Details

sample56.0ms

Algorithm

intervals

Results

21.0ms	138×	body	80	valid
13.0ms	59×	body	1280	valid
6.0ms	35×	body	640	valid
2.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.0b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite94.0ms

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:

8.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt x)
81.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series577.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(cbrt (+ x 1.0))
244.0ms	(cbrt x)
241.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify54.0ms

Counts: 53 → 53

prune203.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
3.0b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite32.0ms

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)
27.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

252.0ms	(cbrt x)
326.0ms	(cbrt x)
291.0ms	(cbrt x)
223.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify98.0ms

Counts: 58 → 58

prune317.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt (cbrt x))
8.9b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt x)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
8×	`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 → 48

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt (cbrt x))
63.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

294.0ms	(cbrt x)
311.0ms	(cbrt x)
370.0ms	(cbrt (cbrt x))
300.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt x)))

simplify160.0ms

Counts: 60 → 60

prune373.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
8.9b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt x)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
10×	`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 → 54

Calls

4 calls:

1.0ms	(cbrt (cbrt x))
1.0ms	(cbrt (cbrt x))
1.0ms	(cbrt (cbrt x))
50.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt x)))

series1.5s

Counts

4 → 12

Calls

4 calls:

418.0ms	(cbrt (cbrt x))
438.0ms	(cbrt (cbrt x))
382.0ms	(cbrt (cbrt x))
269.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt x)))

simplify132.0ms

Counts: 66 → 66

prune499.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.3b

regimes91.0ms

Accuracy

98.9% (0.2b remaining)

Error of 11.9b against oracle of 11.7b and baseline of 29.6b

bsearch123.0ms

Steps

Iters	Range		Point
9	3.244205803610274e-06	1902.9075791774285	0.000284302664009791
9	-1.287840825351744e+65	-4.831460336248242e+57	-4.4346575691912003e+61

simplify139.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

409.0ms	1684×	body	1280	valid
309.0ms	4141×	body	80	valid
197.0ms	1260×	body	640	valid
123.0ms	608×	body	320	valid
24.0ms	307×	body	160	valid