Details

analyze2.6s (13.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4978	427
1	4978	427
0	4	4
1	4	4

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	98.2%	1.8%	7
0%	92%	8%	8
0%	91.2%	8.8%	9
0.4%	89.3%	10.3%	10
7.1%	79.2%	13.6%	11
11.9%	70.2%	17.9%	12
13.8%	67.4%	18.7%	13
16.6%	63.3%	20.1%	14

Compiler

Compiled 41 to 33 computations (19.5% saved)

sample147.0ms (0.8%)

Algorithm

1×

intervals

Results

27.0ms	27×	body	2048	valid
27.0ms	176×	body	128	valid
16.0ms	27×	body	1024	nan
14.0ms	24×	body	1024	valid
13.0ms	17×	body	2048	nan
9.0ms	20×	body	512	nan
8.0ms	56×	body	128	nan
7.0ms	16×	body	512	valid
4.0ms	13×	body	256	valid
2.0ms	8×	body	256	nan

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify57.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5390	61

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

52.9b

Counts

2 → 1

Compiler

Compiled 80 to 59 computations (26.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.6b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
15.9b	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
19.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite100.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`sqrt-div_binary64_5210`
40×	`associate-*r/_binary64_5135`
39×	`*-un-lft-identity_binary64_5193`
36×	`times-frac_binary64_5199`
35×	`add-sqr-sqrt_binary64_5215`
34×	`associate-*l/_binary64_5136`
32×	`add-cube-cbrt_binary64_5228`
25×	`flip-+_binary64_5167` `flip3-+_binary64_5196`
24×	`frac-times_binary64_5203` `frac-sub_binary64_5202`
22×	`flip3--_binary64_5197` `flip--_binary64_5168`
20×	`distribute-neg-frac_binary64_5157` `associate-/l/_binary64_5140`
17×	`pow1_binary64_5254`
16×	`distribute-lft-neg-in_binary64_5150` `distribute-rgt-neg-in_binary64_5151`
15×	`sqrt-prod_binary64_5209`
12×	`associate-/l*_binary64_5138`
8×	`add-cbrt-cube_binary64_5229` `add-exp-log_binary64_5231`
7×	`pow-prod-down_binary64_5264`
5×	`sqrt-pow1_binary64_5211`
4×	`add-log-exp_binary64_5232` `neg-mul-1_binary64_5189` `unpow-prod-down_binary64_5272`
3×	`associate-l_binary64_5134` `distribute-lft-out_binary64_5144` `associate-r_binary64_5133` `associate-/r*_binary64_5137`
2×	`pow1/2_binary64_5273` `associate-/r/_binary64_5139`
1×	`distribute-lft-out--_binary64_5145` `div-sub_binary64_5198` `*-commutative_binary64_5124` `div-inv_binary64_5190` `cbrt-undiv_binary64_5227` `clear-num_binary64_5192` `div-exp_binary64_5244` `rem-sqrt-square_binary64_5206` `prod-exp_binary64_5242` `neg-sub0_binary64_5188` `unswap-sqr_binary64_5161` `cbrt-unprod_binary64_5226` `distribute-frac-neg_binary64_5156` `frac-2neg_binary64_5204`

Counts

4 → 158

Calls

4 calls:

32.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
17.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
12.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
8.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

series864.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

377.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
363.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
62.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
61.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

simplify157.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4948	11070
1	4948	11070

prune659.0ms (3.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	155	15	170
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	15	171

Error

48.0b

Counts

171 → 15

Compiler

Compiled 12042 to 6815 computations (43.4% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

17.8b	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))
20.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite155.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

404×	`sqrt-div_binary64_5210`
136×	`associate-*r/_binary64_5135`
122×	`flip-+_binary64_5167` `flip3-+_binary64_5196`
120×	`frac-times_binary64_5203`
104×	`associate-*l/_binary64_5136`
96×	`frac-sub_binary64_5202`
56×	`distribute-neg-frac_binary64_5157` `associate-/l/_binary64_5140`
45×	`flip3--_binary64_5197` `flip--_binary64_5168`
36×	`times-frac_binary64_5199`
33×	`add-sqr-sqrt_binary64_5215`
31×	`add-cube-cbrt_binary64_5228` `*-un-lft-identity_binary64_5193`
16×	`distribute-lft-neg-in_binary64_5150` `distribute-rgt-neg-in_binary64_5151` `pow1_binary64_5254`
15×	`sqrt-prod_binary64_5209`
12×	`associate-/l*_binary64_5138`
6×	`add-cbrt-cube_binary64_5229` `pow-prod-down_binary64_5264` `add-exp-log_binary64_5231` `sqrt-pow1_binary64_5211`
4×	`add-log-exp_binary64_5232` `neg-mul-1_binary64_5189`
3×	`pow1/2_binary64_5273` `associate-/r*_binary64_5137`
2×	`associate-/r/_binary64_5139` `rem-sqrt-square_binary64_5206`
1×	`div-sub_binary64_5198` `div-inv_binary64_5190` `cbrt-undiv_binary64_5227` `clear-num_binary64_5192` `div-exp_binary64_5244` `neg-sub0_binary64_5188` `distribute-frac-neg_binary64_5156` `frac-2neg_binary64_5204`

Counts

4 → 222

Calls

4 calls:

31.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
23.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

series871.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

375.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
366.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))
68.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
62.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify199.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5558	20240

prune1.4s (7.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	223	11	234
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	228	21	249

Error

48.0b

Counts

249 → 21

Compiler

Compiled 23869 to 12738 computations (46.6% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_5209` `add-sqr-sqrt_binary64_5215`
8×	`sqrt-div_binary64_5210` `add-cube-cbrt_binary64_5228` `*-un-lft-identity_binary64_5193` `pow1_binary64_5254`
4×	`add-cbrt-cube_binary64_5229` `add-log-exp_binary64_5232` `flip-+_binary64_5167` `pow1/2_binary64_5273` `add-exp-log_binary64_5231` `sqrt-pow1_binary64_5211` `flip3-+_binary64_5196` `rem-sqrt-square_binary64_5206`

Counts

4 → 60

Calls

4 calls:

10.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

series271.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
69.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
68.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
62.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify78.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5058	1232

prune539.0ms (2.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	3	17	20
Picked	1	0	1
Done	0	0	0
Total	72	21	93

Error

48.0b

Counts

93 → 21

Compiler

Compiled 7662 to 4474 computations (41.6% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_5209` `add-sqr-sqrt_binary64_5215`
8×	`sqrt-div_binary64_5210` `add-cube-cbrt_binary64_5228` `*-un-lft-identity_binary64_5193` `pow1_binary64_5254`
4×	`add-cbrt-cube_binary64_5229` `add-log-exp_binary64_5232` `flip-+_binary64_5167` `pow1/2_binary64_5273` `add-exp-log_binary64_5231` `sqrt-pow1_binary64_5211` `flip3-+_binary64_5196` `rem-sqrt-square_binary64_5206`

Counts

4 → 60

Calls

4 calls:

10.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

series274.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
68.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
68.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
67.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5058	1232

prune338.0ms (1.8%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	19	20
Picked	0	1	1
Done	0	0	0
Total	72	21	93

Error

48.0b

Counts

93 → 21

Compiler

Compiled 7772 to 4335 computations (44.2% saved)

regimes2.0s (10.6%)

Accuracy

Total 1.6b remaining (3.4%)

Threshold costs 0b (0%)

Compiler

Compiled 34839 to 22595 computations (35.1% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 40 to 32 computations (20% saved)

simplify37.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	590	266
1	590	266

Compiler

Compiled 346 to 234 computations (32.4% saved)

end0.0ms (0%)

sample7.9s (41.9%)

Algorithm

1×

intervals

Results

854.0ms	5562×	body	128	valid
531.0ms	644×	body	2048	valid
523.0ms	849×	body	1024	valid
483.0ms	811×	body	1024	nan
419.0ms	532×	body	2048	nan
371.0ms	2369×	body	128	nan
276.0ms	606×	body	512	valid
271.0ms	589×	body	512	nan
99.0ms	337×	body	256	valid
93.0ms	323×	body	256	nan
2.0ms	2×	body	4096	valid

Compiler

Compiled 5983 to 3882 computations (35.1% saved)

Details

analyze2.6s (13.6%)

sample147.0ms (0.8%)

simplify57.0ms (0.3%)

prune4.0ms (0%)

localize21.0ms (0.1%)

rewrite100.0ms (0.5%)

series864.0ms (4.6%)

simplify157.0ms (0.8%)

prune659.0ms (3.5%)

localize25.0ms (0.1%)

rewrite155.0ms (0.8%)

series871.0ms (4.6%)

simplify199.0ms (1.1%)

prune1.4s (7.2%)

localize31.0ms (0.2%)

rewrite45.0ms (0.2%)

series271.0ms (1.4%)

simplify78.0ms (0.4%)

prune539.0ms (2.9%)

localize34.0ms (0.2%)

rewrite48.0ms (0.3%)

series274.0ms (1.4%)

simplify77.0ms (0.4%)

prune338.0ms (1.8%)

regimes2.0s (10.6%)

bsearch10.0ms (0.1%)

simplify37.0ms (0.2%)

end0.0ms (0%)

sample7.9s (41.9%)

Profiling