Details

analyze274.0ms (4.9%)

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 28 to 26 computations (7.1% saved)

sample42.0ms (0.8%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 47 to 47 computations (0% saved)

simplify284.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (159.0ms)

Iter	Nodes	Cost
0	5644	26

prune7.0ms (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

0.3b

Counts

2 → 1

Compiler

Compiled 32 to 32 computations (0% 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))))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
5×	`pow-prod-down_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`sqrt-pow1_binary64` `sqrt-prod_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 59

Calls

4 calls:

8.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
3.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

series331.0ms (6%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
110.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
67.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
18.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4904	1090
1	4904	1090

prune103.0ms (1.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	6	72

Error

Counts

72 → 6

Compiler

Compiled 1617 to 1256 computations (22.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
0.2b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
0.5b	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`sqrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`pow1_binary64`
19×	`associate-l_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-r_binary64`
9×	`pow-prod-down_binary64`
8×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `log-pow_binary64` `unswap-sqr_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `*-commutative_binary64`
2×	`neg-mul-1_binary64`
1×	`sqrt-unprod_binary64` `rem-sqrt-square_binary64`

Counts

4 → 97

Calls

4 calls:

10.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
8.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
7.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series263.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
85.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
60.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
19.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify51.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4949	1396
1	4949	1396

prune133.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	109	6	115

Error

Counts

115 → 6

Compiler

Compiled 2529 to 1726 computations (31.8% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

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`
11×	`associate-l_binary64`
10×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
9×	`sqrt-prod_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`pow1/2_binary64`
4×	`add-log-exp_binary64`
3×	`sqrt-unprod_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`

Counts

4 → 81

Calls

4 calls:

11.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
8.0ms	(.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)))

series286.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
89.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
71.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
18.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5026	1122

prune127.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	93	6	99

Error

Counts

99 → 6

Compiler

Compiled 2198 to 1775 computations (19.2% 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)

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow-prod-down_binary64`
6×	`-un-lft-identity_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
3×	`sqrt-pow1_binary64`
2×	`associate-l_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `+-commutative_binary64` `sqrt-prod_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 59

Calls

4 calls:

6.0ms	(.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))))

series263.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
76.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
57.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
18.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4843	920
1	4843	920

prune80.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	2	3
Picked	0	1	1
Done	1	1	2
Total	72	5	77

Error

Counts

77 → 5

Compiler

Compiled 1342 to 1007 computations (25% saved)

regimes851.0ms (15.4%)

Accuracy

Total 0.2b remaining (99.8%)

Threshold costs 0.2b (99.8%)

Compiler

Compiled 9215 to 8881 computations (3.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	23
1	19	23

end0.0ms (0%)

sample2.0s (36.9%)

Algorithm

1×

intervals

Results

767.0ms	8000×	body	128	valid
202.0ms	8000×	pre	128	true

Compiler

Compiled 826 to 796 computations (3.6% saved)

Details

analyze274.0ms (4.9%)

sample42.0ms (0.8%)

simplify284.0ms (5.1%)

prune7.0ms (0.1%)

localize14.0ms (0.2%)

rewrite25.0ms (0.5%)

series331.0ms (6%)

simplify85.0ms (1.5%)

prune103.0ms (1.9%)

localize14.0ms (0.2%)

rewrite36.0ms (0.6%)

series263.0ms (4.7%)

simplify51.0ms (0.9%)

prune133.0ms (2.4%)

localize14.0ms (0.3%)

rewrite34.0ms (0.6%)

series286.0ms (5.2%)

simplify74.0ms (1.3%)

prune127.0ms (2.3%)

localize12.0ms (0.2%)

rewrite22.0ms (0.4%)

series263.0ms (4.8%)

simplify70.0ms (1.3%)

prune80.0ms (1.4%)

regimes851.0ms (15.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (36.9%)

Profiling