Details

analyze77.0ms (2.1%)

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 (0.6%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
0.0ms	9×	body	128	nan
0.0ms	8×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify227.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	1030	21
1	1030	21

prune6.0ms (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 82 to 77 computations (6.1% 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)))))
0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite45.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1477`
23×	`*-un-lft-identity_binary64_1455`
17×	`add-cube-cbrt_binary64_1490`
12×	`times-frac_binary64_1461`
11×	`pow1_binary64_1516`
10×	`add-cbrt-cube_binary64_1491` `associate-l_binary64_1396` `add-exp-log_binary64_1493`
8×	`associate-*l/_binary64_1398`
7×	`associate-r_binary64_1395`
6×	`flip--_binary64_1430` `flip3--_binary64_1459`
5×	`sqrt-prod_binary64_1471`
4×	`sqrt-div_binary64_1472` `associate-/r*_binary64_1399` `add-log-exp_binary64_1494` `frac-times_binary64_1465`
3×	`flip-+_binary64_1429` `associate-/l*_binary64_1400` `flip3-+_binary64_1458` `pow-prod-down_binary64_1526`
2×	`prod-exp_binary64_1504` `sqrt-pow1_binary64_1473` `associate-r/_binary64_1397` `associate-/r/_binary64_1401` `distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424` `-commutative_binary64_1386` `cbrt-unprod_binary64_1488` `unswap-sqr_binary64_1423`
1×	`distribute-lft-out_binary64_1406` `distribute-rgt-in_binary64_1405` `div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `distribute-lft-in_binary64_1404` `pow1/2_binary64_1535` `div-inv_binary64_1452`

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)))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series298.0ms (8%)

Counts

4 → 12

Calls

4 calls:

141.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
79.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
43.0ms	(*.f64 (-.f64 a 1/3) 9)
36.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify52.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5478	2236

prune359.0ms (9.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	106	7	113

Merged error: 0b

Counts

113 → 7

Compiler

Compiled 6084 to 5127 computations (15.7% saved)

localize10.0ms (0.3%)

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

rewrite66.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_1477`
70×	`times-frac_binary64_1461`
68×	`*-un-lft-identity_binary64_1455`
46×	`add-cube-cbrt_binary64_1490`
39×	`sqrt-prod_binary64_1471`
35×	`associate-l_binary64_1396`
32×	`add-exp-log_binary64_1493`
20×	`add-cbrt-cube_binary64_1491`
16×	`associate-r_binary64_1395`
11×	`unswap-sqr_binary64_1423`
10×	`pow1_binary64_1516` `div-exp_binary64_1506`
9×	`prod-exp_binary64_1504` `distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424`
8×	`associate-/r*_binary64_1399`
6×	`add-log-exp_binary64_1494` `flip--_binary64_1430` `flip3--_binary64_1459`
5×	`frac-times_binary64_1465` `cbrt-undiv_binary64_1489` `cbrt-unprod_binary64_1488`
4×	`associate-/r/_binary64_1401` `sqrt-div_binary64_1472`
3×	`associate-r/_binary64_1397` `flip-+_binary64_1429` `1-exp_binary64_1499` `pow-flip_binary64_1529` `cancel-sign-sub-inv_binary64_1421` `associate-/l_binary64_1400` `flip3-+_binary64_1458` `div-inv_binary64_1452` `rec-exp_binary64_1505` `associate-*l/_binary64_1398`
2×	`*-commutative_binary64_1386` `pow-prod-down_binary64_1526`
1×	`sqrt-pow1_binary64_1473` `inv-pow_binary64_1540` `distribute-rgt-in_binary64_1405` `clear-num_binary64_1454` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `distribute-lft-in_binary64_1404` `sub-neg_binary64_1448` `pow1/2_binary64_1535`

Counts

4 → 178

Calls

4 calls:

21.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
10.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))))
7.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(-.f64 a 1/3)

series295.0ms (8%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
91.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))))
37.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
27.0ms	(-.f64 a 1/3)

simplify84.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4939	3523
1	4939	3523

prune378.0ms (10.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	191	6	197

Merged error: 0b

Counts

197 → 6

Compiler

Compiled 5928 to 4868 computations (17.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_1477`
22×	`*-un-lft-identity_binary64_1455`
16×	`add-cube-cbrt_binary64_1490`
13×	`associate-r_binary64_1395` `add-log-exp_binary64_1494` `flip--_binary64_1430` `flip3--_binary64_1459`
12×	`sqrt-div_binary64_1472`
11×	`times-frac_binary64_1461`
10×	`frac-add_binary64_1463`
9×	`add-cbrt-cube_binary64_1491` `cancel-sign-sub-inv_binary64_1421` `add-exp-log_binary64_1493`
8×	`associate-l_binary64_1396`
7×	`sqrt-prod_binary64_1471`
6×	`pow1_binary64_1516` `frac-times_binary64_1465` `associate-*l/_binary64_1398`
4×	`associate-+l+_binary64_1388` `unswap-sqr_binary64_1423`
3×	`associate-*r/_binary64_1397` `distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424` `diff-log_binary64_1547` `sub-neg_binary64_1448`
2×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488` `sum-log_binary64_1546`
1×	`distribute-lft-out_binary64_1406` `flip-+_binary64_1429` `associate-+l-_binary64_1390` `div-exp_binary64_1506` `*-commutative_binary64_1386` `cbrt-undiv_binary64_1489` `flip3-+_binary64_1458` `div-inv_binary64_1452` `+-commutative_binary64_1385` `pow-prod-down_binary64_1526`

Counts

4 → 103

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3))
9.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3)))
4.0ms	(-.f64 a 1/3)
4.0ms	(-.f64 a 1/3)

series215.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3))
65.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3)))
27.0ms	(-.f64 a 1/3)
24.0ms	(-.f64 a 1/3)

simplify49.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4945	2197
1	4945	2197

prune171.0ms (4.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	116	5	121

Merged error: 0b

Counts

121 → 5

Compiler

Compiled 2975 to 2316 computations (22.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 a 1/3)
0.0b	(+.f64 (-.f64 a 1/3) (/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) 3))
0.2b	(/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) 3)
0.3b	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64_1455`
19×	`add-sqr-sqrt_binary64_1477`
11×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-cube-cbrt_binary64_1490` `add-exp-log_binary64_1493`
8×	`associate-l_binary64_1396`
6×	`sqrt-prod_binary64_1471` `pow1_binary64_1516` `cancel-sign-sub-inv_binary64_1421`
4×	`sqrt-div_binary64_1472` `associate-+l+_binary64_1388` `flip--_binary64_1430` `flip3--_binary64_1459` `associate-*l/_binary64_1398`
3×	`associate-r_binary64_1395` `distribute-lft-out--_binary64_1407` `associate-/r*_binary64_1399` `times-frac_binary64_1461`
2×	`prod-exp_binary64_1504` `distribute-lft-out_binary64_1406` `difference-of-squares_binary64_1424` `associate-/l/_binary64_1402` `div-exp_binary64_1506` `cbrt-undiv_binary64_1489` `diff-log_binary64_1547` `cbrt-unprod_binary64_1488` `sub-neg_binary64_1448` `sum-log_binary64_1546` `frac-add_binary64_1463` `unswap-sqr_binary64_1423`
1×	`flip-+_binary64_1429` `associate-+l-_binary64_1390` `clear-num_binary64_1454` `-commutative_binary64_1386` `frac-2neg_binary64_1466` `associate-/l_binary64_1400` `flip3-+_binary64_1458` `div-inv_binary64_1452` `+-commutative_binary64_1385` `pow-prod-down_binary64_1526`

Counts

4 → 86

Calls

4 calls:

10.0ms	(+.f64 (-.f64 a 1/3) (/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) 3))
9.0ms	(/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) 3)
8.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
7.0ms	(-.f64 a 1/3)

series281.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) 3)
84.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
76.0ms	(+.f64 (-.f64 a 1/3) (/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) 3))
24.0ms	(-.f64 a 1/3)

simplify64.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5003	1703

prune113.0ms (3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	98	5	103

Merged error: 0b

Counts

103 → 5

Compiler

Compiled 2023 to 1527 computations (24.5% saved)

regimes28.0ms (0.8%)

Compiler: Compiled 168 to 156 computations (7.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	18
1	22	18

end0.0ms (0%)

sample760.0ms (20.5%)

Algorithm

1×

intervals

Results

453.0ms	8000×	body	128	valid
16.0ms	257×	body	128	invalid
15.0ms	286×	body	128	nan

Compiler

Compiled 115 to 107 computations (7% saved)

Details

analyze77.0ms (2.1%)

sample22.0ms (0.6%)

simplify227.0ms (6.1%)

prune6.0ms (0.2%)

localize9.0ms (0.2%)

rewrite45.0ms (1.2%)

series298.0ms (8%)

simplify52.0ms (1.4%)

prune359.0ms (9.7%)

localize10.0ms (0.3%)

rewrite66.0ms (1.8%)

series295.0ms (8%)

simplify84.0ms (2.3%)

prune378.0ms (10.2%)

localize7.0ms (0.2%)

rewrite40.0ms (1.1%)

series215.0ms (5.8%)

simplify49.0ms (1.3%)

prune171.0ms (4.6%)

localize8.0ms (0.2%)

rewrite40.0ms (1.1%)

series281.0ms (7.6%)

simplify64.0ms (1.7%)

prune113.0ms (3%)

regimes28.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample760.0ms (20.5%)

Profiling