Details

analyze86.0ms (1.3%)

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)

sample2.3s (36.3%)

Results

2.2s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify124.0ms (1.9%)

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

prune3.0ms (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)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
✓	0.2b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
✓	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

series296.0ms (4.6%)

Counts

4 → 52

Calls

4 calls:

136.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
134.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
23.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite117.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

362×	`prod-diff_binary64`
268×	`expm1-udef_binary64`
268×	`log1p-udef_binary64`
242×	`fma-udef_binary64`
185×	`fma-neg_binary64`

Counts

4 → 80

Calls

4 calls:

116.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
116.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
116.0ms	(.f64 (.f64 2 (PI.f64)) u2)
116.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	51
1	317	51
2	3390	51
3	4863	51
4	4853	51
5	4886	51
0	0	0
1	0	0

simplify64.0ms (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

132 → 100

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

prune108.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	92	8	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	8	101

Error

Counts

101 → 8

Alt Table

Status	Error	Program
	0.6b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) 3)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
▶	0.3b	(fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(fma.f64 (pow.f64 (sqrt.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))) 2) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	1.2b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))) 3) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) 1) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
	0.7b	(fma.f64 (.f64 1/6 (.f64 (cbrt.f64 (.f64 -2 (log.f64 u1))) (cbrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(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 2324 to 1820 computations (21.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
✓	0.2b	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.3b	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

series176.0ms (2.7%)

Counts

3 → 48

Calls

3 calls:

130.0ms	(fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
25.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
21.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

rewrite110.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

362×	`prod-diff_binary64`
269×	`expm1-udef_binary64`
269×	`log1p-udef_binary64`
242×	`fma-udef_binary64`
190×	`fma-neg_binary64`

Counts

3 → 69

Calls

3 calls:

109.0ms	(fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
109.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
109.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	44
1	320	35
2	3434	35
3	4912	35
4	4908	35
5	4926	35
0	0	0
1	0	0

simplify117.0ms (1.8%)

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

117 → 89

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

prune113.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	108	6	114

Error

Counts

114 → 6

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (exp.f64 (.f64 (log.f64 (.f64 (log.f64 u1) -1/18)) 1/2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (pow.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 1/4) 2) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
▶	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)
	0.6b	(cbrt.f64 (pow.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2) 3))
	0.7b	(fma.f64 (.f64 1/6 (.f64 (cbrt.f64 (.f64 -2 (log.f64 u1))) (cbrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.4b	(fma.f64 (-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)))) 1) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 2155 to 1635 computations (24.1% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)
✓	0.2b	(*.f64 (PI.f64) u2)

series156.0ms (2.4%)

Counts

3 → 32

Calls

3 calls:

132.0ms	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
19.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
5.0ms	(*.f64 (PI.f64) u2)

rewrite59.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

575×	`prod-diff_binary64`
262×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`
157×	`add-sqr-sqrt_binary64`
148×	`log1p-expm1-u_binary64`

Counts

3 → 66

Calls

3 calls:

58.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
58.0ms	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
58.0ms	(*.f64 (PI.f64) u2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	324	33
2	3343	33
3	4983	33
0	0	0
1	0	0

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-neg_binary64`
515×	`associate-r_binary64`
511×	`distribute-rgt-neg-in_binary64`
504×	`associate-l_binary64`
493×	`distribute-lft-neg-in_binary64`

Counts

98 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	846
1	189	830
2	506	804
3	2277	776
4	4739	776
5	4980	776

prune59.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	83	6	89

Error

Counts

89 → 6

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 (exp.f64 (.f64 (log.f64 (.f64 (log.f64 u1) -1/18)) 1/2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (pow.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 1/4) 2) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
✓	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)
	0.6b	(cbrt.f64 (pow.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2) 3))
	0.7b	(fma.f64 (.f64 1/6 (.f64 (cbrt.f64 (.f64 -2 (log.f64 u1))) (cbrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.4b	(fma.f64 (-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)))) 1) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 1873 to 1249 computations (33.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(log.f64 (*.f64 (log.f64 u1) -1/18))
	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.3b	(exp.f64 (.f64 (log.f64 (.f64 (log.f64 u1) -1/18)) 1/2))
✓	0.3b	(*.f64 (log.f64 u1) -1/18)

series457.0ms (7.1%)

Counts

3 → 36

Calls

3 calls:

220.0ms	(exp.f64 (.f64 (log.f64 (.f64 (log.f64 u1) -1/18)) 1/2))
216.0ms	(log.f64 (*.f64 (log.f64 u1) -1/18))
22.0ms	(*.f64 (log.f64 u1) -1/18)

rewrite49.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

663×	`log1p-expm1-u_binary64`
663×	`expm1-log1p-u_binary64`
356×	`log-prod_binary64`
139×	`expm1-udef_binary64`
139×	`log1p-udef_binary64`

Counts

3 → 107

Calls

3 calls:

48.0ms	(log.f64 (*.f64 (log.f64 u1) -1/18))
48.0ms	(exp.f64 (.f64 (log.f64 (.f64 (log.f64 u1) -1/18)) 1/2))
48.0ms	(*.f64 (log.f64 u1) -1/18)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	171	22
2	1762	22
3	5223	22
0	0	0
1	0	0

simplify219.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1383×	`distribute-rgt-in_binary64`
1094×	`distribute-neg-in_binary64`
1053×	`distribute-lft-in_binary64`
899×	`unsub-neg_binary64`
778×	`fma-def_binary64`

Counts

143 → 117

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	280
1	44	280
2	65	280
3	108	280
4	171	280
5	441	280
6	1006	280
7	1833	280
8	2049	280
9	2349	280
10	2467	280
11	2506	280
12	2516	280
13	3326	280
14	3349	280
15	3303	280
16	3429	280
17	3471	280
18	3471	280
19	3513	280
20	3513	280
21	3513	280
22	4761	280
23	5393	280

prune117.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	134	6	140

Error

Counts

140 → 6

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 (exp.f64 (.f64 (log.f64 (.f64 (log.f64 u1) -1/18)) 1/2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (pow.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 1/4) 2) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
✓	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)
	0.6b	(cbrt.f64 (pow.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2) 3))
	0.7b	(fma.f64 (.f64 1/6 (.f64 (cbrt.f64 (.f64 -2 (log.f64 u1))) (cbrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.4b	(fma.f64 (-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)))) 1) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 2901 to 2218 computations (23.5% saved)

regimes1.4s (22.4%)

Accuracy

Total 0.2b remaining (92.5%)

Threshold costs 0.2b (92.5%)

Counts

113 → 1

Compiler

Compiled 25869 to 23023 computations (11% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	23	25
2	25	25
3	26	25
4	26	25

end117.0ms (1.8%)

Compiler: Compiled 148 to 130 computations (12.2% saved)

Details

analyze86.0ms (1.3%)

sample2.3s (36.3%)

simplify124.0ms (1.9%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series296.0ms (4.6%)

rewrite117.0ms (1.8%)

simplify64.0ms (1%)

prune108.0ms (1.7%)

localize12.0ms (0.2%)

series176.0ms (2.7%)

rewrite110.0ms (1.7%)

simplify117.0ms (1.8%)

prune113.0ms (1.8%)

localize11.0ms (0.2%)

series156.0ms (2.4%)

rewrite59.0ms (0.9%)

simplify74.0ms (1.1%)

prune59.0ms (0.9%)

localize12.0ms (0.2%)

series457.0ms (7.1%)

rewrite49.0ms (0.8%)

simplify219.0ms (3.4%)

prune117.0ms (1.8%)

regimes1.4s (22.4%)

simplify2.0ms (0%)

end117.0ms (1.8%)

Profiling