Details

analyze2.4s (14.9%)

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%	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 (0.9%)

Algorithm

1×

intervals

Results

24.0ms	183×	body	128	valid
19.0ms	26×	body	1024	valid
17.0ms	23×	body	2048	valid
17.0ms	23×	body	2048	nan
13.0ms	100×	body	128	nan
12.0ms	23×	body	1024	nan
10.0ms	15×	body	512	valid
7.0ms	18×	body	512	nan
2.0ms	9×	body	256	valid
1.0ms	5×	body	256	nan

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify124.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5613	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

52.3b

Counts

2 → 1

Compiler

Compiled 80 to 59 computations (26.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.8b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
13.0b	(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))))))
24.0b	(/.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)))
38.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite110.0ms (0.7%)

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:

28.0ms	(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))))))
19.0ms	(/.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)))
16.0ms	(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)

series856.0ms (5.4%)

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)))
326.0ms	(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))))))
66.0ms	(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)

simplify138.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4947	11055
1	4947	11055

prune690.0ms (4.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	156	14	170
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	14	171

Error

47.6b

Counts

171 → 14

Compiler

Compiled 11870 to 6701 computations (43.5% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.5b	(/.f64 (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))) (+.f64 A C)))) (-.f64 (.f64 B B) (.f64 C (.f64 A 4))))
12.8b	(.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))) (+.f64 A C)))) (-.f64 (.f64 B B) (.f64 C (.f64 A 4)))))
18.9b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
38.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite125.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`*-un-lft-identity_binary64_2465`
121×	`times-frac_binary64_2471`
89×	`add-sqr-sqrt_binary64_2487`
83×	`add-cube-cbrt_binary64_2500`
75×	`sqrt-prod_binary64_2481`
66×	`associate-r_binary64_2405`
56×	`distribute-lft-neg-in_binary64_2422` `distribute-rgt-neg-in_binary64_2423`
42×	`distribute-lft-out_binary64_2416`
20×	`associate-/l*_binary64_2410`
18×	`sqrt-div_binary64_2482`
13×	`pow1_binary64_2526`
11×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
8×	`associate-*l/_binary64_2408`
7×	`associate-*r/_binary64_2407` `neg-mul-1_binary64_2461`
6×	`flip3-+_binary64_2468` `associate-/l/_binary64_2412` `flip-+_binary64_2439` `distribute-neg-frac_binary64_2429`
5×	`flip--_binary64_2440` `flip3--_binary64_2469`
4×	`add-log-exp_binary64_2504` `associate-/r/_binary64_2411` `pow-prod-down_binary64_2536` `sqrt-pow1_binary64_2483` `frac-add_binary64_2473` `associate-l_binary64_2406`
3×	`associate-/r*_binary64_2409`
2×	`frac-times_binary64_2475` `pow1/2_binary64_2545` `cbrt-undiv_binary64_2499` `unswap-sqr_binary64_2433` `div-exp_binary64_2516` `div-inv_binary64_2462` `prod-exp_binary64_2514` `distribute-frac-neg_binary64_2428` `cbrt-unprod_binary64_2498`
1×	`*-commutative_binary64_2396` `distribute-rgt-neg-out_binary64_2425` `clear-num_binary64_2464` `div-sub_binary64_2470` `rem-sqrt-square_binary64_2478` `frac-2neg_binary64_2476` `neg-sub0_binary64_2460`

Counts

4 → 225

Calls

4 calls:

47.0ms	(.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))) (+.f64 A C)))) (-.f64 (.f64 B B) (.f64 C (.f64 A 4)))))
23.0ms	(/.f64 (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))) (+.f64 A C)))) (-.f64 (.f64 B B) (.f64 C (.f64 A 4))))
8.0ms	(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)))

series800.0ms (5%)

Counts

4 → 12

Calls

4 calls:

381.0ms	(.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))) (+.f64 A C)))) (-.f64 (.f64 B B) (.f64 C (.f64 A 4)))))
205.0ms	(/.f64 (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))) (+.f64 A C)))) (-.f64 (.f64 B B) (.f64 C (.f64 A 4))))
142.0ms	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
71.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify158.0ms (1%)

Algorithm

1×	egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4949	12824
1	4949	12824

prune671.0ms (4.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	231	6	237
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	235	16	251

Error

43.2b

Counts

251 → 16

Compiler

Compiled 14718 to 7854 computations (46.6% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

13.1b	(.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (.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 A C)))) (-.f64 (.f64 B B) (.f64 C (.f64 A 4)))))
18.9b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
38.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
38.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite104.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`associate-r_binary64_2405`
49×	`times-frac_binary64_2471`
46×	`add-sqr-sqrt_binary64_2487`
39×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
26×	`sqrt-prod_binary64_2481`
18×	`distribute-lft-neg-in_binary64_2422` `distribute-rgt-neg-in_binary64_2423`
14×	`pow1_binary64_2526`
10×	`sqrt-div_binary64_2482`
9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
8×	`associate-*l/_binary64_2408`
7×	`associate-*r/_binary64_2407`
5×	`sqrt-pow1_binary64_2483`
4×	`add-log-exp_binary64_2504` `flip--_binary64_2440` `pow-prod-down_binary64_2536` `flip3--_binary64_2469` `associate-l_binary64_2406`
3×	`pow1/2_binary64_2545` `neg-mul-1_binary64_2461`
2×	`flip3-+_binary64_2468` `frac-times_binary64_2475` `flip-+_binary64_2439` `unswap-sqr_binary64_2433` `rem-sqrt-square_binary64_2478` `associate-/r/_binary64_2411` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
1×	`*-commutative_binary64_2396` `distribute-rgt-neg-out_binary64_2425` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `div-inv_binary64_2462` `distribute-frac-neg_binary64_2428`

Counts

4 → 123

Calls

4 calls:

49.0ms	(.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (.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 A C)))) (-.f64 (.f64 B B) (.f64 C (.f64 A 4)))))
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 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))

series644.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

375.0ms	(.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (.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 A C)))) (-.f64 (.f64 B B) (.f64 C (.f64 A 4)))))
132.0ms	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
72.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
64.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify103.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4980	6156
1	4980	6156

prune419.0ms (2.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	134	17	151

Error

43.2b

Counts

151 → 17

Compiler

Compiled 9704 to 5268 computations (45.7% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

38.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
38.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
38.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
38.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_2481` `add-sqr-sqrt_binary64_2487`
8×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526` `sqrt-div_binary64_2482`
4×	`flip3-+_binary64_2468` `add-log-exp_binary64_2504` `pow1/2_binary64_2545` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`

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)))

series286.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
71.0ms	(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)))

simplify75.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5058	1232

prune246.0ms (1.6%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	72	17	89

Error

43.2b

Counts

89 → 17

Compiler

Compiled 6044 to 3186 computations (47.3% saved)

regimes1.3s (8.5%)

Accuracy

Total 5.8b remaining (11.8%)

Threshold costs 0b (0%)

Compiler

Compiled 19493 to 12896 computations (33.8% 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	173	364
1	173	364

end0.0ms (0%)

sample6.3s (39.7%)

Algorithm

1×

intervals

Results

754.0ms	5557×	body	128	valid
476.0ms	874×	body	1024	valid
450.0ms	626×	body	2048	valid
449.0ms	817×	body	1024	nan
432.0ms	603×	body	2048	nan
380.0ms	2827×	body	128	nan
245.0ms	602×	body	512	valid
235.0ms	571×	body	512	nan
89.0ms	337×	body	256	valid
82.0ms	315×	body	256	nan
3.0ms	4×	body	4096	valid

Compiler

Compiled 3472 to 2289 computations (34.1% saved)

Details

analyze2.4s (14.9%)

sample141.0ms (0.9%)

simplify124.0ms (0.8%)

prune4.0ms (0%)

localize21.0ms (0.1%)

rewrite110.0ms (0.7%)

series856.0ms (5.4%)

simplify138.0ms (0.9%)

prune690.0ms (4.3%)

localize21.0ms (0.1%)

rewrite125.0ms (0.8%)

series800.0ms (5%)

simplify158.0ms (1%)

prune671.0ms (4.2%)

localize27.0ms (0.2%)

rewrite104.0ms (0.7%)

series644.0ms (4.1%)

simplify103.0ms (0.7%)

prune419.0ms (2.6%)

localize34.0ms (0.2%)

rewrite44.0ms (0.3%)

series286.0ms (1.8%)

simplify75.0ms (0.5%)

prune246.0ms (1.6%)

regimes1.3s (8.5%)

bsearch7.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample6.3s (39.7%)

Profiling