Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	51×	body	1280	valid
3.0ms	134×	body	80	valid
3.0ms	39×	body	640	valid
1.0ms	25×	body	320	valid
0.0ms	7×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize5.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.2b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
56×	`*-un-lft-identity`
42×	`prod-diff`
41×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
5×	`add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 99

Calls

3 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
49.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series413.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(cbrt (+ x 1.0))
177.0ms	(cbrt x)
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify50.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	430	1315
1	1394	1045
2	5001	981
done	5001	981

prune239.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
2.1b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
26.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series711.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
176.0ms	(cbrt x)
179.0ms	(cbrt x)
175.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify141.0ms

Counts

68 → 68

Iterations

Useful iterations: 3 (136.0ms)

Iter	Nodes	Cost
0	260	403
1	906	328
2	4583	314
3	5001	311
done	5001	311

prune232.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
1.8b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
2.2b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

117×	`cbrt-prod`
104×	`*-un-lft-identity`
84×	`prod-diff`
78×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
47×	`log-prod`
44×	`exp-sum`
16×	`distribute-lft-out`
11×	`log-pow`
10×	`exp-prod`
8×	`difference-of-squares`
7×	`fma-neg`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `cbrt-div` `pow1/3`
1×	`log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `flip--` `flip-+`

Counts

4 → 168

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
94.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
47.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series566.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt (+ x 1.0))
180.0ms	(cbrt x)
148.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
151.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify60.0ms

Counts

180 → 180

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	567	2459
1	1651	1917
2	5001	1581
done	5001	1581

prune382.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.6b

localize16.0ms

Local error

Found 4 expressions with local error:

1.8b	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
1.8b	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
2.2b	(- (cbrt (+ x 1.0)) (cbrt x))
2.2b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

220×	`cbrt-prod`
198×	`*-un-lft-identity`
168×	`prod-diff`
150×	`add-sqr-sqrt`
118×	`add-cube-cbrt`
100×	`log-prod`
94×	`sqrt-prod`
88×	`exp-sum`
30×	`distribute-lft-out`
26×	`log-pow`
22×	`sqrt-pow1`
20×	`exp-prod`
16×	`difference-of-squares`
14×	`fma-neg`
12×	`distribute-lft-out--`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 288

Calls

4 calls:

95.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
96.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
48.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
46.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series1.0s

Counts

4 → 12

Calls

4 calls:

253.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
249.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
147.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
361.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify85.0ms

Counts

300 → 300

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	633	5362
1	1703	4452
2	5002	3896
done	5002	3896

prune802.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.6b

regimes204.0ms

Accuracy

98.8% (0.2b remaining)

Error of 12.1b against oracle of 11.9b and baseline of 30.3b

bsearch89.0ms

Steps

Iters	Range		Point
8	22.544919195950573	6136.975143603057	3466.2851623274805
9	-7.328812839441751e+61	-4.540808272028475e+53	-4.525623377353305e+61

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	51
1	67	51
done	67	51

end0.0ms

sample522.0ms

Algorithm

intervals

Results

173.0ms	1734×	body	1280	valid
94.0ms	1252×	body	640	valid
80.0ms	4040×	body	80	valid
38.0ms	651×	body	320	valid
12.0ms	323×	body	160	valid