Details

analyze76.0ms (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)

sample2.5s (44.2%)

Results

2.4s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify123.0ms (2.1%)

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)

localize11.0ms (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))))

series224.0ms (3.9%)

Counts

4 → 52

Calls

4 calls:

165.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
32.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
24.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite119.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

76× egg-rr

Counts

4 → 76

Calls

2 calls:

118.0ms

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

0.0ms

()

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

simplify63.0ms (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

128 → 98

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

prune102.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	6	99

Error

Counts

99 → 6

Alt Table

Status	Error	Program
	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))
▶	0.2b	(fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(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)
	0.7b	(pow.f64 (sqrt.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)) 2)
	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)
	0.5b	(fma.f64 (exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 2202 to 1718 computations (22% saved)

localize11.0ms (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)

series208.0ms (3.6%)

Counts

3 → 48

Calls

3 calls:

160.0ms	(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))
22.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

rewrite114.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

66× egg-rr

Counts

3 → 66

Calls

2 calls:

112.0ms	((.f64 (.f64 -2 (log.f64 u1)) 1/36) (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2))
0.0ms	()

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

simplify111.0ms (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

114 → 86

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

prune114.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	102	6	108

Error

Counts

108 → 6

Alt Table

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

Compiler

Compiled 2068 to 1570 computations (24.1% saved)

localize12.0ms (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)

series194.0ms (3.4%)

Counts

4 → 36

Calls

4 calls:

164.0ms	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
21.0ms	(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)

rewrite61.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

78× egg-rr

Counts

4 → 78

Calls

2 calls:

59.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	52
1	324	48
2	3343	48
3	4983	48
0	0	0
1	0	0

simplify74.0ms (1.3%)

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

114 → 102

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

prune81.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	102	6	108

Error

Counts

108 → 6

Alt Table

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

Compiler

Compiled 2281 to 1511 computations (33.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (exp.f64 (log.f64 (*.f64 (log.f64 u1) -1/18))))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(*.f64 (log.f64 u1) -1/18)
✓	0.6b	(exp.f64 (log.f64 (*.f64 (log.f64 u1) -1/18)))

series69.0ms (1.2%)

Counts

3 → 36

Calls

3 calls:

24.0ms	(sqrt.f64 (exp.f64 (log.f64 (*.f64 (log.f64 u1) -1/18))))
23.0ms	(exp.f64 (log.f64 (*.f64 (log.f64 u1) -1/18)))
22.0ms	(*.f64 (log.f64 u1) -1/18)

rewrite54.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

129× egg-rr

Counts

3 → 129

Calls

2 calls:

52.0ms	((exp.f64 (log.f64 (.f64 (log.f64 u1) -1/18))) (.f64 (log.f64 u1) -1/18) (sqrt.f64 (exp.f64 (log.f64 (*.f64 (log.f64 u1) -1/18)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	132	20
2	1414	20
3	5210	20
0	0	0
1	0	0

simplify215.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

1383×	`distribute-rgt-in_binary64`
1053×	`distribute-lft-in_binary64`
998×	`distribute-neg-in_binary64`
871×	`unsub-neg_binary64`
748×	`fma-def_binary64`

Counts

165 → 117

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	256
1	33	256
2	51	256
3	95	256
4	154	256
5	409	256
6	949	256
7	1742	256
8	1914	256
9	2189	256
10	2297	256
11	2336	256
12	2346	256
13	3156	256
14	3179	256
15	3133	256
16	3259	256
17	3301	256
18	3301	256
19	3343	256
20	3343	256
21	3343	256
22	4575	256
23	5051	256

prune109.0ms (1.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	133	6	139

Error

Counts

139 → 6

Alt Table

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

Compiler

Compiled 2737 to 2027 computations (25.9% saved)

regimes925.0ms (16.1%)

Accuracy

Total 0.2b remaining (83.5%)

Threshold costs 0.2b (83.5%)

Counts

79 → 1

Compiler

Compiled 16024 to 14231 computations (11.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	16	21
2	16	21

end112.0ms (2%)

Compiler: Compiled 136 to 120 computations (11.8% saved)

Details

analyze76.0ms (1.3%)

sample2.5s (44.2%)

simplify123.0ms (2.1%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series224.0ms (3.9%)

rewrite119.0ms (2.1%)

simplify63.0ms (1.1%)

prune102.0ms (1.8%)

localize11.0ms (0.2%)

series208.0ms (3.6%)

rewrite114.0ms (2%)

simplify111.0ms (1.9%)

prune114.0ms (2%)

localize12.0ms (0.2%)

series194.0ms (3.4%)

rewrite61.0ms (1.1%)

simplify74.0ms (1.3%)

prune81.0ms (1.4%)

localize14.0ms (0.2%)

series69.0ms (1.2%)

rewrite54.0ms (0.9%)

simplify215.0ms (3.7%)

prune109.0ms (1.9%)

regimes925.0ms (16.1%)

simplify2.0ms (0%)

end112.0ms (2%)

Profiling