Details

analyze46.0ms (0.1%)

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)

sample44.0ms (0.1%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify131.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

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

Error

55.0b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b	(*.f64 i (+.f64 (+.f64 alpha beta) i))
0.0b	(*.f64 i (+.f64 (+.f64 alpha beta) i))
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))))
34.4b	(/.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))
47.3b	(/.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))))

rewrite162.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`times-frac_binary64_2408`
66×	`flip3-+_binary64_2405` `flip-+_binary64_2376` `associate-/r/_binary64_2348`
61×	`add-exp-log_binary64_2440` `add-cbrt-cube_binary64_2438`
46×	`add-sqr-sqrt_binary64_2424`
44×	`*-un-lft-identity_binary64_2402` `frac-times_binary64_2412`
34×	`associate-*r/_binary64_2344`
30×	`add-cube-cbrt_binary64_2437`
28×	`difference-of-squares_binary64_2371`
22×	`cbrt-unprod_binary64_2435` `prod-exp_binary64_2451` `associate-*l/_binary64_2345`
19×	`cbrt-undiv_binary64_2436` `div-exp_binary64_2453`
16×	`pow1_binary64_2463`
14×	`associate-/l*_binary64_2347` `difference-of-sqr-1_binary64_2372`
9×	`associate-/l/_binary64_2349` `div-inv_binary64_2399`
7×	`associate-/r*_binary64_2346`
6×	`associate-r_binary64_2342`
4×	`pow-prod-down_binary64_2473` `associate-l_binary64_2343` `add-log-exp_binary64_2441`
3×	`swap-sqr_binary64_2369`
2×	`clear-num_binary64_2401` `*-commutative_binary64_2333` `distribute-rgt-in_binary64_2352` `frac-2neg_binary64_2413` `distribute-lft-in_binary64_2351`
1×	`pow-plus_binary64_2465` `unswap-sqr_binary64_2370` `pow2_binary64_2483` `flip--_binary64_2377` `flip3--_binary64_2406` `pow-prod-up_binary64_2472` `pow-sqr_binary64_2375`

Counts

4 → 228

Calls

8 calls:

47.0ms	(/.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))
28.0ms	(/.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))))
15.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
14.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
0.0ms	(*.f64 i (+.f64 (+.f64 alpha beta) i))

series17.0s (40.7%)

Counts

4 → 106

Calls

4 calls:

15.2s	(/.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))
1.1s	(/.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))))
515.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
268.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 23710 to 16960 computations (28.5% saved)

simplify287.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

334 → 334

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5247	40131

prune2.2s (5.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	327	7	334
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	327	8	335

Error

9.0b

Counts

335 → 8

Compiler

Compiled 34468 to 15565 computations (54.8% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune11.0ms (0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	1	1
Total	8	8

Error

9.0b

Counts

8 → 8

Compiler

Compiled 277 to 158 computations (43% saved)

localize22.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
0.2b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1)) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1)))
0.0b	(*.f64 i (+.f64 (+.f64 alpha beta) i))
0.0b	(*.f64 i (+.f64 (+.f64 alpha beta) i))
0.3b	(/.f64 (/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.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 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
33.3b	(/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
33.8b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite136.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64_2408`
174×	`*-un-lft-identity_binary64_2402`
170×	`add-sqr-sqrt_binary64_2424`
106×	`add-cube-cbrt_binary64_2437`
34×	`associate-/r/_binary64_2348`
32×	`difference-of-squares_binary64_2371`
28×	`associate-/l*_binary64_2347`
25×	`add-exp-log_binary64_2440` `add-cbrt-cube_binary64_2438`
18×	`flip3-+_binary64_2405` `flip-+_binary64_2376`
17×	`associate-/r*_binary64_2346` `div-inv_binary64_2399`
16×	`difference-of-sqr-1_binary64_2372` `distribute-lft-out--_binary64_2354`
11×	`cbrt-undiv_binary64_2436` `div-exp_binary64_2453`
10×	`distribute-lft-out_binary64_2353`
6×	`associate-/l/_binary64_2349`
4×	`clear-num_binary64_2401` `pow1_binary64_2463` `frac-2neg_binary64_2413` `add-log-exp_binary64_2441`
2×	`cbrt-unprod_binary64_2435` `prod-exp_binary64_2451` `associate-*r/_binary64_2344`
1×	`flip--_binary64_2377` `flip3--_binary64_2406`

Counts

4 → 268

Calls

8 calls:

25.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
22.0ms	(/.f64 (/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
14.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
14.0ms	(/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
0.0ms	(*.f64 i (+.f64 (+.f64 alpha beta) i))

series4.6s (11%)

Counts

4 → 109

Calls

4 calls:

2.2s	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
1.8s	(/.f64 (/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
363.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
274.0ms	(/.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

Compiler

Compiled 15944 to 10992 computations (31.1% saved)

simplify242.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

377 → 377

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5016	32781

prune1.7s (4.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	372	5	377
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	375	10	385

Error

8.8b

Counts

385 → 10

Compiler

Compiled 35096 to 15917 computations (54.6% saved)

localize22.0ms (0.1%)

Local error

Found 8 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))
0.2b	(.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 i (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1)))
0.0b	(*.f64 i (+.f64 (+.f64 alpha beta) i))
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 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
33.8b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite162.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

360×	`times-frac_binary64_2408`
348×	`*-un-lft-identity_binary64_2402`
225×	`add-sqr-sqrt_binary64_2424`
161×	`add-cube-cbrt_binary64_2437`
79×	`distribute-lft-out_binary64_2353`
44×	`associate-/l*_binary64_2347`
34×	`associate-/r/_binary64_2348`
32×	`difference-of-squares_binary64_2371`
18×	`flip3-+_binary64_2405` `add-exp-log_binary64_2440` `flip-+_binary64_2376` `add-cbrt-cube_binary64_2438`
17×	`associate-/r*_binary64_2346` `div-inv_binary64_2399`
16×	`difference-of-sqr-1_binary64_2372` `distribute-lft-out--_binary64_2354`
8×	`cbrt-undiv_binary64_2436` `div-exp_binary64_2453`
6×	`associate-/l/_binary64_2349`
4×	`clear-num_binary64_2401` `pow1_binary64_2463` `frac-2neg_binary64_2413` `add-log-exp_binary64_2441`
1×	`flip--_binary64_2377` `flip3--_binary64_2406`

Counts

4 → 340

Calls

8 calls:

29.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
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))
14.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
13.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
0.0ms	(*.f64 i (+.f64 (+.f64 alpha beta) i))

series4.8s (11.4%)

Counts

4 → 111

Calls

4 calls:

2.2s	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
1.9s	(/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
361.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 (+.f64 alpha beta) i))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
269.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

Compiler

Compiled 16482 to 11405 computations (30.8% saved)

simplify274.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

451 → 451

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5357	36854

prune2.2s (5.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	447	4	451
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	450	11	461

Error

0.9b

Counts

461 → 11

Compiler

Compiled 40441 to 18698 computations (53.8% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	440	5302
1	440	5302

regimes715.0ms (1.7%)

Accuracy

Total 10.9b remaining (93.7%)

Threshold costs 0b (0%)

Compiler

Compiled 10608 to 5604 computations (47.2% saved)

bsearch69.0ms (0.2%)

Steps

Iters	Range		Point
5	5.559342826120805e+136	1.141060896543889e+137	1.0061247545788429e+137
6	3.8131776227281808e+112	4.738747114894886e+113	3.8854443850165e+112
3	4.696544043742165e+54	5.8456695486281534e+54	4.9120050759082876e+54

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	66	217
1	66	217

end0.0ms (0%)

sample6.9s (16.4%)

Algorithm

1×

intervals

Results

719.0ms	8000×	body	128	valid
194.0ms	8000×	pre	128	true

Compiler

Compiled 10957 to 5773 computations (47.3% saved)

Pareto

-0.32202100054190974

Details

analyze46.0ms (0.1%)

sample44.0ms (0.1%)

simplify131.0ms (0.3%)

prune4.0ms (0%)

localize16.0ms (0%)

rewrite162.0ms (0.4%)

series17.0s (40.7%)

simplify287.0ms (0.7%)

prune2.2s (5.2%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune11.0ms (0%)

localize22.0ms (0.1%)

rewrite136.0ms (0.3%)

series4.6s (11%)

simplify242.0ms (0.6%)

prune1.7s (4.2%)

localize22.0ms (0.1%)

rewrite162.0ms (0.4%)

series4.8s (11.4%)

simplify274.0ms (0.7%)

prune2.2s (5.4%)

simplify62.0ms (0.1%)

regimes715.0ms (1.7%)

bsearch69.0ms (0.2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.9s (16.4%)

Profiling