Details

analyze446.0ms (7.1%)

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 30 to 26 computations (13.3% saved)

sample52.0ms (0.8%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 53 to 47 computations (11.3% saved)

simplify138.0ms (2.2%)

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 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	26
1	37	26
2	60	26
3	95	26
4	193	26
5	510	26
6	613	26
7	798	26
8	1384	26
9	1423	26
10	1454	26
11	1518	26
12	1524	26
13	1796	26
14	2019	26
15	2440	26
16	3048	26
17	3546	26
18	3979	26
19	4387	26
20	4696	26
21	4801	26

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))

Compiler

Compiled 54 to 48 computations (11.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
0.1b	(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))))

rewrite113.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

14×	`pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`
6×	`add-log-exp_binary64`

Counts

4 → 59

Calls

4 calls:

7.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
3.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

Compiler

Compiled 1319 to 1005 computations (23.8% saved)

series119.0ms (1.9%)

Error

0.2b

Counts

4 → 17

Calls

4 calls:

58.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
25.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
15.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
8.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 897 to 773 computations (13.8% saved)

simplify106.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

479×	`*-commutative_binary64`
393×	`cancel-sign-sub-inv_binary64`
328×	`unswap-sqr_binary64`
275×	`distribute-rgt-neg-in_binary64`
256×	`distribute-lft-neg-in_binary64`

Counts

76 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	1382
1	360	1258
2	1124	1238
3	2040	1228
4	3640	1228
5	4808	1228
6	4931	1228

prune50.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	34	7	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	7	42

Error

0.0b

Counts

42 → 7

Alt Table

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

Compiler

Compiled 965 to 745 computations (22.8% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.2b	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
0.2b	(.f64 (.f64 2 PI.f64) u2)
0.2b	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))

rewrite147.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`pow1_binary64`
19×	`pow-prod-down_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`sqrt-pow1_binary64`

Counts

4 → 81

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
7.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

Compiler

Compiled 1801 to 1453 computations (19.3% saved)

series77.0ms (1.2%)

Error

Counts

4 → 12

Calls

4 calls:

22.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
19.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
16.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
9.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 748 to 675 computations (9.8% saved)

simplify109.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

379×	`associate-*l/_binary64`
369×	`*-commutative_binary64`
239×	`associate-/l/_binary64`
236×	`associate-/l*_binary64`
205×	`sqr-pow_binary64`

Counts

93 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1334
1	261	1130
2	766	1130
3	1059	1122
4	1356	1122
5	2366	1122
6	4478	1122
7	4901	1122

prune73.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	58	7	65

Error

Counts

65 → 7

Alt Table

Status	Error	Program
	0.7b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 1/6) (sqrt.f64 2)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))
✓	0.3b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))
	0.3b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
	0.6b	(.f64 (sqrt.f64 (+.f64 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 PI.f64))))) 1/2)) (sqrt.f64 (+.f64 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64))))) 1/2)))
	0.5b	(exp.f64 (log.f64 (+.f64 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64))))) 1/2)))
▶	0.2b	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
	0.5b	(/.f64 (-.f64 1/4 (.f64 (.f64 (log.f64 u1) -1/18) (.f64 (cos.f64 (.f64 2 (.f64 u2 PI.f64))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))))) (-.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))))))

Compiler

Compiled 1184 to 951 computations (19.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
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)

rewrite105.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

20×	`pow1_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow-prod-down_binary64`
6×	`prod-exp_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `cbrt-unprod_binary64` `add-sqr-sqrt_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`
3×	`sqrt-pow1_binary64`

Counts

4 → 59

Calls

4 calls:

5.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
5.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
3.0ms	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))

Compiler

Compiled 1289 to 984 computations (23.7% saved)

series104.0ms (1.7%)

Error

Counts

4 → 17

Calls

4 calls:

50.0ms	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
14.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
14.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
8.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 841 to 714 computations (15.1% saved)

simplify148.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

455×	`*-commutative_binary64`
389×	`unswap-sqr_binary64`
224×	`associate-l_binary64`
195×	`sqr-pow_binary64`
190×	`distribute-rgt-in_binary64`

Counts

76 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	1314
1	374	1073
2	1142	1053
3	1894	1046
4	3503	1046
5	4778	1046
6	4962	1046
7	4969	1046
8	4831	1046

prune68.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	4	1	5
Picked	1	0	1
Done	1	0	1
Total	58	4	62

Error

Counts

62 → 4

Alt Table

Status	Error	Program
	0.4b	(/.f64 (-.f64 1/4 (.f64 (.f64 -1/18 (log.f64 u1)) (.f64 (cos.f64 (.f64 2 (.f64 u2 PI.f64))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))))) (-.f64 1/2 (.f64 (sqrt.f64 (.f64 -1/18 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64))))))
	0.6b	(.f64 (sqrt.f64 (+.f64 (.f64 (sqrt.f64 (.f64 -1/18 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))) 1/2)) (sqrt.f64 (+.f64 (.f64 (sqrt.f64 (.f64 -1/18 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64)))) 1/2)))
	0.5b	(exp.f64 (log.f64 (+.f64 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64))))) 1/2)))
▶	0.2b	(+.f64 1/2 (.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))

Compiler

Compiled 989 to 726 computations (26.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(log.f64 (pow.f64 u1 -1/18))
0.1b	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))
0.2b	(.f64 (.f64 2 PI.f64) u2)
2.6b	(pow.f64 u1 -1/18)

rewrite111.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`add-exp-log_binary64`
11×	`add-sqr-sqrt_binary64` `pow1_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
7×	`log-prod_binary64`

Counts

4 → 67

Calls

4 calls:

5.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(log.f64 (pow.f64 u1 -1/18))
2.0ms	(pow.f64 u1 -1/18)
1.0ms	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))

Compiler

Compiled 1181 to 932 computations (21.1% saved)

series73.0ms (1.2%)

Error

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))
21.0ms	(log.f64 (pow.f64 u1 -1/18))
15.0ms	(pow.f64 u1 -1/18)
8.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 509 to 450 computations (11.6% saved)

simplify126.0ms (2%)

Algorithm

1×	egg-herbie

Rules

349×	`unswap-sqr_binary64`
319×	`exp-prod_binary64`
317×	`log-prod_binary64`
289×	`*-commutative_binary64`
215×	`sqr-pow_binary64`

Counts

79 → 53

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	116	774
1	218	706
2	636	692
3	1079	677
4	2055	659
5	4052	659
6	4912	659
7	5000	659
8	4822	659

prune49.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	53	4	57

Error

Counts

57 → 4

Alt Table

Status	Error	Program
	0.4b	(/.f64 (-.f64 1/4 (.f64 (.f64 -1/18 (log.f64 u1)) (.f64 (cos.f64 (.f64 2 (.f64 u2 PI.f64))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))))) (-.f64 1/2 (.f64 (sqrt.f64 (.f64 -1/18 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64))))))
	0.6b	(.f64 (sqrt.f64 (+.f64 (.f64 (sqrt.f64 (.f64 -1/18 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))) 1/2)) (sqrt.f64 (+.f64 (.f64 (sqrt.f64 (.f64 -1/18 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64)))) 1/2)))
	0.5b	(exp.f64 (log.f64 (+.f64 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64))))) 1/2)))
	0.2b	(+.f64 1/2 (.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))

Compiler

Compiled 646 to 490 computations (24.1% saved)

regimes2.5s (40%)

Accuracy

Total 0.2b remaining (88.5%)

Threshold costs 0.2b (88.5%)

Compiler

Compiled 38146 to 33042 computations (13.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	20	25
2	20	25

end2.0ms (0%)

Compiler: Compiled 17 to 15 computations (11.8% saved)

sample1.5s (23.5%)

Algorithm

1×

intervals

Results

788.0ms	8000×	body	128	valid
190.0ms	8000×	pre	128	true

Compiler

Compiled 155 to 128 computations (17.4% saved)

Details

analyze446.0ms (7.1%)

sample52.0ms (0.8%)

simplify138.0ms (2.2%)

prune8.0ms (0.1%)

localize14.0ms (0.2%)

rewrite113.0ms (1.8%)

series119.0ms (1.9%)

simplify106.0ms (1.7%)

prune50.0ms (0.8%)

localize18.0ms (0.3%)

rewrite147.0ms (2.4%)

series77.0ms (1.2%)

simplify109.0ms (1.7%)

prune73.0ms (1.2%)

localize12.0ms (0.2%)

rewrite105.0ms (1.7%)

series104.0ms (1.7%)

simplify148.0ms (2.4%)

prune68.0ms (1.1%)

localize13.0ms (0.2%)

rewrite111.0ms (1.8%)

series73.0ms (1.2%)

simplify126.0ms (2%)

prune49.0ms (0.8%)

regimes2.5s (40%)

simplify3.0ms (0.1%)

end2.0ms (0%)

sample1.5s (23.5%)

Profiling