Details

analyze2.5s (10%)

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)

sample144.0ms (0.6%)

Algorithm

1×

intervals

Results

25.0ms	175×	body	128	valid
19.0ms	24×	body	2048	valid
18.0ms	95×	body	128	nan
15.0ms	26×	body	1024	nan
12.0ms	27×	body	512	valid
12.0ms	16×	body	2048	nan
10.0ms	19×	body	1024	valid
9.0ms	22×	body	512	nan
3.0ms	11×	body	256	valid
2.0ms	6×	body	256	nan

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify130.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5613	61

prune5.0ms (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

54.1b

Counts

2 → 1

Compiler

Compiled 80 to 59 computations (26.3% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.7b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
15.4b	(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))))))
22.3b	(/.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)))
34.7b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite102.0ms (0.4%)

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)))
14.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
12.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

series882.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

420.0ms	(/.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)))
329.0ms	(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))))))
67.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
65.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

simplify134.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4947	11055
1	4947	11055

prune671.0ms (2.7%)

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

47.0b

Counts

171 → 16

Compiler

Compiled 11969 to 6774 computations (43.4% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.9b	(/.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)))))
11.4b	(/.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))))))
21.5b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)))
34.7b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite206.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

640×	`times-frac_binary64_3153`
487×	`*-un-lft-identity_binary64_3147`
298×	`add-sqr-sqrt_binary64_3169`
297×	`add-cube-cbrt_binary64_3182`
265×	`sqrt-prod_binary64_3163`
152×	`distribute-lft-neg-in_binary64_3104` `distribute-rgt-neg-in_binary64_3105`
114×	`distribute-lft-out_binary64_3098`
90×	`associate-/r*_binary64_3091`
66×	`sqrt-div_binary64_3164`
37×	`associate-/r/_binary64_3093`
36×	`distribute-neg-frac_binary64_3111`
31×	`flip-+_binary64_3121` `flip3-+_binary64_3150`
24×	`frac-add_binary64_3155`
19×	`neg-mul-1_binary64_3143`
11×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208`
7×	`associate-/l*_binary64_3092` `div-inv_binary64_3144`
4×	`associate-l/_binary64_3090` `associate-/l/_binary64_3094` `cbrt-undiv_binary64_3181` `sqrt-pow1_binary64_3165` `div-exp_binary64_3198` `add-log-exp_binary64_3186` `associate-r/_binary64_3089`
3×	`flip--_binary64_3122` `pow-prod-down_binary64_3218` `flip3--_binary64_3151`
2×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `pow1/2_binary64_3227`
1×	`rem-sqrt-square_binary64_3160` `div-sub_binary64_3152`

Counts

4 → 504

Calls

4 calls:

46.0ms	(/.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))))))
23.0ms	(/.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 2 (.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)))

series860.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

378.0ms	(/.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))))))
248.0ms	(/.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)))))
166.0ms	(sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)))
67.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify388.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

516 → 516

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5241	46794

prune2.7s (11%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	509	7	516
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	515	17	532

Error

45.5b

Counts

532 → 17

Compiler

Compiled 36932 to 20099 computations (45.6% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.7b	(.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)
16.5b	(/.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))))
21.5b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))
34.7b	(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_3169`
16×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
13×	`pow1_binary64_3208`
12×	`times-frac_binary64_3153`
8×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `sqrt-prod_binary64_3163`
6×	`associate-*l/_binary64_3090` `sqrt-div_binary64_3164`
4×	`flip--_binary64_3122` `pow-prod-down_binary64_3218` `flip3--_binary64_3151` `sqrt-pow1_binary64_3165` `add-log-exp_binary64_3186` `associate-/l_binary64_3092` `associate-r/_binary64_3089`
3×	`associate-r_binary64_3087` `associate-/r_binary64_3091` `associate-l*_binary64_3088`
2×	`associate-/l/_binary64_3094` `pow1/2_binary64_3227` `associate-/r/_binary64_3093`
1×	`*-commutative_binary64_3078` `unswap-sqr_binary64_3115` `clear-num_binary64_3146` `flip-+_binary64_3121` `frac-2neg_binary64_3158` `flip3-+_binary64_3150` `rem-sqrt-square_binary64_3160` `prod-exp_binary64_3196` `cbrt-undiv_binary64_3181` `cbrt-unprod_binary64_3180` `div-exp_binary64_3198` `div-inv_binary64_3144`

Counts

4 → 84

Calls

4 calls:

14.0ms	(/.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))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
7.0ms	(.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)
7.0ms	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4))) F)))

series423.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

152.0ms	(/.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))))
138.0ms	(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)))
64.0ms	(.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)

simplify53.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4970	2922
1	4970	2922

prune226.0ms (0.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	96	17	113

Error

45.5b

Counts

113 → 17

Compiler

Compiled 5557 to 3117 computations (43.9% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

11.2b	(/.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 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) (+.f64 A C))))))
21.5b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)))
21.5b	(+.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))) (+.f64 A C))
34.7b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite187.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

580×	`times-frac_binary64_3153`
411×	`*-un-lft-identity_binary64_3147`
257×	`add-sqr-sqrt_binary64_3169`
256×	`add-cube-cbrt_binary64_3182`
225×	`sqrt-prod_binary64_3163`
120×	`distribute-lft-neg-in_binary64_3104` `distribute-rgt-neg-in_binary64_3105`
93×	`distribute-lft-out_binary64_3098`
70×	`associate-/r*_binary64_3091`
60×	`sqrt-div_binary64_3164`
31×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `associate-/r/_binary64_3093`
30×	`distribute-neg-frac_binary64_3111`
24×	`frac-add_binary64_3155` `exp-diff_binary64_3195` `log-div_binary64_3234`
15×	`neg-mul-1_binary64_3143`
11×	`pow1_binary64_3208`
9×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `add-log-exp_binary64_3186`
6×	`div-inv_binary64_3144`
4×	`associate-l/_binary64_3090` `sqrt-pow1_binary64_3165` `associate-/l_binary64_3092` `associate-*r/_binary64_3089`
3×	`pow-prod-down_binary64_3218` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `sum-log_binary64_3238`
2×	`flip--_binary64_3122` `flip3--_binary64_3151` `associate-/l/_binary64_3094` `pow1/2_binary64_3227`
1×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `rem-sqrt-square_binary64_3160` `+-commutative_binary64_3077` `associate-+r+_binary64_3079`

Counts

4 → 419

Calls

4 calls:

49.0ms	(/.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 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) (+.f64 A C))))))
17.0ms	(+.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))) (+.f64 A C))
8.0ms	(sqrt.f64 (.f64 2 (.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)))

series5.5s (22.2%)

Counts

4 → 12

Calls

4 calls:

5.0s	(/.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 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) (+.f64 A C))))))
290.0ms	(+.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))) (+.f64 A C))
135.0ms	(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)))

simplify317.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

431 → 431

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4969	41219
1	4969	41219

prune2.1s (8.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	427	4	431
Fresh	2	13	15
Picked	1	0	1
Done	0	1	1
Total	430	18	448

Error

45.3b

Counts

448 → 18

Compiler

Compiled 31122 to 16879 computations (45.8% saved)

regimes1.1s (4.3%)

Accuracy

Total 5.1b remaining (10.5%)

Threshold costs 0b (0%)

Compiler

Compiled 18041 to 12272 computations (32% saved)

bsearch6.0ms (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	171	385
1	171	385

end0.0ms (0%)

sample6.1s (24.5%)

Algorithm

1×

intervals

Results

760.0ms	5500×	body	128	valid
494.0ms	872×	body	1024	valid
482.0ms	658×	body	2048	valid
453.0ms	836×	body	1024	nan
424.0ms	583×	body	2048	nan
390.0ms	2936×	body	128	nan
255.0ms	636×	body	512	valid
236.0ms	585×	body	512	nan
94.0ms	332×	body	256	valid
87.0ms	340×	body	256	nan
2.0ms	2×	body	4096	valid

Compiler

Compiled 3243 to 2189 computations (32.5% saved)

Details

analyze2.5s (10%)

sample144.0ms (0.6%)

simplify130.0ms (0.5%)

prune5.0ms (0%)

localize25.0ms (0.1%)

rewrite102.0ms (0.4%)

series882.0ms (3.5%)

simplify134.0ms (0.5%)

prune671.0ms (2.7%)

localize25.0ms (0.1%)

rewrite206.0ms (0.8%)

series860.0ms (3.5%)

simplify388.0ms (1.6%)

prune2.7s (11%)

localize21.0ms (0.1%)

rewrite46.0ms (0.2%)

series423.0ms (1.7%)

simplify53.0ms (0.2%)

prune226.0ms (0.9%)

localize28.0ms (0.1%)

rewrite187.0ms (0.7%)

series5.5s (22.2%)

simplify317.0ms (1.3%)

prune2.1s (8.4%)

regimes1.1s (4.3%)

bsearch6.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample6.1s (24.5%)

Profiling