Details

analyze428.0ms (11%)

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample46.0ms (1.2%)

Algorithm

1×

intervals

Results

8.0ms	32×	body	2560	valid
7.0ms	35×	body	1280	valid
7.0ms	160×	body	80	valid
5.0ms	13×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	29×	body	80	nan
1.0ms	2×	body	5120	valid
0.0ms	9×	body	80	invalid
0.0ms	4×	body	160	valid

simplify489.0ms (12.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	713	13
1	713	13

prune20.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 34.9b

Counts

2 → 1

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
21.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite35.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series76.0ms (2%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
21.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
16.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
13.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4936	1587
1	4936	1587

prune143.0ms (3.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	8	102

Merged error: 6.4b

Counts

102 → 8

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.5b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
11.0b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
21.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-/l*_binary64`
10×	`associate-/r/_binary64` `sqrt-prod_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_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 → 126

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
12.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series152.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
52.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
15.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify55.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5022	2592

prune154.0ms (4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	138	8	146

Merged error: 6.2b

Counts

146 → 8

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite30.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

10.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series99.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
15.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify69.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4871	1374
1	4871	1374

prune106.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	93	8	101

Merged error: 6.2b

Counts

101 → 8

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
2.0b	(.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
4.5b	(/.f64 (.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))) a)
21.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite46.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
24×	`associate-r_binary64`
22×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`difference-of-squares_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64`
3×	`associate-/r_binary64` `flip3--_binary64` `associate-l*_binary64` `flip--_binary64`
2×	`associate-*r/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `-commutative_binary64`

Counts

4 → 96

Calls

4 calls:

17.0ms	(.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
13.0ms	(/.f64 (.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))) a)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series147.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
51.0ms	(/.f64 (.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))) a)
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
15.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify59.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4915	1484
1	4915	1484

prune98.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	108	8	116

Merged error: 6.2b

Counts

116 → 8

regimes264.0ms (6.8%)

Accuracy

Total 1.0b remaining (15.5%)

Threshold costs 0b (0%)

bsearch103.0ms (2.7%)

Steps

Iters	Range	Point
10	1.5398840352460444e+91	4.391856722391233e+105	1.4967152907647445e+97
10	3.5591382758316196e-227	4.3444407797197816e-212	7.763327155508912e-220
10	-1.5333361493273752e+162	-1.9944502927471612e+151	-2.989405411627715e+151

Iters

Range

Point

1.5398840352460444e+91

4.391856722391233e+105

1.4967152907647445e+97

3.5591382758316196e-227

4.3444407797197816e-212

7.763327155508912e-220

-1.5333361493273752e+162

-1.9944502927471612e+151

-2.989405411627715e+151

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	179	54
1	179	54

end0.0ms (0%)

sample1.1s (28.6%)

Algorithm

1×

intervals

Results

284.0ms	1083×	body	2560	valid
233.0ms	5103×	body	80	valid
202.0ms	947×	body	1280	valid
66.0ms	401×	body	640	valid
38.0ms	122×	body	5120	valid
33.0ms	243×	body	320	valid
32.0ms	757×	body	80	nan
12.0ms	239×	body	80	invalid
9.0ms	101×	body	160	valid

Details

analyze428.0ms (11%)

sample46.0ms (1.2%)

simplify489.0ms (12.6%)

prune20.0ms (0.5%)

localize12.0ms (0.3%)

rewrite35.0ms (0.9%)

series76.0ms (2%)

simplify62.0ms (1.6%)

prune143.0ms (3.7%)

localize12.0ms (0.3%)

rewrite42.0ms (1.1%)

series152.0ms (3.9%)

simplify55.0ms (1.4%)

prune154.0ms (4%)

localize10.0ms (0.3%)

rewrite30.0ms (0.8%)

series99.0ms (2.5%)

simplify69.0ms (1.8%)

prune106.0ms (2.7%)

localize11.0ms (0.3%)

rewrite46.0ms (1.2%)

series147.0ms (3.8%)

simplify59.0ms (1.5%)

prune98.0ms (2.5%)

regimes264.0ms (6.8%)

bsearch103.0ms (2.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.1s (28.6%)

Profiling