Details

analyze506.0ms (8%)

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)

sample34.0ms (0.5%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
1.0ms	16×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify243.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	1224	54
1	1224	54

prune5.0ms (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: 20.3b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.2b	(+.f64 b (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)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_98`
10×	`*-un-lft-identity_binary64_77`
8×	`add-log-exp_binary64_113`
7×	`sqrt-prod_binary64_92`
6×	`pow1_binary64_135` `add-cube-cbrt_binary64_109`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `sqrt-div_binary64_93`
3×	`flip--_binary64_52` `flip3--_binary64_81`
2×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `difference-of-squares_binary64_46` `pow1/2_binary64_154`
1×	`flip-+_binary64_51` `distribute-lft-out--_binary64_31` `flip3-+_binary64_80` `sub-neg_binary64_70` `+-commutative_binary64_9` `diff-log_binary64_166` `distribute-lft-out_binary64_30` `sum-log_binary64_165`

Counts

4 → 56

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
7.0ms	(+.f64 b (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)))

series482.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
122.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5052	1445

prune153.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 5.5b

Counts

69 → 7

Compiler

Compiled 3190 to 1923 computations (39.7% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

12.5b	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (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)))
25.5b	(sqrt.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

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

Counts

4 → 56

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

series456.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
106.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify43.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5118	1361

prune154.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	68	7	75

Merged error: 5.5b

Counts

75 → 7

Compiler

Compiled 3939 to 2386 computations (39.4% saved)

localize32.0ms (0.5%)

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)))
26.3b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.3b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

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

series574.0ms (9%)

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
168.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4874	1424
1	4874	1424

prune208.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Merged error: 5.5b

Counts

75 → 7

Compiler

Compiled 4948 to 3023 computations (38.9% saved)

localize30.0ms (0.5%)

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

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 60

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

series474.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
104.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4993	1404
1	4993	1404

prune213.0ms (3.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	72	7	79

Merged error: 5.5b

Counts

79 → 7

Compiler

Compiled 5148 to 3044 computations (40.9% saved)

regimes455.0ms (7.1%)

Compiler: Compiled 4998 to 3458 computations (30.8% saved)

bsearch76.0ms (1.2%)

Steps

Iters	Range		Point
11	4.2674410741359733e+105	2.1448977684961606e+126	1.711380925334509e+113
5	-1.2069248715764378e+118	-4.243550660965365e+117	-1.183067257131974e+118

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	144	166
1	144	166

end0.0ms (0%)

sample1.9s (29.7%)

Algorithm

1×

intervals

Results

694.0ms	8000×	body	128	valid
51.0ms	645×	body	128	nan
35.0ms	402×	body	128	invalid

Compiler

Compiled 1379 to 947 computations (31.3% saved)

Details

analyze506.0ms (8%)

sample34.0ms (0.5%)

simplify243.0ms (3.8%)

prune5.0ms (0.1%)

localize22.0ms (0.3%)

rewrite27.0ms (0.4%)

series482.0ms (7.6%)

simplify63.0ms (1%)

prune153.0ms (2.4%)

localize24.0ms (0.4%)

rewrite19.0ms (0.3%)

series456.0ms (7.2%)

simplify43.0ms (0.7%)

prune154.0ms (2.4%)

localize32.0ms (0.5%)

rewrite20.0ms (0.3%)

series574.0ms (9%)

simplify73.0ms (1.1%)

prune208.0ms (3.3%)

localize30.0ms (0.5%)

rewrite21.0ms (0.3%)

series474.0ms (7.4%)

simplify63.0ms (1%)

prune213.0ms (3.3%)

regimes455.0ms (7.1%)

bsearch76.0ms (1.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.9s (29.7%)

Profiling