Details

analyze41.0ms (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)

sample38.0ms (0.3%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify198.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

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: 57.2b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize18.0ms (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)))
0.0b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
41.7b	(/.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))
48.5b	(/.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))))

rewrite173.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`times-frac_binary64_2105`
66×	`flip3-+_binary64_2102` `associate-/r/_binary64_2047` `flip-+_binary64_2073`
61×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
46×	`add-sqr-sqrt_binary64_2120`
44×	`*-un-lft-identity_binary64_2099` `frac-times_binary64_2109`
34×	`associate-*r/_binary64_2043`
30×	`add-cube-cbrt_binary64_2131`
28×	`difference-of-squares_binary64_2068`
22×	`associate-*l/_binary64_2044` `prod-exp_binary64_2145` `cbrt-unprod_binary64_2129`
19×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147`
16×	`pow1_binary64_2157`
14×	`associate-/l*_binary64_2046` `difference-of-sqr-1_binary64_2069`
9×	`associate-/l/_binary64_2048` `div-inv_binary64_2096`
7×	`associate-/r*_binary64_2045`
6×	`associate-r_binary64_2041`
4×	`associate-l_binary64_2042` `add-log-exp_binary64_2135` `pow-prod-down_binary64_2167`
3×	`swap-sqr_binary64_2066`
2×	`distribute-rgt-in_binary64_2051` `*-commutative_binary64_2032` `distribute-lft-in_binary64_2050` `frac-2neg_binary64_2110` `clear-num_binary64_2098`
1×	`pow2_binary64_2177` `pow-plus_binary64_2159` `flip3--_binary64_2103` `flip--_binary64_2074` `unswap-sqr_binary64_2067` `pow-prod-up_binary64_2166` `pow-sqr_binary64_2072`

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))))
21.0ms	(.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))))

series3.7s (26.6%)

Counts

4 → 12

Calls

4 calls:

3.0s	(/.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))
402.0ms	(/.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))))
217.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
104.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify158.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5228	18186

prune736.0ms (5.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	233	7	240
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	234	7	241

Merged error: 38.8b

Counts

241 → 7

Compiler

Compiled 17720 to 6669 computations (62.4% saved)

localize17.0ms (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))
38.4b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
39.3b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite295.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64_2105`
174×	`*-un-lft-identity_binary64_2099`
170×	`add-sqr-sqrt_binary64_2120`
106×	`add-cube-cbrt_binary64_2131`
34×	`associate-/r/_binary64_2047`
32×	`difference-of-squares_binary64_2068`
28×	`associate-/l*_binary64_2046`
25×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
18×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
17×	`associate-/r*_binary64_2045` `div-inv_binary64_2096`
16×	`difference-of-sqr-1_binary64_2069` `distribute-lft-out--_binary64_2053`
11×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147`
10×	`distribute-lft-out_binary64_2052`
6×	`associate-/l/_binary64_2048`
4×	`pow1_binary64_2157` `frac-2neg_binary64_2110` `add-log-exp_binary64_2135` `clear-num_binary64_2098`
2×	`associate-*r/_binary64_2043` `prod-exp_binary64_2145` `cbrt-unprod_binary64_2129`
1×	`flip3--_binary64_2103` `flip--_binary64_2074`

Counts

4 → 268

Calls

4 calls:

160.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
24.0ms	(/.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))
13.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series945.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

390.0ms	(/.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))
216.0ms	(/.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))
210.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
128.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

simplify167.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5091	16880

prune894.0ms (6.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	274	6	280
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	278	9	287

Merged error: 38.7b

Counts

287 → 9

Compiler

Compiled 21368 to 8719 computations (59.2% 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 (+.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))
0.3b	(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
39.3b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite175.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

360×	`times-frac_binary64_2105`
348×	`*-un-lft-identity_binary64_2099`
225×	`add-sqr-sqrt_binary64_2120`
161×	`add-cube-cbrt_binary64_2131`
79×	`distribute-lft-out_binary64_2052`
44×	`associate-/l*_binary64_2046`
34×	`associate-/r/_binary64_2047`
32×	`difference-of-squares_binary64_2068`
18×	`flip3-+_binary64_2102` `add-cbrt-cube_binary64_2132` `flip-+_binary64_2073` `add-exp-log_binary64_2134`
17×	`associate-/r*_binary64_2045` `div-inv_binary64_2096`
16×	`difference-of-sqr-1_binary64_2069` `distribute-lft-out--_binary64_2053`
8×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147`
6×	`associate-/l/_binary64_2048`
4×	`pow1_binary64_2157` `frac-2neg_binary64_2110` `add-log-exp_binary64_2135` `clear-num_binary64_2098`
1×	`flip3--_binary64_2103` `flip--_binary64_2074`

Counts

4 → 340

Calls

4 calls:

29.0ms	(/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
25.0ms	(/.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))
14.0ms	(/.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)))

series844.0ms (6%)

Counts

4 → 12

Calls

4 calls:

372.0ms	(/.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))
216.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
161.0ms	(/.f64 (/.f64 (+.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 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify211.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

352 → 352

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5006	21039

prune1.2s (8.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	349	3	352
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	354	7	361

Merged error: 2.9b

Counts

361 → 7

Compiler

Compiled 26902 to 11346 computations (57.8% 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)))

rewrite188.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

405×	`*-un-lft-identity_binary64_2099`
342×	`times-frac_binary64_2105`
177×	`add-sqr-sqrt_binary64_2120`
152×	`add-cube-cbrt_binary64_2131`
136×	`distribute-lft-out_binary64_2052`
90×	`associate-r_binary64_2041`
29×	`associate-/l*_binary64_2046`
26×	`associate-/r/_binary64_2047`
22×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
14×	`flip3-+_binary64_2102` `associate-/r*_binary64_2045` `flip-+_binary64_2073`
13×	`div-inv_binary64_2096`
8×	`difference-of-squares_binary64_2068` `cbrt-undiv_binary64_2130` `div-exp_binary64_2147`
6×	`pow1_binary64_2157`
5×	`associate-/l/_binary64_2048`
4×	`add-log-exp_binary64_2135` `difference-of-sqr-1_binary64_2069` `distribute-lft-out--_binary64_2053`
3×	`associate-l_binary64_2042` `frac-2neg_binary64_2110` `prod-exp_binary64_2145` `unswap-sqr_binary64_2067` `clear-num_binary64_2098` `cbrt-unprod_binary64_2129`
1×	`associate-r/_binary64_2043` `-commutative_binary64_2032` `pow-prod-down_binary64_2167` `flip3--_binary64_2103` `flip--_binary64_2074`

Counts

4 → 324

Calls

4 calls:

48.0ms	(.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)))
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))
17.0ms	(/.f64 (+.f64 (.f64 alpha 1/4) (+.f64 (.f64 i 1/2) (.f64 beta 1/4))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
17.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series609.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

227.0ms	(.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)))
162.0ms	(/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
119.0ms	(/.f64 (+.f64 (.f64 alpha 1/4) (+.f64 (.f64 i 1/2) (.f64 beta 1/4))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
101.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify168.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4956	14801
1	4956	14801

prune1.4s (9.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	331	5	336
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	333	10	343

Merged error: 2.8b

Counts

343 → 10

Compiler

Compiled 21548 to 11838 computations (45.1% saved)

regimes150.0ms (1.1%)

Compiler: Compiled 1809 to 1086 computations (40% saved)

bsearch22.0ms (0.2%)

Steps

Iters	Range		Point
4	2.0647724486499746e+136	3.096077869614165e+136	3.055689841799785e+136

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	65	210
1	65	210

end0.0ms (0%)

sample1.6s (11.6%)

Algorithm

1×

intervals

Results

701.0ms	8000×	body	128	valid
200.0ms	8000×	pre	128	true

Compiler

Compiled 804 to 466 computations (42% saved)

Details

analyze41.0ms (0.3%)

sample38.0ms (0.3%)

simplify198.0ms (1.4%)

prune4.0ms (0%)

localize18.0ms (0.1%)

rewrite173.0ms (1.2%)

series3.7s (26.6%)

simplify158.0ms (1.1%)

prune736.0ms (5.2%)

localize17.0ms (0.1%)

rewrite295.0ms (2.1%)

series945.0ms (6.7%)

simplify167.0ms (1.2%)

prune894.0ms (6.4%)

localize18.0ms (0.1%)

rewrite175.0ms (1.2%)

series844.0ms (6%)

simplify211.0ms (1.5%)

prune1.2s (8.5%)

localize20.0ms (0.1%)

rewrite188.0ms (1.3%)

series609.0ms (4.3%)

simplify168.0ms (1.2%)

prune1.4s (9.8%)

regimes150.0ms (1.1%)

bsearch22.0ms (0.2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.6s (11.6%)

Profiling