Details

analyze380.0ms (0.6%)

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)

sample37.0ms (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)

simplify247.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (240.0ms)

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

1.5b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize18.0ms (0%)

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 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)))
21.7b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite410.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

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:

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))))
16.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
15.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 6017 to 3676 computations (38.9% saved)

series2.4s (3.9%)

Error

0.1b

Counts

4 → 65

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)))
485.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
350.0ms	(/.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 13703 to 10895 computations (20.5% saved)

simplify143.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4948	11930
1	4948	11930

prune694.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	217	6	223
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	219	6	225

Error

Counts

225 → 6

Compiler

Compiled 10964 to 7446 computations (32.1% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite626.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

133×	`*-un-lft-identity_binary64_1442`
103×	`add-exp-log_binary64_1480`
67×	`times-frac_binary64_1448`
61×	`add-cbrt-cube_binary64_1478`
54×	`add-sqr-sqrt_binary64_1464` `distribute-lft-out_binary64_1393`
42×	`prod-exp_binary64_1491`
37×	`add-cube-cbrt_binary64_1477`
35×	`div-exp_binary64_1493`
27×	`associate-r_binary64_1382`
25×	`associate-l_binary64_1383`
22×	`cbrt-unprod_binary64_1475`
19×	`cbrt-undiv_binary64_1476` `frac-times_binary64_1452`
13×	`flip3-+_binary64_1445` `associate-/l/_binary64_1389` `associate-*r/_binary64_1384` `flip-+_binary64_1416`
11×	`pow1_binary64_1503` `associate-*l/_binary64_1385`
10×	`associate-/r*_binary64_1386`
8×	`associate-/r/_binary64_1388`
6×	`1-exp_binary64_1486` `rec-exp_binary64_1492` `unswap-sqr_binary64_1410`
5×	`associate-/l*_binary64_1387`
4×	`add-log-exp_binary64_1481` `div-inv_binary64_1439` `pow-prod-down_binary64_1513`
2×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `*-commutative_binary64_1373`

Counts

4 → 212

Calls

4 calls:

34.0ms	(*.f64 (/.f64 1 (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))))
30.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))))) (+.f64 alpha (+.f64 beta 3)))
23.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))))
9.0ms	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 8334 to 6054 computations (27.4% saved)

series2.3s (3.8%)

Error

Counts

4 → 62

Calls

4 calls:

1.1s	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))))) (+.f64 alpha (+.f64 beta 3)))
466.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))))
354.0ms	(*.f64 (/.f64 1 (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))))
118.0ms	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 14042 to 11161 computations (20.5% saved)

simplify141.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5313	13662

prune869.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	274	6	280

Error

Counts

280 → 6

Compiler

Compiled 12884 to 9115 computations (29.3% saved)

localize14.0ms (0%)

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

rewrite2.0s (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

838×	`*-un-lft-identity_binary64_1442`
399×	`times-frac_binary64_1448`
360×	`distribute-lft-out_binary64_1393`
248×	`sqrt-prod_binary64_1458`
224×	`add-sqr-sqrt_binary64_1464`
150×	`add-cube-cbrt_binary64_1477`
127×	`swap-sqr_binary64_1409`
45×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
41×	`associate-l_binary64_1383` `associate-r_binary64_1382`
16×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
15×	`associate-/l/_binary64_1389` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
14×	`associate-/r/_binary64_1388`
13×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `flip3-+_binary64_1445` `flip-+_binary64_1416`
11×	`pow1_binary64_1503`
10×	`frac-times_binary64_1452`
9×	`unswap-sqr_binary64_1410`
7×	`div-inv_binary64_1439` `associate-*r/_binary64_1384`
6×	`associate-*l/_binary64_1385`
4×	`add-log-exp_binary64_1481` `sqrt-div_binary64_1459`
3×	`frac-2neg_binary64_1453` `clear-num_binary64_1441`
1×	`pow2_binary64_1523` `pow-prod-down_binary64_1513` `pow-prod-up_binary64_1512` `pow-plus_binary64_1505` `pow-sqr_binary64_1415` `*-commutative_binary64_1373`

Counts

4 → 414

Calls

4 calls:

54.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))
40.0ms	(/.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)))
11.0ms	(/.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 (3.2%)

Error

Counts

4 → 53

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)))
362.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))
121.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
118.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 11433 to 9100 computations (20.4% saved)

simplify207.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

467 → 467

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5700	19926

prune1.8s (3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	467	0	467
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	467	6	473

Error

Counts

473 → 6

Compiler

Compiled 20911 to 15224 computations (27.2% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 alpha (+.f64 2 beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))))) (+.f64 alpha (+.f64 beta 3)))
0.1b	(/.f64 (+.f64 alpha (+.f64 2 beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))
0.2b	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
15.4b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 alpha (+.f64 2 beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))))

rewrite22.0s (36.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6058×	`*-un-lft-identity_binary64_1442`
4965×	`times-frac_binary64_1448`
2553×	`distribute-lft-out_binary64_1393`
1788×	`sqrt-prod_binary64_1458`
1654×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464`
261×	`associate-/r*_binary64_1386`
106×	`associate-/r/_binary64_1388`
58×	`div-inv_binary64_1439`
53×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
40×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
21×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
20×	`associate-/l*_binary64_1387`
11×	`associate-/l/_binary64_1389`
4×	`pow1_binary64_1503` `add-log-exp_binary64_1481` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `sqrt-div_binary64_1459` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
2×	`frac-times_binary64_1452` `associate-*l/_binary64_1385`
1×	`associate-*r/_binary64_1384`

Counts

4 → 2075

Calls

4 calls:

133.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 alpha (+.f64 2 beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))))) (+.f64 alpha (+.f64 beta 3)))
80.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 alpha (+.f64 2 beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))))
32.0ms	(/.f64 (+.f64 alpha (+.f64 2 beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))
11.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 110960 to 83978 computations (24.3% saved)

series2.3s (3.8%)

Error

Counts

4 → 57

Calls

4 calls:

1.3s	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 alpha (+.f64 2 beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))))) (+.f64 alpha (+.f64 beta 3)))
383.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 alpha (+.f64 2 beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))))
214.0ms	(/.f64 (+.f64 alpha (+.f64 2 beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))
125.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 12046 to 9622 computations (20.1% saved)

simplify1.1s (1.8%)

Algorithm

1×	egg-herbie

Counts

2132 → 2132

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5204	116831

prune16.8s (27.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	2132	0	2132
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	2132	6	2138

Error

Counts

2138 → 6

Compiler

Compiled 104432 to 77100 computations (26.2% saved)

regimes623.0ms (1%)

Accuracy

Total 0.1b remaining (92.5%)

Threshold costs 0.1b (92.5%)

Compiler

Compiled 10268 to 7640 computations (25.6% 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 (5.7%)

Algorithm

1×

intervals

Results

500.0ms	8000×	body	128	valid
136.0ms	8000×	pre	128	true

Compiler

Compiled 3465 to 2577 computations (25.6% saved)

Details

analyze380.0ms (0.6%)

sample37.0ms (0.1%)

simplify247.0ms (0.4%)

prune6.0ms (0%)

localize18.0ms (0%)

rewrite410.0ms (0.7%)

series2.4s (3.9%)

simplify143.0ms (0.2%)

prune694.0ms (1.1%)

localize16.0ms (0%)

rewrite626.0ms (1%)

series2.3s (3.8%)

simplify141.0ms (0.2%)

prune869.0ms (1.4%)

localize14.0ms (0%)

rewrite2.0s (3.3%)

series1.9s (3.2%)

simplify207.0ms (0.3%)

prune1.8s (3%)

localize17.0ms (0%)

rewrite22.0s (36.4%)

series2.3s (3.8%)

simplify1.1s (1.8%)

prune16.8s (27.8%)

regimes623.0ms (1%)

bsearch0.0ms (0%)

simplify10.0ms (0%)

end0.0ms (0%)

sample3.5s (5.7%)

Profiling