Details

analyze510.0ms (14.3%)

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

sample39.0ms (1.1%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	80	valid
2.0ms	22×	body	80	nan
1.0ms	13×	body	80	invalid

simplify275.0ms (7.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (272.0ms)

Iter	Nodes	Cost
0	3532	37
1	3532	37

prune9.0ms (0.3%)

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: 21.7b

Counts

2 → 1

localize22.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
1.2b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
7×	`sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `sqrt-div_binary64`
3×	`diff-log_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
1×	`associate--l-_binary64` `neg-sub0_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`

Counts

4 → 58

Calls

4 calls:

10.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series69.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
19.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))

simplify56.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4901	985
1	4901	985

prune156.0ms (4.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	6	71

Merged error: 9.6b

Counts

71 → 6

localize26.0ms (0.7%)

Local error

Found 4 expressions with local error:

5.9b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`
4×	`cbrt-div_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`sqrt-prod_binary64`
2×	`pow1/3_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 52

Calls

4 calls:

10.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series117.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
32.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
27.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify57.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5107	1108

prune164.0ms (4.6%)

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: 9.6b

Counts

70 → 8

localize26.0ms (0.7%)

Local error

Found 4 expressions with local error:

24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite22.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`

Counts

4 → 60

Calls

4 calls:

7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series71.0ms (2%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify51.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5056	932

prune197.0ms (5.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Merged error: 9.6b

Counts

80 → 8

localize30.0ms (0.8%)

Local error

Found 4 expressions with local error:

14.2b	(-.f64 (.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`
4×	`cbrt-div_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`sqrt-prod_binary64`
2×	`pow1/3_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 52

Calls

4 calls:

10.0ms	(-.f64 (.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series109.0ms (3%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(-.f64 (.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
29.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
27.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify40.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4928	1108
1	4928	1108

prune141.0ms (4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	64	8	72

Merged error: 9.6b

Counts

72 → 8

regimes254.0ms (7.1%)

Accuracy

Total 1.2b remaining (13.2%)

Threshold costs 0b (0%)

bsearch53.0ms (1.5%)

Steps

Iters	Range		Point
8	6.093467662767075e+66	1.6571798933176391e+69	1.6435099743363113e+69
6	-1.7832963248470996e+80	-3.612699187479539e+79	-1.7621272729921349e+80

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	149	129
1	149	129

end0.0ms (0%)

sample1.0s (28.1%)

Algorithm

1×

intervals

Results

709.0ms	8000×	body	80	valid
58.0ms	657×	body	80	nan
31.0ms	367×	body	80	invalid

Details

analyze510.0ms (14.3%)

sample39.0ms (1.1%)

simplify275.0ms (7.7%)

prune9.0ms (0.3%)

localize22.0ms (0.6%)

rewrite25.0ms (0.7%)

series69.0ms (1.9%)

simplify56.0ms (1.6%)

prune156.0ms (4.4%)

localize26.0ms (0.7%)

rewrite25.0ms (0.7%)

series117.0ms (3.3%)

simplify57.0ms (1.6%)

prune164.0ms (4.6%)

localize26.0ms (0.7%)

rewrite22.0ms (0.6%)

series71.0ms (2%)

simplify51.0ms (1.4%)

prune197.0ms (5.5%)

localize30.0ms (0.8%)

rewrite25.0ms (0.7%)

series109.0ms (3%)

simplify40.0ms (1.1%)

prune141.0ms (4%)

regimes254.0ms (7.1%)

bsearch53.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (28.1%)

Profiling