Details

analyze259.0ms (4.8%)

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)

simplify268.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (162.0ms)

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

0.4b

Counts

2 → 1

Compiler

Compiled 32 to 32 computations (0% saved)

localize15.0ms (0.3%)

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))))
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

series327.0ms (6.1%)

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))))
105.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
68.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
18.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify87.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4904	1090
1	4904	1090

prune104.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	64	7	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	7	72

Error

Counts

72 → 7

Compiler

Compiled 1609 to 1256 computations (21.9% saved)

localize14.0ms (0.3%)

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 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))))
0.5b	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`sqrt-prod_binary64`
27×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`associate-l_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`pow-prod-down_binary64`
10×	`cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
8×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_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 → 100

Calls

4 calls:

12.0ms	(.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))))
10.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series279.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))))
86.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
57.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
20.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify48.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4990	1752
1	4990	1752

prune144.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	114	5	119

Error

Counts

119 → 5

Compiler

Compiled 2595 to 1787 computations (31.1% saved)

localize15.0ms (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)))

series296.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
100.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
68.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
22.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5026	1122

prune128.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	93	5	98

Error

Counts

98 → 5

Compiler

Compiled 2165 to 1752 computations (19.1% saved)

localize13.0ms (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)

rewrite23.0ms (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))))

series273.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
81.0ms	(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

prune81.0ms (1.5%)

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	0	1	1
Total	71	5	76

Error

Counts

76 → 5

Compiler

Compiled 1342 to 1007 computations (25% saved)

regimes753.0ms (14%)

Accuracy

Total 0.2b remaining (99%)

Threshold costs 0.2b (99%)

Compiler

Compiled 7701 to 7494 computations (2.7% 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%)

sample1.9s (36.1%)

Algorithm

1×

intervals

Results

769.0ms	8000×	body	128	valid
206.0ms	8000×	pre	128	true

Compiler

Compiled 692 to 673 computations (2.7% saved)

Details

analyze259.0ms (4.8%)

sample42.0ms (0.8%)

simplify268.0ms (5%)

prune7.0ms (0.1%)

localize15.0ms (0.3%)

rewrite25.0ms (0.5%)

series327.0ms (6.1%)

simplify87.0ms (1.6%)

prune104.0ms (1.9%)

localize14.0ms (0.3%)

rewrite42.0ms (0.8%)

series279.0ms (5.2%)

simplify48.0ms (0.9%)

prune144.0ms (2.7%)

localize15.0ms (0.3%)

rewrite34.0ms (0.6%)

series296.0ms (5.5%)

simplify74.0ms (1.4%)

prune128.0ms (2.4%)

localize13.0ms (0.2%)

rewrite23.0ms (0.4%)

series273.0ms (5.1%)

simplify70.0ms (1.3%)

prune81.0ms (1.5%)

regimes753.0ms (14%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (36.1%)

Profiling