Details

analyze364.0ms (1.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6300	74
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Symmetry

(sort alpha beta)

Compiler

Compiled 42 to 29 computations (31% saved)

sample42.0ms (0.2%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify238.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (232.0ms)

Iter	Nodes	Cost
0	5023	37

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

1.3b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1)
0.0b	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1)))
0.1b	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
2.7b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))

rewrite2.4s (8.8%)

Algorithm

1×	rewrite-expression-head

Error

1.2b

Rules

804×	`times-frac_binary64_2471`
586×	`*-un-lft-identity_binary64_2465`
340×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
123×	`distribute-lft-out_binary64_2416`
82×	`associate-/l*_binary64_2410`
54×	`associate-/r/_binary64_2411`
29×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
27×	`div-inv_binary64_2462`
20×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
13×	`add-log-exp_binary64_2504`
10×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `associate-/r*_binary64_2409`
6×	`sum-log_binary64_2556`
4×	`pow1_binary64_2526` `associate-/l/_binary64_2412`
3×	`frac-2neg_binary64_2476` `clear-num_binary64_2464`
1×	`associate-+l+_binary64_2398` `+-commutative_binary64_2395`

Counts

4 → 465

Calls

4 calls:

46.0ms	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
21.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1)))
15.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))
9.0ms	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1)

Compiler

Compiled 30783 to 18159 computations (41% saved)

series2.2s (7.9%)

Error

0.1b

Counts

4 → 66

Calls

4 calls:

1.1s	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
486.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1)))
194.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))
53.0ms	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1)

Compiler

Compiled 14120 to 10951 computations (22.4% saved)

simplify313.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

531 → 531

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5022	37357

prune2.2s (7.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	523	8	531
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	524	9	533

Error

0.1b

Counts

533 → 9

Compiler

Compiled 30748 to 16878 computations (45.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha))) (+.f64 alpha (+.f64 beta 3)))
0.0b	(/.f64 1 (+.f64 2 (+.f64 beta alpha)))
0.1b	(.f64 (/.f64 1 (+.f64 2 (+.f64 beta alpha))) (/.f64 (/.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha))) (+.f64 alpha (+.f64 beta 3))))
2.7b	(/.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha)))

rewrite1.4s (5.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

868×	`*-un-lft-identity_binary64_2465`
545×	`times-frac_binary64_2471`
388×	`distribute-lft-out_binary64_2416`
228×	`add-sqr-sqrt_binary64_2487`
198×	`add-cube-cbrt_binary64_2500`
136×	`associate-r_binary64_2405`
54×	`add-exp-log_binary64_2503`
34×	`add-cbrt-cube_binary64_2501`
33×	`associate-/l*_binary64_2410`
32×	`associate-/r/_binary64_2411`
24×	`div-exp_binary64_2516`
21×	`associate-l_binary64_2406`
17×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
16×	`div-inv_binary64_2462`
15×	`associate-/r*_binary64_2409`
14×	`cbrt-undiv_binary64_2499`
12×	`prod-exp_binary64_2514`
9×	`unswap-sqr_binary64_2433`
7×	`pow1_binary64_2526`
6×	`cbrt-unprod_binary64_2498`
4×	`add-log-exp_binary64_2504` `1-exp_binary64_2509` `rec-exp_binary64_2515`
3×	`frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/l/_binary64_2412`
1×	`pow-prod-down_binary64_2536` `frac-times_binary64_2475` `associate-l/_binary64_2408` `associate-r/_binary64_2407` `*-commutative_binary64_2396` `inv-pow_binary64_2550` `pow-flip_binary64_2539`

Counts

4 → 460

Calls

4 calls:

95.0ms	(.f64 (/.f64 1 (+.f64 2 (+.f64 beta alpha))) (/.f64 (/.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha))) (+.f64 alpha (+.f64 beta 3))))
25.0ms	(/.f64 (/.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha))) (+.f64 alpha (+.f64 beta 3)))
15.0ms	(/.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha)))
7.0ms	(/.f64 1 (+.f64 2 (+.f64 beta alpha)))

Compiler

Compiled 21713 to 11455 computations (47.2% saved)

series2.4s (8.7%)

Error

0.1b

Counts

4 → 72

Calls

4 calls:

1.1s	(.f64 (/.f64 1 (+.f64 2 (+.f64 beta alpha))) (/.f64 (/.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha))) (+.f64 alpha (+.f64 beta 3))))
580.0ms	(/.f64 (/.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha))) (+.f64 alpha (+.f64 beta 3)))
190.0ms	(/.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))) (+.f64 2 (+.f64 beta alpha)))
96.0ms	(/.f64 1 (+.f64 2 (+.f64 beta alpha)))

Compiler

Compiled 15724 to 12121 computations (22.9% saved)

simplify240.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

532 → 532

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4969	28750
1	4969	28750

prune1.8s (6.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	530	2	532
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	532	9	541

Error

0.1b

Counts

541 → 9

Compiler

Compiled 27486 to 15181 computations (44.8% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))
0.2b	(/.f64 (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))
2.6b	(sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))
2.6b	(sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))

rewrite404.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

154×	`*-un-lft-identity_binary64_2465`
70×	`times-frac_binary64_2471`
62×	`distribute-lft-out_binary64_2416`
56×	`sqrt-prod_binary64_2481`
48×	`add-sqr-sqrt_binary64_2487`
46×	`add-cube-cbrt_binary64_2500`
14×	`associate-/l*_binary64_2410`
10×	`associate-/r*_binary64_2409`
8×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482`
6×	`pow1_binary64_2526` `flip3-+_binary64_2468` `flip-+_binary64_2439`
4×	`add-log-exp_binary64_2504` `associate-/l/_binary64_2412` `associate-/r/_binary64_2411`
2×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462`

Counts

4 → 158

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))
15.0ms	(/.f64 (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))
8.0ms	(sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))
7.0ms	(sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))

Compiler

Compiled 8434 to 3883 computations (54% saved)

series971.0ms (3.5%)

Error

0.1b

Counts

4 → 48

Calls

4 calls:

300.0ms	(/.f64 (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))
287.0ms	(/.f64 (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))
114.0ms	(sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))
104.0ms	(sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))

Compiler

Compiled 9108 to 6497 computations (28.7% saved)

simplify121.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4965	8388
1	4965	8388

prune543.0ms (2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	206	9	215

Error

0.1b

Counts

215 → 9

Compiler

Compiled 11450 to 6002 computations (47.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
17.9b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite387.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

77×	`*-un-lft-identity_binary64_2465`
34×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `distribute-lft-out_binary64_2416`
24×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
21×	`add-sqr-sqrt_binary64_2487` `associate-r_binary64_2405`
18×	`associate-/r/_binary64_2411`
16×	`frac-times_binary64_2475`
15×	`add-cube-cbrt_binary64_2500`
14×	`times-frac_binary64_2471`
13×	`pow1_binary64_2526`
11×	`swap-sqr_binary64_2432`
10×	`prod-exp_binary64_2514` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `cbrt-unprod_binary64_2498` `associate-*l/_binary64_2408`
9×	`associate-l_binary64_2406`
8×	`associate-*r/_binary64_2407`
7×	`associate-/l/_binary64_2412`
6×	`associate-/r*_binary64_2409`
5×	`associate-/l*_binary64_2410`
4×	`add-log-exp_binary64_2504`
3×	`div-inv_binary64_2462` `unswap-sqr_binary64_2433`
2×	`frac-2neg_binary64_2476` `clear-num_binary64_2464` `pow-prod-down_binary64_2536` `*-commutative_binary64_2396`
1×	`pow2_binary64_2546` `pow-prod-up_binary64_2535` `pow-plus_binary64_2528` `pow-sqr_binary64_2438` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414`

Counts

4 → 158

Calls

4 calls:

27.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
25.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
18.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
15.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 6017 to 3676 computations (38.9% saved)

series2.4s (8.8%)

Error

0.1b

Counts

4 → 72

Calls

4 calls:

1.1s	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
455.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
340.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
133.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 14724 to 11706 computations (20.5% saved)

simplify123.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5134	13209

prune656.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	227	3	230
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	230	9	239

Error

0.0b

Counts

239 → 9

Compiler

Compiled 11685 to 7926 computations (32.2% saved)

regimes1.6s (5.9%)

Accuracy

Total 0.1b remaining (96.1%)

Threshold costs 0.1b (96.1%)

Compiler

Compiled 28399 to 19832 computations (30.2% saved)

bsearch0.0ms (0%)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	24	37

Remove

(sort alpha beta)

Compiler

Compiled 50 to 36 computations (28% saved)

end0.0ms (0%)

sample6.6s (23.9%)

Algorithm

1×

intervals

Results

494.0ms	8000×	body	128	valid
123.0ms	8000×	pre	128	true

Compiler

Compiled 9401 to 6573 computations (30.1% saved)

Details

analyze364.0ms (1.3%)

sample42.0ms (0.2%)

simplify238.0ms (0.9%)

prune5.0ms (0%)

localize12.0ms (0%)

rewrite2.4s (8.8%)

series2.2s (7.9%)

simplify313.0ms (1.1%)

prune2.2s (7.9%)

localize14.0ms (0.1%)

rewrite1.4s (5.2%)

series2.4s (8.7%)

simplify240.0ms (0.9%)

prune1.8s (6.5%)

localize14.0ms (0%)

rewrite404.0ms (1.5%)

series971.0ms (3.5%)

simplify121.0ms (0.4%)

prune543.0ms (2%)

localize14.0ms (0.1%)

rewrite387.0ms (1.4%)

series2.4s (8.8%)

simplify123.0ms (0.4%)

prune656.0ms (2.4%)

regimes1.6s (5.9%)

bsearch0.0ms (0%)

simplify10.0ms (0%)

end0.0ms (0%)

sample6.6s (23.9%)

Profiling