Details

analyze466.0ms (5.2%)

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)

sample41.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	167×	body	128	valid
8.0ms	31×	body	2048	valid
5.0ms	15×	body	4096	valid
4.0ms	22×	body	1024	valid
2.0ms	11×	body	512	valid
1.0ms	10×	body	256	valid
1.0ms	17×	body	128	nan
1.0ms	11×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify402.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (309.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune6.0ms (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

34.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_93`
14×	`*-un-lft-identity_binary64_71`
9×	`add-cbrt-cube_binary64_107` `add-exp-log_binary64_109`
8×	`add-log-exp_binary64_110` `add-cube-cbrt_binary64_106`
6×	`associate-/l*_binary64_16` `sqrt-prod_binary64_87` `difference-of-squares_binary64_40` `times-frac_binary64_77`
5×	`pow1_binary64_132`
4×	`flip--_binary64_46` `flip3--_binary64_75` `cancel-sign-sub-inv_binary64_37`
3×	`distribute-lft-out--_binary64_23`
2×	`sqrt-div_binary64_88` `associate-/l/_binary64_18` `div-exp_binary64_122` `cbrt-undiv_binary64_105` `diff-log_binary64_163` `sub-neg_binary64_64`
1×	`associate-/r*_binary64_15` `clear-num_binary64_70` `div-sub_binary64_76` `div-inv_binary64_68` `sqrt-pow1_binary64_89` `prod-exp_binary64_120` `cbrt-unprod_binary64_104` `rem-sqrt-square_binary64_84` `frac-2neg_binary64_82` `pow1/2_binary64_151`

Counts

4 → 74

Calls

8 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))

series705.0ms (7.9%)

Counts

4 → 71

Calls

4 calls:

230.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
160.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
160.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
155.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

Compiler

Compiled 2110 to 1780 computations (15.6% saved)

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5664	2926

prune230.0ms (2.6%)

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 1728 computations (42.8% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite107.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_77`
439×	`add-sqr-sqrt_binary64_93`
364×	`*-un-lft-identity_binary64_71`
290×	`add-cube-cbrt_binary64_106`
74×	`difference-of-squares_binary64_40`
71×	`associate-/r*_binary64_15`
40×	`sqrt-prod_binary64_87`
37×	`distribute-lft-out--_binary64_23`
25×	`add-exp-log_binary64_109`
17×	`div-inv_binary64_68`
15×	`div-exp_binary64_122`
13×	`add-cbrt-cube_binary64_107`
8×	`add-log-exp_binary64_110`
6×	`cbrt-undiv_binary64_105` `pow1_binary64_132`
5×	`associate-/r/_binary64_17`
4×	`cancel-sign-sub-inv_binary64_37`
3×	`flip--_binary64_46` `rec-exp_binary64_121` `associate-/l*_binary64_16` `flip3--_binary64_75` `1-exp_binary64_115`
2×	`sqrt-div_binary64_88` `diff-log_binary64_163` `sub-neg_binary64_64`
1×	`inv-pow_binary64_156` `clear-num_binary64_70` `sqrt-pow1_binary64_89` `rem-sqrt-square_binary64_84` `frac-2neg_binary64_82` `pow1/2_binary64_151` `pow-flip_binary64_145`

Counts

4 → 356

Calls

8 calls:

29.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.0ms	(/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2))

series689.0ms (7.7%)

Counts

4 → 71

Calls

4 calls:

225.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
160.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
155.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
147.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

Compiler

Compiled 2270 to 1940 computations (14.5% saved)

simplify202.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

427 → 427

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4954	17233
1	4954	17233

prune880.0ms (9.8%)

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 8275 computations (39.9% saved)

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) 2)) (/.f64 a (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) 2))))
0.1b	(/.f64 a (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
0.1b	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2))
0.1b	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_93`
12×	`*-un-lft-identity_binary64_71`
8×	`add-log-exp_binary64_110` `sqrt-prod_binary64_87` `add-cube-cbrt_binary64_106`
6×	`pow1_binary64_132` `cancel-sign-sub-inv_binary64_37`
4×	`sqrt-div_binary64_88` `flip--_binary64_46` `add-cbrt-cube_binary64_107` `add-exp-log_binary64_109` `flip3--_binary64_75` `difference-of-squares_binary64_40`
2×	`distribute-lft-out--_binary64_23` `sqrt-pow1_binary64_89` `rem-sqrt-square_binary64_84` `diff-log_binary64_163` `pow1/2_binary64_151` `sub-neg_binary64_64`

Counts

4 → 64

Calls

8 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.0ms	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2))

series665.0ms (7.4%)

Counts

4 → 74

Calls

4 calls:

175.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
164.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
164.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
162.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

Compiler

Compiled 4256 to 3300 computations (22.5% saved)

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5137	2744

prune245.0ms (2.7%)

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 3185 computations (39.7% saved)

localize17.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_93`
12×	`*-un-lft-identity_binary64_71`
8×	`add-log-exp_binary64_110` `sqrt-prod_binary64_87` `add-cube-cbrt_binary64_106`
6×	`pow1_binary64_132` `cancel-sign-sub-inv_binary64_37`
4×	`sqrt-div_binary64_88` `flip--_binary64_46` `add-cbrt-cube_binary64_107` `add-exp-log_binary64_109` `flip3--_binary64_75` `difference-of-squares_binary64_40`
2×	`distribute-lft-out--_binary64_23` `sqrt-pow1_binary64_89` `rem-sqrt-square_binary64_84` `diff-log_binary64_163` `pow1/2_binary64_151` `sub-neg_binary64_64`

Counts

4 → 64

Calls

8 calls:

11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.0ms	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b))

series669.0ms (7.5%)

Counts

4 → 74

Calls

4 calls:

171.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
167.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
166.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
164.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

Compiler

Compiled 4044 to 3088 computations (23.6% saved)

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5137	2744

prune208.0ms (2.3%)

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 2773 computations (43.1% saved)

regimes822.0ms (9.2%)

Accuracy

Total 4.6b remaining (46.3%)

Threshold costs 0b (0%)

Compiler

Compiled 4488 to 3494 computations (22.1% saved)

bsearch75.0ms (0.8%)

Steps

Iters	Range		Point
9	2.5782589075849317e-38	2.2163939757815603e-33	2.7658541670298186e-38
9	-3.3762185246443427e+123	-2.3479465554301022e+117	-9.934253510808862e+120

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	101	58
1	101	58

end0.0ms (0%)

sample2.2s (24.5%)

Algorithm

1×

intervals

Results

284.0ms	1104×	body	2048	valid
278.0ms	5197×	body	128	valid
147.0ms	731×	body	1024	valid
123.0ms	395×	body	4096	valid
61.0ms	407×	body	512	valid
37.0ms	674×	body	128	nan
21.0ms	405×	body	128	invalid
17.0ms	166×	body	256	valid

Compiler

Compiled 1211 to 934 computations (22.9% saved)

Pareto

Details

analyze466.0ms (5.2%)

sample41.0ms (0.5%)

simplify402.0ms (4.5%)

prune6.0ms (0.1%)

localize11.0ms (0.1%)

rewrite42.0ms (0.5%)

series705.0ms (7.9%)

simplify76.0ms (0.8%)

prune230.0ms (2.6%)

localize13.0ms (0.1%)

rewrite107.0ms (1.2%)

series689.0ms (7.7%)

simplify202.0ms (2.3%)

prune880.0ms (9.8%)

localize15.0ms (0.2%)

rewrite34.0ms (0.4%)

series665.0ms (7.4%)

simplify48.0ms (0.5%)

prune245.0ms (2.7%)

localize17.0ms (0.2%)

rewrite39.0ms (0.4%)

series669.0ms (7.5%)

simplify48.0ms (0.5%)

prune208.0ms (2.3%)

regimes822.0ms (9.2%)

bsearch75.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (24.5%)

Profiling