Details

analyze87.0ms (1.2%)

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)

sample2.4s (33.4%)

Results

2.3s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify122.0ms (1.7%)

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

2 alts after pruning (2 fresh and 0 done)

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

Error

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)

Compiler

Compiled 78 to 68 computations (12.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series438.0ms (6%)

Counts

4 → 60

Calls

4 calls:

247.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
154.0ms	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
34.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite70.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

572×	`prod-diff_binary64`
184×	`add-sqr-sqrt_binary64`
175×	`log1p-expm1-u_binary64`
175×	`expm1-log1p-u_binary64`
172×	`add-log-exp_binary64`

Counts

4 → 85

Calls

4 calls:

67.0ms	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
67.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
67.0ms	(.f64 (.f64 2 (PI.f64)) u2)
67.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	51
1	392	51
2	4174	51
3	5015	51

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Counts

145 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1098
1	172	1050
2	465	1020
3	1647	998
4	3476	998
5	5076	998

prune126.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	99	6	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	6	106

Error

0.0b

Counts

106 → 6

Alt Table

Status	Error	Program
	0.5b	(+.f64 (.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)
	0.6b	(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))
	0.3b	(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	(+.f64 (.f64 (.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)
	0.5b	(/.f64 (-.f64 (.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) 1/4) (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) -1/2))
▶	0.3b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)

Compiler

Compiled 2775 to 2195 computations (20.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series202.0ms (2.8%)

Counts

3 → 48

Calls

3 calls:

149.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
27.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
26.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

rewrite70.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

520×	`prod-diff_binary64`
298×	`log1p-udef_binary64`
167×	`add-sqr-sqrt_binary64`
159×	`add-log-exp_binary64`
159×	`log1p-expm1-u_binary64`

Counts

3 → 79

Calls

3 calls:

68.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
68.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
68.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	351	35
2	3912	35
3	5213	35

simplify112.0ms (1.5%)

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

127 → 99

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

prune131.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	116	6	122

Error

0.0b

Counts

122 → 6

Alt Table

Status	Error	Program
	0.3b	(+.f64 (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (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)
	0.4b	(exp.f64 (log.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)))
	0.7b	(+.f64 (.f64 (.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)
▶	0.3b	(log.f64 (+.f64 1 (expm1.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2))))
	0.5b	(/.f64 (-.f64 (.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) 1/4) (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) -1/2))

Compiler

Compiled 2641 to 2017 computations (23.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(*.f64 (log.f64 u1) -1/18)
✓	1.0b	(expm1.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2))

series214.0ms (2.9%)

Counts

3 → 48

Calls

3 calls:

160.0ms	(expm1.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2))
28.0ms	(*.f64 (log.f64 u1) -1/18)
26.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))

rewrite86.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

469×	`prod-diff_binary64`
253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
228×	`log-pow_binary64`
142×	`add-sqr-sqrt_binary64`

Counts

3 → 66

Calls

3 calls:

84.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))
84.0ms	(*.f64 (log.f64 u1) -1/18)
84.0ms	(expm1.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	294	37
2	3189	37
3	4872	37
4	4949	37

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

936×	`fma-neg_binary64`
426×	`fma-def_binary64`
399×	`*-commutative_binary64`
317×	`distribute-rgt-neg-in_binary64`
312×	`distribute-lft-neg-in_binary64`

Counts

114 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	1134
1	295	1109
2	929	1050
3	2633	1045
4	5120	1045

prune143.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Error

0.0b

Counts

109 → 6

Alt Table

Status	Error	Program
	0.3b	(+.f64 (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (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)
	0.4b	(exp.f64 (log.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)))
	0.5b	(log.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2))) 3)))
	0.7b	(+.f64 (.f64 (.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)
	0.5b	(/.f64 (-.f64 (.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) 1/4) (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) -1/2))

Compiler

Compiled 2903 to 2306 computations (20.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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)

series180.0ms (2.5%)

Counts

4 → 36

Calls

4 calls:

151.0ms	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
24.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
3.0ms	(cos.f64 (.f64 2 (.f64 (PI.f64) u2)))
2.0ms	(*.f64 (PI.f64) u2)

rewrite72.0ms (1%)

Algorithm

1×	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

4 → 108

Calls

4 calls:

70.0ms	(cos.f64 (.f64 2 (.f64 (PI.f64) u2)))
70.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
70.0ms	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
70.0ms	(*.f64 (PI.f64) u2)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	47
1	324	43
2	3343	43
3	4983	43

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Rules

923×	`fma-neg_binary64`
678×	`distribute-rgt-neg-in_binary64`
615×	`associate-r_binary64`
582×	`associate-l_binary64`
245×	`neg-mul-1_binary64`

Counts

144 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	944
1	203	924
2	636	894
3	2836	892
4	4823	892
5	4994	892

prune113.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	132	6	138

Error

0.0b

Counts

138 → 6

Alt Table

Status	Error	Program
	0.3b	(+.f64 (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (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)
	0.4b	(exp.f64 (log.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)))
	0.5b	(log.f64 (+.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2))) 3)))
	0.7b	(+.f64 (.f64 (.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)
	0.5b	(/.f64 (-.f64 (.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) 1/4) (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) -1/2))

Compiler

Compiled 3554 to 2094 computations (41.1% saved)

regimes2.3s (31.8%)

Accuracy

Total 0.2b remaining (91.1%)

Threshold costs 0.2b (91.1%)

Counts

184 → 1

Compiler

Compiled 44534 to 39343 computations (11.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	34
1	29	34
2	30	34
3	28	34

end128.0ms (1.8%)

Compiler: Compiled 182 to 160 computations (12.1% saved)

Details

analyze87.0ms (1.2%)

sample2.4s (33.4%)

simplify122.0ms (1.7%)

prune4.0ms (0.1%)

localize15.0ms (0.2%)

series438.0ms (6%)

rewrite70.0ms (1%)

simplify66.0ms (0.9%)

prune126.0ms (1.7%)

localize11.0ms (0.2%)

series202.0ms (2.8%)

rewrite70.0ms (1%)

simplify112.0ms (1.5%)

prune131.0ms (1.8%)

localize14.0ms (0.2%)

series214.0ms (2.9%)

rewrite86.0ms (1.2%)

simplify56.0ms (0.8%)

prune143.0ms (2%)

localize11.0ms (0.2%)

series180.0ms (2.5%)

rewrite72.0ms (1%)

simplify72.0ms (1%)

prune113.0ms (1.5%)

regimes2.3s (31.8%)

simplify2.0ms (0%)

end128.0ms (1.8%)

Profiling