Details

analyze435.0ms (0.8%)

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)

sample49.0ms (0.1%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify277.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (271.0ms)

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

2.3b

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) 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)))
14.6b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite429.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

77×	`*-un-lft-identity_binary64_1442`
34×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `distribute-lft-out_binary64_1393`
24×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
21×	`add-sqr-sqrt_binary64_1464` `associate-r_binary64_1382`
18×	`associate-/r/_binary64_1388`
16×	`frac-times_binary64_1452`
15×	`add-cube-cbrt_binary64_1477`
14×	`times-frac_binary64_1448`
13×	`pow1_binary64_1503`
11×	`swap-sqr_binary64_1409`
10×	`prod-exp_binary64_1491` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `associate-*l/_binary64_1385`
9×	`associate-l_binary64_1383`
8×	`associate-*r/_binary64_1384`
7×	`associate-/l/_binary64_1389`
6×	`associate-/r*_binary64_1386`
5×	`associate-/l*_binary64_1387`
4×	`add-log-exp_binary64_1481`
3×	`div-inv_binary64_1439` `unswap-sqr_binary64_1410`
2×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373`
1×	`pow2_binary64_1523` `pow-prod-up_binary64_1512` `pow-plus_binary64_1505` `pow-sqr_binary64_1415` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391`

Counts

4 → 158

Calls

4 calls:

43.0ms	(/.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)))
22.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
19.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
19.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 6017 to 3676 computations (38.9% saved)

series2.8s (5.1%)

Error

0.5b

Counts

4 → 72

Calls

4 calls:

1.3s	(/.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)))
541.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
421.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
128.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 14724 to 11706 computations (20.5% saved)

simplify131.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5134	13209

prune1.0s (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	222	8	230
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	224	8	232

Error

0.0b

Counts

232 → 8

Compiler

Compiled 11922 to 8108 computations (32% saved)

localize20.0ms (0%)

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)))

rewrite1.5s (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

826×	`*-un-lft-identity_binary64_1442`
508×	`times-frac_binary64_1448`
374×	`distribute-lft-out_binary64_1393`
191×	`add-sqr-sqrt_binary64_1464`
182×	`add-cube-cbrt_binary64_1477`
136×	`associate-r_binary64_1382`
34×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
31×	`associate-/l*_binary64_1387`
30×	`associate-/r/_binary64_1388`
20×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
15×	`div-inv_binary64_1439` `associate-/r*_binary64_1386`
14×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
8×	`associate-/l/_binary64_1389`
6×	`pow1_binary64_1503` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
4×	`add-log-exp_binary64_1481` `frac-times_binary64_1452` `associate-l/_binary64_1385` `associate-l*_binary64_1383`
3×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `unswap-sqr_binary64_1410`
2×	`associate-*r/_binary64_1384`
1×	`pow-prod-down_binary64_1513` `*-commutative_binary64_1373`

Counts

4 → 422

Calls

4 calls:

75.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))
47.0ms	(/.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)))
24.0ms	(/.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)

series3.1s (5.6%)

Error

0.0b

Counts

4 → 72

Calls

4 calls:

1.5s	(/.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)))
466.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))
447.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))
143.0ms	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 15272 to 12092 computations (20.8% saved)

simplify245.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

494 → 494

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5227	22380

prune2.1s (3.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	492	2	494
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	494	8	502

Error

0.0b

Counts

502 → 8

Compiler

Compiled 22579 to 15663 computations (30.6% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 1 alpha))) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 1 alpha)))) (+.f64 alpha (+.f64 beta 3)))
0.2b	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
0.2b	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
0.3b	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 1 alpha))) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 1 alpha))))

rewrite1.5s (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

160×	`*-un-lft-identity_binary64_1442`
100×	`sqrt-div_binary64_1459`
98×	`frac-times_binary64_1452`
91×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
75×	`times-frac_binary64_1448`
66×	`distribute-lft-out_binary64_1393`
58×	`associate-*r/_binary64_1384`
53×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
48×	`sqrt-prod_binary64_1458`
46×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464`
43×	`pow1_binary64_1503`
42×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
39×	`associate-/l/_binary64_1389`
34×	`associate-*l/_binary64_1385`
24×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
17×	`pow-prod-down_binary64_1513`
15×	`associate-/l_binary64_1387` `associate-/r_binary64_1386`
6×	`associate-/r/_binary64_1388`
4×	`pow-prod-up_binary64_1512` `add-log-exp_binary64_1481` `pow-sqr_binary64_1415`
3×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439`
2×	`pow-plus_binary64_1505`
1×	`pow2_binary64_1523` `swap-sqr_binary64_1409` `associate-l_binary64_1383` `associate-r_binary64_1382` `*-commutative_binary64_1373`

Counts

4 → 283

Calls

4 calls:

67.0ms	(/.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 1 alpha))) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 1 alpha)))) (+.f64 alpha (+.f64 beta 3)))
37.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 1 alpha))) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 1 alpha))))
12.0ms	(/.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 14876 to 11052 computations (25.7% saved)

series2.5s (4.5%)

Error

0.0b

Counts

4 → 60

Calls

4 calls:

1.2s	(/.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 1 alpha))) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 1 alpha)))) (+.f64 alpha (+.f64 beta 3)))
577.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 1 alpha))) (*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 1 alpha))))
150.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
140.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 13584 to 10784 computations (20.6% saved)

simplify174.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

343 → 343

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5033	17273

prune1.6s (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	343	0	343
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	343	8	351

Error

0.0b

Counts

351 → 8

Compiler

Compiled 18402 to 13360 computations (27.4% saved)

localize43.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
0.5b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta 2) alpha)))
0.5b	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta 2) alpha)))) (/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
0.7b	(/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))

rewrite6.9s (12.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

1821×	`*-un-lft-identity_binary64_1442`
1342×	`times-frac_binary64_1448`
855×	`sqrt-prod_binary64_1458`
754×	`distribute-lft-out_binary64_1393`
531×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464`
334×	`associate-r_binary64_1382`
55×	`associate-/l*_binary64_1387`
49×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
42×	`associate-/r/_binary64_1388`
27×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
21×	`div-inv_binary64_1439` `associate-/r*_binary64_1386`
17×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
15×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
10×	`sqrt-div_binary64_1459`
9×	`pow1_binary64_1503` `frac-times_binary64_1452` `associate-*l/_binary64_1385`
5×	`associate-/l/_binary64_1389`
4×	`add-log-exp_binary64_1481`
3×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `pow-prod-down_binary64_1513` `associate-*r/_binary64_1384`
1×	`associate-l_binary64_1383` `*-commutative_binary64_1373` `sqrt-undiv_binary64_1463`

Counts

4 → 919

Calls

4 calls:

113.0ms	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta 2) alpha)))) (/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
37.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
13.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta 2) alpha)))
10.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 52764 to 37989 computations (28% saved)

series15.3s (27.4%)

Error

0.0b

Counts

4 → 64

Calls

4 calls:

11.1s	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta 2) alpha)))) (/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
2.2s	(/.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
393.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta 2) alpha)))
124.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 33797 to 27450 computations (18.8% saved)

simplify537.0ms (1%)

Algorithm

1×	egg-herbie

Counts

983 → 983

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5400	63572

prune9.4s (16.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	983	0	983
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	983	8	991

Error

0.0b

Counts

991 → 8

Compiler

Compiled 65637 to 47344 computations (27.9% saved)

regimes854.0ms (1.5%)

Accuracy

Total 0.1b remaining (96.6%)

Threshold costs 0.1b (96.6%)

Compiler

Compiled 12509 to 9443 computations (24.5% saved)

bsearch0.0ms (0%)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	37
1	28	37

Compiler

Compiled 50 to 38 computations (24% saved)

end0.0ms (0%)

sample4.7s (8.5%)

Algorithm

1×

intervals

Results

586.0ms	8000×	body	128	valid
147.0ms	8000×	pre	128	true

Compiler

Compiled 4212 to 3179 computations (24.5% saved)

Details

analyze435.0ms (0.8%)

sample49.0ms (0.1%)

simplify277.0ms (0.5%)

prune5.0ms (0%)

localize12.0ms (0%)

rewrite429.0ms (0.8%)

series2.8s (5.1%)

simplify131.0ms (0.2%)

prune1.0s (1.9%)

localize20.0ms (0%)

rewrite1.5s (2.8%)

series3.1s (5.6%)

simplify245.0ms (0.4%)

prune2.1s (3.8%)

localize20.0ms (0%)

rewrite1.5s (2.6%)

series2.5s (4.5%)

simplify174.0ms (0.3%)

prune1.6s (2.9%)

localize43.0ms (0.1%)

rewrite6.9s (12.3%)

series15.3s (27.4%)

simplify537.0ms (1%)

prune9.4s (16.8%)

regimes854.0ms (1.5%)

bsearch0.0ms (0%)

simplify11.0ms (0%)

end0.0ms (0%)

sample4.7s (8.5%)

Profiling