Details

sample18.0ms

Algorithm

intervals

Results

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

simplify4.0ms

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

localize8.0ms

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))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3` `distribute-lft-out`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 44

Calls

3 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
38.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series417.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(cbrt (+ x 1.0))
178.0ms	(cbrt x)
151.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify156.0ms

Counts

53 → 53

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	287	358
1	934	344
2	4833	322
3	5001	322
done	5001	322

prune143.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.5b

localize11.0ms

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)))

rewrite26.0ms

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` `add-cbrt-cube`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 46

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
23.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series724.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt x)
179.0ms	(cbrt x)
189.0ms	(cbrt x)
177.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify131.0ms

Counts

58 → 58

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	243	356
1	829	292
2	4198	276
3	5001	276
done	5001	276

prune180.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.5b

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))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`cbrt-prod`
11×	`log-pow`
10×	`exp-prod`
8×	`add-cube-cbrt` `difference-of-squares`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow1` `log-prod`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-lft-out`
2×	`sub-neg` `cbrt-div` `pow1/3` `exp-sum`
1×	`log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `flip--` `flip-+`

Counts

4 → 69

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
83.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
42.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series571.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ x 1.0))
180.0ms	(cbrt x)
152.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
150.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify35.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	336	568
1	1025	536
2	5001	505
done	5001	505

prune240.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.5b

localize11.0ms

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))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
32×	`cbrt-prod`
26×	`log-pow`
22×	`sqrt-pow1`
20×	`exp-prod`
16×	`log-prod` `difference-of-squares`
12×	`distribute-lft-out--`
10×	`add-cube-cbrt` `sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`sub-neg` `exp-sum` `add-cbrt-cube` `distribute-lft-out`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 98

Calls

4 calls:

84.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
85.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
39.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
41.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series979.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
444.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
142.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify36.0ms

Counts

110 → 110

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	360	1078
1	1059	1004
2	5001	982
done	5001	982

prune390.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.5b

regimes109.0ms

Accuracy

99.2% (0.2b remaining)

Error of 12.0b against oracle of 11.8b and baseline of 30.3b

bsearch80.0ms

Steps

Iters	Range		Point
9	0.00021078761332869983	22.544919195950573	0.1408561144889795
9	-7.328812839441751e+61	-4.540808272028475e+53	-4.525623377353305e+61

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	46
1	64	46
2	64	46
done	64	46

end0.0ms

sample507.0ms

Algorithm

intervals

Results

164.0ms	1734×	body	1280	valid
90.0ms	1252×	body	640	valid
79.0ms	4040×	body	80	valid
40.0ms	651×	body	320	valid
11.0ms	323×	body	160	valid