Details

analyze371.0ms (2.4%)

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)

sample38.0ms (0.2%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify246.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (236.0ms)

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

0.7b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.0b	(.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)))
18.7b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite414.0ms (2.7%)

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)))
27.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
17.0ms	(/.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)

series2.1s (13.9%)

Error

0.2b

Counts

4 → 57

Calls

4 calls:

1.0s	(/.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)))
440.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
320.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
115.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 11189 to 8881 computations (20.6% saved)

simplify102.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5363	9621

prune563.0ms (3.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	207	8	215
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	209	8	217

Error

Counts

217 → 8

Compiler

Compiled 9453 to 6379 computations (32.5% saved)

localize15.0ms (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 1 alpha) (+.f64 alpha (+.f64 2 beta)))
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)))

rewrite504.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

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 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
30.0ms	(/.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)))
10.0ms	(/.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)

series1.8s (12.1%)

Error

Counts

4 → 52

Calls

4 calls:

1.0s	(/.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)))
432.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
103.0ms	(/.f64 (+.f64 1 alpha) (+.f64 alpha (+.f64 2 beta)))
98.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 10336 to 8107 computations (21.6% saved)

simplify103.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

254 → 254

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5576	10320

prune566.0ms (3.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	253	1	254
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	255	7	262

Error

Counts

262 → 7

Compiler

Compiled 10651 to 7384 computations (30.7% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite734.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

195×	`*-un-lft-identity_binary64_1442`
97×	`times-frac_binary64_1448`
80×	`distribute-lft-out_binary64_1393`
66×	`add-sqr-sqrt_binary64_1464`
61×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
56×	`add-cube-cbrt_binary64_1477`
50×	`sqrt-prod_binary64_1458`
48×	`associate-r_binary64_1382`
27×	`associate-l_binary64_1383`
22×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `sqrt-div_binary64_1459`
20×	`frac-times_binary64_1452`
19×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
15×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-*l/_binary64_1385`
13×	`associate-/l/_binary64_1389`
12×	`associate-*r/_binary64_1384`
11×	`pow1_binary64_1503`
10×	`associate-/r*_binary64_1386`
8×	`associate-/r/_binary64_1388` `associate-/l*_binary64_1387`
4×	`pow-prod-down_binary64_1513` `add-log-exp_binary64_1481` `div-inv_binary64_1439` `unswap-sqr_binary64_1410`
2×	`*-commutative_binary64_1373` `frac-2neg_binary64_1453` `clear-num_binary64_1441`

Counts

4 → 241

Calls

4 calls:

41.0ms	(/.f64 (.f64 (.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 1 beta))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
34.0ms	(.f64 (.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 1 beta))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
20.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 1 beta)))
11.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 10757 to 7533 computations (30% saved)

series2.3s (14.8%)

Error

Counts

4 → 48

Calls

4 calls:

1.3s	(/.f64 (.f64 (.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 1 beta))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
502.0ms	(.f64 (.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 1 beta))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
179.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta 2) alpha)) (sqrt.f64 (+.f64 1 beta)))
120.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 10986 to 8651 computations (21.3% saved)

simplify126.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5807	12199

prune1.0s (6.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	289	7	296

Error

Counts

296 → 7

Compiler

Compiled 13134 to 9316 computations (29.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cbrt.f64 (+.f64 1 beta)) (cbrt.f64 (+.f64 1 beta)))
0.3b	(cbrt.f64 (+.f64 1 beta))
0.3b	(cbrt.f64 (+.f64 1 beta))
0.3b	(cbrt.f64 (+.f64 1 beta))

rewrite237.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

36×	`cbrt-prod_binary64_1473`
35×	`*-un-lft-identity_binary64_1442`
23×	`add-sqr-sqrt_binary64_1464`
18×	`cbrt-div_binary64_1474`
15×	`add-cube-cbrt_binary64_1477`
11×	`pow1_binary64_1503`
9×	`pow1/3_binary64_1524` `flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-lft-out_binary64_1393` `swap-sqr_binary64_1409`
7×	`associate-l_binary64_1383` `associate-r_binary64_1382`
6×	`add-exp-log_binary64_1480`
4×	`add-log-exp_binary64_1481` `add-cbrt-cube_binary64_1478` `frac-times_binary64_1452` `unswap-sqr_binary64_1410`
2×	`pow-prod-down_binary64_1513` `pow-prod-up_binary64_1512` `pow-sqr_binary64_1415` `associate-l/_binary64_1385` `associate-r/_binary64_1384`
1×	`pow2_binary64_1523` `pow-plus_binary64_1505` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `*-commutative_binary64_1373`

Counts

4 → 95

Calls

4 calls:

11.0ms	(*.f64 (cbrt.f64 (+.f64 1 beta)) (cbrt.f64 (+.f64 1 beta)))
3.0ms	(cbrt.f64 (+.f64 1 beta))
3.0ms	(cbrt.f64 (+.f64 1 beta))
3.0ms	(cbrt.f64 (+.f64 1 beta))

Compiler

Compiled 4163 to 3093 computations (25.7% saved)

series230.0ms (1.5%)

Error

Counts

4 → 29

Calls

4 calls:

52.0ms	(*.f64 (cbrt.f64 (+.f64 1 beta)) (cbrt.f64 (+.f64 1 beta)))
46.0ms	(cbrt.f64 (+.f64 1 beta))
43.0ms	(cbrt.f64 (+.f64 1 beta))
41.0ms	(cbrt.f64 (+.f64 1 beta))

Compiler

Compiled 2712 to 2104 computations (22.4% saved)

simplify101.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4841	1490
1	4841	1490

prune248.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	124	7	131

Error

Counts

131 → 7

Compiler

Compiled 4922 to 3581 computations (27.2% saved)

regimes531.0ms (3.5%)

Accuracy

Total 0.1b remaining (91.1%)

Threshold costs 0.1b (91.1%)

Compiler

Compiled 8315 to 6239 computations (25% saved)

bsearch0.0ms (0%)

simplify10.0ms (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%)

sample2.8s (18.6%)

Algorithm

1×

intervals

Results

516.0ms	8000×	body	128	valid
125.0ms	8000×	pre	128	true

Compiler

Compiled 2814 to 2111 computations (25% saved)

Details

analyze371.0ms (2.4%)

sample38.0ms (0.2%)

simplify246.0ms (1.6%)

prune5.0ms (0%)

localize13.0ms (0.1%)

rewrite414.0ms (2.7%)

series2.1s (13.9%)

simplify102.0ms (0.7%)

prune563.0ms (3.7%)

localize15.0ms (0.1%)

rewrite504.0ms (3.3%)

series1.8s (12.1%)

simplify103.0ms (0.7%)

prune566.0ms (3.7%)

localize22.0ms (0.1%)

rewrite734.0ms (4.8%)

series2.3s (14.8%)

simplify126.0ms (0.8%)

prune1.0s (6.6%)

localize17.0ms (0.1%)

rewrite237.0ms (1.6%)

series230.0ms (1.5%)

simplify101.0ms (0.7%)

prune248.0ms (1.6%)

regimes531.0ms (3.5%)

bsearch0.0ms (0%)

simplify10.0ms (0.1%)

end0.0ms (0%)

sample2.8s (18.6%)

Profiling