Details

analyze2.5s (13.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5334	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%	99.8%	0.2%	7
0%	98.2%	1.8%	8
0%	94.3%	5.7%	9
0.4%	93%	6.6%	10
7.4%	83.3%	9.3%	11
12.4%	75.2%	12.4%	12
14.4%	68.9%	16.7%	13
16.8%	65.4%	17.8%	14

Compiler

Compiled 41 to 33 computations (19.5% saved)

sample141.0ms (0.8%)

Algorithm

1×

intervals

Results

25.0ms	176×	body	128	valid
19.0ms	31×	body	512	valid
16.0ms	28×	body	1024	valid
16.0ms	28×	body	1024	nan
13.0ms	89×	body	128	nan
12.0ms	16×	body	2048	valid
11.0ms	15×	body	2048	nan
6.0ms	14×	body	512	nan
3.0ms	10×	body	256	nan
1.0ms	5×	body	256	valid

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5613	61

prune9.0ms (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

Merged error: 51.8b

Counts

2 → 1

Compiler

Compiled 80 to 59 computations (26.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.8b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
14.9b	(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))))))
23.0b	(/.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)))

rewrite99.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`sqrt-div_binary64_2482`
40×	`associate-*r/_binary64_2407`
39×	`*-un-lft-identity_binary64_2465`
36×	`times-frac_binary64_2471`
35×	`add-sqr-sqrt_binary64_2487`
34×	`associate-*l/_binary64_2408`
32×	`add-cube-cbrt_binary64_2500`
31×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
24×	`frac-times_binary64_2475` `frac-add_binary64_2473`
20×	`associate-/l/_binary64_2412` `distribute-neg-frac_binary64_2429`
17×	`pow1_binary64_2526`
16×	`distribute-lft-neg-in_binary64_2422` `distribute-rgt-neg-in_binary64_2423` `flip--_binary64_2440` `flip3--_binary64_2469`
15×	`sqrt-prod_binary64_2481`
12×	`associate-/l*_binary64_2410`
8×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
7×	`pow-prod-down_binary64_2536`
5×	`sqrt-pow1_binary64_2483`
4×	`add-log-exp_binary64_2504` `unpow-prod-down_binary64_2544` `neg-mul-1_binary64_2461`
3×	`associate-/r_binary64_2409` `associate-r_binary64_2405` `distribute-lft-out_binary64_2416` `associate-l*_binary64_2406`
2×	`pow1/2_binary64_2545` `associate-/r/_binary64_2411`
1×	`*-commutative_binary64_2396` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-sub_binary64_2470` `distribute-lft-out--_binary64_2417` `unswap-sqr_binary64_2433` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `distribute-frac-neg_binary64_2428` `neg-sub0_binary64_2460` `cbrt-unprod_binary64_2498`

Counts

4 → 158

Calls

4 calls:

27.0ms	(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))))))
16.0ms	(/.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	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
11.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

series842.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

406.0ms	(/.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)))
309.0ms	(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)))
61.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

simplify143.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4947	11055
1	4947	11055

prune674.0ms (3.6%)

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

Merged error: 45.7b

Counts

171 → 15

Compiler

Compiled 12009 to 6795 computations (43.4% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.8b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
14.8b	(/.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F))) (/.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))) (+.f64 A C))))))
16.8b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)))
34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite175.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

580×	`times-frac_binary64_2471`
408×	`*-un-lft-identity_binary64_2465`
261×	`add-sqr-sqrt_binary64_2487`
258×	`add-cube-cbrt_binary64_2500`
225×	`sqrt-prod_binary64_2481`
120×	`distribute-lft-neg-in_binary64_2422` `distribute-rgt-neg-in_binary64_2423`
90×	`distribute-lft-out_binary64_2416`
70×	`associate-/r*_binary64_2409`
56×	`sqrt-div_binary64_2482`
31×	`associate-/r/_binary64_2411`
30×	`distribute-neg-frac_binary64_2429`
26×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
20×	`frac-add_binary64_2473`
15×	`neg-mul-1_binary64_2461`
13×	`pow1_binary64_2526`
11×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
6×	`associate-*l/_binary64_2408` `div-inv_binary64_2462`
4×	`add-log-exp_binary64_2504` `associate-r/_binary64_2407` `pow-prod-down_binary64_2536` `sqrt-pow1_binary64_2483` `associate-/l_binary64_2410`
3×	`flip--_binary64_2440` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `associate-r_binary64_2405` `flip3--_binary64_2469` `associate-l_binary64_2406`
2×	`pow1/2_binary64_2545` `associate-/l/_binary64_2412`
1×	`*-commutative_binary64_2396` `clear-num_binary64_2464` `unswap-sqr_binary64_2433` `rem-sqrt-square_binary64_2478` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `cbrt-unprod_binary64_2498`

Counts

4 → 420

Calls

4 calls:

42.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F))) (/.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))) (+.f64 A C))))))
8.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
7.0ms	(sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)))

series641.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

367.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F))) (/.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))) (+.f64 A C))))))
147.0ms	(sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)))
66.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
60.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

simplify339.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

432 → 432

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5325	40691

prune1.9s (10.5%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	422	10	432
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	427	20	447

Merged error: 43.9b

Counts

447 → 20

Compiler

Compiled 31846 to 17324 computations (45.6% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.8b	(.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)
15.8b	(/.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))) (-.f64 (.f64 B B) (.f64 C (.f64 A 4))))
16.8b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_2487`
16×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
13×	`pow1_binary64_2526`
12×	`times-frac_binary64_2471`
8×	`sqrt-prod_binary64_2481` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
6×	`associate-*l/_binary64_2408` `sqrt-div_binary64_2482`
4×	`add-log-exp_binary64_2504` `flip--_binary64_2440` `associate-r/_binary64_2407` `pow-prod-down_binary64_2536` `flip3--_binary64_2469` `sqrt-pow1_binary64_2483` `associate-/l_binary64_2410`
3×	`associate-/r_binary64_2409` `associate-r_binary64_2405` `associate-l*_binary64_2406`
2×	`pow1/2_binary64_2545` `associate-/l/_binary64_2412` `associate-/r/_binary64_2411`
1×	`flip3-+_binary64_2468` `*-commutative_binary64_2396` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `unswap-sqr_binary64_2433` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `cbrt-unprod_binary64_2498`

Counts

4 → 84

Calls

4 calls:

13.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))) (-.f64 (.f64 B B) (.f64 C (.f64 A 4))))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
7.0ms	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
7.0ms	(.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)

series404.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))) (-.f64 (.f64 B B) (.f64 C (.f64 A 4))))
135.0ms	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
66.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
60.0ms	(.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)

simplify55.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4970	2922
1	4970	2922

prune233.0ms (1.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	3	16	19
Picked	1	0	1
Done	0	0	0
Total	98	18	116

Merged error: 43.9b

Counts

116 → 18

Compiler

Compiled 5886 to 3314 computations (43.7% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.8b	(.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)
14.8b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))) (/.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))) (+.f64 A C))))))
16.8b	(sqrt.f64 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))
34.1b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite101.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

190×	`times-frac_binary64_2471`
139×	`*-un-lft-identity_binary64_2465`
82×	`add-sqr-sqrt_binary64_2487`
79×	`add-cube-cbrt_binary64_2500`
70×	`associate-/r*_binary64_2409`
64×	`sqrt-prod_binary64_2481`
48×	`distribute-lft-neg-in_binary64_2422` `distribute-rgt-neg-in_binary64_2423`
36×	`distribute-lft-out_binary64_2416`
26×	`sqrt-div_binary64_2482`
18×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
13×	`associate-/r/_binary64_2411`
12×	`distribute-neg-frac_binary64_2429`
11×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
10×	`pow1_binary64_2526`
8×	`frac-add_binary64_2473`
6×	`associate-*l/_binary64_2408` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `neg-mul-1_binary64_2461`
4×	`add-log-exp_binary64_2504`
3×	`flip--_binary64_2440` `div-inv_binary64_2462` `prod-exp_binary64_2514` `associate-r_binary64_2405` `flip3--_binary64_2469` `sqrt-pow1_binary64_2483` `associate-l_binary64_2406` `cbrt-unprod_binary64_2498`
2×	`pow1/2_binary64_2545` `associate-/l/_binary64_2412` `associate-*r/_binary64_2407` `pow-prod-down_binary64_2536`
1×	`-commutative_binary64_2396` `clear-num_binary64_2464` `unswap-sqr_binary64_2433` `rem-sqrt-square_binary64_2478` `frac-2neg_binary64_2476` `associate-/l_binary64_2410`

Counts

4 → 210

Calls

4 calls:

41.0ms	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))) (/.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))) (+.f64 A C))))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)
5.0ms	(sqrt.f64 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))

series622.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

378.0ms	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))) (/.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))) (+.f64 A C))))))
108.0ms	(sqrt.f64 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))
70.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
66.0ms	(.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)

simplify156.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4975	14127
1	4975	14127

prune668.0ms (3.6%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	220	2	222
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	221	19	240

Merged error: 40.7b

Counts

240 → 19

Compiler

Compiled 13356 to 7068 computations (47.1% saved)

regimes1.5s (8.3%)

Compiler: Compiled 22709 to 15290 computations (32.7% saved)

bsearch7.0ms (0%)

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	161	252
1	161	252

end0.0ms (0%)

sample7.0s (37.9%)

Algorithm

1×

intervals

Results

803.0ms	5581×	body	128	valid
760.0ms	618×	body	2048	valid
519.0ms	886×	body	1024	valid
473.0ms	824×	body	1024	nan
454.0ms	617×	body	2048	nan
417.0ms	2911×	body	128	nan
249.0ms	588×	body	512	valid
246.0ms	562×	body	512	nan
96.0ms	327×	body	256	valid
83.0ms	293×	body	256	nan

Compiler

Compiled 3934 to 2639 computations (32.9% saved)

Details

analyze2.5s (13.7%)

sample141.0ms (0.8%)

simplify41.0ms (0.2%)

prune9.0ms (0%)

localize20.0ms (0.1%)

rewrite99.0ms (0.5%)

series842.0ms (4.5%)

simplify143.0ms (0.8%)

prune674.0ms (3.6%)

localize30.0ms (0.2%)

rewrite175.0ms (0.9%)

series641.0ms (3.5%)

simplify339.0ms (1.8%)

prune1.9s (10.5%)

localize21.0ms (0.1%)

rewrite46.0ms (0.2%)

series404.0ms (2.2%)

simplify55.0ms (0.3%)

prune233.0ms (1.3%)

localize22.0ms (0.1%)

rewrite101.0ms (0.5%)

series622.0ms (3.4%)

simplify156.0ms (0.8%)

prune668.0ms (3.6%)

regimes1.5s (8.3%)

bsearch7.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample7.0s (37.9%)

Profiling