Details

analyze83.0ms (1.7%)

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)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	10×	body	128	nan
1.0ms	9×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify220.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	1030	21
1	1030	21

prune6.0ms (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 82 to 77 computations (6.1% saved)

localize8.0ms (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))

rewrite46.0ms (0.9%)

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)))))
9.0ms	(/.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))

series284.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
82.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
40.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
39.0ms	(*.f64 (-.f64 a 1/3) 9)

simplify50.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5478	2236

prune331.0ms (6.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	107	6	113

Merged error: 0.0b

Counts

113 → 6

Compiler

Compiled 5458 to 4606 computations (15.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.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))
10.4b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

rewrite49.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

17.0ms	(.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)))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series307.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
113.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
41.0ms	(*.f64 (-.f64 a 1/3) 9)
34.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5022	2404

prune221.0ms (4.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	124	5	129

Merged error: 0b

Counts

129 → 5

Compiler

Compiled 3926 to 3031 computations (22.8% saved)

localize9.0ms (0.2%)

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

rewrite138.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

372×	`times-frac_binary64_1461`
248×	`add-sqr-sqrt_binary64_1477`
247×	`*-un-lft-identity_binary64_1455`
223×	`sqrt-prod_binary64_1471`
191×	`add-cube-cbrt_binary64_1490`
33×	`associate-/l*_binary64_1400`
27×	`distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424`
18×	`sqrt-div_binary64_1472`
16×	`associate-/r/_binary64_1401`
14×	`associate-/r*_binary64_1399`
13×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
12×	`flip--_binary64_1430` `flip3--_binary64_1459`
9×	`div-inv_binary64_1452`
7×	`pow1_binary64_1516`
5×	`associate-l_binary64_1396`
4×	`associate-r_binary64_1395` `div-exp_binary64_1506` `add-log-exp_binary64_1494` `frac-times_binary64_1465` `cbrt-undiv_binary64_1489`
3×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
2×	`associate-r/_binary64_1397` `clear-num_binary64_1454` `frac-2neg_binary64_1466` `associate-l/_binary64_1398`
1×	`prod-exp_binary64_1504` `sqrt-pow1_binary64_1473` `distribute-lft-out_binary64_1406` `distribute-rgt-in_binary64_1405` `rem-sqrt-square_binary64_1468` `associate-/l/_binary64_1402` `*-commutative_binary64_1386` `distribute-lft-in_binary64_1404` `cbrt-unprod_binary64_1488` `pow1/2_binary64_1535` `pow-prod-down_binary64_1526` `unswap-sqr_binary64_1423`

Counts

4 → 328

Calls

4 calls:

60.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
16.0ms	(/.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))

series345.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
109.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
83.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
28.0ms	(sqrt.f64 (-.f64 a 1/3))

simplify134.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4947	9006
1	4947	9006

prune605.0ms (12.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	340	0	340
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	340	5	345

Merged error: 0b

Counts

345 → 5

Compiler

Compiled 9033 to 6852 computations (24.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
3.8b	(.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))

rewrite102.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`add-sqr-sqrt_binary64_1477`
103×	`times-frac_binary64_1461`
86×	`*-un-lft-identity_binary64_1455`
78×	`sqrt-prod_binary64_1471`
56×	`add-cube-cbrt_binary64_1490`
41×	`associate-l_binary64_1396`
27×	`associate-r_binary64_1395`
18×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
16×	`sqrt-div_binary64_1472`
15×	`distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424`
12×	`pow1_binary64_1516`
11×	`associate-*l/_binary64_1398`
9×	`unswap-sqr_binary64_1423`
7×	`associate-/r*_binary64_1399`
6×	`associate-/r/_binary64_1401` `flip--_binary64_1430` `flip3--_binary64_1459`
5×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489` `associate-/l*_binary64_1400`
4×	`prod-exp_binary64_1504` `sqrt-pow1_binary64_1473` `add-log-exp_binary64_1494` `cbrt-unprod_binary64_1488`
3×	`div-inv_binary64_1452` `pow-prod-down_binary64_1526`
2×	`associate-/l/_binary64_1402` `pow1/2_binary64_1535`
1×	`associate-r/_binary64_1397` `clear-num_binary64_1454` `frac-times_binary64_1465` `-commutative_binary64_1386` `frac-2neg_binary64_1466` `div-sub_binary64_1460`

Counts

4 → 187

Calls

4 calls:

45.0ms	(.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
14.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series337.0ms (7%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
96.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
34.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
33.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify102.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5005	6062

prune477.0ms (9.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	199	5	204

Merged error: 0b

Counts

204 → 5

Compiler

Compiled 7004 to 5600 computations (20% saved)

regimes30.0ms (0.6%)

Compiler: Compiled 188 to 172 computations (8.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	24
1	24	24

end0.0ms (0%)

sample807.0ms (16.8%)

Algorithm

1×

intervals

Results

488.0ms	8000×	body	128	valid
15.0ms	254×	body	128	invalid
15.0ms	266×	body	128	nan

Compiler

Compiled 129 to 118 computations (8.5% saved)

Details

analyze83.0ms (1.7%)

sample24.0ms (0.5%)

simplify220.0ms (4.6%)

prune6.0ms (0.1%)

localize8.0ms (0.2%)

rewrite46.0ms (0.9%)

series284.0ms (5.9%)

simplify50.0ms (1%)

prune331.0ms (6.9%)

localize8.0ms (0.2%)

rewrite49.0ms (1%)

series307.0ms (6.4%)

simplify69.0ms (1.4%)

prune221.0ms (4.6%)

localize9.0ms (0.2%)

rewrite138.0ms (2.9%)

series345.0ms (7.2%)

simplify134.0ms (2.8%)

prune605.0ms (12.6%)

localize11.0ms (0.2%)

rewrite102.0ms (2.1%)

series337.0ms (7%)

simplify102.0ms (2.1%)

prune477.0ms (9.9%)

regimes30.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample807.0ms (16.8%)

Profiling