Details

analyze72.0ms (1.8%)

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)

sample28.0ms (0.7%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
5.0ms	11×	body	128	invalid
1.0ms	10×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify225.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

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)

localize11.0ms (0.3%)

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))

rewrite48.0ms (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:

17.0ms	(.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)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series293.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
85.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
41.0ms	(*.f64 (-.f64 a 1/3) 9)
36.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify56.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5478	2236

prune419.0ms (10.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	104	7	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	106	7	113

Merged error: 0.0b

Counts

113 → 7

Compiler

Compiled 6836 to 5762 computations (15.7% saved)

localize9.0ms (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 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))))
0.3b	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
0.3b	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))

rewrite64.0ms (1.6%)

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:

22.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
11.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))))
8.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(-.f64 a 1/3)

series313.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
90.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))))
46.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
27.0ms	(-.f64 a 1/3)

simplify86.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4939	3523
1	4939	3523

prune391.0ms (9.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	190	7	197

Merged error: 0b

Counts

197 → 7

Compiler

Compiled 6033 to 4951 computations (17.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite40.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_1477`
20×	`*-un-lft-identity_binary64_1455`
14×	`add-cube-cbrt_binary64_1490`
13×	`associate-r_binary64_1395` `add-log-exp_binary64_1494`
11×	`times-frac_binary64_1461`
9×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
8×	`associate-l_binary64_1396`
7×	`sqrt-prod_binary64_1471`
6×	`pow1_binary64_1516`
4×	`sqrt-div_binary64_1472` `sum-log_binary64_1546` `unswap-sqr_binary64_1423`
3×	`flip--_binary64_1430` `cancel-sign-sub-inv_binary64_1421` `flip3--_binary64_1459`
2×	`prod-exp_binary64_1504` `distribute-lft-out--_binary64_1407` `flip-+_binary64_1429` `difference-of-squares_binary64_1424` `frac-times_binary64_1465` `cbrt-unprod_binary64_1488` `flip3-+_binary64_1458` `+-commutative_binary64_1385` `associate-*l/_binary64_1398`
1×	`distribute-lft-out_binary64_1406` `associate-r/_binary64_1397` `div-exp_binary64_1506` `-commutative_binary64_1386` `cbrt-undiv_binary64_1489` `diff-log_binary64_1547` `sub-neg_binary64_1448` `div-inv_binary64_1452` `pow-prod-down_binary64_1526` `associate-+r+_binary64_1387`

Counts

4 → 84

Calls

4 calls:

16.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3))
7.0ms	(+.f64 a (+.f64 -1/3 (*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3))))
5.0ms	(-.f64 a 1/3)
4.0ms	(+.f64 -1/3 (*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3)))

series265.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3))
69.0ms	(+.f64 -1/3 (*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3)))
64.0ms	(+.f64 a (+.f64 -1/3 (*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3))))
26.0ms	(-.f64 a 1/3)

simplify64.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5268	1788

prune191.0ms (4.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	96	7	103

Merged error: 0b

Counts

103 → 7

Compiler

Compiled 3270 to 2658 computations (18.7% saved)

localize9.0ms (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 rand (.f64 (sqrt.f64 (-.f64 a 1/3)) 3))))
0.2b	(/.f64 rand (*.f64 (sqrt.f64 (-.f64 a 1/3)) 3))
0.4b	(*.f64 (sqrt.f64 (-.f64 a 1/3)) 3)

rewrite45.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_1477`
20×	`*-un-lft-identity_binary64_1455`
13×	`add-cbrt-cube_binary64_1491` `associate-l_binary64_1396` `add-exp-log_binary64_1493`
12×	`add-cube-cbrt_binary64_1490`
8×	`pow1_binary64_1516`
7×	`associate-r_binary64_1395`
6×	`sqrt-prod_binary64_1471` `add-log-exp_binary64_1494` `flip--_binary64_1430` `flip3--_binary64_1459` `associate-*l/_binary64_1398`
4×	`sqrt-div_binary64_1472` `frac-times_binary64_1465`
3×	`prod-exp_binary64_1504` `distribute-lft-out--_binary64_1407` `flip-+_binary64_1429` `difference-of-squares_binary64_1424` `cancel-sign-sub-inv_binary64_1421` `associate-/l*_binary64_1400` `cbrt-unprod_binary64_1488` `flip3-+_binary64_1458` `times-frac_binary64_1461` `unswap-sqr_binary64_1423`
2×	`associate-r/_binary64_1397` `associate-/r/_binary64_1401` `div-exp_binary64_1506` `-commutative_binary64_1386` `cbrt-undiv_binary64_1489` `pow-prod-down_binary64_1526`
1×	`distribute-lft-out_binary64_1406` `distribute-rgt-in_binary64_1405` `clear-num_binary64_1454` `associate-/r*_binary64_1399` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `distribute-lft-in_binary64_1404` `sub-neg_binary64_1448` `div-inv_binary64_1452`

Counts

4 → 96

Calls

4 calls:

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

series284.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(/.f64 rand (*.f64 (sqrt.f64 (-.f64 a 1/3)) 3))
80.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (sqrt.f64 (-.f64 a 1/3)) 3))))
39.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) 3)
30.0ms	(-.f64 a 1/3)

simplify54.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5017	1994

prune138.0ms (3.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	108	7	115

Merged error: 0b

Counts

115 → 7

Compiler

Compiled 2471 to 1942 computations (21.4% saved)

regimes38.0ms (1%)

Compiler: Compiled 316 to 288 computations (8.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	18
1	27	18

end0.0ms (0%)

sample831.0ms (20.8%)

Algorithm

1×

intervals

Results

458.0ms	8000×	body	128	valid
15.0ms	273×	body	128	invalid
15.0ms	276×	body	128	nan

Compiler

Compiled 189 to 173 computations (8.5% saved)

Details

analyze72.0ms (1.8%)

sample28.0ms (0.7%)

simplify225.0ms (5.6%)

prune6.0ms (0.2%)

localize11.0ms (0.3%)

rewrite48.0ms (1.2%)

series293.0ms (7.3%)

simplify56.0ms (1.4%)

prune419.0ms (10.5%)

localize9.0ms (0.2%)

rewrite64.0ms (1.6%)

series313.0ms (7.8%)

simplify86.0ms (2.2%)

prune391.0ms (9.8%)

localize11.0ms (0.3%)

rewrite40.0ms (1%)

series265.0ms (6.6%)

simplify64.0ms (1.6%)

prune191.0ms (4.8%)

localize9.0ms (0.2%)

rewrite45.0ms (1.1%)

series284.0ms (7.1%)

simplify54.0ms (1.3%)

prune138.0ms (3.5%)

regimes38.0ms (1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample831.0ms (20.8%)

Profiling