Details

analyze872.0ms (4.2%)

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	167×	body	128	valid
15.0ms	31×	body	2048	valid
12.0ms	15×	body	4096	valid
9.0ms	22×	body	1024	valid
3.0ms	11×	body	512	valid
2.0ms	10×	body	256	valid
2.0ms	17×	body	128	nan
1.0ms	11×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify715.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (564.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune10.0ms (0%)

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

34.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize23.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite73.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_426`
14×	`*-un-lft-identity_binary64_404`
9×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442`
8×	`add-log-exp_binary64_443` `add-cube-cbrt_binary64_439`
6×	`times-frac_binary64_410` `difference-of-squares_binary64_373` `associate-/l*_binary64_349` `sqrt-prod_binary64_420`
5×	`pow1_binary64_465`
4×	`cancel-sign-sub-inv_binary64_370` `flip3--_binary64_408` `flip--_binary64_379`
3×	`distribute-lft-out--_binary64_356`
2×	`associate-/l/_binary64_351` `div-exp_binary64_455` `sqrt-div_binary64_421` `diff-log_binary64_496` `sub-neg_binary64_397` `cbrt-undiv_binary64_438`
1×	`pow1/2_binary64_484` `sqrt-pow1_binary64_422` `frac-2neg_binary64_415` `div-inv_binary64_401` `associate-/r*_binary64_348` `clear-num_binary64_403` `div-sub_binary64_409` `prod-exp_binary64_453` `rem-sqrt-square_binary64_417` `cbrt-unprod_binary64_437`

Counts

4 → 74

Calls

8 calls:

23.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
20.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
9.0ms	(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))

series1.3s (6.2%)

Counts

4 → 71

Calls

4 calls:

425.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
292.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
288.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
280.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)

Compiler

Compiled 2110 to 1780 computations (15.6% saved)

simplify124.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4940	2926
1	4940	2926

prune407.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	135	10	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	10	146

Error

6.6b

Counts

146 → 10

Compiler

Compiled 3022 to 1613 computations (46.6% saved)

localize26.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.1b	(/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2))
0.0b	(.f64 4 (.f64 a c))
0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite206.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_410`
439×	`add-sqr-sqrt_binary64_426`
364×	`*-un-lft-identity_binary64_404`
290×	`add-cube-cbrt_binary64_439`
74×	`difference-of-squares_binary64_373`
71×	`associate-/r*_binary64_348`
40×	`sqrt-prod_binary64_420`
37×	`distribute-lft-out--_binary64_356`
25×	`add-exp-log_binary64_442`
17×	`div-inv_binary64_401`
15×	`div-exp_binary64_455`
13×	`add-cbrt-cube_binary64_440`
8×	`add-log-exp_binary64_443`
6×	`pow1_binary64_465` `cbrt-undiv_binary64_438`
5×	`associate-/r/_binary64_350`
4×	`cancel-sign-sub-inv_binary64_370`
3×	`1-exp_binary64_448` `rec-exp_binary64_454` `flip3--_binary64_408` `associate-/l*_binary64_349` `flip--_binary64_379`
2×	`sqrt-div_binary64_421` `diff-log_binary64_496` `sub-neg_binary64_397`
1×	`pow-flip_binary64_478` `pow1/2_binary64_484` `sqrt-pow1_binary64_422` `frac-2neg_binary64_415` `clear-num_binary64_403` `inv-pow_binary64_489` `rem-sqrt-square_binary64_417`

Counts

4 → 356

Calls

8 calls:

51.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
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 4 (.f64 a c))

series1.2s (5.9%)

Counts

4 → 71

Calls

4 calls:

410.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
294.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
261.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
259.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)

Compiler

Compiled 2270 to 1940 computations (14.5% saved)

simplify402.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

427 → 427

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4944	17233
1	4944	17233

prune1.6s (7.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	425	2	427
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	426	11	437

Error

6.6b

Counts

437 → 11

Compiler

Compiled 13771 to 7661 computations (44.4% saved)

localize32.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2))
0.1b	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite63.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_426`
12×	`*-un-lft-identity_binary64_404`
8×	`add-log-exp_binary64_443` `add-cube-cbrt_binary64_439` `sqrt-prod_binary64_420`
6×	`pow1_binary64_465` `cancel-sign-sub-inv_binary64_370`
4×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442` `sqrt-div_binary64_421` `flip3--_binary64_408` `difference-of-squares_binary64_373` `flip--_binary64_379`
2×	`pow1/2_binary64_484` `sqrt-pow1_binary64_422` `distribute-lft-out--_binary64_356` `diff-log_binary64_496` `sub-neg_binary64_397` `rem-sqrt-square_binary64_417`

Counts

4 → 64

Calls

8 calls:

16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
8.0ms	(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 4 (.f64 a c))

series1.2s (5.8%)

Counts

4 → 74

Calls

4 calls:

306.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
302.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
302.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
293.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)

Compiler

Compiled 4256 to 3236 computations (24% saved)

simplify165.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4965	2744
1	4965	2744

prune394.0ms (1.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	138	11	149

Error

6.6b

Counts

149 → 11

Compiler

Compiled 5284 to 2955 computations (44.1% saved)

localize31.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
0.1b	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite63.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_426`
12×	`*-un-lft-identity_binary64_404`
8×	`add-log-exp_binary64_443` `add-cube-cbrt_binary64_439` `sqrt-prod_binary64_420`
6×	`pow1_binary64_465` `cancel-sign-sub-inv_binary64_370`
4×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442` `sqrt-div_binary64_421` `flip3--_binary64_408` `difference-of-squares_binary64_373` `flip--_binary64_379`
2×	`pow1/2_binary64_484` `sqrt-pow1_binary64_422` `distribute-lft-out--_binary64_356` `diff-log_binary64_496` `sub-neg_binary64_397` `rem-sqrt-square_binary64_417`

Counts

4 → 64

Calls

8 calls:

18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series1.2s (5.8%)

Counts

4 → 74

Calls

4 calls:

309.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
304.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
300.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
300.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)

Compiler

Compiled 4044 to 3024 computations (25.2% saved)

simplify174.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	4965	2744
1	4965	2744

prune343.0ms (1.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	138	11	149

Error

6.6b

Counts

149 → 11

Compiler

Compiled 4876 to 2545 computations (47.8% saved)

simplify48.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	350	1658
1	350	1658

regimes1.2s (5.9%)

Accuracy

Total 4.7b remaining (48%)

Threshold costs 0b (0%)

Compiler

Compiled 3210 to 2463 computations (23.3% saved)

bsearch118.0ms (0.6%)

Steps

Iters	Range		Point
9	2.5782589075849317e-38	2.2163939757815603e-33	2.7658541670298186e-38
9	-3.3762185246443427e+123	-2.3479465554301022e+117	-1.6128975171429741e+121

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	101	58
1	101	58

end0.0ms (0%)

sample8.7s (41.6%)

Algorithm

1×

intervals

Results

485.0ms	1104×	body	2048	valid
484.0ms	5197×	body	128	valid
252.0ms	731×	body	1024	valid
223.0ms	395×	body	4096	valid
105.0ms	407×	body	512	valid
64.0ms	674×	body	128	nan
36.0ms	405×	body	128	invalid
29.0ms	166×	body	256	valid

Compiler

Compiled 3342 to 2542 computations (23.9% saved)

Pareto

-0.14656934931460033

Details

analyze872.0ms (4.2%)

sample82.0ms (0.4%)

simplify715.0ms (3.4%)

prune10.0ms (0%)

localize23.0ms (0.1%)

rewrite73.0ms (0.4%)

series1.3s (6.2%)

simplify124.0ms (0.6%)

prune407.0ms (2%)

localize26.0ms (0.1%)

rewrite206.0ms (1%)

series1.2s (5.9%)

simplify402.0ms (1.9%)

prune1.6s (7.9%)

localize32.0ms (0.2%)

rewrite63.0ms (0.3%)

series1.2s (5.8%)

simplify165.0ms (0.8%)

prune394.0ms (1.9%)

localize31.0ms (0.1%)

rewrite63.0ms (0.3%)

series1.2s (5.8%)

simplify174.0ms (0.8%)

prune343.0ms (1.6%)

simplify48.0ms (0.2%)

regimes1.2s (5.9%)

bsearch118.0ms (0.6%)

simplify5.0ms (0%)

end0.0ms (0%)

sample8.7s (41.6%)

Profiling