Details

analyze528.0ms (8.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4873	52
1	4873	52
0	2	2
1	2	2

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)

sample49.0ms (0.8%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
13.0ms	256×	pre	128	true

Compiler

Compiled 47 to 47 computations (0% saved)

simplify167.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (161.0ms)

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

rewrite25.0ms (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)))

series337.0ms (5.6%)

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))))
81.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
23.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4904	1090
1	4904	1090

prune106.0ms (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

Error

Counts

72 → 7

Compiler

Compiled 1650 to 1285 computations (22.1% saved)

localize14.0ms (0.2%)

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:

13.0ms	(.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)))

series288.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
86.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
75.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
21.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5026	1122

prune131.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	94	6	100

Error

Counts

100 → 6

Compiler

Compiled 2214 to 1791 computations (19.1% 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:

5.0ms	(.f64 (.f64 2 PI.f64) u2)
5.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
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))))

series270.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
84.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
53.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
23.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4843	920
1	4843	920

prune88.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	72	5	77

Error

Counts

77 → 5

Compiler

Compiled 1406 to 1071 computations (23.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (pow.f64 u1 -1/18))
0.1b	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))
0.2b	(.f64 (.f64 2 PI.f64) u2)
2.8b	(pow.f64 u1 -1/18)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-exp-log_binary64`
11×	`pow1_binary64` `add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`add-cbrt-cube_binary64`
7×	`log-prod_binary64`
6×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `sqrt-prod_binary64`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `rem-log-exp_binary64` `prod-exp_binary64`
2×	`pow-to-exp_binary64` `log-pow_binary64` `sqr-pow_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `pow-pow_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`

Counts

4 → 67

Calls

4 calls:

5.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(pow.f64 u1 -1/18)
2.0ms	(log.f64 (pow.f64 u1 -1/18))
1.0ms	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))

series411.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

164.0ms	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))
140.0ms	(log.f64 (pow.f64 u1 -1/18))
87.0ms	(pow.f64 u1 -1/18)
19.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify106.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4755	671
1	4755	671

prune83.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	79	5	84

Error

Counts

84 → 5

Compiler

Compiled 1349 to 1041 computations (22.8% saved)

regimes896.0ms (15%)

Accuracy

Total 0.2b remaining (99.1%)

Threshold costs 0.2b (99.1%)

Compiler

Compiled 9557 to 9235 computations (3.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	25
1	20	25

end0.0ms (0%)

sample2.1s (35.3%)

Algorithm

1×

intervals

Results

795.0ms	8000×	body	128	valid
207.0ms	8000×	pre	128	true

Compiler

Compiled 853 to 824 computations (3.4% saved)

Details

analyze528.0ms (8.8%)

sample49.0ms (0.8%)

simplify167.0ms (2.8%)

prune7.0ms (0.1%)

localize14.0ms (0.2%)

rewrite25.0ms (0.4%)

series337.0ms (5.6%)

simplify86.0ms (1.4%)

prune106.0ms (1.8%)

localize14.0ms (0.2%)

rewrite35.0ms (0.6%)

series288.0ms (4.8%)

simplify77.0ms (1.3%)

prune131.0ms (2.2%)

localize12.0ms (0.2%)

rewrite22.0ms (0.4%)

series270.0ms (4.5%)

simplify74.0ms (1.2%)

prune88.0ms (1.5%)

localize16.0ms (0.3%)

rewrite16.0ms (0.3%)

series411.0ms (6.9%)

simplify106.0ms (1.8%)

prune83.0ms (1.4%)

regimes896.0ms (15%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.1s (35.3%)

Profiling