Details

analyze261.0ms (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)

sample42.0ms (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 (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (162.0ms)

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

0.4b

Counts

2 → 1

Compiler

Compiled 32 to 32 computations (0% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.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)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.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)))

series508.0ms (9.2%)

Counts

4 → 18

Calls

4 calls:

291.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
112.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
76.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
29.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 628 to 611 computations (2.7% saved)

simplify68.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5116	1290

prune115.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	69	8	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	8	78

Error

Counts

78 → 8

Compiler

Compiled 1794 to 1399 computations (22% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
0.5b	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

rewrite33.0ms (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:

10.0ms	(*.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)))

series300.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
92.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
64.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
31.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 462 to 462 computations (0% saved)

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4949	1396
1	4949	1396

prune138.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	110	7	117

Error

Counts

117 → 7

Compiler

Compiled 2554 to 1751 computations (31.4% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`sqrt-prod_binary64`
21×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`associate-l_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`associate-r_binary64`
8×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `log-pow_binary64`
3×	`*-commutative_binary64`
2×	`neg-mul-1_binary64` `unswap-sqr_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 92

Calls

4 calls:

8.0ms	(.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6) (sqrt.f64 2))
7.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6)
5.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series282.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6) (sqrt.f64 2))
75.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6)
71.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
29.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 462 to 462 computations (0% saved)

simplify66.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5198	1249

prune125.0ms (2.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	104	7	111

Error

Counts

111 → 7

Compiler

Compiled 2417 to 1650 computations (31.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite33.0ms (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)))

series329.0ms (6%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
110.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
71.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
30.0ms	(.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 (60.0ms)

Iter	Nodes	Cost
0	5026	1122

prune123.0ms (2.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	93	7	100

Error

Counts

100 → 7

Compiler

Compiled 2093 to 1680 computations (19.7% saved)

regimes655.0ms (11.9%)

Accuracy

Total 0.2b remaining (98.9%)

Threshold costs 0.2b (98.9%)

Compiler

Compiled 7292 to 6748 computations (7.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	26
1	23	26

end0.0ms (0%)

sample1.9s (34.6%)

Algorithm

1×

intervals

Results

749.0ms	8000×	body	128	valid
206.0ms	8000×	pre	128	true

Compiler

Compiled 759 to 703 computations (7.4% saved)

Details

analyze261.0ms (4.8%)

sample42.0ms (0.8%)

simplify268.0ms (4.9%)

prune7.0ms (0.1%)

localize14.0ms (0.3%)

rewrite24.0ms (0.4%)

series508.0ms (9.2%)

simplify68.0ms (1.2%)

prune115.0ms (2.1%)

localize14.0ms (0.3%)

rewrite33.0ms (0.6%)

series300.0ms (5.5%)

simplify53.0ms (1%)

prune138.0ms (2.5%)

localize14.0ms (0.3%)

rewrite30.0ms (0.6%)

series282.0ms (5.1%)

simplify66.0ms (1.2%)

prune125.0ms (2.3%)

localize17.0ms (0.3%)

rewrite33.0ms (0.6%)

series329.0ms (6%)

simplify76.0ms (1.4%)

prune123.0ms (2.2%)

regimes655.0ms (11.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.9s (34.6%)

Profiling