Details

analyze480.0ms (12.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
57.3%	42.5%	0.1%	12
66.9%	33%	0.1%	13
71.7%	28.2%	0.1%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample18.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 25 to 22 computations (12% saved)

simplify166.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	18
1	20	18

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 36.6b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
34.1b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64_10560`
4×	`add-sqr-sqrt_binary64_10545`
3×	`pow1_binary64_10582` `*-un-lft-identity_binary64_10524` `add-cube-cbrt_binary64_10556` `sqrt-prod_binary64_10539` `sum-log_binary64_10612`
2×	`add-exp-log_binary64_10559` `add-cbrt-cube_binary64_10557` `flip3-+_binary64_10527` `sqrt-div_binary64_10540` `flip-+_binary64_10498`
1×	`rem-sqrt-square_binary64_10537` `+-commutative_binary64_10456` `sqrt-pow1_binary64_10541` `associate-+l+_binary64_10459` `pow1/2_binary64_10601`

Counts

2 → 28

Calls

2 calls:

7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series203.0ms (5.3%)

Counts

2 → 6

Calls

2 calls:

142.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
61.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))

simplify73.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4940	711
1	4940	711

prune32.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	6	35

Merged error: 16.0b

Counts

35 → 6

Compiler

Compiled 686 to 131 computations (80.9% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
0.6b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
34.1b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
34.1b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite61.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`sqrt-prod_binary64_10539`
50×	`add-sqr-sqrt_binary64_10545`
34×	`sqrt-pow1_binary64_10541`
29×	`pow1_binary64_10582`
28×	`sqrt-div_binary64_10540`
18×	`pow1/2_binary64_10601` `*-un-lft-identity_binary64_10524` `add-cube-cbrt_binary64_10556`
15×	`swap-sqr_binary64_10491`
9×	`associate-l_binary64_10467` `unswap-sqr_binary64_10492` `add-log-exp_binary64_10560` `flip3-+_binary64_10527` `flip-+_binary64_10498` `associate-r_binary64_10466` `pow-prod-up_binary64_10591`
6×	`add-exp-log_binary64_10559` `add-cbrt-cube_binary64_10557`
5×	`pow-prod-down_binary64_10592` `pow-sqr_binary64_10497`
4×	`frac-times_binary64_10534`
3×	`sum-log_binary64_10612`
2×	`rem-sqrt-square_binary64_10537` `associate-r/_binary64_10468` `associate-l/_binary64_10469`
1×	`pow-plus_binary64_10584` `prod-exp_binary64_10570` `pow2_binary64_10602` `+-commutative_binary64_10456` `*-commutative_binary64_10457` `cbrt-unprod_binary64_10554` `associate-+l+_binary64_10459` `sqrt-unprod_binary64_10543` `rem-square-sqrt_binary64_10536`

Counts

4 → 126

Calls

4 calls:

22.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
7.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
7.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series515.0ms (13.5%)

Counts

4 → 12

Calls

4 calls:

162.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
148.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
145.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
60.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))

simplify72.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5433	3325

prune114.0ms (3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	138	6	144

Merged error: 16.0b

Counts

144 → 6

Compiler

Compiled 3960 to 461 computations (88.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

34.1b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
35.1b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
35.1b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
35.1b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite69.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`cbrt-div_binary64_10553`
30×	`flip3-+_binary64_10527` `flip-+_binary64_10498`
28×	`frac-times_binary64_10534`
26×	`sqrt-div_binary64_10540`
24×	`pow1_binary64_10582`
15×	`sqrt-pow1_binary64_10541`
14×	`associate-*l/_binary64_10469`
12×	`pow1/3_binary64_10603`
9×	`cbrt-prod_binary64_10552` `pow-prod-up_binary64_10591`
8×	`associate-*r/_binary64_10468`
7×	`add-sqr-sqrt_binary64_10545` `*-un-lft-identity_binary64_10524` `add-cube-cbrt_binary64_10556`
6×	`pow-plus_binary64_10584`
5×	`pow-prod-down_binary64_10592`
4×	`add-exp-log_binary64_10559` `add-cbrt-cube_binary64_10557` `add-log-exp_binary64_10560`
3×	`pow-sqr_binary64_10497`
2×	`pow2_binary64_10602`
1×	`pow3_binary64_10604` `pow1/2_binary64_10601` `sqrt-prod_binary64_10539`

Counts

4 → 89

Calls

4 calls:

31.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
7.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
6.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
6.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series728.0ms (19.1%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
191.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
190.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
153.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))

simplify123.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4970	4630
1	4970	4630

prune138.0ms (3.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	101	6	107

Merged error: 16.0b

Counts

107 → 6

Compiler

Compiled 4942 to 816 computations (83.5% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	3	3
Total	6	6

Merged error: 16.0b

Counts

6 → 6

Compiler

Compiled 0 to 0 computations (0% saved)

regimes236.0ms (6.2%)

Compiler: Compiled 1250 to 689 computations (44.9% saved)

bsearch36.0ms (1%)

Steps

Iters	Range		Point
10	2.351428881698585e+101	8.86092043937918e+112	5.76936148938276e+110
8	-1.028376381863224e+115	-2.882952361683843e+110	-9.992751959244195e+114

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	34
1	27	34

end0.0ms (0%)

sample674.0ms (17.7%)

Algorithm

1×

intervals

Results

338.0ms

8000×

body

128

valid

Compiler

Compiled 141 to 87 computations (38.3% saved)

Details

analyze480.0ms (12.6%)

sample18.0ms (0.5%)

simplify166.0ms (4.4%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

rewrite15.0ms (0.4%)

series203.0ms (5.3%)

simplify73.0ms (1.9%)

prune32.0ms (0.8%)

localize14.0ms (0.4%)

rewrite61.0ms (1.6%)

series515.0ms (13.5%)

simplify72.0ms (1.9%)

prune114.0ms (3%)

localize13.0ms (0.3%)

rewrite69.0ms (1.8%)

series728.0ms (19.1%)

simplify123.0ms (3.2%)

prune138.0ms (3.6%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.2%)

prune1.0ms (0%)

regimes236.0ms (6.2%)

bsearch36.0ms (1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample674.0ms (17.7%)

Profiling