Details

sample46.0ms

Algorithm

intervals

Results

13.0ms	54×	body	1280	valid
8.0ms	44×	body	640	valid
7.0ms	132×	body	80	valid
3.0ms	19×	body	320	valid
1.0ms	7×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize18.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite74.0ms

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×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `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:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
66.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series601.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(cbrt (+ x 1.0))
270.0ms	(cbrt x)
205.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify930.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1404
1	459
0	194

prune424.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ 1.0 x))
0.3b	(cbrt (cbrt (+ 1.0 x)))
0.6b	(cbrt x)
9.3b	(- (* (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x)))) (cbrt x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
14×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div` `prod-diff` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`pow1/3`
2×	`flip3-+` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 69

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 x))
4.0ms	(cbrt (cbrt (+ 1.0 x)))
1.0ms	(cbrt x)
34.0ms	(- (* (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x)))) (cbrt x))

series715.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (+ 1.0 x))
110.0ms	(cbrt (cbrt (+ 1.0 x)))
247.0ms	(cbrt x)
225.0ms	(- (* (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x)))) (cbrt x))

simplify1.1s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1764
1	515
0	212

prune494.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.4b

localize73.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
29.6b	(fma (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x))) (- (cbrt x)))
29.6b	(fma (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x))) (- (cbrt x)))
29.6b	(fma (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x))) (- (cbrt x)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt x)
0.0ms	(fma (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x))) (- (cbrt x)))
1.0ms	(fma (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x))) (- (cbrt x)))
1.0ms	(fma (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x))) (- (cbrt x)))

series1.5s

Counts

4 → 12

Calls

4 calls:

343.0ms	(cbrt x)
369.0ms	(fma (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x))) (- (cbrt x)))
400.0ms	(fma (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x))) (- (cbrt x)))
387.0ms	(fma (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x))) (- (cbrt x)))

simplify1.7s

Counts

55 → 55

Iterations

Iter	Nodes
done	5001
3	2831
2	714
1	223
0	100

prune576.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 7.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cbrt (+ 1.0 x)))
0.3b	(cbrt (cbrt (+ 1.0 x)))
0.6b	(cbrt x)
22.0b	(- (* (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (* (* (cbrt (cbrt (cbrt (+ 1.0 x)))) (cbrt (cbrt (cbrt (+ 1.0 x))))) (cbrt (cbrt (cbrt (+ 1.0 x)))))) (cbrt x))

rewrite396.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
15×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`cbrt-div`
6×	`prod-diff` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`pow1/3`
2×	`flip3-+` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 72

Calls

4 calls:

8.0ms	(cbrt (cbrt (+ 1.0 x)))
7.0ms	(cbrt (cbrt (+ 1.0 x)))
1.0ms	(cbrt x)
377.0ms	(- (* (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (* (* (cbrt (cbrt (cbrt (+ 1.0 x)))) (cbrt (cbrt (cbrt (+ 1.0 x))))) (cbrt (cbrt (cbrt (+ 1.0 x)))))) (cbrt x))

series748.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (cbrt (+ 1.0 x)))
109.0ms	(cbrt (cbrt (+ 1.0 x)))
289.0ms	(cbrt x)
230.0ms	(- (* (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (* (* (cbrt (cbrt (cbrt (+ 1.0 x)))) (cbrt (cbrt (cbrt (+ 1.0 x))))) (cbrt (cbrt (cbrt (+ 1.0 x)))))) (cbrt x))

simplify918.0ms

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	1760
1	498
0	204

prune703.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 7.4b

regimes223.0ms

Accuracy

98.2% (0.4b remaining)

Error of 8.9b against oracle of 8.5b and baseline of 29.2b

bsearch109.0ms

Steps

Iters	Range		Point
6	1.583250720483607e-07	7.294142785006675e-07	2.6276466578463683e-07
10	-185496355225.45163	-22.8286883066892	-4221.179793202217

simplify17.0ms

Iterations

Iter	Nodes
done	67
3	67
2	61
1	51
0	41

end0.0ms

sample1.5s

Algorithm

intervals

Results

690.0ms	1242×	body	640	valid
305.0ms	1672×	body	1280	valid
196.0ms	4176×	body	80	valid
106.0ms	623×	body	320	valid
18.0ms	287×	body	160	valid