Details

analyze343.0ms (2.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2024	42
1	2024	42
0	2	2
1	2	2

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)

sample28.0ms (0.2%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
0.0ms	8×	body	128	nan
0.0ms	7×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune4.0ms (0%)

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)

localize8.0ms (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))
0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

rewrite188.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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)))))
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))

Compiler

Compiled 2373 to 1883 computations (20.6% saved)

series313.0ms (2.2%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

139.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
104.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
33.0ms	(*.f64 (-.f64 a 1/3) 9)
16.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 850 to 737 computations (13.3% saved)

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5010	2067

prune152.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	120	5	125

Error

0.0b

Counts

125 → 5

Compiler

Compiled 2466 to 1942 computations (21.2% saved)

localize9.0ms (0.1%)

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

rewrite869.0ms (6.2%)

Algorithm

1×	rewrite-expression-head

Error

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-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
12×	`flip3--_binary64_1446` `flip--_binary64_1417`
9×	`div-inv_binary64_1439`
7×	`pow1_binary64_1503`
5×	`associate-l_binary64_1383`
4×	`div-exp_binary64_1493` `add-log-exp_binary64_1481` `cbrt-undiv_binary64_1476` `frac-times_binary64_1452` `associate-r_binary64_1382`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
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` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455`

Counts

4 → 328

Calls

4 calls:

59.0ms	(*.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)))
4.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 9369 to 7342 computations (21.6% saved)

series347.0ms (2.5%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

132.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
94.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
89.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
15.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 994 to 863 computations (13.2% saved)

simplify140.0ms (1%)

Algorithm

1×	egg-herbie

Counts

352 → 352

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4958	8590
1	4958	8590

prune599.0ms (4.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	351	1	352
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	353	4	357

Error

Counts

357 → 4

Compiler

Compiled 8497 to 6484 computations (23.7% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite133.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 84

Calls

4 calls:

8.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
8.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
8.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
3.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 1785 to 1369 computations (23.3% saved)

series254.0ms (1.8%)

Error

Counts

4 → 24

Calls

4 calls:

89.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
79.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
59.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
13.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 788 to 671 computations (14.8% saved)

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4934	1567
1	4934	1567

prune106.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	108	4	112

Error

Counts

112 → 4

Compiler

Compiled 1805 to 1378 computations (23.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite3.9s (27.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

1094×	`times-frac_binary64_1448`
740×	`add-sqr-sqrt_binary64_1464`
698×	`sqrt-prod_binary64_1458`
633×	`*-un-lft-identity_binary64_1442`
499×	`add-cube-cbrt_binary64_1477`
277×	`associate-r_binary64_1382`
192×	`cbrt-prod_binary64_1473`
62×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
52×	`add-exp-log_binary64_1480`
40×	`sqrt-div_binary64_1459` `associate-/r/_binary64_1388`
34×	`add-cbrt-cube_binary64_1478`
33×	`associate-/l*_binary64_1387`
31×	`unswap-sqr_binary64_1410`
23×	`div-inv_binary64_1439` `flip3--_binary64_1446` `flip--_binary64_1417`
22×	`div-exp_binary64_1493`
18×	`associate-l_binary64_1383`
17×	`associate-/r*_binary64_1386`
13×	`cbrt-undiv_binary64_1476` `prod-exp_binary64_1491`
8×	`pow1_binary64_1503`
7×	`cbrt-unprod_binary64_1475`
5×	`frac-times_binary64_1452`
4×	`add-log-exp_binary64_1481`
3×	`1-exp_binary64_1486` `rec-exp_binary64_1492` `associate-l/_binary64_1385` `associate-r/_binary64_1384` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373`
1×	`associate-/l/_binary64_1389` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391`

Counts

4 → 750

Calls

4 calls:

312.0ms	(*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 9))) (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9))))
24.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9)))
10.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 9))) (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9))))))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 28719 to 23956 computations (16.6% saved)

series696.0ms (5%)

Error

Counts

4 → 27

Calls

4 calls:

233.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 9))) (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9))))))
190.0ms	(*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 9))) (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9))))
145.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9)))
100.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 1709 to 1557 computations (8.9% saved)

simplify295.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

777 → 777

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4987	24283
1	4987	24283

prune2.9s (21%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	777	0	777
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	777	4	781

Error

Counts

781 → 4

Compiler

Compiled 26363 to 21659 computations (17.8% saved)

regimes450.0ms (3.2%)

Accuracy

Total 0.1b remaining (97.7%)

Threshold costs 0.1b (97.7%)

Compiler

Compiled 5278 to 4714 computations (10.7% 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%)

sample2.0s (14%)

Algorithm

1×

intervals

Results

455.0ms	8000×	body	128	valid
16.0ms	292×	body	128	invalid
13.0ms	261×	body	128	nan

Compiler

Compiled 1343 to 1200 computations (10.6% saved)

Details

analyze343.0ms (2.5%)

sample28.0ms (0.2%)

simplify70.0ms (0.5%)

prune4.0ms (0%)

localize8.0ms (0.1%)

rewrite188.0ms (1.3%)

series313.0ms (2.2%)

simplify66.0ms (0.5%)

prune152.0ms (1.1%)

localize9.0ms (0.1%)

rewrite869.0ms (6.2%)

series347.0ms (2.5%)

simplify140.0ms (1%)

prune599.0ms (4.3%)

localize7.0ms (0%)

rewrite133.0ms (1%)

series254.0ms (1.8%)

simplify72.0ms (0.5%)

prune106.0ms (0.8%)

localize13.0ms (0.1%)

rewrite3.9s (27.9%)

series696.0ms (5%)

simplify295.0ms (2.1%)

prune2.9s (21%)

regimes450.0ms (3.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (14%)

Profiling