Details

analyze133.0ms (3.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
0%	6.2%	93.8%	3
3.1%	3.1%	93.8%	4
3.1%	3.1%	93.8%	5
4.7%	1.6%	93.8%	6
4.7%	1.6%	93.8%	7
5.5%	0.8%	93.8%	8
5.5%	0.8%	93.8%	9
5.8%	0.4%	93.8%	10
5.8%	0.4%	93.8%	11
6%	0.2%	93.8%	12
6%	0.2%	93.8%	13
6.1%	0.1%	93.8%	14

Compiler

Compiled 28 to 26 computations (7.1% saved)

sample42.0ms (1.1%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

Compiler

Compiled 47 to 47 computations (0% saved)

simplify685.0ms (18%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (210.0ms)

Iter	Nodes	Cost
0	5319	26

prune9.0ms (0.2%)

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

Merged error: 0.3b

Counts

2 → 1

Compiler

Compiled 32 to 32 computations (0% saved)

localize14.0ms (0.4%)

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))))

rewrite23.0ms (0.6%)

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)))

series73.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
23.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
18.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
4.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify88.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4903	1090
1	4903	1090

prune88.0ms (2.3%)

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

Merged error: 0.0b

Counts

72 → 7

Compiler

Compiled 1645 to 1282 computations (22.1% saved)

localize14.0ms (0.4%)

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

rewrite30.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`sqrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`pow1_binary64`
19×	`associate-r_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-l_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 1/6 (.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1)))))
9.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1))))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series40.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(.f64 1/6 (.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1)))))
13.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1))))
9.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
3.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify64.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5033	1371

prune111.0ms (2.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	109	7	116

Merged error: 0b

Counts

116 → 7

Compiler

Compiled 2556 to 1759 computations (31.2% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-prod_binary64`
19×	`pow1_binary64`
18×	`associate-r_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
6×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`log-pow_binary64`
2×	`neg-mul-1_binary64` `associate-l_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 81

Calls

4 calls:

9.0ms	(.f64 (.f64 (sqrt.f64 2) 1/6) (sqrt.f64 (neg.f64 (log.f64 u1))))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(+.f64 1/2 (.f64 (.f64 (.f64 (sqrt.f64 2) 1/6) (sqrt.f64 (neg.f64 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series60.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

29.0ms	(+.f64 1/2 (.f64 (.f64 (.f64 (sqrt.f64 2) 1/6) (sqrt.f64 (neg.f64 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
15.0ms	(.f64 (.f64 (sqrt.f64 2) 1/6) (sqrt.f64 (neg.f64 (log.f64 u1))))
12.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
4.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify108.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4889	1507
1	4889	1507

prune91.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Merged error: 0b

Counts

100 → 7

Compiler

Compiled 2240 to 1546 computations (31% saved)

localize14.0ms (0.4%)

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 (sqrt.f64 (neg.f64 (log.f64 u1))))
0.4b	(.f64 (sqrt.f64 2) (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

9.0ms	(*.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1))))
8.0ms	(.f64 (sqrt.f64 2) (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))))
6.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series40.0ms (1%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 2) (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))))
11.0ms	(*.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1))))
10.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
3.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify86.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5199	1226

prune85.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	104	7	111

Merged error: 0b

Counts

111 → 7

Compiler

Compiled 2258 to 1509 computations (33.2% saved)

regimes235.0ms (6.2%)

Compiler: Compiled 1098 to 1070 computations (2.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	30
1	31	30

end0.0ms (0%)

sample1.6s (42.2%)

Algorithm

1×

intervals

Results

780.0ms	8000×	body	80	valid
194.0ms	8000×	pre	80	true

Compiler

Compiled 208 to 202 computations (2.9% saved)

Details

analyze133.0ms (3.5%)

sample42.0ms (1.1%)

simplify685.0ms (18%)

prune9.0ms (0.2%)

localize14.0ms (0.4%)

rewrite23.0ms (0.6%)

series73.0ms (1.9%)

simplify88.0ms (2.3%)

prune88.0ms (2.3%)

localize14.0ms (0.4%)

rewrite30.0ms (0.8%)

series40.0ms (1.1%)

simplify64.0ms (1.7%)

prune111.0ms (2.9%)

localize14.0ms (0.4%)

rewrite23.0ms (0.6%)

series60.0ms (1.6%)

simplify108.0ms (2.8%)

prune91.0ms (2.4%)

localize14.0ms (0.4%)

rewrite28.0ms (0.7%)

series40.0ms (1%)

simplify86.0ms (2.3%)

prune85.0ms (2.2%)

regimes235.0ms (6.2%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.6s (42.2%)

Profiling