Details

analyze459.0ms (3.6%)

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)

sample41.0ms (0.3%)

Algorithm

1×

intervals

Results

8.0ms	165×	body	128	valid
7.0ms	34×	body	1024	valid
6.0ms	26×	body	2048	valid
4.0ms	12×	body	4096	valid
2.0ms	12×	body	512	valid
1.0ms	22×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify418.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (320.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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

36.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite349.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

36.5b

Rules

21×	`add-sqr-sqrt_binary64_100`
14×	`*-un-lft-identity_binary64_78`
9×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
8×	`add-log-exp_binary64_117` `add-cube-cbrt_binary64_113`
6×	`sqrt-prod_binary64_94` `difference-of-squares_binary64_47` `times-frac_binary64_84` `associate-/l*_binary64_23`
5×	`pow1_binary64_139`
4×	`flip3--_binary64_82` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44`
3×	`distribute-lft-out--_binary64_30`
2×	`sqrt-div_binary64_95` `diff-log_binary64_170` `sub-neg_binary64_71` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-/l/_binary64_25`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `div-sub_binary64_83` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/r*_binary64_22`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.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))

Compiler

Compiled 2100 to 1220 computations (41.9% saved)

series690.0ms (5.5%)

Error

6.0b

Counts

4 → 67

Calls

4 calls:

200.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
150.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
147.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
132.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 2931 to 2234 computations (23.8% saved)

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5462	2700

prune151.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	132	9	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	9	142

Error

5.9b

Counts

142 → 9

Compiler

Compiled 2890 to 1533 computations (47% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite1.0s (8%)

Algorithm

1×	rewrite-expression-head

Error

5.9b

Rules

693×	`times-frac_binary64_84`
439×	`add-sqr-sqrt_binary64_100`
364×	`*-un-lft-identity_binary64_78`
290×	`add-cube-cbrt_binary64_113`
74×	`difference-of-squares_binary64_47`
71×	`associate-/r*_binary64_22`
40×	`sqrt-prod_binary64_94`
37×	`distribute-lft-out--_binary64_30`
25×	`add-exp-log_binary64_116`
17×	`div-inv_binary64_75`
15×	`div-exp_binary64_129`
13×	`add-cbrt-cube_binary64_114`
8×	`add-log-exp_binary64_117`
6×	`pow1_binary64_139` `cbrt-undiv_binary64_112`
5×	`associate-/r/_binary64_24`
4×	`cancel-sign-sub-inv_binary64_44`
3×	`flip3--_binary64_82` `flip--_binary64_53` `1-exp_binary64_122` `rec-exp_binary64_128` `associate-/l*_binary64_23`
2×	`sqrt-div_binary64_95` `diff-log_binary64_170` `sub-neg_binary64_71`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `inv-pow_binary64_163` `pow-flip_binary64_152` `frac-2neg_binary64_89` `clear-num_binary64_77`

Counts

4 → 356

Calls

4 calls:

28.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 14021 to 8305 computations (40.8% saved)

series714.0ms (5.7%)

Error

5.9b

Counts

4 → 67

Calls

4 calls:

200.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
169.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
158.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
134.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3193 to 2496 computations (21.8% saved)

simplify211.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4949	17007
1	4949	17007

prune832.0ms (6.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	423	0	423
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	423	9	432

Error

5.9b

Counts

432 → 9

Compiler

Compiled 13598 to 7527 computations (44.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite135.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

5.9b

Rules

28×	`add-sqr-sqrt_binary64_100`
18×	`*-un-lft-identity_binary64_78`
14×	`add-cube-cbrt_binary64_113`
13×	`associate-r_binary64_18`
10×	`times-frac_binary64_84`
9×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
8×	`add-log-exp_binary64_117`
7×	`pow1_binary64_139`
6×	`associate-l_binary64_19`
5×	`flip3--_binary64_82` `flip--_binary64_53` `sqrt-prod_binary64_94`
4×	`cancel-sign-sub-inv_binary64_44` `difference-of-squares_binary64_47`
2×	`sqrt-div_binary64_95` `diff-log_binary64_170` `sub-neg_binary64_71` `distribute-lft-out--_binary64_30` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-times_binary64_88` `unswap-sqr_binary64_46` `associate-*l/_binary64_21`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow-prod-down_binary64_149` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-r/_binary64_20` `div-inv_binary64_75` `-commutative_binary64_9`

Counts

4 → 83

Calls

4 calls:

16.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

Compiler

Compiled 2366 to 1383 computations (41.5% saved)

series701.0ms (5.6%)

Error

5.9b

Counts

4 → 67

Calls

4 calls:

201.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
166.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
149.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
135.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 2931 to 2234 computations (23.8% saved)

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5166	2946

prune148.0ms (1.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	150	9	159

Error

5.9b

Counts

159 → 9

Compiler

Compiled 3088 to 1636 computations (47% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite148.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

5.9b

Rules

10×	`add-sqr-sqrt_binary64_100`
9×	`sqrt-prod_binary64_94`
7×	`pow1_binary64_139` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
4×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `flip3--_binary64_82` `flip--_binary64_53`
3×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91`
1×	`diff-log_binary64_170` `sub-neg_binary64_71` `cancel-sign-sub-inv_binary64_44`

Counts

4 → 57

Calls

4 calls:

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

Compiler

Compiled 3198 to 1798 computations (43.8% saved)

series783.0ms (6.2%)

Error

5.9b

Counts

4 → 72

Calls

4 calls:

179.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
165.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
162.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
156.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 8513 to 5496 computations (35.4% saved)

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4964	2040
1	4964	2040

prune266.0ms (2.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	129	9	138

Error

5.9b

Counts

138 → 9

Compiler

Compiled 6145 to 3319 computations (46% saved)

regimes1.9s (14.8%)

Accuracy

Total 5.2b remaining (49.3%)

Threshold costs 0b (0%)

Compiler

Compiled 10576 to 8034 computations (24% saved)

bsearch61.0ms (0.5%)

Steps

Iters	Range		Point
8	4.9376097014978165e-160	2.4381209893985136e-157	2.412690463248524e-157
5	-1.1334247598495217e+108	-4.186730096836208e+107	-1.1196245350655258e+108

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	101	58
1	101	58

end0.0ms (0%)

sample3.4s (26.7%)

Algorithm

1×

intervals

Results

285.0ms	5223×	body	128	valid
275.0ms	1097×	body	2048	valid
143.0ms	733×	body	1024	valid
121.0ms	395×	body	4096	valid
57.0ms	372×	body	512	valid
34.0ms	698×	body	128	nan
20.0ms	389×	body	128	invalid
18.0ms	180×	body	256	valid

Compiler

Compiled 2691 to 2041 computations (24.2% saved)

Details

analyze459.0ms (3.6%)

sample41.0ms (0.3%)

simplify418.0ms (3.3%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite349.0ms (2.8%)

series690.0ms (5.5%)

simplify69.0ms (0.5%)

prune151.0ms (1.2%)

localize12.0ms (0.1%)

rewrite1.0s (8%)

series714.0ms (5.7%)

simplify211.0ms (1.7%)

prune832.0ms (6.6%)

localize12.0ms (0.1%)

rewrite135.0ms (1.1%)

series701.0ms (5.6%)

simplify75.0ms (0.6%)

prune148.0ms (1.2%)

localize22.0ms (0.2%)

rewrite148.0ms (1.2%)

series783.0ms (6.2%)

simplify60.0ms (0.5%)

prune266.0ms (2.1%)

regimes1.9s (14.8%)

bsearch61.0ms (0.5%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.4s (26.7%)

Profiling