Details

analyze81.0ms (2%)

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 (0.6%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	12×	body	128	invalid
1.0ms	11×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify157.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune8.0ms (0.2%)

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

rewrite46.0ms (1.1%)

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:

16.0ms	(.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)))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series277.0ms (6.8%)

Counts

4 → 22

Calls

4 calls:

147.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
98.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
16.0ms	(*.f64 (-.f64 a 1/3) 9)
16.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 592 to 542 computations (8.4% saved)

simplify67.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5103	2058

prune168.0ms (4.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	115	6	121
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	6	123

Merged error: 0.0b

Counts

123 → 6

Compiler

Compiled 2510 to 1981 computations (21.1% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (*.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))))))
0.2b	(/.f64 rand (sqrt.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))))
0.2b	(.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))
0.3b	(sqrt.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)))

rewrite59.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
17×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
14×	`associate-*l/_binary64_1385`
13×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
12×	`times-frac_binary64_1448`
10×	`associate-r_binary64_1382`
8×	`sqrt-prod_binary64_1458`
7×	`pow-prod-down_binary64_1513`
6×	`flip3--_binary64_1446` `associate-l_binary64_1383` `flip--_binary64_1417`
4×	`associate-/r*_binary64_1386` `cbrt-unprod_binary64_1475` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481` `frac-times_binary64_1452` `prod-exp_binary64_1491`
3×	`sqrt-pow1_binary64_1460` `associate-/l*_binary64_1387` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`associate-r/_binary64_1384` `associate-/r/_binary64_1388` `-commutative_binary64_1373`
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` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`

Counts

4 → 101

Calls

4 calls:

18.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (*.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))))))
12.0ms	(/.f64 rand (sqrt.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))))
10.0ms	(.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))
8.0ms	(sqrt.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)))

series298.0ms (7.3%)

Counts

4 → 22

Calls

4 calls:

157.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (*.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))))))
103.0ms	(/.f64 rand (sqrt.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))))
20.0ms	(.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))
16.0ms	(sqrt.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)))

Compiler

Compiled 592 to 542 computations (8.4% saved)

simplify70.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4973	2092
1	4973	2092

prune151.0ms (3.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	123	6	129

Merged error: 0.0b

Counts

129 → 6

Compiler

Compiled 2610 to 2083 computations (20.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
0.0b	(sqrt.f64 (-.f64 a 1/3))
0.3b	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
0.4b	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1464`
14×	`*-un-lft-identity_binary64_1442`
12×	`pow1_binary64_1503`
11×	`add-cbrt-cube_binary64_1478` `associate-l_binary64_1383` `add-exp-log_binary64_1480` `sqrt-prod_binary64_1458`
10×	`sqrt-div_binary64_1459` `add-cube-cbrt_binary64_1477`
9×	`add-log-exp_binary64_1481`
8×	`associate-*l/_binary64_1385`
7×	`flip3--_binary64_1446` `flip--_binary64_1417`
6×	`associate-*r/_binary64_1384`
4×	`associate-r_binary64_1382` `cbrt-unprod_binary64_1475` `associate-+l+_binary64_1375` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `frac-add_binary64_1450`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`sum-log_binary64_1533` `*-commutative_binary64_1373` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `unswap-sqr_binary64_1410`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `sub-neg_binary64_1435` `+-commutative_binary64_1372` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522` `associate-+l-_binary64_1377`

Counts

4 → 84

Calls

4 calls:

12.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
9.0ms	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
9.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
4.0ms	(sqrt.f64 (-.f64 a 1/3))

series253.0ms (6.2%)

Counts

4 → 24

Calls

4 calls:

91.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
80.0ms	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
69.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
13.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 607 to 550 computations (9.4% saved)

simplify73.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4986	1596
1	4986	1596

prune116.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	107	7	114

Merged error: 0b

Counts

114 → 7

Compiler

Compiled 1897 to 1457 computations (23.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand))
0.0b	(sqrt.f64 (-.f64 a 1/3))
0.3b	(.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand)
0.4b	(*.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1464`
14×	`*-un-lft-identity_binary64_1442`
12×	`pow1_binary64_1503`
11×	`associate-r_binary64_1382` `add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `sqrt-prod_binary64_1458`
10×	`sqrt-div_binary64_1459` `add-cube-cbrt_binary64_1477`
9×	`add-log-exp_binary64_1481`
8×	`associate-*r/_binary64_1384`
7×	`flip3--_binary64_1446` `flip--_binary64_1417`
6×	`associate-*l/_binary64_1385`
4×	`cbrt-unprod_binary64_1475` `associate-+l+_binary64_1375` `associate-l_binary64_1383` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `frac-add_binary64_1450`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`sum-log_binary64_1533` `*-commutative_binary64_1373` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `unswap-sqr_binary64_1410`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `sub-neg_binary64_1435` `+-commutative_binary64_1372` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522` `associate-+l-_binary64_1377`

Counts

4 → 84

Calls

4 calls:

10.0ms	(.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand)
9.0ms	(*.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))
9.0ms	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand))
4.0ms	(sqrt.f64 (-.f64 a 1/3))

series210.0ms (5.1%)

Counts

4 → 21

Calls

4 calls:

97.0ms	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand))
82.0ms	(.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand)
17.0ms	(*.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))
14.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 517 to 473 computations (8.5% saved)

simplify91.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4860	1552
1	4860	1552

prune103.0ms (2.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	105	7	112

Merged error: 0b

Counts

112 → 7

Compiler

Compiled 1728 to 1326 computations (23.3% saved)

regimes299.0ms (7.3%)

Compiler: Compiled 3178 to 2802 computations (11.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	24
1	24	24

end0.0ms (0%)

sample1.4s (34.9%)

Algorithm

1×

intervals

Results

464.0ms	8000×	body	128	valid
17.0ms	256×	body	128	invalid
14.0ms	265×	body	128	nan

Compiler

Compiled 818 to 722 computations (11.7% saved)

Details

analyze81.0ms (2%)

sample23.0ms (0.6%)

simplify157.0ms (3.8%)

prune8.0ms (0.2%)

localize9.0ms (0.2%)

rewrite46.0ms (1.1%)

series277.0ms (6.8%)

simplify67.0ms (1.6%)

prune168.0ms (4.1%)

localize11.0ms (0.3%)

rewrite59.0ms (1.4%)

series298.0ms (7.3%)

simplify70.0ms (1.7%)

prune151.0ms (3.7%)

localize7.0ms (0.2%)

rewrite41.0ms (1%)

series253.0ms (6.2%)

simplify73.0ms (1.8%)

prune116.0ms (2.8%)

localize7.0ms (0.2%)

rewrite38.0ms (0.9%)

series210.0ms (5.1%)

simplify91.0ms (2.2%)

prune103.0ms (2.5%)

regimes299.0ms (7.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (34.9%)

Profiling