Details

analyze77.0ms (1.9%)

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)

sample23.0ms (0.6%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	11×	body	128	invalid
0.0ms	5×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify223.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

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)))
0.3b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite50.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1446`
23×	`*-un-lft-identity_binary64_1425`
17×	`add-cube-cbrt_binary64_1457`
12×	`times-frac_binary64_1431`
11×	`pow1_binary64_1483`
10×	`associate-l_binary64_1368` `add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
8×	`associate-*l/_binary64_1370`
7×	`associate-r_binary64_1367`
6×	`flip--_binary64_1400` `flip3--_binary64_1429`
5×	`sqrt-prod_binary64_1440`
4×	`associate-/r*_binary64_1371` `sqrt-div_binary64_1441` `add-log-exp_binary64_1461` `frac-times_binary64_1435`
3×	`flip3-+_binary64_1428` `flip-+_binary64_1399` `associate-/l*_binary64_1372` `pow-prod-down_binary64_1493`
2×	`distribute-lft-out--_binary64_1379` `unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `associate-r/_binary64_1369` `sqrt-pow1_binary64_1442` `associate-/r/_binary64_1373` `difference-of-squares_binary64_1394` `-commutative_binary64_1358`
1×	`distribute-lft-in_binary64_1376` `frac-2neg_binary64_1436` `pow1/2_binary64_1502` `clear-num_binary64_1424` `distribute-lft-out_binary64_1378` `distribute-rgt-in_binary64_1377` `div-inv_binary64_1422` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`

Counts

4 → 99

Calls

4 calls:

16.0ms	(.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)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series293.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
83.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
50.0ms	(*.f64 (-.f64 a 1/3) 9)
37.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify50.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5372	2236

prune164.0ms (4.1%)

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 2628 to 2047 computations (22.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.3b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
5.6b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

rewrite55.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_1446`
25×	`times-frac_binary64_1431`
24×	`*-un-lft-identity_binary64_1425`
22×	`add-cube-cbrt_binary64_1457`
18×	`associate-r_binary64_1367`
14×	`flip--_binary64_1400` `flip3--_binary64_1429`
12×	`associate-*l/_binary64_1370`
11×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
10×	`frac-add_binary64_1433`
9×	`pow1_binary64_1483` `add-log-exp_binary64_1461`
8×	`sqrt-prod_binary64_1440`
6×	`sqrt-div_binary64_1441` `frac-times_binary64_1435`
5×	`associate-l_binary64_1368`
4×	`associate-/r*_binary64_1371` `associate-/r/_binary64_1373`
3×	`associate-r/_binary64_1369` `associate-/l_binary64_1372`
2×	`unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `sqrt-pow1_binary64_1442` `div-inv_binary64_1422` `sum-log_binary64_1513` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456` `pow-prod-down_binary64_1493`
1×	`diff-log_binary64_1514` `frac-2neg_binary64_1436` `distribute-lft-out--_binary64_1379` `flip3-+_binary64_1428` `pow1/2_binary64_1502` `sub-neg_binary64_1418` `clear-num_binary64_1424` `associate-+l+_binary64_1360` `difference-of-squares_binary64_1394` `flip-+_binary64_1399` `associate-+l-_binary64_1362` `+-commutative_binary64_1357` `*-commutative_binary64_1358`

Counts

4 → 113

Calls

4 calls:

21.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
9.0ms	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
8.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series370.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
111.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
94.0ms	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
41.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify92.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4921	3244
1	4921	3244

prune174.0ms (4.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	128	4	132

Merged error: 0b

Counts

132 → 4

Compiler

Compiled 3278 to 2421 computations (26.1% saved)

localize9.0ms (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 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
0.4b	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
0.5b	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

rewrite265.0ms (6.7%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`add-sqr-sqrt_binary64_1446`
115×	`*-un-lft-identity_binary64_1425`
110×	`times-frac_binary64_1431`
70×	`sqrt-prod_binary64_1440`
57×	`add-cube-cbrt_binary64_1457`
46×	`associate-l_binary64_1368`
29×	`distribute-lft-out--_binary64_1379` `difference-of-squares_binary64_1394`
22×	`associate-r_binary64_1367`
18×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
11×	`add-log-exp_binary64_1461`
9×	`unswap-sqr_binary64_1393` `pow1_binary64_1483`
8×	`associate-/r*_binary64_1371`
7×	`flip--_binary64_1400` `flip3--_binary64_1429`
6×	`frac-add_binary64_1433`
5×	`div-exp_binary64_1473` `associate-/l*_binary64_1372` `cbrt-undiv_binary64_1456`
4×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `sqrt-div_binary64_1441` `associate-/r/_binary64_1373`
3×	`associate-r/_binary64_1369` `div-inv_binary64_1422` `associate-l/_binary64_1370` `frac-times_binary64_1435`
2×	`diff-log_binary64_1514` `sub-neg_binary64_1418` `pow-div_binary64_1497` `sum-log_binary64_1513` `associate-/l/_binary64_1374`
1×	`frac-2neg_binary64_1436` `flip3-+_binary64_1428` `pow1/2_binary64_1502` `clear-num_binary64_1424` `div-sub_binary64_1430` `sqrt-pow1_binary64_1442` `associate-+l+_binary64_1360` `flip-+_binary64_1399` `associate-+l-_binary64_1362` `+-commutative_binary64_1357` `*-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

4 → 202

Calls

4 calls:

217.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
10.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))
8.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
4.0ms	(-.f64 a 1/3)

series277.0ms (7%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
98.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
40.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))
24.0ms	(-.f64 a 1/3)

simplify78.0ms (2%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5703	4352

prune329.0ms (8.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	214	4	218

Merged error: 0b

Counts

218 → 4

Compiler

Compiled 5129 to 3935 computations (23.3% 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))))))
0.2b	(.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
0.3b	(/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.3b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite51.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1446`
27×	`*-un-lft-identity_binary64_1425`
26×	`times-frac_binary64_1431`
24×	`add-cube-cbrt_binary64_1457`
21×	`associate-r_binary64_1367`
19×	`add-exp-log_binary64_1460`
15×	`pow1_binary64_1483`
13×	`add-cbrt-cube_binary64_1458`
8×	`associate-l_binary64_1368` `sqrt-prod_binary64_1440` `associate-*l/_binary64_1370`
6×	`flip--_binary64_1400` `sqrt-div_binary64_1441` `flip3--_binary64_1429`
5×	`prod-exp_binary64_1471`
4×	`pow-flip_binary64_1496` `associate-/r*_binary64_1371` `unswap-sqr_binary64_1393` `sqrt-pow1_binary64_1442` `associate-/r/_binary64_1373` `div-exp_binary64_1473` `add-log-exp_binary64_1461` `frac-times_binary64_1435` `pow-prod-down_binary64_1493`
3×	`flip3-+_binary64_1428` `cbrt-unprod_binary64_1455` `associate-r/_binary64_1369` `flip-+_binary64_1399` `associate-/l_binary64_1372`
2×	`pow1/2_binary64_1502` `div-inv_binary64_1422` `1-exp_binary64_1466` `cbrt-undiv_binary64_1456` `rec-exp_binary64_1472` `*-commutative_binary64_1358`
1×	`distribute-lft-in_binary64_1376` `frac-2neg_binary64_1436` `inv-pow_binary64_1507` `distribute-lft-out--_binary64_1379` `un-div-inv_binary64_1423` `clear-num_binary64_1424` `distribute-rgt-in_binary64_1377` `difference-of-squares_binary64_1394`

Counts

4 → 124

Calls

4 calls:

15.0ms	(.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
9.0ms	(.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))

series298.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
85.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))))
53.0ms	(/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
34.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4945	2772
1	4945	2772

prune182.0ms (4.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	136	4	140

Merged error: 0b

Counts

140 → 4

Compiler

Compiled 3182 to 2537 computations (20.3% saved)

regimes25.0ms (0.6%)

Compiler: Compiled 142 to 132 computations (7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	24
1	24	24

end0.0ms (0%)

sample764.0ms (19.3%)

Algorithm

1×

intervals

Results

469.0ms	8000×	body	128	valid
15.0ms	259×	body	128	invalid
14.0ms	267×	body	128	nan

Compiler

Compiled 106 to 98 computations (7.5% saved)

Details

analyze77.0ms (1.9%)

sample23.0ms (0.6%)

simplify223.0ms (5.6%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite50.0ms (1.3%)

series293.0ms (7.4%)

simplify50.0ms (1.3%)

prune164.0ms (4.1%)

localize9.0ms (0.2%)

rewrite55.0ms (1.4%)

series370.0ms (9.4%)

simplify92.0ms (2.3%)

prune174.0ms (4.4%)

localize9.0ms (0.2%)

rewrite265.0ms (6.7%)

series277.0ms (7%)

simplify78.0ms (2%)

prune329.0ms (8.3%)

localize10.0ms (0.2%)

rewrite51.0ms (1.3%)

series298.0ms (7.5%)

simplify76.0ms (1.9%)

prune182.0ms (4.6%)

regimes25.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample764.0ms (19.3%)

Profiling