Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample19.0ms (0.5%)

Algorithm

1×

intervals

Results

6.0ms	64×	body	1024	valid
4.0ms	138×	body	128	valid
2.0ms	30×	body	512	valid
1.0ms	9×	body	2048	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify175.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (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

Merged error: 29.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
3.4b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_1440` `add-sqr-sqrt_binary64_1446` `*-un-lft-identity_binary64_1425`
4×	`difference-of-squares_binary64_1394` `add-log-exp_binary64_1461`
3×	`add-cube-cbrt_binary64_1457` `distribute-lft-out--_binary64_1379` `pow1_binary64_1483`
2×	`sqrt-div_binary64_1441` `distribute-lft-out_binary64_1378` `add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
1×	`flip--_binary64_1400` `diff-log_binary64_1514` `flip3-+_binary64_1428` `pow1/2_binary64_1502` `sub-neg_binary64_1418` `sqrt-pow1_binary64_1442` `flip-+_binary64_1399` `rem-sqrt-square_binary64_1438` `flip3--_binary64_1429`

Counts

2 → 34

Calls

2 calls:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series102.0ms (2.5%)

Counts

2 → 6

Calls

2 calls:

73.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
29.0ms	(sqrt.f64 (+.f64 x 1))

simplify90.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4907	747
1	4907	747

prune48.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	4	41

Merged error: 0.2b

Counts

41 → 4

Compiler

Compiled 662 to 443 computations (33.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1425`
24×	`sqrt-prod_binary64_1440`
21×	`distribute-lft-out_binary64_1378`
18×	`times-frac_binary64_1431`
16×	`add-sqr-sqrt_binary64_1446`
15×	`add-cube-cbrt_binary64_1457`
7×	`add-exp-log_binary64_1460`
6×	`associate-/r*_binary64_1371`
5×	`add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `add-log-exp_binary64_1461`
3×	`flip3-+_binary64_1428` `flip-+_binary64_1399` `associate-/l*_binary64_1372`
2×	`sqrt-div_binary64_1441` `associate-/r/_binary64_1373` `div-exp_binary64_1473`
1×	`frac-2neg_binary64_1436` `pow-flip_binary64_1496` `inv-pow_binary64_1507` `pow1/2_binary64_1502` `clear-num_binary64_1424` `sqrt-pow1_binary64_1442` `div-inv_binary64_1422` `sum-log_binary64_1513` `+-commutative_binary64_1357` `1-exp_binary64_1466` `rem-sqrt-square_binary64_1438` `cbrt-undiv_binary64_1456` `rec-exp_binary64_1472`

Counts

3 → 75

Calls

3 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series135.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

61.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
44.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
30.0ms	(sqrt.f64 (+.f64 x 1))

simplify64.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5545	1516

prune100.0ms (2.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	79	9	88

Merged error: 0.0b

Counts

88 → 9

Compiler

Compiled 1528 to 1091 computations (28.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

rewrite69.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`sqrt-prod_binary64_1440`
62×	`add-sqr-sqrt_binary64_1446`
46×	`*-un-lft-identity_binary64_1425`
40×	`sqrt-pow1_binary64_1442`
32×	`sqrt-div_binary64_1441` `pow1_binary64_1483`
28×	`add-cube-cbrt_binary64_1457`
20×	`pow1/2_binary64_1502`
18×	`swap-sqr_binary64_1392`
10×	`associate-l_binary64_1368` `associate-r_binary64_1367` `add-exp-log_binary64_1460`
9×	`times-frac_binary64_1431` `unswap-sqr_binary64_1393` `flip3-+_binary64_1428` `flip-+_binary64_1399` `pow-prod-up_binary64_1492`
8×	`distribute-lft-out_binary64_1378` `add-cbrt-cube_binary64_1458`
5×	`pow-sqr_binary64_1398` `pow-prod-down_binary64_1493`
4×	`rem-sqrt-square_binary64_1438` `add-log-exp_binary64_1461` `frac-times_binary64_1435`
3×	`associate-/r_binary64_1371` `associate-/l_binary64_1372`
2×	`associate-r/_binary64_1369` `associate-/r/_binary64_1373` `div-exp_binary64_1473` `associate-l/_binary64_1370`
1×	`frac-2neg_binary64_1436` `pow-flip_binary64_1496` `inv-pow_binary64_1507` `prod-exp_binary64_1471` `pow-plus_binary64_1485` `cbrt-unprod_binary64_1455` `clear-num_binary64_1424` `rem-square-sqrt_binary64_1437` `pow2_binary64_1503` `sqrt-unprod_binary64_1444` `div-inv_binary64_1422` `1-exp_binary64_1466` `cbrt-undiv_binary64_1456` `rec-exp_binary64_1472` `*-commutative_binary64_1358`

Counts

4 → 165

Calls

4 calls:

19.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
17.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

series179.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
43.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
41.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
31.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

simplify84.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5041	2482

prune212.0ms (5.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	177	9	186

Merged error: 0.0b

Counts

186 → 9

Compiler

Compiled 3443 to 2576 computations (25.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

rewrite167.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Rules

742×	`*-un-lft-identity_binary64_1425`
700×	`sqrt-prod_binary64_1440`
594×	`times-frac_binary64_1431`
280×	`distribute-lft-out_binary64_1378`
254×	`add-sqr-sqrt_binary64_1446`
252×	`add-cube-cbrt_binary64_1457`
36×	`associate-/l*_binary64_1372`
28×	`sqrt-div_binary64_1441`
24×	`associate-/r/_binary64_1373`
18×	`associate-/r*_binary64_1371`
17×	`add-exp-log_binary64_1460`
14×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
12×	`div-inv_binary64_1422`
11×	`add-cbrt-cube_binary64_1458`
8×	`div-exp_binary64_1473` `pow1_binary64_1483`
4×	`cbrt-undiv_binary64_1456` `add-log-exp_binary64_1461`
3×	`pow-flip_binary64_1496` `pow1/2_binary64_1502` `sqrt-pow1_binary64_1442`
2×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `1-exp_binary64_1466` `rem-sqrt-square_binary64_1438` `rec-exp_binary64_1472`
1×	`inv-pow_binary64_1507` `associate-/l/_binary64_1374`

Counts

4 → 453

Calls

4 calls:

38.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
14.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
10.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
9.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series329.0ms (8%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
86.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
74.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
68.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

simplify219.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4902	17550
1	4902	17550

prune1.2s (28.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	461	4	465
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	465	9	474

Merged error: 0.0b

Counts

474 → 9

Compiler

Compiled 12982 to 9495 computations (26.9% saved)

regimes28.0ms (0.7%)

Compiler: Compiled 222 to 177 computations (20.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	13	26

end0.0ms (0%)

sample811.0ms (19.8%)

Algorithm

1×

intervals

Results

193.0ms	1971×	body	1024	valid
128.0ms	4331×	body	128	valid
69.0ms	964×	body	512	valid
28.0ms	222×	body	2048	valid
25.0ms	512×	body	256	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 253 to 205 computations (19% saved)

Details

analyze2.0ms (0.1%)

sample19.0ms (0.5%)

simplify175.0ms (4.3%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite16.0ms (0.4%)

series102.0ms (2.5%)

simplify90.0ms (2.2%)

prune48.0ms (1.2%)

localize6.0ms (0.1%)

rewrite30.0ms (0.7%)

series135.0ms (3.3%)

simplify64.0ms (1.6%)

prune100.0ms (2.4%)

localize9.0ms (0.2%)

rewrite69.0ms (1.7%)

series179.0ms (4.4%)

simplify84.0ms (2.1%)

prune212.0ms (5.2%)

localize13.0ms (0.3%)

rewrite167.0ms (4.1%)

series329.0ms (8%)

simplify219.0ms (5.3%)

prune1.2s (28.7%)

regimes28.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample811.0ms (19.8%)

Profiling