Details

analyze495.0ms (1.8%)

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)

sample47.0ms (0.2%)

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)

simplify311.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (305.0ms)

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

1.7b

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)))
18.5b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite471.0ms (1.7%)

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:

32.0ms	(/.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)))
30.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
24.0ms	(.f64 (+.f64 alpha 1) (/.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)

series2.9s (10.8%)

Error

0.2b

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)))
559.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
424.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
145.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 14724 to 11706 computations (20.5% saved)

simplify169.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5134	13209

prune892.0ms (3.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	223	7	230
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	224	8	232

Error

0.0b

Counts

232 → 8

Compiler

Compiled 11934 to 8105 computations (32.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite617.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
26×	`associate-l_binary64_1383` `associate-r_binary64_1382`
15×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `associate-/r*_binary64_1386`
10×	`associate-/r/_binary64_1388`
9×	`associate-/l*_binary64_1387`
8×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
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×	`frac-2neg_binary64_1453` `clear-num_binary64_1441`
2×	`frac-times_binary64_1452` `associate-l/_binary64_1385` `associate-r/_binary64_1384`
1×	`pow-prod-down_binary64_1513` `*-commutative_binary64_1373`

Counts

4 → 202

Calls

4 calls:

34.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
34.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
15.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
9.0ms	(/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 7414 to 4981 computations (32.8% saved)

series2.6s (9.4%)

Error

0.0b

Counts

4 → 72

Calls

4 calls:

1.2s	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
544.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
181.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
175.0ms	(/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 14336 to 11243 computations (21.6% saved)

simplify202.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5186	14138

prune1.1s (3.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	269	5	274
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	273	9	282

Error

0.0b

Counts

282 → 9

Compiler

Compiled 13460 to 9282 computations (31% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite998.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

156×	`*-un-lft-identity_binary64_1442`
143×	`add-exp-log_binary64_1480`
102×	`add-cbrt-cube_binary64_1478`
81×	`times-frac_binary64_1448`
62×	`div-exp_binary64_1493`
60×	`distribute-lft-out_binary64_1393`
54×	`prod-exp_binary64_1491`
51×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464`
39×	`cbrt-undiv_binary64_1476`
36×	`cbrt-unprod_binary64_1475` `sqrt-prod_binary64_1458`
25×	`associate-l_binary64_1383`
15×	`associate-/r*_binary64_1386`
12×	`associate-/l*_binary64_1387`
11×	`associate-/l/_binary64_1389`
10×	`1-exp_binary64_1486` `frac-times_binary64_1452` `associate-*r/_binary64_1384`
9×	`pow1_binary64_1503`
6×	`associate-*l/_binary64_1385` `associate-/r/_binary64_1388`
5×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
4×	`add-log-exp_binary64_1481` `div-inv_binary64_1439`
3×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `pow-prod-down_binary64_1513`
2×	`sqrt-div_binary64_1459`
1×	`associate-r_binary64_1382` `*-commutative_binary64_1373`

Counts

4 → 233

Calls

4 calls:

50.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) 1) (.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (/.f64 (sqrt.f64 (+.f64 1 alpha)) (+.f64 (+.f64 beta 2) alpha))))
44.0ms	(/.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) 1) (.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (/.f64 (sqrt.f64 (+.f64 1 alpha)) (+.f64 (+.f64 beta 2) alpha)))) (+.f64 alpha (+.f64 beta 3)))
12.0ms	(/.f64 (sqrt.f64 (+.f64 1 alpha)) (+.f64 (+.f64 beta 2) alpha))
10.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha))

Compiler

Compiled 10984 to 8216 computations (25.2% saved)

series2.6s (9.6%)

Error

0.0b

Counts

4 → 72

Calls

4 calls:

1.2s	(/.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) 1) (.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (/.f64 (sqrt.f64 (+.f64 1 alpha)) (+.f64 (+.f64 beta 2) alpha)))) (+.f64 alpha (+.f64 beta 3)))
478.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) 1) (.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (/.f64 (sqrt.f64 (+.f64 1 alpha)) (+.f64 (+.f64 beta 2) alpha))))
233.0ms	(/.f64 (sqrt.f64 (+.f64 1 alpha)) (+.f64 (+.f64 beta 2) alpha))
140.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha))

Compiler

Compiled 15092 to 11941 computations (20.9% saved)

simplify178.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5035	16487

prune1.4s (5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	305	0	305
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	305	9	314

Error

0.0b

Counts

314 → 9

Compiler

Compiled 16131 to 11709 computations (27.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite2.0s (7.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

899×	`*-un-lft-identity_binary64_1442`
549×	`times-frac_binary64_1448`
405×	`distribute-lft-out_binary64_1393`
221×	`add-sqr-sqrt_binary64_1464`
200×	`add-cube-cbrt_binary64_1477`
136×	`associate-r_binary64_1382`
34×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `associate-/l*_binary64_1387`
32×	`associate-/r/_binary64_1388`
26×	`associate-l_binary64_1383`
18×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
16×	`div-inv_binary64_1439`
15×	`associate-/r*_binary64_1386`
14×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
6×	`pow1_binary64_1503` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410`
5×	`associate-/l/_binary64_1389`
4×	`add-log-exp_binary64_1481`
3×	`frac-2neg_binary64_1453` `clear-num_binary64_1441`
1×	`pow-prod-down_binary64_1513` `frac-times_binary64_1452` `associate-l/_binary64_1385` `associate-r/_binary64_1384` `*-commutative_binary64_1373`

Counts

4 → 460

Calls

4 calls:

106.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 3) alpha)))
28.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 3) alpha))
10.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha))
10.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha))

Compiler

Compiled 18398 to 13240 computations (28% saved)

series2.5s (9.2%)

Error

0.0b

Counts

4 → 72

Calls

4 calls:

1.3s	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 3) alpha)))
492.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 3) alpha))
174.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha))
156.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 beta 2) alpha))

Compiler

Compiled 14216 to 11164 computations (21.5% saved)

simplify281.0ms (1%)

Algorithm

1×	egg-herbie

Counts

532 → 532

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5137	24309

prune2.5s (9.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	530	2	532
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	532	9	541

Error

Counts

541 → 9

Compiler

Compiled 23665 to 16751 computations (29.2% saved)

regimes833.0ms (3%)

Accuracy

Total 0.1b remaining (95.2%)

Threshold costs 0.1b (95.2%)

Compiler

Compiled 11195 to 8324 computations (25.6% saved)

bsearch0.0ms (0%)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	37
1	28	37

Remove

(sort alpha beta)

Compiler

Compiled 50 to 38 computations (24% saved)

end0.0ms (0%)

sample4.2s (15.4%)

Algorithm

1×

intervals

Results

552.0ms	8000×	body	128	valid
162.0ms	8000×	pre	128	true

Compiler

Compiled 3774 to 2806 computations (25.6% saved)

Details

analyze495.0ms (1.8%)

sample47.0ms (0.2%)

simplify311.0ms (1.1%)

prune5.0ms (0%)

localize12.0ms (0%)

rewrite471.0ms (1.7%)

series2.9s (10.8%)

simplify169.0ms (0.6%)

prune892.0ms (3.3%)

localize20.0ms (0.1%)

rewrite617.0ms (2.3%)

series2.6s (9.4%)

simplify202.0ms (0.7%)

prune1.1s (3.9%)

localize20.0ms (0.1%)

rewrite998.0ms (3.6%)

series2.6s (9.6%)

simplify178.0ms (0.7%)

prune1.4s (5%)

localize16.0ms (0.1%)

rewrite2.0s (7.1%)

series2.5s (9.2%)

simplify281.0ms (1%)

prune2.5s (9.2%)

regimes833.0ms (3%)

bsearch0.0ms (0%)

simplify17.0ms (0.1%)

end0.0ms (0%)

sample4.2s (15.4%)

Profiling