Details

analyze431.0ms (4%)

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)

sample77.0ms (0.7%)

Algorithm

1×

intervals

Results

45.0ms	256×	body	128	valid
13.0ms	256×	pre	128	true

Compiler

Compiled 47 to 47 computations (0% saved)

simplify462.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (285.0ms)

Iter	Nodes	Cost
0	5644	26

prune12.0ms (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

Merged error: 0.4b

Counts

2 → 1

Compiler

Compiled 32 to 32 computations (0% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.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)
0.3b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

rewrite42.0ms (0.4%)

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:

13.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
9.0ms	(.f64 (.f64 2 PI.f64) u2)
6.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
4.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

series543.0ms (5%)

Counts

4 → 12

Calls

4 calls:

216.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
166.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
128.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
33.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify151.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4904	1090
1	4904	1090

prune193.0ms (1.8%)

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: 0b

Counts

72 → 7

Compiler

Compiled 1615 to 1260 computations (22% saved)

localize28.0ms (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)
0.3b	(.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))))
0.4b	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

rewrite74.0ms (0.7%)

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:

21.0ms	(.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))))
18.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
10.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series510.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

215.0ms	(.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))))
143.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
119.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
32.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify87.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4990	1752
1	4990	1752

prune263.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	113	6	119

Merged error: 0b

Counts

119 → 6

Compiler

Compiled 2613 to 1799 computations (31.2% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
0.2b	(.f64 (.f64 (.f64 u2 u2) (.f64 (sqrt.f64 2) (pow.f64 PI.f64 2))) -1/3)
0.2b	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (+.f64 (.f64 (sqrt.f64 2) 1/6) (.f64 (.f64 (.f64 u2 u2) (.f64 (sqrt.f64 2) (pow.f64 PI.f64 2))) -1/3)))
0.2b	(.f64 (.f64 u2 u2) (*.f64 (sqrt.f64 2) (pow.f64 PI.f64 2)))

rewrite97.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-exp-log_binary64`
46×	`prod-exp_binary64`
36×	`add-cbrt-cube_binary64`
25×	`pow1_binary64` `sqrt-prod_binary64`
22×	`cbrt-unprod_binary64`
18×	`add-sqr-sqrt_binary64`
17×	`associate-l_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow-prod-down_binary64`
8×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`associate-r_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `log-pow_binary64` `pow-exp_binary64`
3×	`*-commutative_binary64`
2×	`associate-*r/_binary64` `neg-mul-1_binary64` `unswap-sqr_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 110

Calls

4 calls:

24.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (+.f64 (.f64 (sqrt.f64 2) 1/6) (.f64 (.f64 (.f64 u2 u2) (.f64 (sqrt.f64 2) (pow.f64 PI.f64 2))) -1/3)))
22.0ms	(.f64 (.f64 (.f64 u2 u2) (.f64 (sqrt.f64 2) (pow.f64 PI.f64 2))) -1/3)
18.0ms	(.f64 (.f64 u2 u2) (*.f64 (sqrt.f64 2) (pow.f64 PI.f64 2)))
4.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series706.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

390.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (+.f64 (.f64 (sqrt.f64 2) 1/6) (.f64 (.f64 (.f64 u2 u2) (.f64 (sqrt.f64 2) (pow.f64 PI.f64 2))) -1/3)))
126.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
108.0ms	(.f64 (.f64 (.f64 u2 u2) (.f64 (sqrt.f64 2) (pow.f64 PI.f64 2))) -1/3)
82.0ms	(.f64 (.f64 u2 u2) (*.f64 (sqrt.f64 2) (pow.f64 PI.f64 2)))

simplify164.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	5060	2696

prune334.0ms (3.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	122	6	128

Merged error: 0b

Counts

128 → 6

Compiler

Compiled 3558 to 2400 computations (32.5% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite51.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`pow1_binary64`
14×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64`
6×	`pow-prod-down_binary64`
5×	`prod-exp_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `log-pow_binary64` `associate-l_binary64`
2×	`log-prod_binary64` `rem-log-exp_binary64` `*-commutative_binary64`
1×	`rem-exp-log_binary64` `unswap-sqr_binary64` `exp-sum_binary64` `sqrt-prod_binary64`

Counts

4 → 63

Calls

4 calls:

12.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
11.0ms	(exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))))
10.0ms	(log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))
10.0ms	(.f64 (.f64 2 PI.f64) u2)

series816.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

360.0ms	(exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))))
271.0ms	(log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))
150.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
35.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify132.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4959	905
1	4959	905

prune171.0ms (1.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	75	6	81

Merged error: 0b

Counts

81 → 6

Compiler

Compiled 1613 to 1267 computations (21.5% saved)

regimes1.6s (15%)

Compiler: Compiled 9902 to 9332 computations (5.8% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	39
1	35	39

end0.0ms (0%)

sample3.8s (35%)

Algorithm

1×

intervals

Results

1.4s	8000×	body	128	valid
388.0ms	8000×	pre	128	true

Compiler

Compiled 842 to 793 computations (5.8% saved)

Details

analyze431.0ms (4%)

sample77.0ms (0.7%)

simplify462.0ms (4.2%)

prune12.0ms (0.1%)

localize26.0ms (0.2%)

rewrite42.0ms (0.4%)

series543.0ms (5%)

simplify151.0ms (1.4%)

prune193.0ms (1.8%)

localize28.0ms (0.3%)

rewrite74.0ms (0.7%)

series510.0ms (4.7%)

simplify87.0ms (0.8%)

prune263.0ms (2.4%)

localize34.0ms (0.3%)

rewrite97.0ms (0.9%)

series706.0ms (6.5%)

simplify164.0ms (1.5%)

prune334.0ms (3.1%)

localize31.0ms (0.3%)

rewrite51.0ms (0.5%)

series816.0ms (7.5%)

simplify132.0ms (1.2%)

prune171.0ms (1.6%)

regimes1.6s (15%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample3.8s (35%)

Profiling