Details

analyze874.0ms (4.3%)

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)

sample82.0ms (0.4%)

Algorithm

1×

intervals

Results

17.0ms	35×	body	2048	valid
16.0ms	167×	body	128	valid
13.0ms	16×	body	4096	valid
7.0ms	18×	body	1024	valid
4.0ms	13×	body	512	valid
2.0ms	22×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify772.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (601.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune10.0ms (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

Error

36.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize26.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite57.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_404`
15×	`add-sqr-sqrt_binary64_426`
14×	`add-cube-cbrt_binary64_439`
12×	`times-frac_binary64_410`
8×	`add-log-exp_binary64_443`
6×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442`
5×	`pow1_binary64_465` `distribute-lft-out_binary64_355`
4×	`associate-/l*_binary64_349`
3×	`associate-/r*_binary64_348` `sqrt-prod_binary64_420`
2×	`associate-/l/_binary64_351` `sqrt-div_binary64_421` `flip3-+_binary64_407` `flip3--_binary64_408` `flip-+_binary64_378` `flip--_binary64_379`
1×	`div-exp_binary64_455` `cancel-sign-sub-inv_binary64_370` `pow1/2_binary64_484` `sqrt-pow1_binary64_422` `frac-2neg_binary64_415` `div-inv_binary64_401` `sum-log_binary64_495` `diff-log_binary64_496` `clear-num_binary64_403` `sub-neg_binary64_397` `cbrt-undiv_binary64_438` `+-commutative_binary64_334` `rem-sqrt-square_binary64_417`

Counts

4 → 72

Calls

8 calls:

16.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
12.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.0ms	(.f64 4 (.f64 a c))

series1.1s (5.2%)

Counts

4 → 63

Calls

4 calls:

368.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
288.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
213.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
197.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

Compiler

Compiled 1784 to 1524 computations (14.6% saved)

simplify150.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4975	2734
1	4975	2734

prune381.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	125	10	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	10	136

Error

7.3b

Counts

136 → 10

Compiler

Compiled 2862 to 1551 computations (45.8% saved)

localize26.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 -1/2 (/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) a))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
2.9b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
11.6b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite114.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_410`
59×	`add-sqr-sqrt_binary64_426`
44×	`*-un-lft-identity_binary64_404`
30×	`add-cube-cbrt_binary64_439`
27×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442`
14×	`difference-of-squares_binary64_373`
13×	`associate-/l*_binary64_349` `sqrt-prod_binary64_420`
10×	`div-exp_binary64_455` `associate-/r/_binary64_350` `cbrt-undiv_binary64_438`
9×	`associate-/r*_binary64_348`
7×	`distribute-lft-out--_binary64_356` `flip3--_binary64_408` `flip--_binary64_379`
6×	`cancel-sign-sub-inv_binary64_370` `div-inv_binary64_401` `add-log-exp_binary64_443` `prod-exp_binary64_453` `cbrt-unprod_binary64_437`
5×	`pow1_binary64_465`
2×	`frac-2neg_binary64_415` `sqrt-div_binary64_421` `clear-num_binary64_403`
1×	`associate-/l/_binary64_351` `pow1/2_binary64_484` `sqrt-pow1_binary64_422` `diff-log_binary64_496` `sub-neg_binary64_397` `rem-sqrt-square_binary64_417`

Counts

4 → 136

Calls

8 calls:

33.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
24.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
14.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 -1/2 (/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) a))

series1.8s (8.8%)

Counts

4 → 75

Calls

4 calls:

589.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
518.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
386.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
293.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3010 to 2350 computations (21.9% saved)

simplify175.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4974	6566
1	4974	6566

prune538.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	213	8	221

Error

7.3b

Counts

221 → 8

Compiler

Compiled 6282 to 3307 computations (47.4% saved)

localize30.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
0.0b	(.f64 -1/2 (.f64 4 (.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))))
0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite67.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_426`
28×	`*-un-lft-identity_binary64_404`
18×	`times-frac_binary64_410` `add-cube-cbrt_binary64_439`
11×	`sqrt-prod_binary64_420`
10×	`difference-of-squares_binary64_373`
8×	`add-log-exp_binary64_443`
7×	`cancel-sign-sub-inv_binary64_370`
6×	`add-cbrt-cube_binary64_440` `associate-/r*_binary64_348` `add-exp-log_binary64_442`
5×	`pow1_binary64_465` `distribute-lft-out--_binary64_356`
4×	`flip3--_binary64_408` `flip--_binary64_379`
3×	`associate-/l*_binary64_349`
2×	`sqrt-div_binary64_421` `associate-/r/_binary64_350` `diff-log_binary64_496` `sub-neg_binary64_397`
1×	`div-exp_binary64_455` `pow1/2_binary64_484` `sqrt-pow1_binary64_422` `frac-2neg_binary64_415` `div-inv_binary64_401` `clear-num_binary64_403` `cbrt-undiv_binary64_438` `rem-sqrt-square_binary64_417`

Counts

4 → 88

Calls

8 calls:

17.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
16.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 -1/2 (.f64 4 (.f64 1 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))))

series1.5s (7.1%)

Counts

4 → 80

Calls

4 calls:

513.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
357.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
292.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
290.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2861 to 2446 computations (14.5% saved)

simplify155.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4954	3941
1	4954	3941

prune386.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	168	8	176

Error

7.3b

Counts

176 → 8

Compiler

Compiled 4427 to 2629 computations (40.6% saved)

localize26.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.1b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.1b	(/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite85.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64_410`
82×	`*-un-lft-identity_binary64_404`
57×	`add-sqr-sqrt_binary64_426`
56×	`add-cube-cbrt_binary64_439`
18×	`associate-/r*_binary64_348`
15×	`add-exp-log_binary64_442`
13×	`distribute-lft-out_binary64_355`
9×	`add-cbrt-cube_binary64_440` `associate-/r/_binary64_350`
8×	`add-log-exp_binary64_443`
7×	`div-exp_binary64_455`
6×	`pow1_binary64_465`
5×	`div-inv_binary64_401` `flip3-+_binary64_407` `flip-+_binary64_378`
3×	`cbrt-undiv_binary64_438` `associate-/l*_binary64_349` `sqrt-prod_binary64_420`
2×	`1-exp_binary64_448` `sqrt-div_binary64_421` `rec-exp_binary64_454` `flip3--_binary64_408` `flip--_binary64_379`
1×	`pow-flip_binary64_478` `cancel-sign-sub-inv_binary64_370` `pow1/2_binary64_484` `sqrt-pow1_binary64_422` `frac-2neg_binary64_415` `sum-log_binary64_495` `diff-log_binary64_496` `clear-num_binary64_403` `inv-pow_binary64_489` `sub-neg_binary64_397` `+-commutative_binary64_334` `rem-sqrt-square_binary64_417`

Counts

4 → 135

Calls

8 calls:

24.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
13.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.0ms	(.f64 4 (.f64 a c))

series1.1s (5.3%)

Counts

4 → 63

Calls

4 calls:

373.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
274.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
212.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
209.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

Compiler

Compiled 1924 to 1664 computations (13.5% saved)

simplify194.0ms (1%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4912	5220
1	4912	5220

prune401.0ms (2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	197	9	206

Error

7.3b

Counts

206 → 9

Compiler

Compiled 4923 to 2723 computations (44.7% saved)

simplify87.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	1070	1593
1	1070	1593

regimes842.0ms (4.1%)

Accuracy

Total 1.4b remaining (22.4%)

Threshold costs 0b (0%)

Compiler

Compiled 3144 to 2388 computations (24% saved)

bsearch198.0ms (1%)

Steps

Iters	Range	Point
10	3.8530791125633152e+65	1.6148340927808046e+81	1.1102892118009466e+81
8	7.407819669024023e-264	1.1267988616538363e-260	6.382555368342549e-262
8	-2.896882628819812e+127	-9.970494331055357e+124	-3.675391325498039e+126

Iters

Range

Point

3.8530791125633152e+65

1.6148340927808046e+81

1.1102892118009466e+81

7.407819669024023e-264

1.1267988616538363e-260

6.382555368342549e-262

-2.896882628819812e+127

-9.970494331055357e+124

-3.675391325498039e+126

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	117	91
1	117	91

end0.0ms (0%)

sample9.3s (45.6%)

Algorithm

1×

intervals

Results

560.0ms	1148×	body	2048	valid
502.0ms	5152×	body	128	valid
283.0ms	731×	body	1024	valid
230.0ms	381×	body	4096	valid
117.0ms	407×	body	512	valid
69.0ms	689×	body	128	nan
35.0ms	363×	body	128	invalid
34.0ms	181×	body	256	valid

Compiler

Compiled 3320 to 2499 computations (24.7% saved)

Pareto

-0.09669508024149041

Details

analyze874.0ms (4.3%)

sample82.0ms (0.4%)

simplify772.0ms (3.8%)

prune10.0ms (0.1%)

localize26.0ms (0.1%)

rewrite57.0ms (0.3%)

series1.1s (5.2%)

simplify150.0ms (0.7%)

prune381.0ms (1.9%)

localize26.0ms (0.1%)

rewrite114.0ms (0.6%)

series1.8s (8.8%)

simplify175.0ms (0.9%)

prune538.0ms (2.6%)

localize30.0ms (0.1%)

rewrite67.0ms (0.3%)

series1.5s (7.1%)

simplify155.0ms (0.8%)

prune386.0ms (1.9%)

localize26.0ms (0.1%)

rewrite85.0ms (0.4%)

series1.1s (5.3%)

simplify194.0ms (1%)

prune401.0ms (2%)

simplify87.0ms (0.4%)

regimes842.0ms (4.1%)

bsearch198.0ms (1%)

simplify6.0ms (0%)

end0.0ms (0%)

sample9.3s (45.6%)

Profiling