Details

analyze661.0ms (1.7%)

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

Compiler

Compiled 42 to 29 computations (31% saved)

sample59.0ms (0.1%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify427.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (417.0ms)

Iter	Nodes	Cost
0	5023	37

prune10.0ms (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

1.2b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize32.0ms (0.1%)

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

rewrite191.0ms (0.5%)

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:

49.0ms	(/.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)))
42.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
31.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
27.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

series3.5s (8.7%)

Counts

4 → 72

Calls

4 calls:

1.8s	(/.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)))
807.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
611.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
213.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 7596 to 6128 computations (19.3% saved)

simplify236.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5134	13209

prune1.6s (4%)

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 12008 to 7920 computations (34% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite207.0ms (0.5%)

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:

72.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
50.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
25.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
18.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))

series3.1s (7.8%)

Counts

4 → 72

Calls

4 calls:

1.8s	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
814.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
260.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))
219.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 7316 to 5835 computations (20.2% saved)

simplify292.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4943	14138
1	4943	14138

prune1.6s (4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	271	3	274
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	274	10	284

Error

Counts

284 → 10

Compiler

Compiled 13495 to 8867 computations (34.3% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite369.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

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-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
41×	`associate-r_binary64_1382` `associate-l_binary64_1383`
16×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
15×	`associate-/r_binary64_1386` `associate-/l/_binary64_1389` `associate-/l_binary64_1387`
14×	`associate-/r/_binary64_1388`
13×	`cbrt-unprod_binary64_1475` `flip3-+_binary64_1445` `flip-+_binary64_1416` `prod-exp_binary64_1491`
11×	`pow1_binary64_1503`
10×	`frac-times_binary64_1452`
9×	`unswap-sqr_binary64_1410`
7×	`associate-*r/_binary64_1384` `div-inv_binary64_1439`
6×	`associate-*l/_binary64_1385`
4×	`sqrt-div_binary64_1459` `add-log-exp_binary64_1481`
3×	`clear-num_binary64_1441` `frac-2neg_binary64_1453`
1×	`pow2_binary64_1523` `pow-plus_binary64_1505` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `pow-sqr_binary64_1415` `pow-prod-up_binary64_1512`

Counts

4 → 414

Calls

4 calls:

98.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
71.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
28.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
22.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

series2.9s (7.3%)

Counts

4 → 60

Calls

4 calls:

1.9s	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
604.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
211.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
211.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 6476 to 5218 computations (19.4% saved)

simplify401.0ms (1%)

Algorithm

1×	egg-herbie

Counts

474 → 474

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	6107	20915

prune3.0s (7.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	474	0	474
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	474	10	484

Error

Counts

484 → 10

Compiler

Compiled 21811 to 14786 computations (32.2% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))
0.1b	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
0.6b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
0.6b	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))

rewrite1.8s (4.4%)

Algorithm

1×	rewrite-expression-head

Rules

2156×	`*-un-lft-identity_binary64_1442`
1592×	`times-frac_binary64_1448`
917×	`distribute-lft-out_binary64_1393`
679×	`add-sqr-sqrt_binary64_1464`
569×	`add-cube-cbrt_binary64_1477`
550×	`sqrt-prod_binary64_1458`
214×	`associate-r_binary64_1382` `associate-l_binary64_1383`
78×	`associate-/r/_binary64_1388`
56×	`associate-/l*_binary64_1387`
52×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
40×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
39×	`div-inv_binary64_1439`
25×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`
21×	`associate-/r*_binary64_1386`
9×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
8×	`sqrt-div_binary64_1459`
6×	`pow1_binary64_1503`
4×	`associate-/l/_binary64_1389` `add-log-exp_binary64_1481`
3×	`clear-num_binary64_1441` `frac-2neg_binary64_1453`
1×	`associate-r/_binary64_1384` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-times_binary64_1452` `associate-*l/_binary64_1385`

Counts

4 → 1046

Calls

4 calls:

1.2s	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
47.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
47.0ms	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
20.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))

series3.7s (9.2%)

Counts

4 → 60

Calls

4 calls:

1.9s	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
742.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
712.0ms	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
281.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 8145 to 6508 computations (20.1% saved)

simplify1.0s (2.6%)

Algorithm

1×	egg-herbie

Counts

1106 → 1106

Iterations

Useful iterations: 0 (208.0ms)

Iter	Nodes	Cost
0	4961	57871
1	4961	57871

prune9.8s (24.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	1106	0	1106
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	1106	10	1116

Error

Counts

1116 → 10

Compiler

Compiled 57721 to 38846 computations (32.7% saved)

regimes691.0ms (1.7%)

Accuracy

Total 0.1b remaining (95.8%)

Threshold costs 0.1b (95.8%)

Compiler

Compiled 5558 to 4115 computations (26% saved)

bsearch0.0ms (0%)

simplify18.0ms (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%)

sample4.3s (10.7%)

Algorithm

1×

intervals

Results

972.0ms	8000×	body	128	valid
255.0ms	8000×	pre	128	true

Compiler

Compiled 1895 to 1402 computations (26% saved)

Details

analyze661.0ms (1.7%)

sample59.0ms (0.1%)

simplify427.0ms (1.1%)

prune10.0ms (0%)

localize32.0ms (0.1%)

rewrite191.0ms (0.5%)

series3.5s (8.7%)

simplify236.0ms (0.6%)

prune1.6s (4%)

localize34.0ms (0.1%)

rewrite207.0ms (0.5%)

series3.1s (7.8%)

simplify292.0ms (0.7%)

prune1.6s (4%)

localize27.0ms (0.1%)

rewrite369.0ms (0.9%)

series2.9s (7.3%)

simplify401.0ms (1%)

prune3.0s (7.5%)

localize38.0ms (0.1%)

rewrite1.8s (4.4%)

series3.7s (9.2%)

simplify1.0s (2.6%)

prune9.8s (24.5%)

regimes691.0ms (1.7%)

bsearch0.0ms (0%)

simplify18.0ms (0%)

end0.0ms (0%)

sample4.3s (10.7%)

Profiling