Details

analyze459.0ms (11.7%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample44.0ms (1.1%)

Algorithm

1×

intervals

Results

11.0ms	167×	body	80	valid
9.0ms	30×	body	2560	valid
7.0ms	30×	body	1280	valid
3.0ms	17×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	22×	body	80	nan
1.0ms	5×	body	320	valid
1.0ms	12×	body	80	invalid
0.0ms	3×	body	160	valid

simplify239.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (236.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune7.0ms (0.2%)

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: 38.2b

Counts

2 → 1

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
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)))

series78.0ms (2%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
17.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
12.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))

simplify47.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4921	1309
1	4921	1309

prune139.0ms (3.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 7.6b

Counts

83 → 8

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
3.4b	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
11.6b	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64`
77×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
19×	`distribute-lft-out_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `pow1_binary64`
4×	`div-inv_binary64`
3×	`flip3-+_binary64` `div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 158

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
12.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.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))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series153.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
54.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4977	3981
1	4977	3981

prune287.0ms (7.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	168	2	170
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	172	6	178

Merged error: 7.5b

Counts

178 → 6

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
6.0ms	(+.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)))

series104.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
20.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4930	1299
1	4930	1299

prune118.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	83	6	89

Merged error: 7.5b

Counts

89 → 6

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
3.4b	(/.f64 (.f64 (/.f64 (neg.f64 (.f64 4.0 a)) (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))))) (/.f64 c (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))))) (*.f64 a 2.0))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`sqrt-div_binary64`
3×	`associate-/l/_binary64` `flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-frac-neg_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `distribute-lft-neg-out_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 78

Calls

4 calls:

26.0ms	(/.f64 (.f64 (/.f64 (neg.f64 (.f64 4.0 a)) (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))))) (/.f64 c (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))))) (*.f64 a 2.0))
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)))

series106.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(/.f64 (.f64 (/.f64 (neg.f64 (.f64 4.0 a)) (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))))) (/.f64 c (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))))) (*.f64 a 2.0))
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))

simplify59.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4992	2038
1	4992	2038

prune150.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	90	6	96

Merged error: 7.5b

Counts

96 → 6

regimes241.0ms (6.1%)

Accuracy

Total 1.1b remaining (16.1%)

Threshold costs 0b (0%)

bsearch79.0ms (2%)

Steps

Iters	Range	Point
6	1.5254191584927803e+91	1.9406410536970233e+92	2.4801938863971876e+91
8	-8.878839583541517e-240	-5.411190655501986e-243	-2.6603754368549326e-241
8	-3.476586232975515e+112	-9.977119098877996e+107	-5.948493915058576e+108

Iters

Range

Point

1.5254191584927803e+91

1.9406410536970233e+92

2.4801938863971876e+91

-8.878839583541517e-240

-5.411190655501986e-243

-2.6603754368549326e-241

-3.476586232975515e+112

-9.977119098877996e+107

-5.948493915058576e+108

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	125	63
1	125	63

end0.0ms (0%)

sample1.3s (32.8%)

Algorithm

1×

intervals

Results

321.0ms	1039×	body	2560	valid
282.0ms	5148×	body	80	valid
231.0ms	919×	body	1280	valid
94.0ms	460×	body	640	valid
41.0ms	106×	body	5120	valid
34.0ms	671×	body	80	nan
34.0ms	230×	body	320	valid
21.0ms	396×	body	80	invalid
10.0ms	98×	body	160	valid

Details

analyze459.0ms (11.7%)

sample44.0ms (1.1%)

simplify239.0ms (6.1%)

prune7.0ms (0.2%)

localize10.0ms (0.3%)

rewrite31.0ms (0.8%)

series78.0ms (2%)

simplify47.0ms (1.2%)

prune139.0ms (3.6%)

localize12.0ms (0.3%)

rewrite41.0ms (1%)

series153.0ms (3.9%)

simplify62.0ms (1.6%)

prune287.0ms (7.3%)

localize13.0ms (0.3%)

rewrite26.0ms (0.7%)

series104.0ms (2.6%)

simplify67.0ms (1.7%)

prune118.0ms (3%)

localize16.0ms (0.4%)

rewrite42.0ms (1.1%)

series106.0ms (2.7%)

simplify59.0ms (1.5%)

prune150.0ms (3.8%)

regimes241.0ms (6.1%)

bsearch79.0ms (2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (32.8%)

Profiling