Details

analyze95.0ms (1.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 13 to 13 computations (0% saved)

sample40.0ms (0.5%)

Algorithm

1×

intervals

Results

20.0ms	64×	body	2048	valid
6.0ms	34×	body	1024	valid
5.0ms	135×	body	128	valid
2.0ms	18×	body	512	valid
0.0ms	5×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 15.4b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(hypot.f64 1 x)
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
2.0b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_1442`
24×	`add-sqr-sqrt_binary64_1464`
15×	`add-cube-cbrt_binary64_1477`
12×	`sqrt-prod_binary64_1458`
9×	`times-frac_binary64_1448`
7×	`cancel-sign-sub-inv_binary64_1408`
6×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
5×	`pow1_binary64_1503`
4×	`difference-of-squares_binary64_1411`
3×	`associate-/r_binary64_1386` `associate-/l_binary64_1387` `distribute-lft-out_binary64_1393` `distribute-lft-out--_binary64_1394`
2×	`sqrt-div_binary64_1459`
1×	`sqrt-pow1_binary64_1460` `cbrt-undiv_binary64_1476` `rem-sqrt-square_binary64_1455` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `flip3--_binary64_1446` `flip--_binary64_1417` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522` `div-exp_binary64_1493`

Counts

4 → 75

Calls

4 calls:

10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
1.0ms	(hypot.f64 1 x)

series327.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
55.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
21.0ms	(/.f64 1/2 (hypot.f64 1 x))
3.0ms	(hypot.f64 1 x)

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4821	1307
1	4821	1307

prune93.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 14.9b

Counts

88 → 4

Compiler

Compiled 1393 to 1266 computations (9.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
1.5b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
28×	`times-frac_binary64_1448`
27×	`add-cube-cbrt_binary64_1477`
13×	`cancel-sign-sub-inv_binary64_1408`
8×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
6×	`associate-/r_binary64_1386` `associate-/l_binary64_1387`
4×	`distribute-lft-out_binary64_1393` `pow1_binary64_1503`
3×	`div-inv_binary64_1439`
2×	`cbrt-undiv_binary64_1476` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `sqrt-prod_binary64_1458` `difference-of-squares_binary64_1411` `div-exp_binary64_1493`
1×	`sum-log_binary64_1533` `sub-neg_binary64_1435` `flip3--_binary64_1446` `+-commutative_binary64_1372` `flip--_binary64_1417` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-lft-out--_binary64_1394`

Counts

4 → 95

Calls

4 calls:

8.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

series146.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
45.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
24.0ms	(/.f64 1/2 (hypot.f64 1 x))
21.0ms	(/.f64 1/2 (hypot.f64 1 x))

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4940	1445
1	4940	1445

prune151.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	108	3	111

Merged error: 14.6b

Counts

111 → 3

Compiler

Compiled 2500 to 2240 computations (10.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3/2))
0.0b	(/.f64 (-.f64 1 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)) (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3/2)))
0.5b	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)
1.5b	(-.f64 1 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3))

rewrite108.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

191×	`*-un-lft-identity_binary64_1442`
149×	`add-sqr-sqrt_binary64_1464`
84×	`difference-of-squares_binary64_1411`
80×	`times-frac_binary64_1448`
58×	`distribute-lft-out_binary64_1393`
44×	`sqrt-prod_binary64_1458`
42×	`cube-prod_binary64_1470` `unpow-prod-down_binary64_1521`
37×	`add-cube-cbrt_binary64_1477`
20×	`cancel-sign-sub-inv_binary64_1408`
16×	`associate-/l*_binary64_1387` `sqr-pow_binary64_1414`
11×	`add-log-exp_binary64_1481`
7×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `distribute-lft-out--_binary64_1394`
6×	`pow1_binary64_1503`
5×	`associate-/r*_binary64_1386` `flip3-+_binary64_1445` `flip-+_binary64_1416`
4×	`associate-/r/_binary64_1388` `frac-add_binary64_1450`
3×	`sum-log_binary64_1533` `pow-unpow_binary64_1519` `pow-pow_binary64_1514`
2×	`cube-mult_binary64_1472` `associate-/l/_binary64_1389` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417` `unpow3_binary64_1508` `cube-div_binary64_1471`
1×	`sqrt-pow1_binary64_1460` `cbrt-undiv_binary64_1476` `pow-exp_binary64_1510` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `+-commutative_binary64_1372` `rem-cube-cbrt_binary64_1465` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `pow1/2_binary64_1522` `div-sub_binary64_1447` `sqrt-pow2_binary64_1461` `associate-+r+_binary64_1374` `div-exp_binary64_1493` `pow-to-exp_binary64_1511`

Counts

4 → 217

Calls

4 calls:

39.0ms	(/.f64 (-.f64 1 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)) (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3/2)))
16.0ms	(+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3/2))
14.0ms	(-.f64 1 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3))
8.0ms	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)

series648.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

341.0ms	(/.f64 (-.f64 1 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)) (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3/2)))
141.0ms	(-.f64 1 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3))
84.0ms	(+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3/2))
82.0ms	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)

simplify163.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4918	10993
1	4918	10993

prune984.0ms (12.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	229	3	232

Merged error: 14.6b

Counts

232 → 3

Compiler

Compiled 10020 to 9042 computations (9.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (+.f64 1 (sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3))) (/.f64 (-.f64 1 (sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3))) (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3/2))))
0.5b	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)
0.5b	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)
1.5b	(-.f64 1 (sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)))

rewrite161.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

216×	`*-un-lft-identity_binary64_1442`
172×	`add-sqr-sqrt_binary64_1464`
147×	`sqrt-prod_binary64_1458`
103×	`associate-r_binary64_1382`
96×	`times-frac_binary64_1448`
84×	`difference-of-squares_binary64_1411`
65×	`distribute-lft-out_binary64_1393`
46×	`add-cube-cbrt_binary64_1477`
45×	`cube-prod_binary64_1470` `unpow-prod-down_binary64_1521`
23×	`cancel-sign-sub-inv_binary64_1408`
15×	`sqr-pow_binary64_1414`
12×	`distribute-lft-out--_binary64_1394`
11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
10×	`pow1_binary64_1503`
6×	`pow-unpow_binary64_1519` `add-log-exp_binary64_1481` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow-pow_binary64_1514`
5×	`associate-l_binary64_1383`
4×	`associate-/r/_binary64_1388` `sqrt-div_binary64_1459` `cube-div_binary64_1471`
3×	`cube-mult_binary64_1472` `unpow3_binary64_1508`
2×	`sqrt-pow1_binary64_1460` `cbrt-unprod_binary64_1475` `pow-exp_binary64_1510` `rem-cube-cbrt_binary64_1465` `frac-times_binary64_1452` `pow1/2_binary64_1522` `prod-exp_binary64_1491` `frac-add_binary64_1450` `sqrt-pow2_binary64_1461` `associate-*l/_binary64_1385` `pow-to-exp_binary64_1511` `unswap-sqr_binary64_1410`
1×	`associate-r/_binary64_1384` `cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `sub-neg_binary64_1435` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `flip--_binary64_1417` `diff-log_binary64_1534` `div-exp_binary64_1493`

Counts

4 → 250

Calls

4 calls:

76.0ms	(*.f64 (+.f64 1 (sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3))) (/.f64 (-.f64 1 (sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3))) (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3/2))))
16.0ms	(-.f64 1 (sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)))
8.0ms	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)
8.0ms	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)

series1.1s (13.8%)

Counts

4 → 12

Calls

4 calls:

673.0ms	(*.f64 (+.f64 1 (sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3))) (/.f64 (-.f64 1 (sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3))) (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3/2))))
219.0ms	(-.f64 1 (sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)))
88.0ms	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)
88.0ms	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)

simplify145.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5007	11009

prune1.6s (20.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	261	1	262
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	262	3	265

Merged error: 14.6b

Counts

265 → 3

Compiler

Compiled 15402 to 14038 computations (8.9% saved)

regimes233.0ms (3%)

Compiler: Compiled 2936 to 2768 computations (5.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	27
1	30	27

end0.0ms (0%)

sample1.5s (19.9%)

Algorithm

1×

intervals

Results

503.0ms	2033×	body	2048	valid
178.0ms	973×	body	1024	valid
177.0ms	4272×	body	128	valid
61.0ms	465×	body	512	valid
21.0ms	257×	body	256	valid

Compiler

Compiled 437 to 413 computations (5.5% saved)

Details

analyze95.0ms (1.2%)

sample40.0ms (0.5%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite24.0ms (0.3%)

series327.0ms (4.2%)

simplify84.0ms (1.1%)

prune93.0ms (1.2%)

localize9.0ms (0.1%)

rewrite28.0ms (0.4%)

series146.0ms (1.9%)

simplify74.0ms (1%)

prune151.0ms (2%)

localize12.0ms (0.2%)

rewrite108.0ms (1.4%)

series648.0ms (8.4%)

simplify163.0ms (2.1%)

prune984.0ms (12.7%)

localize17.0ms (0.2%)

rewrite161.0ms (2.1%)

series1.1s (13.8%)

simplify145.0ms (1.9%)

prune1.6s (20.1%)

regimes233.0ms (3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.5s (19.9%)

Profiling