Details

analyze384.0ms (4.7%)

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)

sample45.0ms (0.6%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 47 to 47 computations (0% saved)

simplify310.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (167.0ms)

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:

0.1b	(+.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)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

rewrite25.0ms (0.3%)

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)))

series480.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

176.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
167.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
111.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
25.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify148.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4904	1090
1	4904	1090

prune202.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	8	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	8	72

Error

0.0b

Counts

72 → 8

Compiler

Compiled 1669 to 1306 computations (21.7% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
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))
0.3b	(.f64 (.f64 2 PI.f64) u2)

rewrite71.0ms (0.9%)

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:

22.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
16.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
10.0ms	(.f64 (.f64 2 PI.f64) u2)
5.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

series425.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

141.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
124.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
123.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
37.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify115.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5026	1122

prune220.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	94	7	101

Error

Counts

101 → 7

Compiler

Compiled 2252 to 1831 computations (18.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))
0.2b	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(*.f64 (log.f64 u1) -1/3)

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`associate-l_binary64`
10×	`pow-prod-down_binary64` `-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
6×	`sqrt-pow1_binary64` `sqrt-prod_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`pow1/2_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`log-pow_binary64` `sqrt-unprod_binary64`

Counts

4 → 75

Calls

4 calls:

8.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
5.0ms	(*.f64 (log.f64 u1) -1/3)
2.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))

series366.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

163.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
132.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))
52.0ms	(*.f64 (log.f64 u1) -1/3)
19.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify109.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5161	940

prune141.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	87	7	94

Error

Counts

94 → 7

Compiler

Compiled 1923 to 1515 computations (21.2% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
0.9b	(exp.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))

rewrite20.0ms (0.2%)

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×	`pow1/2_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
2.0ms	(exp.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))

series419.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(exp.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))
122.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
92.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
19.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify140.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4884	772
1	4884	772

prune136.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	70	7	77

Error

Counts

77 → 7

Compiler

Compiled 1495 to 1176 computations (21.3% saved)

regimes1.2s (15%)

Accuracy

Total 0.2b remaining (99.3%)

Threshold costs 0.2b (99.3%)

Compiler

Compiled 8860 to 8532 computations (3.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	23
1	20	23

end0.0ms (0%)

sample3.0s (37.2%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
304.0ms	8000×	pre	128	true

Compiler

Compiled 855 to 823 computations (3.7% saved)

Details

analyze384.0ms (4.7%)

sample45.0ms (0.6%)

simplify310.0ms (3.8%)

prune7.0ms (0.1%)

localize14.0ms (0.2%)

rewrite25.0ms (0.3%)

series480.0ms (5.9%)

simplify148.0ms (1.8%)

prune202.0ms (2.5%)

localize30.0ms (0.4%)

rewrite71.0ms (0.9%)

series425.0ms (5.2%)

simplify115.0ms (1.4%)

prune220.0ms (2.7%)

localize14.0ms (0.2%)

rewrite26.0ms (0.3%)

series366.0ms (4.5%)

simplify109.0ms (1.3%)

prune141.0ms (1.7%)

localize24.0ms (0.3%)

rewrite20.0ms (0.2%)

series419.0ms (5.2%)

simplify140.0ms (1.7%)

prune136.0ms (1.7%)

regimes1.2s (15%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample3.0s (37.2%)

Profiling