Details

analyze2.6s (15.6%)

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)

sample152.0ms (0.9%)

Algorithm

1×

intervals

Results

24.0ms	170×	body	128	valid
22.0ms	28×	body	1024	valid
19.0ms	25×	body	2048	valid
16.0ms	27×	body	1024	nan
16.0ms	20×	body	2048	nan
13.0ms	89×	body	128	nan
10.0ms	24×	body	512	valid
7.0ms	16×	body	512	nan
3.0ms	9×	body	256	valid
2.0ms	6×	body	256	nan

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify38.0ms (0.2%)

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

51.5b

Counts

2 → 1

Compiler

Compiled 80 to 59 computations (26.3% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.4b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
12.6b	(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))))))
18.7b	(/.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)))
33.8b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite102.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`sqrt-div_binary64_3164`
40×	`associate-*r/_binary64_3089`
39×	`*-un-lft-identity_binary64_3147`
36×	`times-frac_binary64_3153`
35×	`add-sqr-sqrt_binary64_3169`
34×	`associate-*l/_binary64_3090`
32×	`add-cube-cbrt_binary64_3182`
31×	`flip-+_binary64_3121` `flip3-+_binary64_3150`
24×	`frac-times_binary64_3157` `frac-add_binary64_3155`
20×	`distribute-neg-frac_binary64_3111` `associate-/l/_binary64_3094`
17×	`pow1_binary64_3208`
16×	`flip--_binary64_3122` `flip3--_binary64_3151` `distribute-lft-neg-in_binary64_3104` `distribute-rgt-neg-in_binary64_3105`
15×	`sqrt-prod_binary64_3163`
12×	`associate-/l*_binary64_3092`
8×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
7×	`pow-prod-down_binary64_3218`
5×	`sqrt-pow1_binary64_3165`
4×	`unpow-prod-down_binary64_3226` `neg-mul-1_binary64_3143` `add-log-exp_binary64_3186`
3×	`associate-r_binary64_3087` `associate-/r_binary64_3091` `distribute-lft-out_binary64_3098` `associate-l*_binary64_3088`
2×	`pow1/2_binary64_3227` `associate-/r/_binary64_3093`
1×	`*-commutative_binary64_3078` `unswap-sqr_binary64_3115` `clear-num_binary64_3146` `distribute-frac-neg_binary64_3110` `frac-2neg_binary64_3158` `rem-sqrt-square_binary64_3160` `distribute-lft-out--_binary64_3099` `prod-exp_binary64_3196` `neg-sub0_binary64_3142` `div-sub_binary64_3152` `cbrt-undiv_binary64_3181` `cbrt-unprod_binary64_3180` `div-exp_binary64_3198` `div-inv_binary64_3144`

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))))))
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)

series867.0ms (5.2%)

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)))
328.0ms	(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)))
66.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4947	11055
1	4947	11055

prune665.0ms (4%)

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

44.9b

Counts

171 → 14

Compiler

Compiled 11903 to 6723 computations (43.5% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.9b	(/.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))))
11.9b	(.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)))))
15.3b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
33.8b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite126.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`*-un-lft-identity_binary64_3147`
121×	`times-frac_binary64_3153`
89×	`add-sqr-sqrt_binary64_3169`
83×	`add-cube-cbrt_binary64_3182`
75×	`sqrt-prod_binary64_3163`
66×	`associate-r_binary64_3087`
56×	`distribute-lft-neg-in_binary64_3104` `distribute-rgt-neg-in_binary64_3105`
42×	`distribute-lft-out_binary64_3098`
20×	`associate-/l*_binary64_3092`
18×	`sqrt-div_binary64_3164`
13×	`pow1_binary64_3208`
11×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
8×	`associate-*l/_binary64_3090`
7×	`neg-mul-1_binary64_3143` `associate-*r/_binary64_3089`
6×	`distribute-neg-frac_binary64_3111` `flip-+_binary64_3121` `flip3-+_binary64_3150` `associate-/l/_binary64_3094`
5×	`flip--_binary64_3122` `flip3--_binary64_3151`
4×	`frac-add_binary64_3155` `pow-prod-down_binary64_3218` `sqrt-pow1_binary64_3165` `add-log-exp_binary64_3186` `associate-l_binary64_3088` `associate-/r/_binary64_3093`
3×	`associate-/r*_binary64_3091`
2×	`frac-times_binary64_3157` `unswap-sqr_binary64_3115` `distribute-frac-neg_binary64_3110` `prod-exp_binary64_3196` `cbrt-undiv_binary64_3181` `pow1/2_binary64_3227` `cbrt-unprod_binary64_3180` `div-exp_binary64_3198` `div-inv_binary64_3144`
1×	`*-commutative_binary64_3078` `clear-num_binary64_3146` `distribute-rgt-neg-out_binary64_3107` `frac-2neg_binary64_3158` `rem-sqrt-square_binary64_3160` `neg-sub0_binary64_3142` `div-sub_binary64_3152`

Counts

4 → 225

Calls

4 calls:

44.0ms	(.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)))

series799.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

386.0ms	(.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)))))
210.0ms	(/.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))))
137.0ms	(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)))

simplify146.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4949	12824
1	4949	12824

prune681.0ms (4.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	231	6	237
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	234	17	251

Error

43.7b

Counts

251 → 17

Compiler

Compiled 14873 to 7942 computations (46.6% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

11.9b	(.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)))))
15.3b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
33.8b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
33.8b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite99.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`associate-r_binary64_3087`
49×	`times-frac_binary64_3153`
46×	`add-sqr-sqrt_binary64_3169`
39×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
26×	`sqrt-prod_binary64_3163`
18×	`distribute-lft-neg-in_binary64_3104` `distribute-rgt-neg-in_binary64_3105`
14×	`pow1_binary64_3208`
10×	`sqrt-div_binary64_3164`
9×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
8×	`associate-*l/_binary64_3090`
7×	`associate-*r/_binary64_3089`
5×	`sqrt-pow1_binary64_3165`
4×	`flip--_binary64_3122` `pow-prod-down_binary64_3218` `flip3--_binary64_3151` `add-log-exp_binary64_3186` `associate-l_binary64_3088`
3×	`neg-mul-1_binary64_3143` `pow1/2_binary64_3227`
2×	`frac-times_binary64_3157` `unswap-sqr_binary64_3115` `flip-+_binary64_3121` `flip3-+_binary64_3150` `rem-sqrt-square_binary64_3160` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `associate-/r/_binary64_3093`
1×	`*-commutative_binary64_3078` `distribute-rgt-neg-out_binary64_3107` `distribute-frac-neg_binary64_3110` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `div-inv_binary64_3144`

Counts

4 → 123

Calls

4 calls:

52.0ms	(.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)))

series661.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

382.0ms	(.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)))))
146.0ms	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
68.0ms	(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)))

simplify98.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4980	6156
1	4980	6156

prune423.0ms (2.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	134	18	152

Error

43.7b

Counts

152 → 18

Compiler

Compiled 10001 to 5441 computations (45.6% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

15.3b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
33.8b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.9b	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.9b	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite43.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64_3208`
8×	`add-sqr-sqrt_binary64_3169`
7×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
6×	`cbrt-prod_binary64_3178`
4×	`cbrt-div_binary64_3179` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `sqrt-pow1_binary64_3165` `add-log-exp_binary64_3186` `sqrt-div_binary64_3164` `sqrt-prod_binary64_3163`
3×	`flip-+_binary64_3121` `pow-prod-down_binary64_3218` `flip3-+_binary64_3150`
2×	`pow1/3_binary64_3229` `associate-l/_binary64_3090` `pow1/2_binary64_3227` `associate-r/_binary64_3089`
1×	`flip--_binary64_3122` `flip3--_binary64_3151` `rem-sqrt-square_binary64_3160`

Counts

4 → 55

Calls

4 calls:

9.0ms	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
8.0ms	(cbrt.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	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

series509.0ms (3%)

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
150.0ms	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
138.0ms	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
67.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify50.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4949	1420
1	4949	1420

prune208.0ms (1.2%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	63	22	85

Error

43.7b

Counts

85 → 22

Compiler

Compiled 4936 to 2662 computations (46.1% saved)

regimes1.5s (8.9%)

Accuracy

Total 1.9b remaining (4.2%)

Threshold costs 0b (0%)

Compiler

Compiled 21947 to 14432 computations (34.2% saved)

bsearch7.0ms (0%)

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

simplify27.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	170	385
1	170	385

Compiler

Compiled 502 to 316 computations (37.1% saved)

end0.0ms (0%)

sample6.7s (40.1%)

Algorithm

1×

intervals

Results

833.0ms	5611×	body	128	valid
504.0ms	845×	body	1024	valid
474.0ms	787×	body	1024	nan
473.0ms	614×	body	2048	valid
438.0ms	570×	body	2048	nan
430.0ms	2872×	body	128	nan
254.0ms	585×	body	512	valid
244.0ms	555×	body	512	nan
97.0ms	344×	body	256	valid
94.0ms	341×	body	256	nan
1.0ms	1×	body	4096	valid

Compiler

Compiled 3894 to 2547 computations (34.6% saved)

Details

analyze2.6s (15.6%)

sample152.0ms (0.9%)

simplify38.0ms (0.2%)

prune4.0ms (0%)

localize23.0ms (0.1%)

rewrite102.0ms (0.6%)

series867.0ms (5.2%)

simplify133.0ms (0.8%)

prune665.0ms (4%)

localize22.0ms (0.1%)

rewrite126.0ms (0.8%)

series799.0ms (4.8%)

simplify146.0ms (0.9%)

prune681.0ms (4.1%)

localize23.0ms (0.1%)

rewrite99.0ms (0.6%)

series661.0ms (3.9%)

simplify98.0ms (0.6%)

prune423.0ms (2.5%)

localize31.0ms (0.2%)

rewrite43.0ms (0.3%)

series509.0ms (3%)

simplify50.0ms (0.3%)

prune208.0ms (1.2%)

regimes1.5s (8.9%)

bsearch7.0ms (0%)

simplify27.0ms (0.2%)

end0.0ms (0%)

sample6.7s (40.1%)

Profiling