Details

analyze265.0ms (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)

sample43.0ms (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)

simplify262.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (157.0ms)

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

Merged error: 0.3b

Counts

2 → 1

Compiler

Compiled 32 to 32 computations (0% saved)

localize14.0ms (0.3%)

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))))

rewrite24.0ms (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:

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

series317.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
104.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
66.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
18.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify84.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4904	1090
1	4904	1090

prune103.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	7	72

Merged error: 0b

Counts

72 → 7

Compiler

Compiled 1602 to 1245 computations (22.3% 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))

rewrite35.0ms (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:

10.0ms	(.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)))

series293.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
98.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
65.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
20.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5026	1122

prune129.0ms (2.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	93	7	100

Merged error: 0b

Counts

100 → 7

Compiler

Compiled 2208 to 1787 computations (19.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.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:

5.0ms	(.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))))

series322.0ms (5.8%)

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))))
80.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
53.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
29.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify68.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4843	920
1	4843	920

prune86.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	2	2	4
Picked	0	1	1
Done	1	1	2
Total	72	6	78

Merged error: 0b

Counts

78 → 6

Compiler

Compiled 1431 to 1090 computations (23.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 2 PI.f64) u2)
0.3b	(log.f64 (sqrt.f64 (*.f64 (log.f64 u1) -1/18)))
0.3b	(exp.f64 (log.f64 (sqrt.f64 (*.f64 (log.f64 u1) -1/18))))
0.4b	(*.f64 (log.f64 u1) -1/18)

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64`
12×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`log-pow_binary64`
8×	`log-prod_binary64`
7×	`exp-prod_binary64`
6×	`pow-prod-down_binary64` `associate-r_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `exp-sum_binary64` `prod-exp_binary64`
2×	`pow1/2_binary64` `sqrt-prod_binary64` `*-commutative_binary64`
1×	`rem-log-exp_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64`

Counts

4 → 72

Calls

4 calls:

5.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(exp.f64 (log.f64 (sqrt.f64 (*.f64 (log.f64 u1) -1/18))))
4.0ms	(*.f64 (log.f64 u1) -1/18)
3.0ms	(log.f64 (sqrt.f64 (*.f64 (log.f64 u1) -1/18)))

series389.0ms (7%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(exp.f64 (log.f64 (sqrt.f64 (*.f64 (log.f64 u1) -1/18))))
141.0ms	(log.f64 (sqrt.f64 (*.f64 (log.f64 u1) -1/18)))
52.0ms	(*.f64 (log.f64 u1) -1/18)
18.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify60.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4916	832
1	4916	832

prune92.0ms (1.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	84	6	90

Merged error: 0b

Counts

90 → 6

Compiler

Compiled 1605 to 1214 computations (24.4% saved)

regimes788.0ms (14.2%)

Compiler: Compiled 8501 to 8163 computations (4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	23
1	19	23

end0.0ms (0%)

sample2.0s (36%)

Algorithm

1×

intervals

Results

785.0ms	8000×	body	128	valid
211.0ms	8000×	pre	128	true

Compiler

Compiled 765 to 734 computations (4.1% saved)

Details

analyze265.0ms (4.8%)

sample43.0ms (0.8%)

simplify262.0ms (4.7%)

prune7.0ms (0.1%)

localize14.0ms (0.3%)

rewrite24.0ms (0.4%)

series317.0ms (5.7%)

simplify84.0ms (1.5%)

prune103.0ms (1.9%)

localize15.0ms (0.3%)

rewrite35.0ms (0.6%)

series293.0ms (5.3%)

simplify73.0ms (1.3%)

prune129.0ms (2.3%)

localize12.0ms (0.2%)

rewrite22.0ms (0.4%)

series322.0ms (5.8%)

simplify68.0ms (1.2%)

prune86.0ms (1.6%)

localize15.0ms (0.3%)

rewrite25.0ms (0.5%)

series389.0ms (7%)

simplify60.0ms (1.1%)

prune92.0ms (1.7%)

regimes788.0ms (14.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (36%)

Profiling