Details

analyze371.0ms (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)

sample38.0ms (0.1%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify232.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (227.0ms)

Iter	Nodes	Cost
0	5023	37

prune6.0ms (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

0.5b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.0b	(.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)))
20.1b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite396.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

77×	`*-un-lft-identity_binary64_1101`
34×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `distribute-lft-out_binary64_1052`
24×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
21×	`add-sqr-sqrt_binary64_1123` `associate-r_binary64_1041`
18×	`associate-/r/_binary64_1047`
16×	`frac-times_binary64_1111`
15×	`add-cube-cbrt_binary64_1136`
14×	`times-frac_binary64_1107`
13×	`pow1_binary64_1162`
11×	`swap-sqr_binary64_1068`
10×	`prod-exp_binary64_1150` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134` `associate-*l/_binary64_1044`
9×	`associate-l_binary64_1042`
8×	`associate-*r/_binary64_1043`
7×	`associate-/l/_binary64_1048`
6×	`associate-/r*_binary64_1045`
5×	`associate-/l*_binary64_1046`
4×	`add-log-exp_binary64_1140`
3×	`div-inv_binary64_1098` `unswap-sqr_binary64_1069`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `pow-prod-down_binary64_1172` `*-commutative_binary64_1032`
1×	`pow2_binary64_1182` `pow-prod-up_binary64_1171` `pow-plus_binary64_1164` `pow-sqr_binary64_1074` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`

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)))
23.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
17.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
14.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 6017 to 3676 computations (38.9% saved)

series2.4s (8.6%)

Error

0.1b

Counts

4 → 66

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)))
468.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
352.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
120.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 14062 to 11184 computations (20.5% saved)

simplify136.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4953	12303
1	4953	12303

prune718.0ms (2.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	217	7	224
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	219	7	226

Error

0.0b

Counts

226 → 7

Compiler

Compiled 11292 to 7687 computations (31.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite1.3s (4.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

826×	`*-un-lft-identity_binary64_1101`
508×	`times-frac_binary64_1107`
374×	`distribute-lft-out_binary64_1052`
191×	`add-sqr-sqrt_binary64_1123`
182×	`add-cube-cbrt_binary64_1136`
136×	`associate-r_binary64_1041`
34×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
31×	`associate-/l*_binary64_1046`
30×	`associate-/r/_binary64_1047`
20×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
15×	`div-inv_binary64_1098` `associate-/r*_binary64_1045`
14×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
8×	`associate-/l/_binary64_1048`
6×	`pow1_binary64_1162` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
4×	`add-log-exp_binary64_1140` `frac-times_binary64_1111` `associate-l/_binary64_1044` `associate-l*_binary64_1042`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `unswap-sqr_binary64_1069`
2×	`associate-*r/_binary64_1043`
1×	`pow-prod-down_binary64_1172` `*-commutative_binary64_1032`

Counts

4 → 422

Calls

4 calls:

53.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))
34.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
20.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))
9.0ms	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 16960 to 11567 computations (31.8% saved)

series2.3s (8.4%)

Error

0.0b

Counts

4 → 64

Calls

4 calls:

1.0s	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
461.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))
348.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))
120.0ms	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 14444 to 11448 computations (20.7% saved)

simplify188.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

486 → 486

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4958	21304
1	4958	21304

prune1.8s (6.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	484	2	486
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	486	7	493

Error

Counts

493 → 7

Compiler

Compiled 21713 to 15093 computations (30.5% saved)

localize195.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))) (+.f64 alpha (+.f64 beta 3)))
0.1b	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
0.1b	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
0.3b	(*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))

rewrite1.7s (6.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

838×	`*-un-lft-identity_binary64_1101`
399×	`times-frac_binary64_1107`
360×	`distribute-lft-out_binary64_1052`
248×	`sqrt-prod_binary64_1117`
224×	`add-sqr-sqrt_binary64_1123`
150×	`add-cube-cbrt_binary64_1136`
127×	`swap-sqr_binary64_1068`
45×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
41×	`associate-l_binary64_1042` `associate-r_binary64_1041`
16×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
15×	`associate-/l/_binary64_1048` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
14×	`associate-/r/_binary64_1047`
13×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `flip3-+_binary64_1104` `flip-+_binary64_1075`
11×	`pow1_binary64_1162`
10×	`frac-times_binary64_1111`
9×	`unswap-sqr_binary64_1069`
7×	`div-inv_binary64_1098` `associate-*r/_binary64_1043`
6×	`associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100`
1×	`pow2_binary64_1182` `pow-prod-down_binary64_1172` `pow-prod-up_binary64_1171` `pow-plus_binary64_1164` `pow-sqr_binary64_1074` `*-commutative_binary64_1032`

Counts

4 → 414

Calls

4 calls:

48.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))
34.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))) (+.f64 alpha (+.f64 beta 3)))
14.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
10.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 19079 to 14248 computations (25.3% saved)

series1.9s (7%)

Error

Counts

4 → 56

Calls

4 calls:

1.1s	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))) (+.f64 alpha (+.f64 beta 3)))
353.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))
124.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
114.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 11964 to 9521 computations (20.4% saved)

simplify188.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

470 → 470

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5969	20352

prune2.1s (7.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	470	0	470
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	470	7	477

Error

Counts

477 → 7

Compiler

Compiled 21283 to 15494 computations (27.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))
0.0b	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
0.1b	(/.f64 (+.f64 (+.f64 beta 3) alpha) (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))))
0.3b	(/.f64 1 (/.f64 (+.f64 (+.f64 beta 3) alpha) (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))))

rewrite2.0s (7.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

821×	`*-un-lft-identity_binary64_1101`
550×	`times-frac_binary64_1107`
365×	`distribute-lft-out_binary64_1052`
203×	`add-sqr-sqrt_binary64_1123`
194×	`add-cube-cbrt_binary64_1136`
136×	`associate-r_binary64_1041`
82×	`add-exp-log_binary64_1139`
52×	`add-cbrt-cube_binary64_1137` `associate-/r/_binary64_1047`
44×	`div-exp_binary64_1152`
34×	`associate-/l*_binary64_1046`
26×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
25×	`cbrt-undiv_binary64_1135`
20×	`associate-/r*_binary64_1045`
19×	`div-inv_binary64_1098`
15×	`prod-exp_binary64_1150`
12×	`frac-times_binary64_1111` `associate-*l/_binary64_1044`
9×	`cbrt-unprod_binary64_1134`
7×	`pow1_binary64_1162`
6×	`associate-*r/_binary64_1043`
5×	`1-exp_binary64_1145` `rec-exp_binary64_1151`
4×	`add-log-exp_binary64_1140` `associate-l_binary64_1042`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `unswap-sqr_binary64_1069`
1×	`inv-pow_binary64_1186` `pow-flip_binary64_1175` `pow-prod-down_binary64_1172` `*-commutative_binary64_1032`

Counts

4 → 469

Calls

4 calls:

52.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
40.0ms	(/.f64 (+.f64 (+.f64 beta 3) alpha) (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))))
38.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 beta 3) alpha) (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))))
27.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))

Compiler

Compiled 20007 to 14657 computations (26.7% saved)

series2.8s (10%)

Error

Counts

4 → 70

Calls

4 calls:

1.1s	(/.f64 1 (/.f64 (+.f64 (+.f64 beta 3) alpha) (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))))
459.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
404.0ms	(/.f64 (+.f64 (+.f64 beta 3) alpha) (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))))
347.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))

Compiler

Compiled 17078 to 13584 computations (20.5% saved)

simplify277.0ms (1%)

Algorithm

1×	egg-herbie

Counts

539 → 539

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4952	26331
1	4952	26331

prune2.3s (8.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	539	0	539
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	539	7	546

Error

Counts

546 → 7

Compiler

Compiled 25045 to 17907 computations (28.5% saved)

regimes620.0ms (2.2%)

Accuracy

Total 0.1b remaining (90.8%)

Threshold costs 0.1b (90.8%)

Compiler

Compiled 10274 to 7796 computations (24.1% 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

Compiler

Compiled 50 to 36 computations (28% saved)

end0.0ms (0%)

sample3.5s (12.8%)

Algorithm

1×

intervals

Results

508.0ms	8000×	body	128	valid
145.0ms	8000×	pre	128	true

Compiler

Compiled 3467 to 2629 computations (24.2% saved)

Details

analyze371.0ms (1.3%)

sample38.0ms (0.1%)

simplify232.0ms (0.8%)

prune6.0ms (0%)

localize17.0ms (0.1%)

rewrite396.0ms (1.4%)

series2.4s (8.6%)

simplify136.0ms (0.5%)

prune718.0ms (2.6%)

localize14.0ms (0.1%)

rewrite1.3s (4.8%)

series2.3s (8.4%)

simplify188.0ms (0.7%)

prune1.8s (6.3%)

localize195.0ms (0.7%)

rewrite1.7s (6.3%)

series1.9s (7%)

simplify188.0ms (0.7%)

prune2.1s (7.6%)

localize14.0ms (0.1%)

rewrite2.0s (7.3%)

series2.8s (10%)

simplify277.0ms (1%)

prune2.3s (8.5%)

regimes620.0ms (2.2%)

bsearch0.0ms (0%)

simplify10.0ms (0%)

end0.0ms (0%)

sample3.5s (12.8%)

Profiling