Details

analyze314.0ms (0.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5646	316
0	3	3
1	3	3

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)

sample80.0ms (0.1%)

Algorithm

1×

intervals

Results

43.0ms	256×	body	128	valid
10.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify81.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5395	79

prune8.0ms (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

54.5b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize31.0ms (0%)

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))))
36.5b	(/.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))
46.6b	(/.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))))

rewrite285.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`times-frac_binary64_2471`
66×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-/r/_binary64_2411`
61×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
46×	`add-sqr-sqrt_binary64_2487`
44×	`*-un-lft-identity_binary64_2465` `frac-times_binary64_2475`
34×	`associate-*r/_binary64_2407`
30×	`add-cube-cbrt_binary64_2500`
28×	`difference-of-squares_binary64_2434`
22×	`associate-*l/_binary64_2408` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
19×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516`
16×	`pow1_binary64_2526`
14×	`difference-of-sqr-1_binary64_2435` `associate-/l*_binary64_2410`
9×	`associate-/l/_binary64_2412` `div-inv_binary64_2462`
7×	`associate-/r*_binary64_2409`
6×	`associate-r_binary64_2405`
4×	`add-log-exp_binary64_2504` `pow-prod-down_binary64_2536` `associate-l_binary64_2406`
3×	`swap-sqr_binary64_2432`
2×	`distribute-lft-in_binary64_2414` `*-commutative_binary64_2396` `clear-num_binary64_2464` `distribute-rgt-in_binary64_2415` `frac-2neg_binary64_2476`
1×	`pow-plus_binary64_2528` `flip--_binary64_2440` `unswap-sqr_binary64_2433` `pow2_binary64_2546` `flip3--_binary64_2469` `pow-sqr_binary64_2438` `pow-prod-up_binary64_2535`

Counts

4 → 228

Calls

4 calls:

82.0ms	(/.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))
51.0ms	(/.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))))
25.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
24.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))

series15.0s (19.6%)

Counts

4 → 92

Calls

4 calls:

12.3s	(/.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))
1.4s	(/.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))))
845.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
464.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 15739 to 10997 computations (30.1% saved)

simplify420.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5767	25129

prune2.2s (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	311	9	320
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	312	9	321

Error

9.9b

Counts

321 → 9

Compiler

Compiled 24457 to 10198 computations (58.3% saved)

localize1.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune29.0ms (0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Error

9.9b

Counts

9 → 9

Compiler

Compiled 401 to 225 computations (43.9% saved)

localize38.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.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))
0.1b	(.f64 (/.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)) (/.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)))
35.2b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
35.6b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite444.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64_2471`
200×	`*-un-lft-identity_binary64_2465`
198×	`add-sqr-sqrt_binary64_2487`
117×	`add-cube-cbrt_binary64_2500`
111×	`associate-r_binary64_2405`
74×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
42×	`associate-/r/_binary64_2411` `associate-l_binary64_2406`
35×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516`
30×	`difference-of-squares_binary64_2434`
22×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
21×	`div-inv_binary64_2462`
19×	`distribute-lft-out_binary64_2416`
17×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
15×	`difference-of-sqr-1_binary64_2435` `distribute-lft-out--_binary64_2417`
13×	`associate-/l*_binary64_2410`
10×	`associate-/r*_binary64_2409`
6×	`unswap-sqr_binary64_2433` `pow1_binary64_2526`
5×	`associate-/l/_binary64_2412`
4×	`add-log-exp_binary64_2504`
3×	`associate-*r/_binary64_2407` `clear-num_binary64_2464` `frac-2neg_binary64_2476`
1×	`associate-l/_binary64_2408` `-commutative_binary64_2396` `frac-times_binary64_2475` `flip--_binary64_2440` `pow-prod-down_binary64_2536` `flip3--_binary64_2469`

Counts

4 → 319

Calls

4 calls:

221.0ms	(.f64 (/.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)) (/.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)))
46.0ms	(/.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))
29.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
21.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series14.9s (19.4%)

Counts

4 → 90

Calls

4 calls:

12.6s	(.f64 (/.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)) (/.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)))
1.3s	(/.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))
629.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
447.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

Compiler

Compiled 17592 to 12330 computations (29.9% saved)

simplify508.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

409 → 409

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5454	31209

prune2.9s (3.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	404	5	409
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	407	11	418

Error

9.5b

Counts

418 → 11

Compiler

Compiled 33291 to 14655 computations (56% saved)

localize37.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (/.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))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
0.1b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (/.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)))
35.2b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
35.6b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite374.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

190×	`times-frac_binary64_2471`
152×	`add-sqr-sqrt_binary64_2487`
132×	`*-un-lft-identity_binary64_2465`
111×	`associate-r_binary64_2405`
94×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
83×	`add-cube-cbrt_binary64_2500`
43×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516`
30×	`difference-of-squares_binary64_2434`
25×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
24×	`associate-/r/_binary64_2411`
15×	`difference-of-sqr-1_binary64_2435` `distribute-lft-out--_binary64_2417`
13×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
12×	`div-inv_binary64_2462`
10×	`associate-/r*_binary64_2409`
9×	`associate-l_binary64_2406`
7×	`associate-/l/_binary64_2412`
6×	`pow1_binary64_2526`
5×	`associate-/l*_binary64_2410`
4×	`add-log-exp_binary64_2504` `associate-*r/_binary64_2407`
3×	`clear-num_binary64_2464` `unswap-sqr_binary64_2433` `frac-2neg_binary64_2476`
2×	`associate-*l/_binary64_2408` `frac-times_binary64_2475` `distribute-lft-out_binary64_2416`
1×	`*-commutative_binary64_2396` `flip--_binary64_2440` `pow-prod-down_binary64_2536` `flip3--_binary64_2469`

Counts

4 → 253

Calls

4 calls:

116.0ms	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (/.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)))
94.0ms	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (/.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))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
29.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
21.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series29.0s (37.8%)

Counts

4 → 91

Calls

4 calls:

15.0s	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (/.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)))
12.9s	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (/.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))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
607.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
472.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

Compiler

Compiled 25461 to 18216 computations (28.5% saved)

simplify464.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4982	32151
1	4982	32151

prune2.8s (3.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	341	3	344
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	345	10	355

Error

1.2b

Counts

355 → 10

Compiler

Compiled 31618 to 14164 computations (55.2% saved)

regimes1.5s (1.9%)

Accuracy

Total 8.8b remaining (91.6%)

Threshold costs 0b (0%)

Compiler

Compiled 12912 to 6861 computations (46.9% saved)

bsearch143.0ms (0.2%)

Steps

Iters	Range	Point
6	9.73820724333152e+193	1.0858503186080343e+195	9.93925909258039e+193
7	5.7701757933133484e+181	1.3378708075165643e+184	1.3118580258271777e+184
4	3.5462956141267525e+143	5.182614852116433e+143	3.5774238846229697e+143

Iters

Range

Point

9.73820724333152e+193

1.0858503186080343e+195

9.93925909258039e+193

5.7701757933133484e+181

1.3378708075165643e+184

1.3118580258271777e+184

3.5462956141267525e+143

5.182614852116433e+143

3.5774238846229697e+143

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify24.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	65
1	38	65

Compiler

Compiled 88 to 64 computations (27.3% saved)

end0.0ms (0%)

sample5.1s (6.7%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
316.0ms	8000×	pre	128	true

Compiler

Compiled 3267 to 1745 computations (46.6% saved)

Details

analyze314.0ms (0.4%)

sample80.0ms (0.1%)

simplify81.0ms (0.1%)

prune8.0ms (0%)

localize31.0ms (0%)

rewrite285.0ms (0.4%)

series15.0s (19.6%)

simplify420.0ms (0.5%)

prune2.2s (2.8%)

localize1.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify12.0ms (0%)

prune29.0ms (0%)

localize38.0ms (0%)

rewrite444.0ms (0.6%)

series14.9s (19.4%)

simplify508.0ms (0.7%)

prune2.9s (3.8%)

localize37.0ms (0%)

rewrite374.0ms (0.5%)

series29.0s (37.8%)

simplify464.0ms (0.6%)

prune2.8s (3.6%)

regimes1.5s (1.9%)

bsearch143.0ms (0.2%)

simplify24.0ms (0%)

end0.0ms (0%)

sample5.1s (6.7%)

Profiling