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)

sample33.0ms (0.3%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify322.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (225.0ms)

Iter	Nodes	Cost
0	5023	37

prune5.0ms (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

Error

0.3b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize16.0ms (0.2%)

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)))
7.3b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
8.1b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))

rewrite117.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64_1442`
34×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `distribute-lft-out_binary64_1393`
24×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
21×	`associate-r_binary64_1382` `add-sqr-sqrt_binary64_1464`
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×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `prod-exp_binary64_1491` `associate-*l/_binary64_1385` `div-exp_binary64_1493`
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×	`clear-num_binary64_1441` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `frac-2neg_binary64_1453`
1×	`pow2_binary64_1523` `pow-plus_binary64_1505` `pow-sqr_binary64_1415` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `pow-prod-up_binary64_1512`

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))))
19.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
17.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

series276.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.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)))
96.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
52.0ms	(/.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))

simplify90.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4964	3959
1	4964	3959

prune296.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	162	8	170
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	164	8	172

Error

0.0b

Counts

172 → 8

Compiler

Compiled 5331 to 3456 computations (35.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite123.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

192×	`*-un-lft-identity_binary64_1442`
89×	`times-frac_binary64_1448`
82×	`distribute-lft-out_binary64_1393`
60×	`add-sqr-sqrt_binary64_1464`
48×	`add-cube-cbrt_binary64_1477`
38×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
26×	`associate-r_binary64_1382` `associate-l_binary64_1383`
15×	`cbrt-undiv_binary64_1476` `associate-/r*_binary64_1386` `div-exp_binary64_1493`
10×	`associate-/r/_binary64_1388`
9×	`associate-/l*_binary64_1387`
8×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
7×	`associate-/l/_binary64_1389` `flip3-+_binary64_1445` `flip-+_binary64_1416`
6×	`pow1_binary64_1503`
5×	`div-inv_binary64_1439`
4×	`add-log-exp_binary64_1481` `unswap-sqr_binary64_1410`
3×	`clear-num_binary64_1441` `frac-2neg_binary64_1453`
2×	`associate-r/_binary64_1384` `frac-times_binary64_1452` `associate-l/_binary64_1385`
1×	`pow-prod-down_binary64_1513` `*-commutative_binary64_1373`

Counts

4 → 202

Calls

4 calls:

42.0ms	(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
32.0ms	(/.f64 (*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
11.0ms	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

series246.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(/.f64 (*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
89.0ms	(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
28.0ms	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))
25.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4953	5499
1	4953	5499

prune356.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	210	4	214
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	215	7	222

Error

Counts

222 → 7

Compiler

Compiled 7071 to 4470 computations (36.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite174.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`*-un-lft-identity_binary64_1442`
113×	`times-frac_binary64_1448`
96×	`add-sqr-sqrt_binary64_1464`
84×	`distribute-lft-out_binary64_1393`
83×	`associate-r_binary64_1382`
82×	`sqrt-prod_binary64_1458`
64×	`add-cube-cbrt_binary64_1477`
58×	`sqrt-div_binary64_1459`
53×	`frac-times_binary64_1452`
52×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
47×	`pow1_binary64_1503`
33×	`associate-*l/_binary64_1385`
32×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
25×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
19×	`associate-*r/_binary64_1384` `pow-prod-down_binary64_1513`
15×	`associate-l_binary64_1383`
12×	`unswap-sqr_binary64_1410`
9×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
7×	`associate-/l*_binary64_1387`
6×	`associate-/r/_binary64_1388`
5×	`associate-/r*_binary64_1386`
4×	`pow-sqr_binary64_1415` `add-log-exp_binary64_1481` `pow-prod-up_binary64_1512`
3×	`div-inv_binary64_1439` `*-commutative_binary64_1373`
2×	`associate-/l/_binary64_1389` `pow-plus_binary64_1505`
1×	`pow2_binary64_1523` `swap-sqr_binary64_1409` `clear-num_binary64_1441` `frac-2neg_binary64_1453`

Counts

4 → 286

Calls

4 calls:

43.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))))
35.0ms	(*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2)))
31.0ms	(*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2)))
13.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))

series453.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

163.0ms	(*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2)))
159.0ms	(*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2)))
99.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))))
32.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))

simplify135.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4993	7935
1	4993	7935

prune874.0ms (8.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	298	0	298
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	298	7	305

Error

Counts

305 → 7

Compiler

Compiled 12797 to 8716 computations (31.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
0.1b	(*.f64 (/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
0.1b	(/.f64 (*.f64 (/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
0.5b	(/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))

rewrite387.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Rules

1158×	`*-un-lft-identity_binary64_1442`
821×	`times-frac_binary64_1448`
492×	`distribute-lft-out_binary64_1393`
343×	`add-sqr-sqrt_binary64_1464`
306×	`add-cube-cbrt_binary64_1477`
279×	`sqrt-prod_binary64_1458`
214×	`associate-l_binary64_1383`
61×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
44×	`associate-/r/_binary64_1388`
31×	`associate-/l*_binary64_1387`
29×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
26×	`associate-r_binary64_1382`
23×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
22×	`div-inv_binary64_1439`
21×	`associate-/r*_binary64_1386`
12×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
10×	`unswap-sqr_binary64_1410`
6×	`associate-/l/_binary64_1389` `sqrt-div_binary64_1459` `pow1_binary64_1503`
4×	`add-log-exp_binary64_1481`
3×	`clear-num_binary64_1441` `frac-2neg_binary64_1453`
2×	`associate-r/_binary64_1384` `frac-times_binary64_1452` `associate-l/_binary64_1385`
1×	`pow-prod-down_binary64_1513` `*-commutative_binary64_1373`

Counts

4 → 624

Calls

4 calls:

151.0ms	(*.f64 (/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
56.0ms	(/.f64 (*.f64 (/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
27.0ms	(/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
11.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

series274.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(/.f64 (*.f64 (/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
96.0ms	(*.f64 (/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
45.0ms	(/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
26.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

simplify387.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

636 → 636

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4995	25802
1	4995	25802

prune2.6s (26.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	636	0	636
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	636	7	643

Error

Counts

643 → 7

Compiler

Compiled 29682 to 19812 computations (33.3% saved)

regimes392.0ms (4%)

Accuracy

Total 0.1b remaining (94.5%)

Threshold costs 0.1b (94.5%)

Compiler

Compiled 5682 to 4295 computations (24.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	24	37

end0.0ms (0%)

sample2.1s (21.8%)

Algorithm

1×

intervals

Results

469.0ms	8000×	body	128	valid
141.0ms	8000×	pre	128	true

Compiler

Compiled 1901 to 1437 computations (24.4% saved)

Details

analyze5.0ms (0%)

sample33.0ms (0.3%)

simplify322.0ms (3.3%)

prune5.0ms (0.1%)

localize16.0ms (0.2%)

rewrite117.0ms (1.2%)

series276.0ms (2.8%)

simplify90.0ms (0.9%)

prune296.0ms (3%)

localize12.0ms (0.1%)

rewrite123.0ms (1.3%)

series246.0ms (2.5%)

simplify97.0ms (1%)

prune356.0ms (3.6%)

localize18.0ms (0.2%)

rewrite174.0ms (1.8%)

series453.0ms (4.6%)

simplify135.0ms (1.4%)

prune874.0ms (8.9%)

localize18.0ms (0.2%)

rewrite387.0ms (3.9%)

series274.0ms (2.8%)

simplify387.0ms (3.9%)

prune2.6s (26.2%)

regimes392.0ms (4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.1s (21.8%)

Profiling