Details

analyze394.0ms (5.5%)

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)

sample51.0ms (0.7%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 53 to 47 computations (11.3% saved)

simplify365.0ms (5.1%)

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 → 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

prune3.0ms (0%)

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)

localize12.0ms (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)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

rewrite102.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

14×	`pow1_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`

Counts

4 → 59

Calls

4 calls:

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

series110.0ms (1.5%)

Error

0.2b

Counts

4 → 17

Calls

4 calls:

72.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
13.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
11.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
6.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 897 to 773 computations (13.8% saved)

simplify122.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

681×	`distribute-rgt-in_binary64`
438×	`*-commutative_binary64`
282×	`cancel-sign-sub-inv_binary64`
260×	`unswap-sqr_binary64`
218×	`distribute-rgt-neg-in_binary64`

Counts

76 → 39

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	1382
1	353	1258
2	1059	1238
3	1851	1228
4	3264	1228
5	4927	1228
6	4998	1228
7	4877	1228

prune40.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	32	7	39
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	33	7	40

Error

0.0b

Counts

40 → 7

Alt Table

Status	Error	Program
	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)))))))
	0.6b	(+.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))))
	0.6b	(cbrt.f64 (pow.f64 (+.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64)))))) 3))
	0.4b	(+.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))))
▶	0.3b	(+.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))))
	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 PI.f64))))))) (cbrt.f64 (+.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 PI.f64)))))))) (cbrt.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	(exp.f64 (log.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 1010 to 778 computations (23% saved)

localize15.0ms (0.2%)

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

rewrite112.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 81

Calls

4 calls:

9.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
6.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
4.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

Compiler

Compiled 1801 to 1453 computations (19.3% saved)

series57.0ms (0.8%)

Error

Counts

4 → 12

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
14.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
11.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
6.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 773 to 697 computations (9.8% saved)

simplify106.0ms (1.5%)

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	259	1130
2	768	1130
3	1059	1122
4	1356	1122
5	2366	1122
6	4478	1122
7	4901	1122

prune49.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	59	6	65

Error

Counts

65 → 6

Alt Table

Status	Error	Program
	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	(+.f64 1/2 (.f64 (exp.f64 (log.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 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))))
▶	0.3b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
	0.6b	(cbrt.f64 (pow.f64 (+.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 u2 PI.f64)))))) 3))
	0.5b	(exp.f64 (log.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 1126 to 905 computations (19.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
0.2b	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2)))
0.3b	(.f64 (.f64 2 PI.f64) u2)

rewrite91.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

24×	`sqrt-prod_binary64`
19×	`pow1_binary64`
16×	`associate-l_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`

Counts

4 → 81

Calls

4 calls:

9.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2)))
4.0ms	(.f64 (.f64 2 PI.f64) u2)
3.0ms	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

Compiler

Compiled 1808 to 1178 computations (34.8% saved)

series100.0ms (1.4%)

Error

Counts

4 → 17

Calls

4 calls:

53.0ms	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
17.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2)))
11.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
6.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 1034 to 870 computations (15.9% saved)

simplify111.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

598×	`*-commutative_binary64`
462×	`distribute-rgt-neg-in_binary64`
409×	`distribute-lft-neg-in_binary64`
374×	`cancel-sign-sub-inv_binary64`
338×	`neg-mul-1_binary64`

Counts

98 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	181	1865
1	426	1730
2	1346	1698
3	2576	1684
4	4619	1684
5	4982	1684

prune55.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	67	6	73

Error

Counts

73 → 6

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
	0.3b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1)))) (-.f64 (+.f64 1/6 (.f64 1/9 (.f64 (pow.f64 u2 4) (pow.f64 PI.f64 4)))) (.f64 1/3 (.f64 (*.f64 u2 u2) (pow.f64 PI.f64 2))))))
	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	(+.f64 1/2 (.f64 (exp.f64 (log.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 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 1/2 (.f64 (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 3)) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))

Compiler

Compiled 1424 to 985 computations (30.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))
0.2b	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(*.f64 (log.f64 u1) -1/3)

rewrite92.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

22×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
11×	`associate-l_binary64`

Counts

4 → 75

Calls

4 calls:

6.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
4.0ms	(.f64 (.f64 2 PI.f64) u2)
3.0ms	(*.f64 (log.f64 u1) -1/3)
2.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))

Compiler

Compiled 1464 to 1122 computations (23.4% saved)

series48.0ms (0.7%)

Error

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
11.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))
10.0ms	(*.f64 (log.f64 u1) -1/3)
6.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 636 to 566 computations (11% saved)

simplify96.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

605×	`distribute-rgt-in_binary64`
519×	`distribute-lft-in_binary64`
317×	`*-commutative_binary64`
185×	`associate-l_binary64`
175×	`distribute-rgt-neg-out_binary64`

Counts

87 → 62

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	132	1035
1	255	940
2	772	940
3	1029	940
4	1551	940
5	4681	940
6	4944	940

prune59.0ms (0.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	62	6	68

Error

Counts

68 → 6

Alt Table

Status	Error	Program
	0.3b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
	0.3b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1)))) (-.f64 (+.f64 1/6 (.f64 1/9 (.f64 (pow.f64 u2 4) (pow.f64 PI.f64 4)))) (.f64 1/3 (.f64 (*.f64 u2 u2) (pow.f64 PI.f64 2))))))
	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	(+.f64 1/2 (.f64 (exp.f64 (log.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 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))))
	0.5b	(+.f64 1/2 (.f64 (.f64 (.f64 (sqrt.f64 1/6) (sqrt.f64 (sqrt.f64 (.f64 -1/3 (log.f64 u1))))) (sqrt.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/3)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))

Compiler

Compiled 1117 to 867 computations (22.4% saved)

regimes3.2s (44.7%)

Accuracy

Total 0.2b remaining (92%)

Threshold costs 0.2b (92%)

Compiler

Compiled 52788 to 45830 computations (13.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	20	23
2	20	23

end1.0ms (0%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

sample1.8s (24.4%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
217.0ms	8000×	pre	128	true

Compiler

Compiled 206 to 175 computations (15% saved)

Details

analyze394.0ms (5.5%)

sample51.0ms (0.7%)

simplify365.0ms (5.1%)

prune3.0ms (0%)

localize12.0ms (0.2%)

rewrite102.0ms (1.4%)

series110.0ms (1.5%)

simplify122.0ms (1.7%)

prune40.0ms (0.6%)

localize15.0ms (0.2%)

rewrite112.0ms (1.6%)

series57.0ms (0.8%)

simplify106.0ms (1.5%)

prune49.0ms (0.7%)

localize13.0ms (0.2%)

rewrite91.0ms (1.3%)

series100.0ms (1.4%)

simplify111.0ms (1.5%)

prune55.0ms (0.8%)

localize15.0ms (0.2%)

rewrite92.0ms (1.3%)

series48.0ms (0.7%)

simplify96.0ms (1.3%)

prune59.0ms (0.8%)

regimes3.2s (44.7%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.8s (24.4%)

Profiling