Details

analyze125.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample40.0ms (0.3%)

Algorithm

1×

intervals

Results

14.0ms	201×	body	128	valid
6.0ms	256×	pre	128	true
5.0ms	21×	body	1024	valid
3.0ms	18×	body	512	valid
2.0ms	14×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify267.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4894	43
1	4894	43

prune3.0ms (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: 26.8b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.3b

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

3.4b

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

20.7b

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite98.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_2493`
47×	`*-un-lft-identity_binary64_2487`
25×	`add-cube-cbrt_binary64_2522` `add-sqr-sqrt_binary64_2509`
17×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
14×	`associate-/r/_binary64_2433`
11×	`distribute-lft-out_binary64_2438` `flip-+_binary64_2461` `flip3-+_binary64_2490`
10×	`associate-/l*_binary64_2432`
9×	`associate-/l/_binary64_2434`
7×	`associate-/r*_binary64_2431` `div-inv_binary64_2484` `div-exp_binary64_2538` `cbrt-undiv_binary64_2521`
5×	`add-log-exp_binary64_2526`
4×	`frac-times_binary64_2497`
3×	`flip--_binary64_2462` `pow1_binary64_2548` `flip3--_binary64_2491`
2×	`associate-l/_binary64_2430` `prod-exp_binary64_2536` `frac-2neg_binary64_2498` `clear-num_binary64_2486` `cbrt-unprod_binary64_2520` `associate-r/_binary64_2429`
1×	`+-commutative_binary64_2417` `sum-log_binary64_2578`

Counts

3 → 111

Calls

3 calls:

37.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

24.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

20.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.4s (9.1%)

Counts

3 → 9

Calls

3 calls:

683.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

593.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

127.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify103.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4935	5261
1	4935	5261

prune861.0ms (5.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 5.8b

Counts

121 → 10

Compiler

Compiled 22664 to 13562 computations (40.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
0.3b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
3.6b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
5.1b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite177.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

321×	`times-frac_binary64_2493`
290×	`*-un-lft-identity_binary64_2487`
211×	`add-sqr-sqrt_binary64_2509`
140×	`add-cube-cbrt_binary64_2522`
90×	`associate-r_binary64_2427`
44×	`distribute-lft-out_binary64_2438`
31×	`difference-of-squares_binary64_2456` `distribute-lft-out--_binary64_2439`
26×	`associate-/l*_binary64_2432`
24×	`associate-/r/_binary64_2433`
20×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
15×	`flip-+_binary64_2461` `flip3-+_binary64_2490`
12×	`div-inv_binary64_2484`
7×	`associate-/r*_binary64_2431` `div-exp_binary64_2538` `cbrt-undiv_binary64_2521`
6×	`pow1_binary64_2548` `add-log-exp_binary64_2526`
4×	`associate-l_binary64_2428`
3×	`unswap-sqr_binary64_2455` `prod-exp_binary64_2536` `div-sub_binary64_2492` `cbrt-unprod_binary64_2520` `associate-/l/_binary64_2434`
2×	`associate-*l/_binary64_2430` `frac-2neg_binary64_2498` `frac-times_binary64_2497` `clear-num_binary64_2486`
1×	`flip--_binary64_2462` `-commutative_binary64_2418` `+-commutative_binary64_2417` `sum-log_binary64_2578` `pow-prod-down_binary64_2558` `associate-r/_binary64_2429` `flip3--_binary64_2491`

Counts

4 → 295

Calls

4 calls:

51.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
32.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
23.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
13.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.7s (11.1%)

Counts

4 → 12

Calls

4 calls:

689.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
586.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
328.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
116.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify156.0ms (1%)

Algorithm

1×	egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4969	13438
1	4969	13438

prune1.1s (6.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	302	5	307
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	306	11	317

Merged error: 5.8b

Counts

317 → 11

Compiler

Compiled 21458 to 12100 computations (43.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
3.6b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
5.1b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
5.1b	(log.f64 (exp.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)))

rewrite163.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64_2493`
151×	`*-un-lft-identity_binary64_2487`
116×	`add-sqr-sqrt_binary64_2509`
90×	`associate-r_binary64_2427`
75×	`add-cube-cbrt_binary64_2522`
22×	`distribute-lft-out_binary64_2438`
16×	`difference-of-squares_binary64_2456` `distribute-lft-out--_binary64_2439`
15×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
12×	`associate-/r/_binary64_2433`
9×	`flip-+_binary64_2461` `flip3-+_binary64_2490`
7×	`pow1_binary64_2548`
6×	`div-inv_binary64_2484` `add-log-exp_binary64_2526`
5×	`associate-/l*_binary64_2432`
4×	`div-exp_binary64_2538` `log-prod_binary64_2573` `associate-l_binary64_2428` `log-pow_binary64_2576` `cbrt-undiv_binary64_2521`
3×	`unswap-sqr_binary64_2455` `prod-exp_binary64_2536` `associate-/r*_binary64_2431` `exp-prod_binary64_2539` `cbrt-unprod_binary64_2520`
2×	`associate-*l/_binary64_2430` `frac-times_binary64_2497` `associate-/l/_binary64_2434`
1×	`flip--_binary64_2462` `-commutative_binary64_2418` `frac-2neg_binary64_2498` `rem-log-exp_binary64_2528` `clear-num_binary64_2486` `div-sub_binary64_2492` `+-commutative_binary64_2417` `sum-log_binary64_2578` `pow-prod-down_binary64_2558` `exp-sum_binary64_2533` `associate-r/_binary64_2429` `flip3--_binary64_2491`

Counts

4 → 184

Calls

4 calls:

49.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
35.0ms	(log.f64 (exp.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)))
32.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
15.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series2.5s (16%)

Counts

4 → 12

Calls

4 calls:

1.1s	(log.f64 (exp.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)))
657.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
566.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
116.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify92.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4990	7173
1	4990	7173

prune497.0ms (3.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	195	12	207

Merged error: 5.7b

Counts

207 → 12

Compiler

Compiled 10185 to 5630 computations (44.7% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.6b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
3.6b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
5.1b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
5.1b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite239.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

294×	`times-frac_binary64_2493`
258×	`*-un-lft-identity_binary64_2487`
188×	`add-sqr-sqrt_binary64_2509`
180×	`associate-r_binary64_2427`
122×	`add-cube-cbrt_binary64_2522`
44×	`distribute-lft-out_binary64_2438`
24×	`difference-of-squares_binary64_2456` `distribute-lft-out--_binary64_2439`
22×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
20×	`associate-/r/_binary64_2433`
16×	`flip-+_binary64_2461` `flip3-+_binary64_2490`
10×	`div-inv_binary64_2484`
8×	`pow1_binary64_2548` `add-log-exp_binary64_2526` `associate-l_binary64_2428`
6×	`unswap-sqr_binary64_2455` `prod-exp_binary64_2536` `cbrt-unprod_binary64_2520` `div-exp_binary64_2538` `cbrt-undiv_binary64_2521`
4×	`associate-*l/_binary64_2430` `frac-times_binary64_2497`
2×	`-commutative_binary64_2418` `+-commutative_binary64_2417` `sum-log_binary64_2578` `pow-prod-down_binary64_2558` `associate-r/_binary64_2429`

Counts

4 → 256

Calls

4 calls:

54.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
51.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
32.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
32.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

series2.5s (16.1%)

Counts

4 → 12

Calls

4 calls:

676.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
671.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
580.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
567.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

simplify130.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5206	10534

prune1.5s (9.7%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	268	12	280

Merged error: 5.7b

Counts

280 → 12

Compiler

Compiled 21816 to 12009 computations (45% saved)

regimes181.0ms (1.2%)

Compiler: Compiled 2248 to 1448 computations (35.6% saved)

bsearch109.0ms (0.7%)

Steps

Iters	Range		Point
8	8.489737402972492e+210	1.3466033699607912e+215	2.9136664706659033e+211
6	7.678961252145001e+85	1.0656915599992308e+87	9.854544423750154e+86
10	24425790.248319037	4.2719404142716026e+17	3193849138179.12

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	77	185
1	77	185

end0.0ms (0%)

sample1.5s (9.8%)

Algorithm

1×

intervals

Results

390.0ms	6458×	body	128	valid
191.0ms	8000×	pre	128	true
159.0ms	665×	body	1024	valid
90.0ms	521×	body	512	valid
38.0ms	320×	body	256	valid
11.0ms	36×	body	2048	valid

Compiler

Compiled 720 to 463 computations (35.7% saved)

Details

analyze125.0ms (0.8%)

sample40.0ms (0.3%)

simplify267.0ms (1.7%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite98.0ms (0.6%)

series1.4s (9.1%)

simplify103.0ms (0.7%)

prune861.0ms (5.6%)

localize14.0ms (0.1%)

rewrite177.0ms (1.1%)

series1.7s (11.1%)

simplify156.0ms (1%)

prune1.1s (6.8%)

localize17.0ms (0.1%)

rewrite163.0ms (1.1%)

series2.5s (16%)

simplify92.0ms (0.6%)

prune497.0ms (3.2%)

localize23.0ms (0.2%)

rewrite239.0ms (1.5%)

series2.5s (16.1%)

simplify130.0ms (0.8%)

prune1.5s (9.7%)

regimes181.0ms (1.2%)

bsearch109.0ms (0.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.5s (9.8%)

Profiling