Details

analyze5.0ms (0%)

Algorithm

1×

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

Compiler

Compiled 42 to 29 computations (31% saved)

sample34.0ms (0.3%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify420.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (263.0ms)

Iter	Nodes	Cost
0	5111	37

prune9.0ms (0.1%)

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

Merged error: 2.1b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize12.0ms (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 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
7.7b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
12.0b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite113.0ms (1%)

Algorithm

1×	rewrite-expression-head

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×	`associate-*l/_binary64_2408` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
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×	`unswap-sqr_binary64_2433` `div-inv_binary64_2462`
2×	`*-commutative_binary64_2396` `clear-num_binary64_2464` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536`
1×	`distribute-lft-in_binary64_2414` `pow-plus_binary64_2528` `distribute-rgt-in_binary64_2415` `pow2_binary64_2546` `pow-sqr_binary64_2438` `pow-prod-up_binary64_2535`

Counts

4 → 158

Calls

4 calls:

30.0ms	(/.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)))
26.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
20.0ms	(*.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)))

series552.0ms (5%)

Counts

4 → 12

Calls

4 calls:

230.0ms	(/.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)))
194.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
94.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
34.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify89.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4982	3959
1	4982	3959

prune289.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	160	10	170
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	162	10	172

Merged error: 0.0b

Counts

172 → 10

Compiler

Compiled 5392 to 3509 computations (34.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
0.1b	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
7.7b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))

rewrite213.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

826×	`*-un-lft-identity_binary64_2465`
508×	`times-frac_binary64_2471`
374×	`distribute-lft-out_binary64_2416`
191×	`add-sqr-sqrt_binary64_2487`
182×	`add-cube-cbrt_binary64_2500`
136×	`associate-r_binary64_2405`
34×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
31×	`associate-/l*_binary64_2410`
30×	`associate-/r/_binary64_2411`
20×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
15×	`associate-/r*_binary64_2409` `div-inv_binary64_2462`
14×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516`
8×	`associate-/l/_binary64_2412`
6×	`pow1_binary64_2526` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
4×	`associate-l/_binary64_2408` `add-log-exp_binary64_2504` `frac-times_binary64_2475` `associate-l*_binary64_2406`
3×	`clear-num_binary64_2464` `unswap-sqr_binary64_2433` `frac-2neg_binary64_2476`
2×	`associate-*r/_binary64_2407`
1×	`*-commutative_binary64_2396` `pow-prod-down_binary64_2536`

Counts

4 → 422

Calls

4 calls:

60.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))
42.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
23.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

series587.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
203.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))
103.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
53.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

simplify163.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

434 → 434

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4941	12598
1	4941	12598

prune1.0s (9.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	431	3	434
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	437	7	444

Merged error: 0b

Counts

444 → 7

Compiler

Compiled 15515 to 9817 computations (36.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))) (+.f64 alpha (+.f64 beta 3)))
3.1b	(*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))
4.6b	(.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1))))

rewrite262.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

783×	`*-un-lft-identity_binary64_2465`
491×	`times-frac_binary64_2471`
354×	`distribute-lft-out_binary64_2416`
192×	`add-sqr-sqrt_binary64_2487`
174×	`add-cube-cbrt_binary64_2500`
143×	`associate-l_binary64_2406`
52×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482`
40×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
34×	`frac-times_binary64_2475`
28×	`associate-/r/_binary64_2411`
27×	`associate-/l*_binary64_2410`
24×	`associate-*r/_binary64_2407`
18×	`associate-/l/_binary64_2412`
17×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
14×	`div-inv_binary64_2462`
11×	`associate-*l/_binary64_2408` `sqrt-prod_binary64_2481` `pow1_binary64_2526`
10×	`associate-/r*_binary64_2409`
8×	`associate-r_binary64_2405`
6×	`unswap-sqr_binary64_2433`
4×	`add-log-exp_binary64_2504` `pow-prod-down_binary64_2536`
2×	`*-commutative_binary64_2396` `clear-num_binary64_2464` `frac-2neg_binary64_2476`

Counts

4 → 440

Calls

4 calls:

56.0ms	(*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))
51.0ms	(/.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))) (+.f64 alpha (+.f64 beta 3)))
44.0ms	(.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1))))
23.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))

series720.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

230.0ms	(/.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))) (+.f64 alpha (+.f64 beta 3)))
209.0ms	(.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1))))
178.0ms	(*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))
102.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))

simplify202.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4941	15228
1	4941	15228

prune1.4s (12.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	452	0	452
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	452	7	459

Merged error: 0b

Counts

459 → 7

Compiler

Compiled 19019 to 12704 computations (33.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
0.2b	(pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)
7.7b	(*.f64 (+.f64 alpha 1) (/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)) (+.f64 (+.f64 alpha beta) 2)))
9.6b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3))

rewrite329.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

958×	`*-un-lft-identity_binary64_2465`
599×	`times-frac_binary64_2471`
428×	`distribute-lft-out_binary64_2416`
354×	`cbrt-prod_binary64_2496`
311×	`associate-r_binary64_2405`
245×	`add-sqr-sqrt_binary64_2487`
221×	`add-cube-cbrt_binary64_2500`
184×	`cube-prod_binary64_2493` `unpow-prod-down_binary64_2544`
32×	`associate-/r/_binary64_2411`
21×	`add-exp-log_binary64_2503`
20×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
19×	`add-cbrt-cube_binary64_2501`
16×	`div-inv_binary64_2462`
8×	`unswap-sqr_binary64_2433` `sqr-pow_binary64_2437`
7×	`unpow3_binary64_2531` `cube-mult_binary64_2495` `pow1_binary64_2526`
6×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516`
5×	`associate-/r*_binary64_2409` `associate-/l/_binary64_2412`
4×	`associate-l/_binary64_2408` `add-log-exp_binary64_2504` `frac-times_binary64_2475` `prod-exp_binary64_2514` `associate-l*_binary64_2406` `cbrt-unprod_binary64_2498`
3×	`pow-unpow_binary64_2542`
2×	`rem-cube-cbrt_binary64_2488` `associate-*r/_binary64_2407` `pow-exp_binary64_2533` `cube-div_binary64_2494`
1×	`-commutative_binary64_2396` `clear-num_binary64_2464` `cbrt-div_binary64_2497` `pow-to-exp_binary64_2534` `pow1/3_binary64_2547` `pow-pow_binary64_2537` `frac-2neg_binary64_2476` `rem-cbrt-cube_binary64_2489` `pow-prod-down_binary64_2536` `associate-/l_binary64_2410`

Counts

4 → 515

Calls

4 calls:

120.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)) (+.f64 (+.f64 alpha beta) 2)))
64.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
18.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3))
15.0ms	(pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)

series595.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
199.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)) (+.f64 (+.f64 alpha beta) 2)))
117.0ms	(pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3)
51.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) 3))

simplify171.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

527 → 527

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5063	13022

prune1.5s (13.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	527	0	527
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	527	7	534

Merged error: 0b

Counts

534 → 7

Compiler

Compiled 20133 to 13054 computations (35.2% saved)

regimes484.0ms (4.4%)

Compiler: Compiled 3918 to 3041 computations (22.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	24	37

end0.0ms (0%)

sample1.8s (16.3%)

Algorithm

1×

intervals

Results

484.0ms	8000×	body	128	valid
142.0ms	8000×	pre	128	true

Compiler

Compiled 1313 to 1019 computations (22.4% saved)

Details

analyze5.0ms (0%)

sample34.0ms (0.3%)

simplify420.0ms (3.8%)

prune9.0ms (0.1%)

localize12.0ms (0.1%)

rewrite113.0ms (1%)

series552.0ms (5%)

simplify89.0ms (0.8%)

prune289.0ms (2.6%)

localize15.0ms (0.1%)

rewrite213.0ms (1.9%)

series587.0ms (5.4%)

simplify163.0ms (1.5%)

prune1.0s (9.2%)

localize15.0ms (0.1%)

rewrite262.0ms (2.4%)

series720.0ms (6.6%)

simplify202.0ms (1.8%)

prune1.4s (12.5%)

localize15.0ms (0.1%)

rewrite329.0ms (3%)

series595.0ms (5.4%)

simplify171.0ms (1.6%)

prune1.5s (13.7%)

regimes484.0ms (4.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (16.3%)

Profiling