Details

analyze86.0ms (1.1%)

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 (32.6%)

Results

2.2s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify121.0ms (1.6%)

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%)

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

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(+.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)

localize14.0ms (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)
✓	0.4b	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))

series419.0ms (5.6%)

Counts

4 → 60

Calls

4 calls:

241.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
145.0ms	(+.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)
29.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite72.0ms (1%)

Algorithm

2×	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 → 83

Calls

4 calls:

71.0ms	(+.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)
71.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
71.0ms	(.f64 (.f64 2 (PI.f64)) u2)
71.0ms	(.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
0	0	0
1	0	0

simplify67.0ms (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

143 → 104

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	98	6	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	6	105

Error

Counts

105 → 6

Alt Table

Status	Error	Program
	0.6b	(+.f64 (.f64 (.f64 (/.f64 1 6) (.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (pow.f64 (.f64 -2 (log.f64 u1)) 1/4))) (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)
	0.5b	(-.f64 (/.f64 (.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) -1/2)) (/.f64 1/4 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) -1/2)))
	0.6b	(+.f64 (.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	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	1.1b	(+.f64 (.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)

Compiler

Compiled 2790 to 2206 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)

series198.0ms (2.6%)

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)
25.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
24.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

rewrite69.0ms (0.9%)

Algorithm

2×	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 → 77

Calls

3 calls:

67.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
67.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
67.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

Iterations

Useful iterations: 0 (0.0ms)

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

simplify113.0ms (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

125 → 97

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

prune138.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	113	6	119

Error

Counts

119 → 6

Alt Table

Status	Error	Program
	0.5b	(-.f64 (/.f64 (.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) -1/2)) (/.f64 1/4 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) -1/2)))
▶	0.2b	(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	(+.f64 (.f64 (.f64 (/.f64 1 6) (.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (pow.f64 (.f64 -2 (log.f64 u1)) 1/4))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.5b	(+.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3/2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
	0.3b	(+.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
✓	0.2b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)

Compiler

Compiled 2615 to 1997 computations (23.6% saved)

localize11.0ms (0.1%)

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)

series181.0ms (2.4%)

Counts

4 → 36

Calls

4 calls:

147.0ms	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
25.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
6.0ms	(.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))))
2.0ms	(*.f64 (PI.f64) u2)

rewrite66.0ms (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:

65.0ms	(.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))))
65.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
65.0ms	(fma.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/18) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2)))) 1/2)
65.0ms	(*.f64 (PI.f64) u2)

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

simplify79.0ms (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

prune90.0ms (1.2%)

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
	0.5b	(-.f64 (/.f64 (.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) -1/2)) (/.f64 1/4 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) -1/2)))
✓	0.2b	(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	(+.f64 (.f64 (.f64 (/.f64 1 6) (.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (pow.f64 (.f64 -2 (log.f64 u1)) 1/4))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.5b	(+.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3/2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
▶	0.3b	(+.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
✓	0.2b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)

Compiler

Compiled 2370 to 1580 computations (33.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(*.f64 (log.f64 u1) -1/18)
✓	0.5b	(cbrt.f64 (pow.f64 (*.f64 (log.f64 u1) -1/18) 3))
✓	0.8b	(pow.f64 (*.f64 (log.f64 u1) -1/18) 3)

series89.0ms (1.2%)

Counts

3 → 36

Calls

3 calls:

39.0ms	(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)

rewrite54.0ms (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:

49.0ms	(*.f64 (log.f64 u1) -1/18)
49.0ms	(cbrt.f64 (pow.f64 (*.f64 (log.f64 u1) -1/18) 3))
49.0ms	(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

prune161.0ms (2.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	141	5	146

Error

Counts

146 → 5

Alt Table

Status	Error	Program
	0.5b	(-.f64 (/.f64 (.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) -1/2)) (/.f64 1/4 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) -1/2)))
✓	0.2b	(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 (.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 1/34012224 (pow.f64 (log.f64 u1) 6))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
	0.6b	(+.f64 (.f64 (.f64 (/.f64 1 6) (.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (pow.f64 (.f64 -2 (log.f64 u1)) 1/4))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.2b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)

Compiler

Compiled 3238 to 2491 computations (23.1% saved)

regimes2.7s (35.5%)

Accuracy

Total 0.2b remaining (88.9%)

Threshold costs 0.2b (88.9%)

Counts

200 → 1

Compiler

Compiled 50155 to 43724 computations (12.8% 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	17	26
1	26	26
2	27	26
3	25	26

end116.0ms (1.5%)

Compiler: Compiled 170 to 146 computations (14.1% saved)

Details

analyze86.0ms (1.1%)

sample2.4s (32.6%)

simplify121.0ms (1.6%)

prune3.0ms (0%)

localize14.0ms (0.2%)

series419.0ms (5.6%)

rewrite72.0ms (1%)

simplify67.0ms (0.9%)

prune126.0ms (1.7%)

localize11.0ms (0.2%)

series198.0ms (2.6%)

rewrite69.0ms (0.9%)

simplify113.0ms (1.5%)

prune138.0ms (1.8%)

localize11.0ms (0.1%)

series181.0ms (2.4%)

rewrite66.0ms (0.9%)

simplify79.0ms (1.1%)

prune90.0ms (1.2%)

localize12.0ms (0.2%)

series89.0ms (1.2%)

rewrite54.0ms (0.7%)

simplify97.0ms (1.3%)

prune161.0ms (2.1%)

regimes2.7s (35.5%)

simplify2.0ms (0%)

end116.0ms (1.5%)

Profiling