Details

analyze88.0ms (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)

sample3.3s (45.4%)

Results

3.1s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify151.0ms (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

prune6.0ms (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)

localize21.0ms (0.3%)

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)))
✓	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.3b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

series411.0ms (5.6%)

Counts

4 → 52

Calls

4 calls:

193.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
166.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
45.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
6.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite119.0ms (1.6%)

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 → 76

Calls

4 calls:

117.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
117.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
117.0ms	(.f64 (.f64 2 (PI.f64)) u2)
117.0ms	(.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

simplify70.0ms (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

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

prune108.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	7	99

Error

0.0b

Counts

99 → 7

Alt Table

Status	Error	Program
	0.6b	(fma.f64 (.f64 1/6 (pow.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) 2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(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)
▶	0.2b	(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 (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)
	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)
	0.6b	(expm1.f64 (log1p.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)))
	0.6b	(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)

Compiler

Compiled 2242 to 1754 computations (21.8% saved)

localize11.0ms (0.1%)

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))
	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

series203.0ms (2.8%)

Counts

3 → 48

Calls

3 calls:

159.0ms	(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)

rewrite116.0ms (1.6%)

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 → 66

Calls

3 calls:

115.0ms	(fma.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
115.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
115.0ms	(.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

simplify115.0ms (1.6%)

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 (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	104	5	109

Error

0.0b

Counts

109 → 5

Alt Table

Status	Error	Program
▶	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	(expm1.f64 (log1p.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)))
	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)
	0.3b	(fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (.f64 1/6 (pow.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) 2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 2053 to 1557 computations (24.2% saved)

localize11.0ms (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	(*.f64 (PI.f64) u2)
✓	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)

series199.0ms (2.7%)

Counts

4 → 36

Calls

4 calls:

167.0ms	(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)

rewrite68.0ms (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

4 → 78

Calls

4 calls:

66.0ms	(.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))))
66.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
66.0ms	(*.f64 (PI.f64) u2)
66.0ms	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)

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

simplify80.0ms (1.1%)

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

prune76.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	101	6	107

Error

Counts

107 → 6

Alt Table

Status	Error	Program
✓	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	(expm1.f64 (log1p.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)))
	1.2b	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (-.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))))) 1) 1/2)
	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)
▶	0.3b	(fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (.f64 1/6 (pow.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) 2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 2308 to 1536 computations (33.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(*.f64 (log.f64 u1) -1/18)
✓	0.5b	(cbrt.f64 (pow.f64 (*.f64 (log.f64 u1) -1/18) 3))
✓	0.7b	(pow.f64 (*.f64 (log.f64 u1) -1/18) 3)

series93.0ms (1.3%)

Counts

3 → 36

Calls

3 calls:

43.0ms	(cbrt.f64 (pow.f64 (*.f64 (log.f64 u1) -1/18) 3))
29.0ms	(pow.f64 (*.f64 (log.f64 u1) -1/18) 3)
21.0ms	(*.f64 (log.f64 u1) -1/18)

rewrite53.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

563×	`log1p-expm1-u_binary64`
563×	`expm1-log1p-u_binary64`
520×	`unpow-prod-down_binary64`
291×	`log-prod_binary64`
161×	`pow2_binary64`

Counts

3 → 134

Calls

3 calls:

51.0ms	(*.f64 (log.f64 u1) -1/18)
51.0ms	(cbrt.f64 (pow.f64 (*.f64 (log.f64 u1) -1/18) 3))
51.0ms	(pow.f64 (*.f64 (log.f64 u1) -1/18) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	146	21
2	1501	21
3	5466	21
0	0	0
1	0	0

simplify97.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1117×	`unsub-neg_binary64`
437×	`neg-sub0_binary64`
400×	`sub-neg_binary64`
389×	`neg-mul-1_binary64`
370×	`unswap-sqr_binary64`

Counts

170 → 124

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	276
1	69	276
2	167	276
3	423	276
4	1380	276
5	2378	276
6	3959	276
7	4917	276
8	4999	276
9	4827	276

prune125.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	140	6	146

Error

Counts

146 → 6

Alt Table

Status	Error	Program
	0.2b	(fma.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (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	(expm1.f64 (log1p.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)))
	1.2b	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (-.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))))) 1) 1/2)
	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)
✓	0.3b	(fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 3070 to 2331 computations (24.1% saved)

regimes1.5s (20.8%)

Accuracy

Total 0.2b remaining (89.9%)

Threshold costs 0.2b (89.9%)

Counts

124 → 1

Compiler

Compiled 25867 to 22954 computations (11.3% 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

end108.0ms (1.5%)

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

Details

analyze88.0ms (1.2%)

sample3.3s (45.4%)

simplify151.0ms (2.1%)

prune6.0ms (0.1%)

localize21.0ms (0.3%)

series411.0ms (5.6%)

rewrite119.0ms (1.6%)

simplify70.0ms (1%)

prune108.0ms (1.5%)

localize11.0ms (0.1%)

series203.0ms (2.8%)

rewrite116.0ms (1.6%)

simplify115.0ms (1.6%)

prune114.0ms (1.6%)

localize11.0ms (0.2%)

series199.0ms (2.7%)

rewrite68.0ms (0.9%)

simplify80.0ms (1.1%)

prune76.0ms (1%)

localize12.0ms (0.2%)

series93.0ms (1.3%)

rewrite53.0ms (0.7%)

simplify97.0ms (1.3%)

prune125.0ms (1.7%)

regimes1.5s (20.8%)

simplify2.0ms (0%)

end108.0ms (1.5%)

Profiling