Details

analyze79.0ms (1.2%)

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)

sample26.0ms (0.4%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid
1.0ms	10×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify156.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	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

Error

0.1b

Counts

2 → 2

Compiler

Compiled 48 to 45 computations (6.3% saved)

localize9.0ms (0.1%)

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

rewrite194.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

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

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)))))
9.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.0ms	(*.f64 (-.f64 a 1/3) 9)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 2373 to 1883 computations (20.6% saved)

series301.0ms (4.5%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

133.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
100.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
31.0ms	(*.f64 (-.f64 a 1/3) 9)
14.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 850 to 737 computations (13.3% saved)

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5010	2067

prune160.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	116	9	125

Error

Counts

125 → 9

Compiler

Compiled 2553 to 2019 computations (20.9% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite115.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

20×	`add-sqr-sqrt_binary64_1464`
16×	`*-un-lft-identity_binary64_1442`
11×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
10×	`add-cube-cbrt_binary64_1477`
9×	`associate-r_binary64_1382`
8×	`add-log-exp_binary64_1481`
6×	`associate-r/_binary64_1384` `associate-l*_binary64_1383` `sqrt-prod_binary64_1458` `cancel-sign-sub-inv_binary64_1408`
4×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417`
3×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
2×	`*-commutative_binary64_1373` `unswap-sqr_binary64_1410` `diff-log_binary64_1534` `sub-neg_binary64_1435`

Counts

4 → 78

Calls

4 calls:

11.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
8.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(-.f64 a 1/3)
4.0ms	(-.f64 a 1/3)

Compiler

Compiled 1445 to 1112 computations (23% saved)

series193.0ms (2.9%)

Error

Counts

4 → 24

Calls

4 calls:

75.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
56.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
23.0ms	(-.f64 a 1/3)
21.0ms	(-.f64 a 1/3)

Compiler

Compiled 806 to 676 computations (16.1% saved)

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5203	922

prune100.0ms (1.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	103	8	111

Error

Counts

111 → 8

Compiler

Compiled 1670 to 1284 computations (23.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite103.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

18×	`add-sqr-sqrt_binary64_1464`
16×	`*-un-lft-identity_binary64_1442`
11×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `associate-r_binary64_1382`
10×	`add-cube-cbrt_binary64_1477`
8×	`add-log-exp_binary64_1481`
6×	`cancel-sign-sub-inv_binary64_1408`
5×	`sqrt-prod_binary64_1458`
4×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `associate-l_binary64_1383`
3×	`flip3--_binary64_1446` `flip--_binary64_1417` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
2×	`-commutative_binary64_1373` `sqrt-div_binary64_1459` `associate-r/_binary64_1384` `diff-log_binary64_1534` `sub-neg_binary64_1435`
1×	`unswap-sqr_binary64_1410`

Counts

4 → 75

Calls

4 calls:

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

Compiler

Compiled 1348 to 1043 computations (22.6% saved)

series159.0ms (2.4%)

Error

Counts

4 → 21

Calls

4 calls:

84.0ms	(.f64 (.f64 1/3 rand) (sqrt.f64 (-.f64 a 1/3)))
21.0ms	(-.f64 a 1/3)
21.0ms	(-.f64 a 1/3)
18.0ms	(*.f64 1/3 rand)

Compiler

Compiled 681 to 578 computations (15.1% saved)

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4890	767
1	4890	767

prune93.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	96	8	104

Error

Counts

104 → 8

Compiler

Compiled 1546 to 1194 computations (22.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.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)))

rewrite842.0ms (12.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

372×	`times-frac_binary64_1448`
247×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
218×	`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`
16×	`sqrt-div_binary64_1459` `associate-/r/_binary64_1388`
14×	`associate-/r*_binary64_1386`
13×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
12×	`flip3--_binary64_1446` `flip--_binary64_1417`
9×	`div-inv_binary64_1439`
6×	`pow1_binary64_1503` `add-log-exp_binary64_1481`
5×	`associate-l_binary64_1383`
4×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-times_binary64_1452` `associate-r_binary64_1382`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `cancel-sign-sub-inv_binary64_1408`
2×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-l/_binary64_1385` `associate-r/_binary64_1384`
1×	`associate-/l/_binary64_1389` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `distribute-lft-out_binary64_1393` `*-commutative_binary64_1373` `diff-log_binary64_1534` `sub-neg_binary64_1435`

Counts

4 → 327

Calls

4 calls:

55.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
19.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(-.f64 a 1/3)

Compiler

Compiled 9338 to 7317 computations (21.6% saved)

series389.0ms (5.8%)

Error

Counts

4 → 27

Calls

4 calls:

146.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
101.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
99.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
24.0ms	(-.f64 a 1/3)

Compiler

Compiled 1065 to 926 computations (13.1% saved)

simplify136.0ms (2%)

Algorithm

1×	egg-herbie

Counts

354 → 354

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4981	8537
1	4981	8537

prune579.0ms (8.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	353	1	354
Fresh	1	3	4
Picked	0	1	1
Done	0	3	3
Total	354	8	362

Error

Counts

362 → 8

Compiler

Compiled 8452 to 6438 computations (23.8% saved)

regimes555.0ms (8.3%)

Accuracy

Total 0.1b remaining (98.3%)

Threshold costs 0.1b (98.3%)

Compiler

Compiled 6290 to 5538 computations (12% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	24
1	27	24

end0.0ms (0%)

sample2.3s (33.8%)

Algorithm

1×

intervals

Results

473.0ms	8000×	body	128	valid
14.0ms	255×	body	128	invalid
14.0ms	266×	body	128	nan

Compiler

Compiled 1596 to 1406 computations (11.9% saved)

Details

analyze79.0ms (1.2%)

sample26.0ms (0.4%)

simplify156.0ms (2.3%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

rewrite194.0ms (2.9%)

series301.0ms (4.5%)

simplify65.0ms (1%)

prune160.0ms (2.4%)

localize7.0ms (0.1%)

rewrite115.0ms (1.7%)

series193.0ms (2.9%)

simplify65.0ms (1%)

prune100.0ms (1.5%)

localize7.0ms (0.1%)

rewrite103.0ms (1.5%)

series159.0ms (2.4%)

simplify69.0ms (1%)

prune93.0ms (1.4%)

localize10.0ms (0.2%)

rewrite842.0ms (12.6%)

series389.0ms (5.8%)

simplify136.0ms (2%)

prune579.0ms (8.7%)

regimes555.0ms (8.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.3s (33.8%)

Profiling