Details

analyze258.0ms (5%)

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)

sample41.0ms (0.8%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 47 to 47 computations (0% saved)

simplify262.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (156.0ms)

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: 0.4b

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 (0.5%)

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)))

series439.0ms (8.6%)

Counts

4 → 15

Calls

4 calls:

247.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
107.0ms	(.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)

simplify73.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4907	1168
1	4907	1168

prune109.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	66	8	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	8	75

Merged error: 0.0b

Counts

75 → 8

Compiler

Compiled 1691 to 1322 computations (21.8% saved)

localize14.0ms (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 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
0.4b	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`sqrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`pow1_binary64`
19×	`associate-l_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-r_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:

9.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
8.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series262.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
85.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
61.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
18.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify51.0ms (1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4949	1396
1	4949	1396

prune138.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	109	8	117

Merged error: 0b

Counts

117 → 8

Compiler

Compiled 2539 to 1746 computations (31.2% 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))

rewrite34.0ms (0.7%)

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:

11.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
7.0ms	(.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)))

series294.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
100.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
68.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
19.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify74.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5026	1122

prune129.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	95	6	101

Merged error: 0b

Counts

101 → 6

Compiler

Compiled 2191 to 1778 computations (18.8% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite24.0ms (0.5%)

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:

7.0ms	(.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))

series235.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
69.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))
50.0ms	(*.f64 (log.f64 u1) -1/3)
18.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5161	940

prune101.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	87	6	93

Merged error: 0b

Counts

93 → 6

Compiler

Compiled 1781 to 1381 computations (22.5% saved)

regimes589.0ms (11.5%)

Compiler: Compiled 6222 to 6018 computations (3.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	27
1	23	27

end0.0ms (0%)

sample1.8s (35.4%)

Algorithm

1×

intervals

Results

740.0ms	8000×	body	128	valid
207.0ms	8000×	pre	128	true

Compiler

Compiled 653 to 631 computations (3.4% saved)

Details

analyze258.0ms (5%)

sample41.0ms (0.8%)

simplify262.0ms (5.1%)

prune7.0ms (0.1%)

localize14.0ms (0.3%)

rewrite24.0ms (0.5%)

series439.0ms (8.6%)

simplify73.0ms (1.4%)

prune109.0ms (2.1%)

localize14.0ms (0.3%)

rewrite32.0ms (0.6%)

series262.0ms (5.1%)

simplify51.0ms (1%)

prune138.0ms (2.7%)

localize15.0ms (0.3%)

rewrite34.0ms (0.7%)

series294.0ms (5.8%)

simplify74.0ms (1.5%)

prune129.0ms (2.5%)

localize13.0ms (0.3%)

rewrite24.0ms (0.5%)

series235.0ms (4.6%)

simplify69.0ms (1.4%)

prune101.0ms (2%)

regimes589.0ms (11.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (35.4%)

Profiling