Details

analyze239.0ms (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

Symmetry

(sort alpha beta)

Compiler

Compiled 63 to 34 computations (46% saved)

sample51.0ms (0.1%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify44.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5395	79

prune7.0ms (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

55.8b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize17.0ms (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))
47.8b	(/.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))))

rewrite1.3s (2%)

Algorithm

1×	rewrite-expression-head

Error

39.5b

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×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `associate-*l/_binary64_2408`
19×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499`
16×	`pow1_binary64_2526`
14×	`associate-/l*_binary64_2410` `difference-of-sqr-1_binary64_2435`
9×	`div-inv_binary64_2462` `associate-/l/_binary64_2412`
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×	`frac-2neg_binary64_2476` `clear-num_binary64_2464` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `*-commutative_binary64_2396`
1×	`flip3--_binary64_2469` `flip--_binary64_2440` `pow2_binary64_2546` `pow-prod-up_binary64_2535` `pow-plus_binary64_2528` `pow-sqr_binary64_2438` `unswap-sqr_binary64_2433`

Counts

4 → 228

Calls

4 calls:

45.0ms	(/.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))
26.0ms	(/.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))))
14.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
13.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))

Compiler

Compiled 17673 to 6571 computations (62.8% saved)

series13.9s (21.2%)

Error

11.3b

Counts

4 → 94

Calls

4 calls:

11.4s	(/.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))
982.0ms	(/.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))))
785.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
376.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 20323 to 13805 computations (32.1% saved)

simplify212.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

322 → 322

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5620	24882

prune971.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	315	7	322
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	316	7	323

Error

8.8b

Counts

323 → 7

Compiler

Compiled 16272 to 7228 computations (55.6% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

8.8b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 8.8b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune14.0ms (0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Error

8.8b

Counts

7 → 7

Compiler

Compiled 311 to 183 computations (41.2% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1))
0.3b	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
36.4b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
36.9b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

rewrite1.3s (2%)

Algorithm

1×	rewrite-expression-head

Error

8.7b

Rules

376×	`*-un-lft-identity_binary64_2465`
342×	`times-frac_binary64_2471`
205×	`add-sqr-sqrt_binary64_2487`
129×	`add-cube-cbrt_binary64_2500`
91×	`distribute-lft-out_binary64_2416`
38×	`associate-/r/_binary64_2411` `difference-of-squares_binary64_2434` `distribute-lft-out--_binary64_2417`
32×	`associate-/l*_binary64_2410`
25×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
21×	`associate-/r*_binary64_2409`
20×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
19×	`div-inv_binary64_2462` `difference-of-sqr-1_binary64_2435`
11×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499`
6×	`associate-/l/_binary64_2412`
4×	`pow1_binary64_2526` `add-log-exp_binary64_2504` `frac-2neg_binary64_2476` `clear-num_binary64_2464`
2×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `associate-*r/_binary64_2407`
1×	`flip3--_binary64_2469` `flip--_binary64_2440`

Counts

4 → 333

Calls

4 calls:

22.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1))
20.0ms	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
15.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
10.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

Compiler

Compiled 17784 to 8516 computations (52.1% saved)

series5.5s (8.5%)

Error

8.5b

Counts

4 → 97

Calls

4 calls:

2.8s	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1))
1.6s	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
524.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
320.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 19118 to 12925 computations (32.4% saved)

simplify221.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

430 → 430

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5124	27488

prune1.3s (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	424	6	430
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	428	9	437

Error

8.5b

Counts

437 → 9

Compiler

Compiled 20825 to 10156 computations (51.2% saved)

localize29.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)) (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))
0.3b	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
36.4b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
36.9b	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))

rewrite1.1s (1.8%)

Algorithm

1×	rewrite-expression-head

Error

8.4b

Rules

315×	`*-un-lft-identity_binary64_2465`
252×	`times-frac_binary64_2471`
105×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
101×	`distribute-lft-out_binary64_2416`
31×	`associate-/r/_binary64_2411` `associate-/r*_binary64_2409`
25×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
19×	`associate-/l*_binary64_2410` `distribute-lft-out--_binary64_2417`
18×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
16×	`div-inv_binary64_2462`
11×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499`
7×	`associate-/l/_binary64_2412`
4×	`pow1_binary64_2526` `add-log-exp_binary64_2504` `frac-2neg_binary64_2476` `clear-num_binary64_2464`
2×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `associate-*r/_binary64_2407`
1×	`associate-+r-_binary64_2399` `div-sub_binary64_2470`

Counts

4 → 277

Calls

4 calls:

22.0ms	(/.f64 (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)) (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))
20.0ms	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
12.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
10.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))

Compiler

Compiled 15781 to 7933 computations (49.7% saved)

series4.9s (7.5%)

Error

8.5b

Counts

4 → 99

Calls

4 calls:

2.1s	(/.f64 (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)) (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))
1.6s	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
525.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))
323.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 19981 to 13161 computations (34.1% saved)

simplify190.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5523	22631

prune1.4s (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	372	4	376
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	376	9	385

Error

8.4b

Counts

385 → 9

Compiler

Compiled 19855 to 9971 computations (49.8% saved)

regimes30.4s (46.6%)

Accuracy

Total 3.9b remaining (33.3%)

Threshold costs 0b (0%)

Compiler

Compiled 292996 to 180404 computations (38.4% saved)

bsearch217.0ms (0.3%)

Steps

Iters	Range		Point
7	9.073204483351882e+137	1.5019809588951115e+140	9.287113942396901e+137
6	4.407309740674861e+95	3.5695578754989237e+96	3.5191541943214098e+96
4	2.2956826746031863e+62	4.154704606333708e+62	3.84695951150349e+62

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	78	236
1	78	236

end25.0ms (0%)

Compiler: Compiled 474 to 264 computations (44.3% saved)

sample1.8s (2.7%)

Algorithm

1×

intervals

Results

666.0ms	8000×	body	128	valid
176.0ms	8000×	pre	128	true

Compiler

Compiled 794 to 486 computations (38.8% saved)

Details

analyze239.0ms (0.4%)

sample51.0ms (0.1%)

simplify44.0ms (0.1%)

prune7.0ms (0%)

localize17.0ms (0%)

rewrite1.3s (2%)

series13.9s (21.2%)

simplify212.0ms (0.3%)

prune971.0ms (1.5%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0%)

prune14.0ms (0%)

localize19.0ms (0%)

rewrite1.3s (2%)

series5.5s (8.5%)

simplify221.0ms (0.3%)

prune1.3s (2%)

localize29.0ms (0%)

rewrite1.1s (1.8%)

series4.9s (7.5%)

simplify190.0ms (0.3%)

prune1.4s (2.1%)

regimes30.4s (46.6%)

bsearch217.0ms (0.3%)

simplify4.0ms (0%)

end25.0ms (0%)

sample1.8s (2.7%)

Profiling