Details

analyze374.0ms (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)

simplify244.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (233.0ms)

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

1.1b

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) 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)))
16.4b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite410.0ms (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:

26.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
25.0ms	(/.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)))
16.0ms	(/.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 (8.2%)

Error

0.0b

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)))
459.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
336.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
126.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 14724 to 11706 computations (20.5% saved)

simplify125.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5134	13209

prune688.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	220	10	230
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	222	10	232

Error

0.0b

Counts

232 → 10

Compiler

Compiled 12091 to 8225 computations (32% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite1.4s (4.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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:

52.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))
33.0ms	(/.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)))
19.0ms	(/.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)

series2.6s (8.8%)

Error

0.0b

Counts

4 → 72

Calls

4 calls:

1.2s	(/.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)))
456.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))
334.0ms	(/.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 15272 to 12092 computations (20.8% saved)

simplify201.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

494 → 494

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5227	22380

prune2.0s (6.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	491	3	494
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	497	7	504

Error

0.0b

Counts

504 → 7

Compiler

Compiled 22522 to 15607 computations (30.7% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 (+.f64 beta 2) alpha))) (/.f64 (/.f64 (+.f64 1 beta) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
0.0b	(*.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 (+.f64 beta 2) alpha)))
0.1b	(/.f64 (.f64 (.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 (+.f64 beta 2) alpha))) (/.f64 (/.f64 (+.f64 1 beta) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
0.7b	(/.f64 (+.f64 1 beta) (sqrt.f64 (+.f64 alpha (+.f64 2 beta))))

rewrite2.7s (9.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

797×	`*-un-lft-identity_binary64_1101`
614×	`times-frac_binary64_1107`
375×	`sqrt-prod_binary64_1117`
331×	`associate-r_binary64_1041`
314×	`distribute-lft-out_binary64_1052`
255×	`add-sqr-sqrt_binary64_1123`
248×	`add-cube-cbrt_binary64_1136`
152×	`add-exp-log_binary64_1139`
94×	`add-cbrt-cube_binary64_1137`
61×	`div-exp_binary64_1152`
58×	`prod-exp_binary64_1150`
36×	`cbrt-undiv_binary64_1135`
32×	`cbrt-unprod_binary64_1134`
24×	`associate-/r/_binary64_1047`
23×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
22×	`frac-times_binary64_1111` `associate-*l/_binary64_1044`
20×	`sqrt-div_binary64_1118`
15×	`associate-/l/_binary64_1048`
13×	`associate-/r*_binary64_1045`
12×	`div-inv_binary64_1098`
11×	`pow1_binary64_1162`
7×	`1-exp_binary64_1145` `rec-exp_binary64_1151` `associate-*r/_binary64_1043`
5×	`associate-/l_binary64_1046` `un-div-inv_binary64_1099` `associate-l*_binary64_1042`
4×	`add-log-exp_binary64_1140` `pow-prod-down_binary64_1172`
3×	`unswap-sqr_binary64_1069`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `*-commutative_binary64_1032`

Counts

4 → 529

Calls

4 calls:

88.0ms	(.f64 (.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 (+.f64 beta 2) alpha))) (/.f64 (/.f64 (+.f64 1 beta) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
56.0ms	(/.f64 (.f64 (.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 (+.f64 beta 2) alpha))) (/.f64 (/.f64 (+.f64 1 beta) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
21.0ms	(*.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 (+.f64 beta 2) alpha)))
12.0ms	(/.f64 (+.f64 1 beta) (sqrt.f64 (+.f64 alpha (+.f64 2 beta))))

Compiler

Compiled 28141 to 20087 computations (28.6% saved)

series2.2s (7.5%)

Error

0.0b

Counts

4 → 66

Calls

4 calls:

1.0s	(/.f64 (.f64 (.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 (+.f64 beta 2) alpha))) (/.f64 (/.f64 (+.f64 1 beta) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
465.0ms	(.f64 (.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 (+.f64 beta 2) alpha))) (/.f64 (/.f64 (+.f64 1 beta) (sqrt.f64 (+.f64 alpha (+.f64 2 beta)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
171.0ms	(/.f64 (+.f64 1 beta) (sqrt.f64 (+.f64 alpha (+.f64 2 beta))))
132.0ms	(*.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 (+.f64 beta 2) alpha)))

Compiler

Compiled 14802 to 11633 computations (21.4% saved)

simplify240.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

595 → 595

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5351	25650

prune2.8s (9.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	594	1	595
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	594	8	602

Error

Counts

602 → 8

Compiler

Compiled 30018 to 21051 computations (29.9% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 beta 1) (+.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))))
1.0b	(/.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)))))

rewrite1.4s (4.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

467×	`*-un-lft-identity_binary64_1101`
320×	`times-frac_binary64_1107`
203×	`distribute-lft-out_binary64_1052`
136×	`associate-r_binary64_1041`
127×	`add-sqr-sqrt_binary64_1123`
118×	`add-cube-cbrt_binary64_1136`
79×	`add-exp-log_binary64_1139`
49×	`add-cbrt-cube_binary64_1137`
42×	`div-exp_binary64_1152`
40×	`associate-/r/_binary64_1047`
23×	`cbrt-undiv_binary64_1135`
21×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
20×	`associate-/r*_binary64_1045`
15×	`prod-exp_binary64_1150`
13×	`div-inv_binary64_1098`
12×	`frac-times_binary64_1111` `associate-l/_binary64_1044` `associate-/l_binary64_1046`
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_1048` `associate-l_binary64_1042`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `unswap-sqr_binary64_1069`
1×	`inv-pow_binary64_1186` `pow-flip_binary64_1175` `pow-prod-down_binary64_1172` `*-commutative_binary64_1032`

Counts

4 → 336

Calls

4 calls:

57.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
40.0ms	(/.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)))))
35.0ms	(/.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))))
10.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha))

Compiler

Compiled 14085 to 10291 computations (26.9% saved)

series2.5s (8.3%)

Error

Counts

4 → 78

Calls

4 calls:

1.0s	(/.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)))))
461.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
392.0ms	(/.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))))
123.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha))

Compiler

Compiled 16686 to 13159 computations (21.1% saved)

simplify193.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

414 → 414

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5554	21268

prune1.8s (6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	414	0	414
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	414	8	422

Error

Counts

422 → 8

Compiler

Compiled 20159 to 14262 computations (29.3% saved)

regimes913.0ms (3.1%)

Accuracy

Total 0.1b remaining (95.1%)

Threshold costs 0.1b (95.1%)

Compiler

Compiled 14966 to 11216 computations (25.1% saved)

bsearch0.0ms (0%)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	37
1	28	37

Removed

()

Compiler

Compiled 50 to 38 computations (24% saved)

end0.0ms (0%)

sample4.3s (14.5%)

Algorithm

1×

intervals

Results

499.0ms	8000×	body	128	valid
130.0ms	8000×	pre	128	true

Compiler

Compiled 5031 to 3770 computations (25.1% saved)

Details

analyze374.0ms (1.3%)

sample38.0ms (0.1%)

simplify244.0ms (0.8%)

prune5.0ms (0%)

localize12.0ms (0%)

rewrite410.0ms (1.4%)

series2.4s (8.2%)

simplify125.0ms (0.4%)

prune688.0ms (2.3%)

localize14.0ms (0%)

rewrite1.4s (4.7%)

series2.6s (8.8%)

simplify201.0ms (0.7%)

prune2.0s (6.6%)

localize25.0ms (0.1%)

rewrite2.7s (9.2%)

series2.2s (7.5%)

simplify240.0ms (0.8%)

prune2.8s (9.6%)

localize14.0ms (0%)

rewrite1.4s (4.7%)

series2.5s (8.3%)

simplify193.0ms (0.7%)

prune1.8s (6%)

regimes913.0ms (3.1%)

bsearch0.0ms (0%)

simplify9.0ms (0%)

end0.0ms (0%)

sample4.3s (14.5%)

Profiling