Details

analyze40.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

Compiler

Compiled 63 to 34 computations (46% saved)

sample40.0ms (0.3%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify194.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5395	79

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

Merged error: 54.3b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
37.5b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
46.3b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite164.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`times-frac_binary64_2493`
66×	`associate-/r/_binary64_2433` `flip-+_binary64_2461` `flip3-+_binary64_2490`
61×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
46×	`add-sqr-sqrt_binary64_2509`
44×	`*-un-lft-identity_binary64_2487` `frac-times_binary64_2497`
34×	`associate-*r/_binary64_2429`
30×	`add-cube-cbrt_binary64_2522`
28×	`difference-of-squares_binary64_2456`
22×	`associate-*l/_binary64_2430` `prod-exp_binary64_2536` `cbrt-unprod_binary64_2520`
19×	`div-exp_binary64_2538` `cbrt-undiv_binary64_2521`
16×	`pow1_binary64_2548`
14×	`difference-of-sqr-1_binary64_2457` `associate-/l*_binary64_2432`
9×	`div-inv_binary64_2484` `associate-/l/_binary64_2434`
7×	`associate-/r*_binary64_2431`
6×	`associate-r_binary64_2427`
4×	`pow-prod-down_binary64_2558` `add-log-exp_binary64_2526` `associate-l_binary64_2428`
3×	`swap-sqr_binary64_2454`
2×	`distribute-rgt-in_binary64_2437` `distribute-lft-in_binary64_2436` `*-commutative_binary64_2418` `frac-2neg_binary64_2498` `clear-num_binary64_2486`
1×	`unswap-sqr_binary64_2455` `flip--_binary64_2462` `pow-plus_binary64_2550` `pow-prod-up_binary64_2557` `pow-sqr_binary64_2460` `pow2_binary64_2568` `flip3--_binary64_2491`

Counts

4 → 228

Calls

4 calls:

46.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
30.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
19.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
15.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))

series3.6s (23.4%)

Counts

4 → 12

Calls

4 calls:

2.9s	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
400.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
202.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
98.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify151.0ms (1%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5255	18181

prune1.3s (8.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	231	9	240
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	232	9	241

Merged error: 34.5b

Counts

241 → 9

Compiler

Compiled 37855 to 16033 computations (57.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.3b	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
35.3b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
36.3b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite135.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64_2493`
174×	`*-un-lft-identity_binary64_2487`
170×	`add-sqr-sqrt_binary64_2509`
106×	`add-cube-cbrt_binary64_2522`
34×	`associate-/r/_binary64_2433`
32×	`difference-of-squares_binary64_2456`
28×	`associate-/l*_binary64_2432`
25×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
18×	`flip-+_binary64_2461` `flip3-+_binary64_2490`
17×	`associate-/r*_binary64_2431` `div-inv_binary64_2484`
16×	`difference-of-sqr-1_binary64_2457` `distribute-lft-out--_binary64_2439`
11×	`div-exp_binary64_2538` `cbrt-undiv_binary64_2521`
10×	`distribute-lft-out_binary64_2438`
6×	`associate-/l/_binary64_2434`
4×	`frac-2neg_binary64_2498` `clear-num_binary64_2486` `pow1_binary64_2548` `add-log-exp_binary64_2526`
2×	`prod-exp_binary64_2536` `cbrt-unprod_binary64_2520` `associate-*r/_binary64_2429`
1×	`flip--_binary64_2462` `flip3--_binary64_2491`

Counts

4 → 268

Calls

4 calls:

28.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
24.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
15.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
12.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series947.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

386.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
229.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
218.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
114.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

simplify160.0ms (1%)

Algorithm

1×	egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5138	16880

prune1.1s (7.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	275	5	280
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	281	8	289

Merged error: 34.5b

Counts

289 → 8

Compiler

Compiled 30919 to 13279 computations (57.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
0.3b	(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
0.3b	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
36.3b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite161.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

360×	`times-frac_binary64_2493`
348×	`*-un-lft-identity_binary64_2487`
225×	`add-sqr-sqrt_binary64_2509`
161×	`add-cube-cbrt_binary64_2522`
79×	`distribute-lft-out_binary64_2438`
44×	`associate-/l*_binary64_2432`
34×	`associate-/r/_binary64_2433`
32×	`difference-of-squares_binary64_2456`
18×	`add-exp-log_binary64_2525` `flip-+_binary64_2461` `flip3-+_binary64_2490` `add-cbrt-cube_binary64_2523`
17×	`associate-/r*_binary64_2431` `div-inv_binary64_2484`
16×	`difference-of-sqr-1_binary64_2457` `distribute-lft-out--_binary64_2439`
8×	`div-exp_binary64_2538` `cbrt-undiv_binary64_2521`
6×	`associate-/l/_binary64_2434`
4×	`frac-2neg_binary64_2498` `clear-num_binary64_2486` `pow1_binary64_2548` `add-log-exp_binary64_2526`
1×	`flip--_binary64_2462` `flip3--_binary64_2491`

Counts

4 → 340

Calls

4 calls:

26.0ms	(/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
24.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
17.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
12.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series849.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

389.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
211.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
150.0ms	(/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
99.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify221.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

352 → 352

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5061	21039

prune1.4s (8.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	349	3	352
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	354	6	360

Merged error: 2.5b

Counts

360 → 6

Compiler

Compiled 31134 to 13470 computations (56.7% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 i (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
0.2b	(/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
0.2b	(/.f64 (+.f64 (.f64 alpha 1/4) (+.f64 (.f64 i 1/2) (.f64 beta 1/4))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
0.3b	(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite182.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

405×	`*-un-lft-identity_binary64_2487`
342×	`times-frac_binary64_2493`
177×	`add-sqr-sqrt_binary64_2509`
152×	`add-cube-cbrt_binary64_2522`
136×	`distribute-lft-out_binary64_2438`
90×	`associate-r_binary64_2427`
29×	`associate-/l*_binary64_2432`
26×	`associate-/r/_binary64_2433`
22×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
14×	`associate-/r*_binary64_2431` `flip-+_binary64_2461` `flip3-+_binary64_2490`
13×	`div-inv_binary64_2484`
8×	`difference-of-squares_binary64_2456` `div-exp_binary64_2538` `cbrt-undiv_binary64_2521`
6×	`pow1_binary64_2548`
5×	`associate-/l/_binary64_2434`
4×	`difference-of-sqr-1_binary64_2457` `distribute-lft-out--_binary64_2439` `add-log-exp_binary64_2526`
3×	`unswap-sqr_binary64_2455` `prod-exp_binary64_2536` `frac-2neg_binary64_2498` `clear-num_binary64_2486` `cbrt-unprod_binary64_2520` `associate-l_binary64_2428`
1×	`flip--_binary64_2462` `-commutative_binary64_2418` `pow-prod-down_binary64_2558` `associate-r/_binary64_2429` `flip3--_binary64_2491`

Counts

4 → 324

Calls

4 calls:

50.0ms	(.f64 i (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
27.0ms	(/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
20.0ms	(/.f64 (+.f64 (.f64 alpha 1/4) (+.f64 (.f64 i 1/2) (.f64 beta 1/4))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
14.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series590.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(.f64 i (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
157.0ms	(/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
116.0ms	(/.f64 (+.f64 (.f64 alpha 1/4) (+.f64 (.f64 i 1/2) (.f64 beta 1/4))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
104.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify173.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4932	15019
1	4932	15019

prune2.3s (15.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	330	6	336
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	332	10	342

Merged error: 2.4b

Counts

342 → 10

Compiler

Compiled 53128 to 30245 computations (43.1% saved)

regimes173.0ms (1.1%)

Compiler: Compiled 2112 to 1185 computations (43.9% saved)

bsearch106.0ms (0.7%)

Steps

Iters	Range		Point
7	2.8076895841586733e+150	8.749287135151516e+151	5.193139048227797e+150
7	9.598822262776831e+127	1.262452854391747e+130	9.537261936518884e+128
10	4.097258852272462e+80	2.1527236044154613e+90	2.6436317829303763e+83

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	150
1	72	150

end0.0ms (0%)

sample1.4s (9%)

Algorithm

1×

intervals

Results

617.0ms	8000×	body	128	valid
182.0ms	8000×	pre	128	true

Compiler

Compiled 865 to 488 computations (43.6% saved)

Details

analyze40.0ms (0.3%)

sample40.0ms (0.3%)

simplify194.0ms (1.2%)

prune4.0ms (0%)

localize19.0ms (0.1%)

rewrite164.0ms (1.1%)

series3.6s (23.4%)

simplify151.0ms (1%)

prune1.3s (8.3%)

localize18.0ms (0.1%)

rewrite135.0ms (0.9%)

series947.0ms (6.1%)

simplify160.0ms (1%)

prune1.1s (7.3%)

localize18.0ms (0.1%)

rewrite161.0ms (1%)

series849.0ms (5.5%)

simplify221.0ms (1.4%)

prune1.4s (8.7%)

localize20.0ms (0.1%)

rewrite182.0ms (1.2%)

series590.0ms (3.8%)

simplify173.0ms (1.1%)

prune2.3s (15.1%)

regimes173.0ms (1.1%)

bsearch106.0ms (0.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.4s (9%)

Profiling