Details

analyze76.0ms (1.4%)

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)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	14×	body	128	nan
1.0ms	9×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify231.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	1030	21
1	1030	21

prune4.0ms (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	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite52.0ms (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:

20.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
9.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
7.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series300.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
78.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
40.0ms	(*.f64 (-.f64 a 1/3) 9)
38.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5478	2236

prune163.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Merged error: 0.0b

Counts

113 → 8

Compiler

Compiled 2615 to 2037 computations (22.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
0.2b	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
1.0b	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))

rewrite67.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_1448`
69×	`*-un-lft-identity_binary64_1442`
68×	`add-sqr-sqrt_binary64_1464`
64×	`add-cube-cbrt_binary64_1477`
19×	`associate-/r*_binary64_1386` `add-exp-log_binary64_1480`
17×	`sqrt-prod_binary64_1458`
13×	`add-cbrt-cube_binary64_1478`
10×	`pow1_binary64_1503`
8×	`div-exp_binary64_1493`
7×	`div-inv_binary64_1439` `associate-/l*_binary64_1387`
6×	`associate-*l/_binary64_1385`
5×	`associate-r_binary64_1382` `flip3--_binary64_1446` `associate-l_binary64_1383` `flip--_binary64_1417`
4×	`cbrt-undiv_binary64_1476` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481` `frac-times_binary64_1452`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`sqrt-pow1_binary64_1460` `associate-*r/_binary64_1384` `associate-/l/_binary64_1389` `clear-num_binary64_1441` `1-exp_binary64_1486` `pow-prod-down_binary64_1513` `rec-exp_binary64_1492` `distribute-lft-out_binary64_1393` `frac-2neg_binary64_1453`
1×	`inv-pow_binary64_1527` `cbrt-unprod_binary64_1475` `associate-/r/_binary64_1388` `*-commutative_binary64_1373` `pow-flip_binary64_1516` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `pow1/2_binary64_1522` `prod-exp_binary64_1491` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `unswap-sqr_binary64_1410`

Counts

4 → 166

Calls

4 calls:

25.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
11.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))
9.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series381.0ms (7%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))
123.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
80.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
34.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify91.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4943	4358
1	4943	4358

prune279.0ms (5.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	176	10	186

Merged error: 0.0b

Counts

186 → 10

Compiler

Compiled 4656 to 3601 computations (22.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))))
0.3b	(.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
0.3b	(/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite52.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1464`
27×	`*-un-lft-identity_binary64_1442`
26×	`times-frac_binary64_1448`
24×	`add-cube-cbrt_binary64_1477`
21×	`associate-r_binary64_1382`
19×	`add-exp-log_binary64_1480`
15×	`pow1_binary64_1503`
13×	`add-cbrt-cube_binary64_1478`
8×	`associate-l_binary64_1383` `sqrt-prod_binary64_1458` `associate-*l/_binary64_1385`
6×	`flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417`
5×	`prod-exp_binary64_1491`
4×	`sqrt-pow1_binary64_1460` `associate-/r*_binary64_1386` `associate-/r/_binary64_1388` `pow-prod-down_binary64_1513` `add-log-exp_binary64_1481` `pow-flip_binary64_1516` `frac-times_binary64_1452` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`
3×	`associate-r/_binary64_1384` `cbrt-unprod_binary64_1475` `associate-/l_binary64_1387` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `1-exp_binary64_1486` `*-commutative_binary64_1373` `rec-exp_binary64_1492` `pow1/2_binary64_1522`
1×	`inv-pow_binary64_1527` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `un-div-inv_binary64_1440` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`

Counts

4 → 124

Calls

4 calls:

16.0ms	(.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
10.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))))
9.0ms	(/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series309.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

136.0ms	(.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
89.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))))
45.0ms	(/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
38.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5023	2772

prune195.0ms (3.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	136	10	146

Merged error: 0b

Counts

146 → 10

Compiler

Compiled 3388 to 2714 computations (19.9% saved)

localize13.0ms (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 rand (sqrt.f64 (-.f64 a 1/3)))
0.2b	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))

rewrite139.0ms (2.5%)

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:

66.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
17.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(sqrt.f64 (-.f64 a 1/3))

series355.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

137.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
103.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
89.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
25.0ms	(sqrt.f64 (-.f64 a 1/3))

simplify134.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4947	9006
1	4947	9006

prune666.0ms (12.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	339	1	340
Fresh	4	3	7
Picked	0	1	1
Done	0	2	2
Total	343	7	350

Merged error: 0b

Counts

350 → 7

Compiler

Compiled 8653 to 6512 computations (24.7% saved)

regimes322.0ms (5.9%)

Compiler: Compiled 3694 to 3226 computations (12.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	24
1	24	24

end0.0ms (0%)

sample1.5s (26.9%)

Algorithm

1×

intervals

Results

449.0ms	8000×	body	128	valid
15.0ms	267×	body	128	invalid
13.0ms	249×	body	128	nan

Compiler

Compiled 947 to 828 computations (12.6% saved)

Details

analyze76.0ms (1.4%)

sample22.0ms (0.4%)

simplify231.0ms (4.2%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite52.0ms (1%)

series300.0ms (5.5%)

simplify53.0ms (1%)

prune163.0ms (3%)

localize10.0ms (0.2%)

rewrite67.0ms (1.2%)

series381.0ms (7%)

simplify91.0ms (1.7%)

prune279.0ms (5.1%)

localize10.0ms (0.2%)

rewrite52.0ms (1%)

series309.0ms (5.6%)

simplify58.0ms (1.1%)

prune195.0ms (3.6%)

localize13.0ms (0.2%)

rewrite139.0ms (2.5%)

series355.0ms (6.5%)

simplify134.0ms (2.5%)

prune666.0ms (12.2%)

regimes322.0ms (5.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.5s (26.9%)

Profiling