules-14-rev_binary64`

Counts

165 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	1776
1	58	1752
2	154	1704
3	507	1704
4	2111	1704
5	4246	1704
6	4977	1704
7	4929	1704

prune232.0ms (2.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	134	6	140

Error

0.7b

Counts

140 → 6

Alt Table

Status	Error	Program
▶	0.8b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
	2.2b	(/.f64 (-.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3) (pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3)) (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 3)) (+.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))))))
	2.2b	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) 2) 3) (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 3)) (+.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (fma.f64 (cbrt.f64 (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 4)) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) 2) (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (/.f64 (PI.f64) 2)))))
	2.9b	(+.f64 (fma.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (pow.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) 2) (neg.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) 2) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))))
	2.2b	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) 2) 3) (log1p.f64 (expm1.f64 (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 3)))) (+.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))))))
	2.2b	(.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))) 2))

Compiler

Compiled 9256 to 6320 computations (31.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

series2.0ms (0%)

Counts

1 → 0

Calls

1 calls:

2.0ms

(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

rewrite55.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

716×	`log1p-expm1-u_binary64`
716×	`expm1-log1p-u_binary64`
140×	`prod-diff_binary64`
78×	`add-sqr-sqrt_binary64`
74×	`add-cbrt-cube_binary64`

Counts

1 → 40

Calls

1 calls:

54.0ms

(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	187	14
2	2101	14
3	4872	14
0	0	0
1	0	0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune56.0ms (0.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	38	8	46

Error

0.7b

Counts

46 → 8

Alt Table

Status	Error	Program
✓	0.8b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
▶	2.2b	(/.f64 (-.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3) (pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3)) (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 3)) (+.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))))))
	2.3b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 1 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))) (fma.f64 -1 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)) (*.f64 1 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))))
	2.9b	(+.f64 (fma.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (pow.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) 2) (neg.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) 2) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))))
	2.2b	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) 2) 3) (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 3)) (+.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (fma.f64 (cbrt.f64 (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 4)) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) 2) (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (/.f64 (PI.f64) 2)))))
	2.3b	(*.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 2))
	2.3b	(+.f64 (fma.f64 (/.f64 (PI.f64) 2) 1 (neg.f64 (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))))))
	2.2b	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) 2) 3) (log1p.f64 (expm1.f64 (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 3)))) (+.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))))))

Compiler

Compiled 2216 to 1655 computations (25.3% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(sqrt.f64 (/.f64 (PI.f64) 2))
✓	1.0b	(*.f64 (pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3) (pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3))
✓	1.6b	(pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3)
	1.8b	(+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))))

series0.0ms (0%)

Counts

3 → 0

Calls

3 calls:

0.0ms	(pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3)
0.0ms	(*.f64 (pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3) (pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3))
0.0ms	(sqrt.f64 (/.f64 (PI.f64) 2))

rewrite85.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

640×	`log1p-expm1-u_binary64`
640×	`expm1-log1p-u_binary64`
476×	`fma-neg_binary64`
272×	`egg-rr`
157×	`prod-diff_binary64`

Counts

3 → 272

Calls

3 calls:

81.0ms	(sqrt.f64 (/.f64 (PI.f64) 2))
81.0ms	(*.f64 (pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3) (pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3))
81.0ms	(pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	191	23
2	1951	23
3	5151	23
0	0	0
1	0	0

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune865.0ms (10.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	458	2	460
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	461	7	468

Error

0.7b

Counts

468 → 7

Alt Table

Status	Error	Program
✓	0.8b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
	1.6b	(/.f64 (-.f64 (.f64 (pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3) (pow.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) 3)) (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 3)) (+.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (fma.f64 (cbrt.f64 (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 4)) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) 2) (.f64 (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1))) (/.f64 (PI.f64) 2)))))
	2.9b	(/.f64 (-.f64 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) 2) 3) (/.f64 (PI.f64) 2) 0) (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 3)) (+.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))))))
	2.3b	(*.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 2))
	2.3b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 1 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))) (fma.f64 -1 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)) (*.f64 1 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))))
	2.3b	(+.f64 (fma.f64 (/.f64 (PI.f64) 2) 1 (neg.f64 (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))))))
	2.2b	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) 2) 3) (log1p.f64 (expm1.f64 (pow.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) 3)))) (+.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (+.f64 (.f64 (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 (.f64 v v) -5 1) (fma.f64 v v -1)))) (.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 (*.f64 v v) -5 1) (fma.f64 v v -1)))))))

Compiler

Compiled 40842 to 28621 computations (29.9% saved)

regimes430.0ms (5.4%)

Accuracy

Total 0.0b remaining (1.7%)

Threshold costs 0.0b (1.7%)

Counts

67 → 1

Compiler

Compiled 14110 to 10215 computations (27.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	16	23
2	15	23

end307.0ms (3.8%)

Compiler: Compiled 477 to 354 computations (25.8% saved)

Details

analyze1.2s (15.1%)

sample3.9s (49.4%)

simplify70.0ms (0.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series6.0ms (0.1%)

rewrite60.0ms (0.8%)

simplify36.0ms (0.5%)

prune88.0ms (1.1%)

localize19.0ms (0.2%)

series254.0ms (3.2%)

rewrite101.0ms (1.3%)

simplify116.0ms (1.4%)

prune232.0ms (2.9%)

localize6.0ms (0.1%)

series2.0ms (0%)

rewrite55.0ms (0.7%)

simplify7.0ms (0.1%)

prune56.0ms (0.7%)

localize20.0ms (0.3%)

series0.0ms (0%)

rewrite85.0ms (1.1%)

simplify12.0ms (0.2%)

prune865.0ms (10.8%)

regimes430.0ms (5.4%)

simplify2.0ms (0%)

end307.0ms (3.8%)

Profiling