Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	55×	body	1280	valid
4.0ms	142×	body	80	valid
3.0ms	37×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	8×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.0b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite68.0ms

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)
62.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series616.0ms

Counts

3 → 9

Calls

3 calls:

130.0ms	(cbrt (+ x 1.0))
278.0ms	(cbrt x)
207.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify79.0ms

Counts: 53 → 53

prune268.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.0b	(- (cbrt (+ x 1.0)) (cbrt x))
9.0b	(log (- (cbrt (+ x 1.0)) (cbrt x)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
58.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
39.0ms	(log (- (cbrt (+ x 1.0)) (cbrt x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt (+ x 1.0))
321.0ms	(cbrt x)
282.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
302.0ms	(log (- (cbrt (+ x 1.0)) (cbrt x)))

simplify41.0ms

Counts: 77 → 77

prune391.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.0b

localize40.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (cbrt (+ x 1.0)) (cbrt x))
9.0b	(log (- (cbrt (+ x 1.0)) (cbrt x)))
9.0b	(log (- (cbrt (+ x 1.0)) (cbrt x)))
9.0b	(log (- (cbrt (+ x 1.0)) (cbrt x)))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
32×	`cbrt-prod`
30×	`log-prod`
16×	`difference-of-squares`
12×	`distribute-lft-out--`
7×	`pow1` `add-exp-log` `add-cube-cbrt`
6×	`log-div` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out`
3×	`rem-log-exp` `log-pow`
1×	`sub-neg` `diff-log`

Counts

4 → 82

Calls

4 calls:

75.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
36.0ms	(log (- (cbrt (+ x 1.0)) (cbrt x)))
45.0ms	(log (- (cbrt (+ x 1.0)) (cbrt x)))
57.0ms	(log (- (cbrt (+ x 1.0)) (cbrt x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

264.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
277.0ms	(log (- (cbrt (+ x 1.0)) (cbrt x)))
283.0ms	(log (- (cbrt (+ x 1.0)) (cbrt x)))
291.0ms	(log (- (cbrt (+ x 1.0)) (cbrt x)))

simplify166.0ms

Counts: 94 → 94

prune646.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt (* (cbrt x) (cbrt x)))
0.6b	(cbrt (cbrt x))
9.8b	(- (cbrt (+ x 1.0)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

13×	`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--`

Counts

4 → 46

Calls

4 calls:

1.0ms	(cbrt x)
6.0ms	(cbrt (* (cbrt x) (cbrt x)))
2.0ms	(cbrt (cbrt x))
80.0ms	(- (cbrt (+ x 1.0)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))

series1.4s

Counts

4 → 12

Calls

4 calls:

297.0ms	(cbrt x)
467.0ms	(cbrt (* (cbrt x) (cbrt x)))
389.0ms	(cbrt (cbrt x))
258.0ms	(- (cbrt (+ x 1.0)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))

simplify87.0ms

Counts: 58 → 58

prune249.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.8b

regimes111.0ms

Accuracy

98.5% (0.3b remaining)

Error of 11.4b against oracle of 11.2b and baseline of 29.5b

bsearch127.0ms

Steps

Iters	Range		Point
7	-3.84051392789859e-308	1.722088704518556e-307	4.64969669863363e-310
11	-2.526251423771835e+75	-8.875265822373592e+51	-4.434414446652679e+61

simplify76.0ms

end0.0ms

sample1.1s

Algorithm

intervals

Results

436.0ms	1703×	body	1280	valid
215.0ms	1284×	body	640	valid
182.0ms	4036×	body	80	valid
97.0ms	653×	body	320	valid
22.0ms	324×	body	160	valid