Details

analyze550.0ms (13.2%)

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
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

sample42.0ms (1%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	80	valid
1.0ms	14×	body	80	nan
1.0ms	7×	body	80	invalid

simplify672.0ms (16.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (266.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune21.0ms (0.5%)

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: 21.9b

Counts

2 → 1

localize24.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

10.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

series91.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
23.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
19.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
19.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)

simplify80.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4874	1082
1	4874	1082

prune170.0ms (4.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	65	8	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	8	74

Merged error: 10.6b

Counts

74 → 8

localize24.0ms (0.6%)

Local error

Found 4 expressions with local error:

8.4b	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

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

series76.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))))
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify58.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5629	983

prune162.0ms (3.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	71	8	79

Merged error: 10.6b

Counts

79 → 8

localize26.0ms (0.6%)

Local error

Found 4 expressions with local error:

10.5b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))) b)
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
25.9b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
25.9b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite25.0ms (0.6%)

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

series118.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))) b)
32.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
28.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify41.0ms (1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5043	1108

prune156.0ms (3.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	63	9	72

Merged error: 10.6b

Counts

72 → 9

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
3.4b	(/.f64 (-.f64 (-.f64 (.f64 2.0 (/.f64 (.f64 c a) b)) b) b) (*.f64 2.0 a))
7.1b	(/.f64 (*.f64 c a) b)
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite37.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `times-frac_binary64`
6×	`associate-/l*_binary64`
5×	`pow1_binary64`
4×	`associate-/r*_binary64` `cbrt-undiv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `sqrt-prod_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `neg-log_binary64`

Counts

4 → 81

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (-.f64 (.f64 2.0 (/.f64 (.f64 c a) b)) b) b) (*.f64 2.0 a))
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
5.0ms	(/.f64 (*.f64 c a) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

series67.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(/.f64 (-.f64 (-.f64 (.f64 2.0 (/.f64 (.f64 c a) b)) b) b) (*.f64 2.0 a))
20.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
6.0ms	(/.f64 (*.f64 c a) b)

simplify44.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5193	1257

prune165.0ms (4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	88	14	102

Merged error: 9.4b

Counts

102 → 14

regimes370.0ms (8.9%)

Accuracy

Total 0.9b remaining (12.6%)

Threshold costs 0.9b (12.6%)

bsearch60.0ms (1.4%)

Steps

Iters	Range		Point
9	4.133558150256362e+100	2.0370040434721257e+109	1.827145917976237e+108
9	-7.796098687113796e+132	-3.0791589294299004e+127	-3.6419385251769567e+130

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	170	123
1	170	123

end0.0ms (0%)

sample1.0s (24.1%)

Algorithm

1×

intervals

Results

712.0ms	8000×	body	80	valid
54.0ms	663×	body	80	nan
32.0ms	375×	body	80	invalid

Details

analyze550.0ms (13.2%)

sample42.0ms (1%)

simplify672.0ms (16.1%)

prune21.0ms (0.5%)

localize24.0ms (0.6%)

rewrite32.0ms (0.8%)

series91.0ms (2.2%)

simplify80.0ms (1.9%)

prune170.0ms (4.1%)

localize24.0ms (0.6%)

rewrite21.0ms (0.5%)

series76.0ms (1.8%)

simplify58.0ms (1.4%)

prune162.0ms (3.9%)

localize26.0ms (0.6%)

rewrite25.0ms (0.6%)

series118.0ms (2.8%)

simplify41.0ms (1%)

prune156.0ms (3.8%)

localize25.0ms (0.6%)

rewrite37.0ms (0.9%)

series67.0ms (1.6%)

simplify44.0ms (1.1%)

prune165.0ms (4%)

regimes370.0ms (8.9%)

bsearch60.0ms (1.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (24.1%)

Profiling