Details

analyze100.0ms (1.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
3.1%	3.1%	93.8%	2
3.1%	3.1%	93.8%	3
4.7%	1.6%	93.8%	4
4.7%	1.6%	93.8%	5
5.5%	0.8%	93.8%	6
5.5%	0.8%	93.8%	7
5.8%	0.4%	93.8%	8
5.8%	0.4%	93.8%	9
6%	0.2%	93.8%	10
6%	0.2%	93.8%	11
6.1%	0.1%	93.8%	12
6.1%	0.1%	93.8%	13
6.2%	0%	93.8%	14

Compiler

Compiled 36 to 30 computations (16.7% saved)

sample2.5s (36.2%)

Results

2.3s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify151.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

909×	`cube-prod_binary64`
818×	`unswap-sqr_binary64`
698×	`fabs-mul_binary64`
671×	`sqr-pow_binary64`
541×	`cube-mult_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	24
1	38	24
2	63	24
3	101	24
4	203	24
5	528	24
6	667	24
7	856	24
8	1442	24
9	1481	24
10	1512	24
11	1576	24
12	1582	24
13	1854	24
14	2077	24
15	2498	24
16	3106	24
17	3604	24
18	4037	24
19	4445	24
20	4754	24
21	4859	24

prune4.0ms (0.1%)

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

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 70 to 60 computations (14.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
✓	0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

series305.0ms (4.4%)

Counts

4 → 52

Calls

4 calls:

157.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
114.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
31.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite293.0ms (4.3%)

Algorithm

4×	egg-rewrite

Rules

56×	`egg`
51×	`egg`
35×	`egg`
28×	`egg`

Counts

4 → 170

Calls

4 calls:

120.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
88.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
41.0ms	(.f64 (.f64 2 (PI.f64)) u2)
40.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	157	11
2	1647	11
3	4880	11
0	6	8
1	121	8
2	1359	8
3	5038	8
0	6	8
1	116	8
2	1228	8
3	4927	8
4	6317	8
0	16	24
1	317	24
2	3390	24
3	4863	24
4	4853	24
5	4886	24

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

728×	`unswap-sqr_binary64`
433×	`fma-neg_binary64`
309×	`distribute-rgt-neg-in_binary64`
302×	`distribute-lft-neg-in_binary64`
289×	`associate-l_binary64`

Counts

222 → 192

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1086
1	172	1038
2	465	968
3	1647	922
4	3490	922
5	5076	922

prune190.0ms (2.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	186	6	192
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	6	193

Error

Counts

193 → 6

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
▶	0.2b	(fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) 1/6)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (.f64 1/6 (cbrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 3/2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(fma.f64 (.f64 (cbrt.f64 (.f64 -2 (log.f64 u1))) (.f64 (cbrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))) 1/6)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2) 3))

Compiler

Compiled 4395 to 3350 computations (23.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
✓	0.1b	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

series202.0ms (2.9%)

Counts

3 → 48

Calls

3 calls:

158.0ms	(fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
23.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
21.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

rewrite213.0ms (3.1%)

Algorithm

3×	egg-rewrite

Rules

49×	`egg`
36×	`egg`
34×	`egg`

Counts

3 → 119

Calls

3 calls:

122.0ms	(fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
45.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
43.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	140	6
2	1482	6
3	5308	6
0	8	11
1	160	8
2	1693	8
3	4890	8
0	16	24
1	320	21
2	3434	21
3	4912	21
4	4908	21
5	4926	21

simplify131.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

728×	`unswap-sqr_binary64`
416×	`fma-neg_binary64`
311×	`distribute-rgt-neg-in_binary64`
302×	`distribute-lft-neg-in_binary64`
266×	`associate-r_binary64`

Counts

167 → 135

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	69	826
1	153	814
2	406	786
3	1564	774
4	3319	774
5	4907	768
6	4966	768
7	4998	768
8	4970	768

prune205.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	188	4	192
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	192	6	198

Error

Counts

198 → 6

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
✓	0.2b	(fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
▶	0.3b	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
	0.5b	(fma.f64 (.f64 1/6 (cbrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 3/2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.4b	(fma.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (.f64 (log.f64 u1) -1/18)))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.3b	(fma.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (log.f64 u1) 3) -1/5832))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 4035 to 3035 computations (24.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))))
✓	0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
✓	0.2b	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
✓	0.3b	(*.f64 (PI.f64) u2)

series189.0ms (2.8%)

Counts

4 → 36

Calls

4 calls:

158.0ms	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
22.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
7.0ms	(.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))))
2.0ms	(*.f64 (PI.f64) u2)

rewrite302.0ms (4.4%)

Algorithm

4×	egg-rewrite

Rules

43×	`egg`
29×	`egg`
25×	`egg`
2×	`egg`

Counts

4 → 99

Calls

4 calls:

99.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
81.0ms	(*.f64 (PI.f64) u2)
60.0ms	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
59.0ms	(.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	4	5
1	78	5
2	896	5
3	4544	5
4	5520	5
0	16	25
1	324	23
2	3343	23
3	4983	23
0	5	3
1	99	3
2	892	1
3	2020	1
4	4977	1
5	4698	1
0	10	15
1	205	15
2	2277	15
3	6284	15

simplify85.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

682×	`distribute-rgt-neg-in_binary64`
672×	`associate-l_binary64`
654×	`distribute-lft-neg-in_binary64`
624×	`associate-r_binary64`
355×	`neg-mul-1_binary64`

Counts

135 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	982
1	212	962
2	656	914
3	2980	914
4	4772	914
5	5053	914

prune103.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	121	6	127

Error

Counts

127 → 6

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
✓	0.2b	(fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
✓	0.3b	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
	0.5b	(fma.f64 (.f64 1/6 (cbrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 3/2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.4b	(fma.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (.f64 (log.f64 u1) -1/18)))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
▶	0.3b	(fma.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (log.f64 u1) 3) -1/5832))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 2791 to 1777 computations (36.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.5b	(*.f64 (pow.f64 (log.f64 u1) 3) -1/5832)
✓	0.5b	(cbrt.f64 (*.f64 (pow.f64 (log.f64 u1) 3) -1/5832))
✓	0.7b	(pow.f64 (log.f64 u1) 3)

series106.0ms (1.5%)

Counts

3 → 32

Calls

3 calls:

38.0ms	(cbrt.f64 (*.f64 (pow.f64 (log.f64 u1) 3) -1/5832))
36.0ms	(pow.f64 (log.f64 u1) 3)
31.0ms	(*.f64 (pow.f64 (log.f64 u1) 3) -1/5832)

rewrite192.0ms (2.8%)

Algorithm

3×	egg-rewrite

Rules

47×	`egg`
43×	`egg`
27×	`egg`

Counts

3 → 117

Calls

3 calls:

76.0ms	(pow.f64 (log.f64 u1) 3)
74.0ms	(cbrt.f64 (*.f64 (pow.f64 (log.f64 u1) 3) -1/5832))
41.0ms	(*.f64 (pow.f64 (log.f64 u1) 3) -1/5832)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	100	6
2	1014	6
3	4849	6
4	5773	6
0	8	8
1	159	8
2	1634	8
3	4991	8
4	4871	8
0	7	9
1	141	9
2	1435	9
3	5054	9

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1070×	`unsub-neg_binary64`
599×	`distribute-neg-in_binary64`
424×	`neg-mul-1_binary64`
372×	`neg-sub0_binary64`
348×	`distribute-rgt-neg-in_binary64`

Counts

149 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	284
1	64	284
2	169	252
3	416	252
4	1387	252
5	2363	252
6	3711	252
7	4967	252
8	4882	252

prune169.0ms (2.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	181	6	187

Error

Counts

187 → 6

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
✓	0.2b	(fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
✓	0.3b	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
	0.5b	(fma.f64 (.f64 1/6 (cbrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 3/2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.4b	(fma.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (.f64 (log.f64 u1) -1/18)))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
✓	0.3b	(fma.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (log.f64 u1) 3) -1/5832))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 3873 to 2954 computations (23.7% saved)

regimes1.1s (16.4%)

Accuracy

Total 0.2b remaining (90.3%)

Threshold costs 0.2b (90.3%)

Counts

95 → 1

Compiler

Compiled 20053 to 17742 computations (11.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	20	26
2	20	26

end111.0ms (1.6%)

Compiler: Compiled 141 to 125 computations (11.3% saved)

Details

analyze100.0ms (1.5%)

sample2.5s (36.2%)

simplify151.0ms (2.2%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series305.0ms (4.4%)

rewrite293.0ms (4.3%)

simplify73.0ms (1.1%)

prune190.0ms (2.8%)

localize10.0ms (0.2%)

series202.0ms (2.9%)

rewrite213.0ms (3.1%)

simplify131.0ms (1.9%)

prune205.0ms (3%)

localize13.0ms (0.2%)

series189.0ms (2.8%)

rewrite302.0ms (4.4%)

simplify85.0ms (1.2%)

prune103.0ms (1.5%)

localize12.0ms (0.2%)

series106.0ms (1.5%)

rewrite192.0ms (2.8%)

simplify89.0ms (1.3%)

prune169.0ms (2.5%)

regimes1.1s (16.4%)

simplify2.0ms (0%)

end111.0ms (1.6%)

Profiling