Details

sample30.0ms

Algorithm

intervals

Results

8.0ms	56×	body	1280	valid
4.0ms	39×	body	640	valid
4.0ms	123×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	13×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.7b	(cbrt x)
4.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite49.0ms

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)
43.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series629.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(cbrt (+ x 1.0))
246.0ms	(cbrt x)
232.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify4.0s

Counts

53 → 53

Iterations

Useful iterations: 4 (2.1s)

Iter	Nodes	Cost
0	131	649
1	290	597
2	672	573
3	1717	521
4	4878	501
done	5000	501

prune246.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.7b	(cbrt x)
3.6b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
4.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite227.0ms

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)
161.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
60.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series879.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(cbrt (+ x 1.0))
297.0ms	(cbrt x)
264.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
194.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.2s

Counts

81 → 81

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	166	1057
1	338	936
2	737	887
3	1819	812
done	5000	783

prune281.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.3b

localize12.0ms

Local error

Found 4 expressions with local error:

3.6b	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
3.6b	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
4.3b	(- (cbrt (+ x 1.0)) (cbrt x))
4.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite337.0ms

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:

114.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
132.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
43.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
41.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series1.2s

Counts

4 → 12

Calls

4 calls:

365.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
440.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
200.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
200.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.9s

Counts

110 → 110

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	175	1770
1	360	1628
2	818	1526
3	2047	1424
done	5000	1384

prune613.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
3.6b	(log (exp (* (sqrt (- (cbrt (+ x 1.0)) (cbrt x))) (sqrt (- (cbrt (+ x 1.0)) (cbrt x))))))
4.3b	(- (cbrt (+ x 1.0)) (cbrt x))
4.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`cbrt-prod`
9×	`add-log-exp`
8×	`difference-of-squares`
6×	`add-cube-cbrt` `distribute-lft-out--`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`log-prod` `log-pow`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`exp-prod` `exp-to-pow` `pow1/3` `rem-log-exp`

Counts

4 → 63

Calls

4 calls:

1.0ms	(cbrt x)
3.0ms	(log (exp (* (sqrt (- (cbrt (+ x 1.0)) (cbrt x))) (sqrt (- (cbrt (+ x 1.0)) (cbrt x))))))
54.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
61.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series988.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(cbrt x)
262.0ms	(log (exp (* (sqrt (- (cbrt (+ x 1.0)) (cbrt x))) (sqrt (- (cbrt (+ x 1.0)) (cbrt x))))))
210.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
235.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify3.5s

Counts

75 → 75

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	127	1270
1	258	1010
2	589	945
3	1497	864
4	4534	833
done	5001	833

prune337.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.1b

regimes156.0ms

Accuracy

98.5% (0.3b remaining)

Error of 8.1b against oracle of 7.8b and baseline of 29.7b

bsearch167.0ms

Steps

Iters	Range		Point
7	4.772092826529504e-10	9.85435867085541e-08	4.799156511993158e-08
8	-66911392.43097515	-3231.0590912120524	-3865.3828611493445
9	-2.519337225575135e+155	-3.305070260551137e+146	-1.3369489205631287e+154

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	64	99
1	78	97
done	78	97

end0.0ms

sample826.0ms

Algorithm

intervals

Results

272.0ms	1742×	body	1280	valid
149.0ms	1256×	body	640	valid
133.0ms	4104×	body	80	valid
50.0ms	592×	body	320	valid
18.0ms	306×	body	160	valid