Details

analyze367.0ms (3.7%)

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)

sample28.0ms (0.3%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify229.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (223.0ms)

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

1.5b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize12.0ms (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)))
17.3b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite103.0ms (1%)

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:

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)))
24.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
20.0ms	(/.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))

series265.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(/.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)))
95.0ms	(.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)))
17.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4964	3959
1	4964	3959

prune273.0ms (2.8%)

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 5348 to 3473 computations (35.1% saved)

localize14.0ms (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 (+.f64 beta alpha) 2))
0.0b	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 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)))

rewrite106.0ms (1.1%)

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:

34.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
28.0ms	(/.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)))
13.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))
10.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

series247.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(/.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)))
90.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
28.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
24.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))

simplify109.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4954	5499
1	4954	5499

prune366.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	210	4	214
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	215	7	222

Error

Counts

222 → 7

Compiler

Compiled 7056 to 4461 computations (36.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite341.0ms (3.5%)

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:

134.0ms	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
49.0ms	(/.f64 (*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.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))))
26.0ms	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
10.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))

series268.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(/.f64 (*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.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))))
92.0ms	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
44.0ms	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
24.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))

simplify256.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

636 → 636

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4995	25798
1	4995	25798

prune2.5s (25.6%)

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 29872 to 19944 computations (33.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (+.f64 alpha (+.f64 beta 3)))
0.3b	(cbrt.f64 (+.f64 alpha (+.f64 beta 3)))
0.3b	(cbrt.f64 (+.f64 alpha (+.f64 beta 3)))
0.6b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 alpha (+.f64 beta 3))))

rewrite102.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

571×	`*-un-lft-identity_binary64_1442`
388×	`times-frac_binary64_1448`
243×	`distribute-lft-out_binary64_1393`
151×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477`
150×	`cbrt-prod_binary64_1473`
26×	`associate-/l*_binary64_1387`
20×	`associate-/r/_binary64_1388`
13×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
10×	`div-inv_binary64_1439`
9×	`add-exp-log_binary64_1480`
8×	`associate-/r*_binary64_1386` `cbrt-div_binary64_1474`
7×	`add-cbrt-cube_binary64_1478`
4×	`add-log-exp_binary64_1481` `pow1_binary64_1503`
3×	`cbrt-undiv_binary64_1476` `pow1/3_binary64_1524` `div-exp_binary64_1493`
1×	`associate-/l/_binary64_1389` `clear-num_binary64_1441` `frac-2neg_binary64_1453`

Counts

4 → 304

Calls

4 calls:

26.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 alpha (+.f64 beta 3))))
5.0ms	(cbrt.f64 (+.f64 alpha (+.f64 beta 3)))
5.0ms	(cbrt.f64 (+.f64 alpha (+.f64 beta 3)))
5.0ms	(cbrt.f64 (+.f64 alpha (+.f64 beta 3)))

series353.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

150.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 alpha (+.f64 beta 3))))
70.0ms	(cbrt.f64 (+.f64 alpha (+.f64 beta 3)))
67.0ms	(cbrt.f64 (+.f64 alpha (+.f64 beta 3)))
65.0ms	(cbrt.f64 (+.f64 alpha (+.f64 beta 3)))

simplify169.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4911	12750
1	4911	12750

prune1.2s (12.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	316	0	316
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	316	7	323

Error

Counts

323 → 7

Compiler

Compiled 17110 to 11561 computations (32.4% saved)

regimes346.0ms (3.5%)

Accuracy

Total 0.1b remaining (95.5%)

Threshold costs 0.1b (95.5%)

Compiler

Compiled 4935 to 3725 computations (24.5% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

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%)

sample2.0s (20.6%)

Algorithm

1×

intervals

Results

460.0ms	8000×	body	128	valid
149.0ms	8000×	pre	128	true

Compiler

Compiled 1652 to 1247 computations (24.5% saved)

Details

analyze367.0ms (3.7%)

sample28.0ms (0.3%)

simplify229.0ms (2.3%)

prune5.0ms (0.1%)

localize12.0ms (0.1%)

rewrite103.0ms (1%)

series265.0ms (2.7%)

simplify85.0ms (0.9%)

prune273.0ms (2.8%)

localize14.0ms (0.1%)

rewrite106.0ms (1.1%)

series247.0ms (2.5%)

simplify109.0ms (1.1%)

prune366.0ms (3.7%)

localize15.0ms (0.1%)

rewrite341.0ms (3.5%)

series268.0ms (2.7%)

simplify256.0ms (2.6%)

prune2.5s (25.6%)

localize17.0ms (0.2%)

rewrite102.0ms (1%)

series353.0ms (3.6%)

simplify169.0ms (1.7%)

prune1.2s (12.1%)

regimes346.0ms (3.5%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.0s (20.6%)

Profiling