Details

analyze475.0ms (11.8%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample44.0ms (1.1%)

Algorithm

1×

intervals

Results

11.0ms	37×	body	2560	valid
9.0ms	166×	body	80	valid
5.0ms	20×	body	1280	valid
4.0ms	20×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	22×	body	80	nan
1.0ms	7×	body	320	valid
1.0ms	12×	body	80	invalid
0.0ms	2×	body	160	valid

simplify212.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (209.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune9.0ms (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: 36.7b

Counts

2 → 1

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))) b) (.f64 3.0 a))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))) b)
26.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 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 3.0 a) c))) b) (.f64 3.0 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))

series79.0ms (2%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))) b) (.f64 3.0 a))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))) b)
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
12.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))

simplify37.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4931	1311
1	4931	1311

prune152.0ms (3.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 5.2b

Counts

83 → 10

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
3.9b	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))))) (.f64 3.0 a))
9.3b	(/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))))
26.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite46.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64`
79×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
20×	`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×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`cbrt-unprod_binary64` `neg-sub0_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 159

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))))) (.f64 3.0 a))
10.0ms	(/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series163.0ms (4%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))))
53.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))))) (.f64 3.0 a))
20.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

simplify63.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4996	3913
1	4996	3913

prune293.0ms (7.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	168	3	171
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	171	10	181

Merged error: 5.1b

Counts

181 → 10

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3.0 a) c)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
1.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
26.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite22.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
5.0ms	(.f64 (.f64 3.0 a) c)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series52.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
12.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
4.0ms	(.f64 (.f64 3.0 a) c)

simplify28.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5122	753

prune102.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	68	10	78

Merged error: 5.1b

Counts

78 → 10

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
1.7b	(.f64 (neg.f64 (.f64 3.0 a)) (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))))
3.9b	(/.f64 (.f64 (neg.f64 (.f64 3.0 a)) (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c)))))) (.f64 3.0 a))
26.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite43.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
14×	`add-cube-cbrt_binary64` `times-frac_binary64`
9×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`distribute-lft-out_binary64`
3×	`sqrt-prod_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `distribute-lft-neg-out_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-inv_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-/r_binary64` `pow1/2_binary64` `flip3--_binary64` `neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `+-commutative_binary64` `distribute-frac-neg_binary64` `flip--_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 95

Calls

4 calls:

14.0ms	(.f64 (neg.f64 (.f64 3.0 a)) (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))))
14.0ms	(/.f64 (.f64 (neg.f64 (.f64 3.0 a)) (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c)))))) (.f64 3.0 a))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series158.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(.f64 (neg.f64 (.f64 3.0 a)) (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))))
52.0ms	(/.f64 (.f64 (neg.f64 (.f64 3.0 a)) (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c)))))) (.f64 3.0 a))
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
18.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))

simplify53.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4964	1769
1	4964	1769

prune137.0ms (3.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	107	10	117

Merged error: 5.1b

Counts

117 → 10

regimes440.0ms (10.9%)

Accuracy

Total 0.9b remaining (14%)

Threshold costs 0.9b (14%)

bsearch87.0ms (2.2%)

Steps

Iters	Range	Point
7	7.023815571878041e+127	3.7086927817372e+129	2.7144293381871665e+129
10	-1.0074435914629907e-302	1.2174472353976405e-303	-4.511854892223982e-306
8	-5.886835373009713e+149	-1.5910644516223008e+147	-1.3740666575718133e+149

Iters

Range

Point

7.023815571878041e+127

3.7086927817372e+129

2.7144293381871665e+129

-1.0074435914629907e-302

1.2174472353976405e-303

-4.511854892223982e-306

-5.886835373009713e+149

-1.5910644516223008e+147

-1.3740666575718133e+149

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	120	59
1	120	59

end0.0ms (0%)

sample1.3s (31.2%)

Algorithm

1×

intervals

Results

323.0ms	1048×	body	2560	valid
270.0ms	5111×	body	80	valid
222.0ms	924×	body	1280	valid
95.0ms	494×	body	640	valid
40.0ms	106×	body	5120	valid
35.0ms	670×	body	80	nan
34.0ms	224×	body	320	valid
21.0ms	395×	body	80	invalid
9.0ms	93×	body	160	valid

Details

analyze475.0ms (11.8%)

sample44.0ms (1.1%)

simplify212.0ms (5.3%)

prune9.0ms (0.2%)

localize9.0ms (0.2%)

rewrite31.0ms (0.8%)

series79.0ms (2%)

simplify37.0ms (0.9%)

prune152.0ms (3.8%)

localize12.0ms (0.3%)

rewrite46.0ms (1.1%)

series163.0ms (4%)

simplify63.0ms (1.6%)

prune293.0ms (7.3%)

localize10.0ms (0.3%)

rewrite22.0ms (0.6%)

series52.0ms (1.3%)

simplify28.0ms (0.7%)

prune102.0ms (2.5%)

localize12.0ms (0.3%)

rewrite43.0ms (1.1%)

series158.0ms (3.9%)

simplify53.0ms (1.3%)

prune137.0ms (3.4%)

regimes440.0ms (10.9%)

bsearch87.0ms (2.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (31.2%)

Profiling