Details

analyze2.6s (13.7%)

Algorithm

1×

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)

sample129.0ms (0.7%)

Algorithm

1×

intervals

Results

28.0ms	176×	body	128	valid
19.0ms	27×	body	2048	valid
13.0ms	27×	body	1024	nan
13.0ms	24×	body	1024	valid
12.0ms	17×	body	2048	nan
8.0ms	20×	body	512	nan
7.0ms	56×	body	128	nan
6.0ms	16×	body	512	valid
3.0ms	13×	body	256	valid
2.0ms	8×	body	256	nan

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify153.0ms (0.8%)

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)))

rewrite101.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`sqrt-div_binary64_5551`
40×	`associate-*r/_binary64_5476`
39×	`*-un-lft-identity_binary64_5534`
36×	`times-frac_binary64_5540`
35×	`add-sqr-sqrt_binary64_5556`
34×	`associate-*l/_binary64_5477`
32×	`add-cube-cbrt_binary64_5569`
25×	`flip-+_binary64_5508` `flip3-+_binary64_5537`
24×	`frac-sub_binary64_5543` `frac-times_binary64_5544`
22×	`flip--_binary64_5509` `flip3--_binary64_5538`
20×	`associate-/l/_binary64_5481` `distribute-neg-frac_binary64_5498`
17×	`pow1_binary64_5595`
16×	`distribute-rgt-neg-in_binary64_5492` `distribute-lft-neg-in_binary64_5491`
15×	`sqrt-prod_binary64_5550`
12×	`associate-/l*_binary64_5479`
8×	`add-cbrt-cube_binary64_5570` `add-exp-log_binary64_5572`
7×	`pow-prod-down_binary64_5605`
5×	`sqrt-pow1_binary64_5552`
4×	`add-log-exp_binary64_5573` `neg-mul-1_binary64_5530` `unpow-prod-down_binary64_5613`
3×	`associate-l_binary64_5475` `associate-/r_binary64_5478` `associate-r*_binary64_5474` `distribute-lft-out_binary64_5485`
2×	`pow1/2_binary64_5614` `associate-/r/_binary64_5480`
1×	`div-inv_binary64_5531` `cbrt-unprod_binary64_5567` `distribute-lft-out--_binary64_5486` `div-exp_binary64_5585` `*-commutative_binary64_5465` `frac-2neg_binary64_5545` `clear-num_binary64_5533` `rem-sqrt-square_binary64_5547` `div-sub_binary64_5539` `unswap-sqr_binary64_5502` `distribute-frac-neg_binary64_5497` `prod-exp_binary64_5583` `cbrt-undiv_binary64_5568` `neg-sub0_binary64_5529`

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)))
11.0ms	(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)

series833.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

361.0ms	(/.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)))
349.0ms	(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))))))
65.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
58.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

simplify171.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4948	11070
1	4948	11070

prune623.0ms (3.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	154	16	170
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	16	171

Error

48.0b

Counts

171 → 16

Compiler

Compiled 12075 to 6841 computations (43.3% saved)

localize24.0ms (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)))

rewrite152.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

404×	`sqrt-div_binary64_5551`
136×	`associate-*r/_binary64_5476`
122×	`flip-+_binary64_5508` `flip3-+_binary64_5537`
120×	`frac-times_binary64_5544`
104×	`associate-*l/_binary64_5477`
96×	`frac-sub_binary64_5543`
56×	`associate-/l/_binary64_5481` `distribute-neg-frac_binary64_5498`
45×	`flip--_binary64_5509` `flip3--_binary64_5538`
36×	`times-frac_binary64_5540`
33×	`add-sqr-sqrt_binary64_5556`
31×	`*-un-lft-identity_binary64_5534` `add-cube-cbrt_binary64_5569`
16×	`distribute-rgt-neg-in_binary64_5492` `distribute-lft-neg-in_binary64_5491` `pow1_binary64_5595`
15×	`sqrt-prod_binary64_5550`
12×	`associate-/l*_binary64_5479`
6×	`add-cbrt-cube_binary64_5570` `sqrt-pow1_binary64_5552` `add-exp-log_binary64_5572` `pow-prod-down_binary64_5605`
4×	`add-log-exp_binary64_5573` `neg-mul-1_binary64_5530`
3×	`associate-/r*_binary64_5478` `pow1/2_binary64_5614`
2×	`rem-sqrt-square_binary64_5547` `associate-/r/_binary64_5480`
1×	`div-inv_binary64_5531` `div-exp_binary64_5585` `frac-2neg_binary64_5545` `clear-num_binary64_5533` `div-sub_binary64_5539` `distribute-frac-neg_binary64_5497` `cbrt-undiv_binary64_5568` `neg-sub0_binary64_5529`

Counts

4 → 222

Calls

4 calls:

29.0ms	(/.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)))
22.0ms	(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))))))))
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)))

series866.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

370.0ms	(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))))))))
366.0ms	(/.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)))
69.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
60.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify233.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5558	20240

prune1.4s (7.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	220	14	234
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	225	25	250

Error

48.0b

Counts

250 → 25

Compiler

Compiled 24241 to 12965 computations (46.5% saved)

localize36.0ms (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)))

rewrite42.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_5550` `add-sqr-sqrt_binary64_5556`
8×	`sqrt-div_binary64_5551` `*-un-lft-identity_binary64_5534` `add-cube-cbrt_binary64_5569` `pow1_binary64_5595`
4×	`flip-+_binary64_5508` `flip3-+_binary64_5537` `add-cbrt-cube_binary64_5570` `add-log-exp_binary64_5573` `sqrt-pow1_binary64_5552` `add-exp-log_binary64_5572` `rem-sqrt-square_binary64_5547` `pow1/2_binary64_5614`

Counts

4 → 60

Calls

4 calls:

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

series278.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
70.0ms	(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)))
65.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5058	1232

prune339.0ms (1.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	3	21	24
Picked	1	0	1
Done	0	0	0
Total	72	25	97

Error

48.0b

Counts

97 → 25

Compiler

Compiled 8034 to 4701 computations (41.5% saved)

localize39.0ms (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)))

rewrite47.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_5550` `add-sqr-sqrt_binary64_5556`
8×	`sqrt-div_binary64_5551` `*-un-lft-identity_binary64_5534` `add-cube-cbrt_binary64_5569` `pow1_binary64_5595`
4×	`flip-+_binary64_5508` `flip3-+_binary64_5537` `add-cbrt-cube_binary64_5570` `add-log-exp_binary64_5573` `sqrt-pow1_binary64_5552` `add-exp-log_binary64_5572` `rem-sqrt-square_binary64_5547` `pow1/2_binary64_5614`

Counts

4 → 60

Calls

4 calls:

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

series277.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
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)))
66.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify82.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5058	1232

prune370.0ms (2%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	23	24
Picked	0	1	1
Done	0	0	0
Total	72	25	97

Error

48.0b

Counts

97 → 25

Compiler

Compiled 7772 to 4335 computations (44.2% saved)

regimes2.0s (10.6%)

Accuracy

Total 2.9b remaining (5.7%)

Threshold costs 0b (0%)

Compiler

Compiled 37023 to 23933 computations (35.4% saved)

bsearch11.0ms (0.1%)

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

simplify24.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	589	280
1	589	280

end0.0ms (0%)

sample7.7s (41.4%)

Algorithm

1×

intervals

Results

775.0ms	5562×	body	128	valid
477.0ms	849×	body	1024	valid
465.0ms	644×	body	2048	valid
449.0ms	811×	body	1024	nan
364.0ms	532×	body	2048	nan
327.0ms	2369×	body	128	nan
241.0ms	606×	body	512	valid
231.0ms	589×	body	512	nan
95.0ms	337×	body	256	valid
84.0ms	323×	body	256	nan
2.0ms	2×	body	4096	valid

Compiler

Compiled 6357 to 4112 computations (35.3% saved)

Details

analyze2.6s (13.7%)

sample129.0ms (0.7%)

simplify153.0ms (0.8%)

prune4.0ms (0%)

localize21.0ms (0.1%)

rewrite101.0ms (0.5%)

series833.0ms (4.5%)

simplify171.0ms (0.9%)

prune623.0ms (3.3%)

localize24.0ms (0.1%)

rewrite152.0ms (0.8%)

series866.0ms (4.6%)

simplify233.0ms (1.2%)

prune1.4s (7.8%)

localize36.0ms (0.2%)

rewrite42.0ms (0.2%)

series278.0ms (1.5%)

simplify79.0ms (0.4%)

prune339.0ms (1.8%)

localize39.0ms (0.2%)

rewrite47.0ms (0.3%)

series277.0ms (1.5%)

simplify82.0ms (0.4%)

prune370.0ms (2%)

regimes2.0s (10.6%)

bsearch11.0ms (0.1%)

simplify24.0ms (0.1%)

end0.0ms (0%)

sample7.7s (41.4%)

Profiling