Details

analyze80.0ms (1.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

Compiler

Compiled 21 to 20 computations (4.8% saved)

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
0.0ms	9×	body	128	nan
0.0ms	4×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify160.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

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

Merged error: 0.1b

Counts

2 → 2

Compiler

Compiled 48 to 45 computations (6.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.2b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1464`
23×	`*-un-lft-identity_binary64_1442`
17×	`add-cube-cbrt_binary64_1477`
12×	`times-frac_binary64_1448`
11×	`pow1_binary64_1503`
10×	`add-cbrt-cube_binary64_1478` `associate-l_binary64_1383` `add-exp-log_binary64_1480`
8×	`associate-*l/_binary64_1385`
7×	`associate-r_binary64_1382`
6×	`flip3--_binary64_1446` `flip--_binary64_1417`
5×	`sqrt-prod_binary64_1458`
4×	`associate-/r*_binary64_1386` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481` `frac-times_binary64_1452`
3×	`associate-/l*_binary64_1387` `pow-prod-down_binary64_1513` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `cbrt-unprod_binary64_1475` `associate-/r/_binary64_1388` `-commutative_binary64_1373` `prod-exp_binary64_1491` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `unswap-sqr_binary64_1410`
1×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `clear-num_binary64_1441` `distribute-lft-out_binary64_1393` `frac-2neg_binary64_1453` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `pow1/2_binary64_1522` `div-exp_binary64_1493`

Counts

4 → 99

Calls

4 calls:

15.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
8.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.0ms	(*.f64 (-.f64 a 1/3) 9)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series150.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
42.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
20.0ms	(*.f64 (-.f64 a 1/3) 9)
19.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify52.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4954	2236
1	4954	2236

prune156.0ms (3.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	108	5	113

Merged error: 0b

Counts

113 → 5

Compiler

Compiled 2535 to 1969 computations (22.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a 1/3))
0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
0.2b	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
0.2b	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

rewrite121.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

372×	`times-frac_binary64_1448`
248×	`add-sqr-sqrt_binary64_1464`
247×	`*-un-lft-identity_binary64_1442`
223×	`sqrt-prod_binary64_1458`
191×	`add-cube-cbrt_binary64_1477`
33×	`associate-/l*_binary64_1387`
27×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
18×	`sqrt-div_binary64_1459`
16×	`associate-/r/_binary64_1388`
14×	`associate-/r*_binary64_1386`
13×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
12×	`flip3--_binary64_1446` `flip--_binary64_1417`
9×	`div-inv_binary64_1439`
7×	`pow1_binary64_1503`
5×	`associate-l_binary64_1383`
4×	`associate-r_binary64_1382` `cbrt-undiv_binary64_1476` `add-log-exp_binary64_1481` `frac-times_binary64_1452` `div-exp_binary64_1493`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`associate-r/_binary64_1384` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `associate-l/_binary64_1385`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `cbrt-unprod_binary64_1475` `associate-/l/_binary64_1389` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `distribute-lft-out_binary64_1393` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `pow1/2_binary64_1522` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`

Counts

4 → 328

Calls

4 calls:

56.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
15.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
3.0ms	(sqrt.f64 (-.f64 a 1/3))

series183.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
61.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
44.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
15.0ms	(sqrt.f64 (-.f64 a 1/3))

simplify125.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5225	8870

prune636.0ms (14.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	339	1	340
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	340	5	345

Merged error: 0b

Counts

345 → 5

Compiler

Compiled 8646 to 6554 computations (24.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.2b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
9.5b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

rewrite49.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1464`
28×	`*-un-lft-identity_binary64_1442`
25×	`times-frac_binary64_1448`
24×	`add-cube-cbrt_binary64_1477`
21×	`associate-r_binary64_1382`
13×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
11×	`pow1_binary64_1503`
10×	`associate-l_binary64_1383` `associate-*l/_binary64_1385`
8×	`sqrt-prod_binary64_1458`
6×	`flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417`
4×	`associate-/r*_binary64_1386` `associate-/r/_binary64_1388` `add-log-exp_binary64_1481`
3×	`cbrt-unprod_binary64_1475` `associate-/l*_binary64_1387` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`
2×	`sqrt-pow1_binary64_1460` `cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `*-commutative_binary64_1373` `frac-times_binary64_1452` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `div-exp_binary64_1493`
1×	`associate-*r/_binary64_1384` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `pow1/2_binary64_1522`

Counts

4 → 111

Calls

4 calls:

16.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
11.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.0ms	(*.f64 (-.f64 a 1/3) 9)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series157.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
57.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
23.0ms	(*.f64 (-.f64 a 1/3) 9)
18.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify51.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5036	2404

prune165.0ms (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	123	5	128

Merged error: 0b

Counts

128 → 5

Compiler

Compiled 3017 to 2235 computations (25.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a 1/3))
0.0b	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
0.3b	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
0.5b	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

rewrite81.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`add-sqr-sqrt_binary64_1464`
117×	`*-un-lft-identity_binary64_1442`
110×	`times-frac_binary64_1448`
75×	`sqrt-prod_binary64_1458`
59×	`add-cube-cbrt_binary64_1477`
46×	`associate-l_binary64_1383`
29×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
22×	`associate-r_binary64_1382`
18×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
10×	`pow1_binary64_1503`
9×	`add-log-exp_binary64_1481` `unswap-sqr_binary64_1410`
8×	`associate-/r*_binary64_1386`
7×	`flip3--_binary64_1446` `flip--_binary64_1417`
6×	`sqrt-div_binary64_1459` `frac-add_binary64_1450`
5×	`cbrt-undiv_binary64_1476` `associate-/l*_binary64_1387` `div-exp_binary64_1493`
4×	`cbrt-unprod_binary64_1475` `associate-+l+_binary64_1375` `associate-/r/_binary64_1388` `prod-exp_binary64_1491`
3×	`associate-r/_binary64_1384` `cancel-sign-sub-inv_binary64_1408` `div-inv_binary64_1439` `frac-times_binary64_1452` `associate-l/_binary64_1385`
2×	`sqrt-pow1_binary64_1460` `sum-log_binary64_1533` `associate-/l/_binary64_1389` `pow-div_binary64_1517` `pow1/2_binary64_1522`
1×	`rem-sqrt-square_binary64_1455` `sub-neg_binary64_1435` `clear-num_binary64_1441` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416` `div-sub_binary64_1447` `associate-+l-_binary64_1377`

Counts

4 → 209

Calls

4 calls:

33.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
10.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))
7.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
3.0ms	(sqrt.f64 (-.f64 a 1/3))

series139.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
47.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
20.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))
15.0ms	(sqrt.f64 (-.f64 a 1/3))

simplify98.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4942	4585
1	4942	4585

prune340.0ms (7.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	1	1	2
Picked	1	0	1
Done	1	1	2
Total	223	3	226

Merged error: 0b

Counts

226 → 3

Compiler

Compiled 5292 to 4045 computations (23.6% saved)

regimes253.0ms (5.7%)

Compiler: Compiled 2598 to 2314 computations (10.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	21
1	25	21

end0.0ms (0%)

sample1.3s (29.6%)

Algorithm

1×

intervals

Results

479.0ms	8000×	body	128	valid
14.0ms	247×	body	128	invalid
13.0ms	243×	body	128	nan

Compiler

Compiled 671 to 599 computations (10.7% saved)

Details

analyze80.0ms (1.8%)

sample23.0ms (0.5%)

simplify160.0ms (3.6%)

prune5.0ms (0.1%)

localize9.0ms (0.2%)

rewrite43.0ms (1%)

series150.0ms (3.4%)

simplify52.0ms (1.2%)

prune156.0ms (3.5%)

localize9.0ms (0.2%)

rewrite121.0ms (2.7%)

series183.0ms (4.1%)

simplify125.0ms (2.8%)

prune636.0ms (14.4%)

localize9.0ms (0.2%)

rewrite49.0ms (1.1%)

series157.0ms (3.6%)

simplify51.0ms (1.2%)

prune165.0ms (3.7%)

localize10.0ms (0.2%)

rewrite81.0ms (1.8%)

series139.0ms (3.2%)

simplify98.0ms (2.2%)

prune340.0ms (7.7%)

regimes253.0ms (5.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (29.6%)

Profiling