Details

analyze267.0ms (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)

sample45.0ms (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)

simplify268.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (162.0ms)

Iter	Nodes	Cost
0	5644	26

prune9.0ms (0.2%)

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

0.4b

Counts

2 → 1

Compiler

Compiled 32 to 32 computations (0% saved)

localize14.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0b	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
0.0b	(.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)))
0.0b	(cos.f64 (.f64 (.f64 2 PI.f64) u2))
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)
0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

rewrite26.0ms (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

8 calls:

8.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(+.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)))
0.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

series495.0ms (8.8%)

Counts

4 → 18

Calls

4 calls:

282.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
106.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
80.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
26.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 628 to 611 computations (2.7% saved)

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5116	1290

prune144.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	68	9	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	9	78

Error

Counts

78 → 9

Compiler

Compiled 1821 to 1422 computations (21.9% saved)

localize15.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))
0.0b	(.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)))
0.0b	(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)
0.2b	(.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))

rewrite36.0ms (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

8 calls:

11.0ms	(.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))
8.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0ms	(.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)))

series330.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
96.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
82.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
28.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 522 to 522 computations (0% saved)

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5026	1122

prune157.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	94	8	102

Error

Counts

102 → 8

Compiler

Compiled 2286 to 1855 computations (18.9% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
0.0b	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
0.0b	(.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)))
0.0b	(cos.f64 (.f64 (.f64 2 PI.f64) u2))
0.0b	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
0.2b	(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)

rewrite23.0ms (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

8 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))))
0.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

series430.0ms (7.7%)

Counts

4 → 18

Calls

4 calls:

256.0ms	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
82.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
62.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
30.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 574 to 557 computations (3% saved)

simplify66.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4887	1115
1	4887	1115

prune112.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	78	7	85

Error

Counts

85 → 7

Compiler

Compiled 1628 to 1241 computations (23.8% saved)

localize14.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b	(log.f64 (pow.f64 u1 -1/18))
0.0b	(+.f64 1/2 (.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
0.0b	(.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)))
0.0b	(cos.f64 (.f64 (.f64 2 PI.f64) u2))
0.1b	(log.f64 (pow.f64 u1 -1/18))
0.2b	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))
0.2b	(.f64 (.f64 2 PI.f64) u2)
2.7b	(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

8 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)))
0.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

series351.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))
123.0ms	(log.f64 (pow.f64 u1 -1/18))
66.0ms	(pow.f64 u1 -1/18)
28.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 394 to 394 computations (0% saved)

simplify104.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4755	671
1	4755	671

prune82.0ms (1.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	79	7	86

Error

Counts

86 → 7

Compiler

Compiled 1349 to 1041 computations (22.8% saved)

simplify21.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	359	1246
1	359	1246

regimes359.0ms (6.4%)

Compiler: Compiled 3825 to 3695 computations (3.4% saved)

bsearch0.0ms (0%)

regimes32.0ms (0.6%)

Compiler: Compiled 65 to 95 computations (-46.2% saved)

bsearch0.0ms (0%)

regimes15.0ms (0.3%)

Accuracy

Total 0.2b remaining (99.3%)

Threshold costs 0.2b (99.3%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch3.0ms (0%)

Compiler: Compiled 22 to 25 computations (-13.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	35
1	24	35

end0.0ms (0%)

sample2.0s (35.9%)

Algorithm

1×

intervals

Results

753.0ms	8000×	body	128	valid
200.0ms	8000×	pre	128	true

Compiler

Compiled 809 to 784 computations (3.1% saved)

Pareto

0.32640108250146643

Details

analyze267.0ms (4.8%)

sample45.0ms (0.8%)

simplify268.0ms (4.8%)

prune9.0ms (0.2%)

localize14.0ms (0.3%)

rewrite26.0ms (0.5%)

series495.0ms (8.8%)

simplify70.0ms (1.2%)

prune144.0ms (2.6%)

localize15.0ms (0.3%)

rewrite36.0ms (0.6%)

series330.0ms (5.9%)

simplify76.0ms (1.4%)

prune157.0ms (2.8%)

localize13.0ms (0.2%)

rewrite23.0ms (0.4%)

series430.0ms (7.7%)

simplify66.0ms (1.2%)

prune112.0ms (2%)

localize14.0ms (0.2%)

rewrite16.0ms (0.3%)

series351.0ms (6.3%)

simplify104.0ms (1.9%)

prune82.0ms (1.5%)

simplify21.0ms (0.4%)

regimes359.0ms (6.4%)

bsearch0.0ms (0%)

regimes32.0ms (0.6%)

bsearch0.0ms (0%)

regimes15.0ms (0.3%)

bsearch3.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.0s (35.9%)

Profiling