Details

analyze465.0ms (7.6%)

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample40.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	171×	body	128	valid
9.0ms	34×	body	2048	valid
6.0ms	28×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	24×	body	128	nan
1.0ms	7×	body	512	valid
1.0ms	5×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify219.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (0.1%)

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: 34.4b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 4 a) c)
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_435`
10×	`pow1_binary64_472`
9×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`*-un-lft-identity_binary64_414` `add-log-exp_binary64_450`
6×	`add-cube-cbrt_binary64_446`
4×	`sqrt-prod_binary64_429`
3×	`flip3--_binary64_418` `prod-exp_binary64_460` `pow-prod-down_binary64_482` `associate-r_binary64_356` `flip--_binary64_389` `cbrt-unprod_binary64_444`
2×	`sqrt-div_binary64_430` `difference-of-squares_binary64_383` `diff-log_binary64_503` `sub-neg_binary64_407`
1×	`distribute-lft-out--_binary64_368` `-commutative_binary64_347` `sqrt-pow1_binary64_431` `associate-l*_binary64_357` `pow1/2_binary64_491` `rem-sqrt-square_binary64_427`

Counts

4 → 58

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
8.0ms	(.f64 (.f64 4 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series359.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
126.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
75.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
28.0ms	(.f64 (.f64 4 a) c)

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4886	1207
1	4886	1207

prune96.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	62	8	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	9	71

Merged error: 12.9b

Counts

71 → 9

Compiler

Compiled 1718 to 1045 computations (39.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.4b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
8.0b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite54.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
22×	`times-frac_binary64_420`
21×	`*-un-lft-identity_binary64_414`
17×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
13×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
12×	`add-sqr-sqrt_binary64_435`
11×	`add-cube-cbrt_binary64_446` `associate-/l*_binary64_361`
6×	`associate-/r/_binary64_362` `add-log-exp_binary64_450`
5×	`pow1_binary64_472` `distribute-lft-out_binary64_367` `associate-/r*_binary64_360`
4×	`flip3-+_binary64_417` `div-inv_binary64_411` `flip-+_binary64_388`
3×	`sqrt-prod_binary64_429`
2×	`clear-num_binary64_413` `sqrt-div_binary64_430` `frac-2neg_binary64_425`
1×	`flip3--_binary64_418` `sqrt-pow1_binary64_431` `+-commutative_binary64_346` `pow1/2_binary64_491` `flip--_binary64_389` `associate-/l/_binary64_363` `sum-log_binary64_502` `rem-sqrt-square_binary64_427`

Counts

4 → 102

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series932.0ms (15.2%)

Counts

4 → 12

Calls

4 calls:

387.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
298.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
131.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify88.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4940	3121
1	4940	3121

prune161.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	107	7	114
Fresh	6	1	7
Picked	1	0	1
Done	0	1	1
Total	114	9	123

Merged error: 8.2b

Counts

123 → 9

Compiler

Compiled 3290 to 2029 computations (38.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 4 a) c)
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64_472`
9×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`*-un-lft-identity_binary64_414` `add-log-exp_binary64_450`
7×	`add-sqr-sqrt_binary64_435`
6×	`add-cube-cbrt_binary64_446`
3×	`prod-exp_binary64_460` `sqrt-prod_binary64_429` `pow-prod-down_binary64_482` `associate-r_binary64_356` `cbrt-unprod_binary64_444`
2×	`flip3--_binary64_418` `sqrt-div_binary64_430` `flip--_binary64_389`
1×	`flip3-+_binary64_417` `diff-log_binary64_503` `-commutative_binary64_347` `sqrt-pow1_binary64_431` `+-commutative_binary64_346` `sub-neg_binary64_407` `associate-l*_binary64_357` `flip-+_binary64_388` `distribute-lft-out_binary64_367` `pow1/2_binary64_491` `sum-log_binary64_502` `rem-sqrt-square_binary64_427`

Counts

4 → 56

Calls

4 calls:

7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
6.0ms	(.f64 (.f64 4 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series338.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
121.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
27.0ms	(.f64 (.f64 4 a) c)

simplify60.0ms (1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4871	1116
1	4871	1116

prune76.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	71	6	77

Merged error: 7.2b

Counts

77 → 6

Compiler

Compiled 1643 to 1045 computations (36.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4)))
1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.4b	(/.f64 (/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4))) (*.f64 a 2))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite69.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac_binary64_420`
74×	`*-un-lft-identity_binary64_414`
53×	`add-sqr-sqrt_binary64_435`
52×	`add-cube-cbrt_binary64_446`
45×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
32×	`associate-/l*_binary64_361`
23×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
14×	`div-inv_binary64_411`
11×	`distribute-lft-out_binary64_367`
9×	`associate-/r*_binary64_360`
7×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
6×	`add-log-exp_binary64_450`
5×	`pow1_binary64_472`
3×	`associate-/r/_binary64_362` `sqrt-prod_binary64_429`
2×	`clear-num_binary64_413` `sqrt-div_binary64_430` `frac-2neg_binary64_425`
1×	`flip3--_binary64_418` `flip3-+_binary64_417` `sqrt-pow1_binary64_431` `+-commutative_binary64_346` `flip-+_binary64_388` `pow1/2_binary64_491` `flip--_binary64_389` `associate-/l/_binary64_363` `sum-log_binary64_502` `rem-sqrt-square_binary64_427`

Counts

4 → 165

Calls

4 calls:

19.0ms	(/.f64 (/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4))) (*.f64 a 2))
12.0ms	(/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4)))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series1.0s (16.4%)

Counts

4 → 12

Calls

4 calls:

427.0ms	(/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4)))
351.0ms	(/.f64 (/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 c -4))) (*.f64 a 2))
122.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
109.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4997	6019
1	4997	6019

prune260.0ms (4.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	175	8	183

Merged error: 7.2b

Counts

183 → 8

Compiler

Compiled 5521 to 3234 computations (41.4% saved)

regimes129.0ms (2.1%)

Compiler: Compiled 402 to 345 computations (14.2% saved)

bsearch110.0ms (1.8%)

Steps

Iters	Range	Point
8	6.787489049073195e+118	7.133955408180205e+122	5.134094891995538e+120
9	2.173626231849138e-227	1.6620553427918547e-219	2.227512516590462e-227
8	-9.73333868460494e+156	-4.49823275505298e+152	-1.3249665758399062e+154

Iters

Range

Point

6.787489049073195e+118

7.133955408180205e+122

5.134094891995538e+120

2.173626231849138e-227

1.6620553427918547e-219

2.227512516590462e-227

-9.73333868460494e+156

-4.49823275505298e+152

-1.3249665758399062e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	122	104
1	122	104

end0.0ms (0%)

sample1.4s (22.8%)

Algorithm

1×

intervals

Results

292.0ms	5258×	body	128	valid
287.0ms	1104×	body	2048	valid
142.0ms	682×	body	1024	valid
131.0ms	398×	body	4096	valid
58.0ms	372×	body	512	valid
35.0ms	662×	body	128	nan
21.0ms	186×	body	256	valid
20.0ms	360×	body	128	invalid

Compiler

Compiled 220 to 172 computations (21.8% saved)

Details

analyze465.0ms (7.6%)

sample40.0ms (0.6%)

simplify219.0ms (3.6%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite32.0ms (0.5%)

series359.0ms (5.8%)

simplify72.0ms (1.2%)

prune96.0ms (1.6%)

localize15.0ms (0.2%)

rewrite54.0ms (0.9%)

series932.0ms (15.2%)

simplify88.0ms (1.4%)

prune161.0ms (2.6%)

localize14.0ms (0.2%)

rewrite26.0ms (0.4%)

series338.0ms (5.5%)

simplify60.0ms (1%)

prune76.0ms (1.2%)

localize14.0ms (0.2%)

rewrite69.0ms (1.1%)

series1.0s (16.4%)

simplify93.0ms (1.5%)

prune260.0ms (4.2%)

regimes129.0ms (2.1%)

bsearch110.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (22.8%)

Profiling