Details

analyze488.0ms (8.6%)

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample33.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
1.0ms	16×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify237.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	1224	54
1	1224	54

prune6.0ms (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: 23.4b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_113` `add-sqr-sqrt_binary64_98`
6×	`sqrt-prod_binary64_92` `pow1_binary64_135` `add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `sqrt-div_binary64_93` `flip--_binary64_52` `flip3--_binary64_81`
2×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `sub-neg_binary64_70` `pow1/2_binary64_154` `diff-log_binary64_166`

Counts

4 → 52

Calls

4 calls:

6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series385.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
72.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify53.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5020	1222

prune134.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	6	65

Merged error: 9.7b

Counts

65 → 6

Compiler

Compiled 2984 to 1806 computations (39.5% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

8.6b	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_98`
7×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
6×	`add-log-exp_binary64_113` `cbrt-prod_binary64_105`
5×	`pow1_binary64_135`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `cbrt-div_binary64_106`
3×	`sqrt-prod_binary64_92` `flip--_binary64_52` `flip3--_binary64_81`
2×	`sqrt-div_binary64_93` `pow1/3_binary64_156`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `flip-+_binary64_51` `flip3-+_binary64_80` `+-commutative_binary64_9` `pow1/2_binary64_154` `sum-log_binary64_165`

Counts

4 → 52

Calls

4 calls:

5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))

series676.0ms (11.9%)

Counts

4 → 12

Calls

4 calls:

217.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
174.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
173.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5027	1684

prune162.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	62	8	70

Merged error: 9.7b

Counts

70 → 8

Compiler

Compiled 3979 to 2437 computations (38.8% saved)

localize31.0ms (0.6%)

Local error

Found 4 expressions with local error:

25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_98`
9×	`sqrt-prod_binary64_92`
8×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
7×	`pow1_binary64_135`
6×	`sqrt-div_binary64_93`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `flip--_binary64_52` `flip3--_binary64_81`
3×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-prod_binary64_105` `pow1/2_binary64_154`
2×	`cbrt-div_binary64_106`
1×	`pow1/3_binary64_156`

Counts

4 → 58

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series523.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4874	1408
1	4874	1408

prune214.0ms (3.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	70	8	78

Merged error: 9.7b

Counts

78 → 8

Compiler

Compiled 5100 to 3110 computations (39% saved)

localize33.0ms (0.6%)

Local error

Found 4 expressions with local error:

25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_98`
9×	`sqrt-prod_binary64_92`
8×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
7×	`pow1_binary64_135`
6×	`sqrt-div_binary64_93`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `flip--_binary64_52` `flip3--_binary64_81`
3×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-prod_binary64_105` `pow1/2_binary64_154`
2×	`cbrt-div_binary64_106`
1×	`pow1/3_binary64_156`

Counts

4 → 58

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series540.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4874	1408
1	4874	1408

prune190.0ms (3.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	70	8	78

Merged error: 9.7b

Counts

78 → 8

Compiler

Compiled 4809 to 2909 computations (39.5% saved)

regimes150.0ms (2.7%)

Compiler: Compiled 1212 to 843 computations (30.4% saved)

bsearch95.0ms (1.7%)

Steps

Iters	Range		Point
9	2.7667221834522944e+79	6.980360605296595e+84	3.148606068148581e+83
9	-7.769097205397194e+154	-3.112609503432856e+149	-1.3610757459905584e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	149	212
1	149	212

end0.0ms (0%)

sample1.4s (24.3%)

Algorithm

1×

intervals

Results

676.0ms	8000×	body	128	valid
59.0ms	724×	body	128	nan
33.0ms	380×	body	128	invalid

Compiler

Compiled 581 to 392 computations (32.5% saved)

Details

analyze488.0ms (8.6%)

sample33.0ms (0.6%)

simplify237.0ms (4.2%)

prune6.0ms (0.1%)

localize22.0ms (0.4%)

rewrite22.0ms (0.4%)

series385.0ms (6.8%)

simplify53.0ms (0.9%)

prune134.0ms (2.4%)

localize27.0ms (0.5%)

rewrite19.0ms (0.3%)

series676.0ms (11.9%)

simplify55.0ms (1%)

prune162.0ms (2.9%)

localize31.0ms (0.6%)

rewrite21.0ms (0.4%)

series523.0ms (9.2%)

simplify73.0ms (1.3%)

prune214.0ms (3.8%)

localize33.0ms (0.6%)

rewrite22.0ms (0.4%)

series540.0ms (9.5%)

simplify71.0ms (1.3%)

prune190.0ms (3.4%)

regimes150.0ms (2.7%)

bsearch95.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (24.3%)

Profiling