Details

sample19.0ms

Algorithm

intervals

Results

6.0ms	57×	body	1280	valid
3.0ms	39×	body	640	valid
3.0ms	133×	body	80	valid
1.0ms	19×	body	320	valid
0.0ms	8×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize9.0ms

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))

rewrite35.0ms

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

2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
29.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series426.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(cbrt (+ x 1.0))
179.0ms	(cbrt x)
156.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.3s

Counts

108 → 108

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	194	2160
1	427	1776
2	1032	1468
3	3259	1349
done	5001	1335

prune222.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

120×	`cbrt-prod`
104×	`*-un-lft-identity`
84×	`prod-diff`
78×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
16×	`distribute-lft-out`
14×	`fma-neg`
8×	`add-log-exp` `difference-of-squares`
6×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--`

Counts

4 → 166

Calls

4 calls:

0.0ms	(cbrt x)
1.0ms	(cbrt x)
30.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
28.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series677.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
188.0ms	(cbrt x)
151.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
156.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.1s

Counts

178 → 178

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	172	3858
1	371	3142
2	880	2528
3	2817	2186
done	5001	2158

prune411.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.7b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

228×	`cbrt-prod`
200×	`*-un-lft-identity`
168×	`prod-diff`
148×	`add-sqr-sqrt`
116×	`add-cube-cbrt`
32×	`distribute-lft-out`
28×	`fma-neg`
16×	`difference-of-squares`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 280

Calls

4 calls:

29.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
28.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
31.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
27.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series627.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
157.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
151.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
161.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.1s

Counts

292 → 292

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	165	7432
1	361	6044
2	855	5048
3	2755	4476
done	5001	4420

prune750.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
0.6b	(cbrt x)
29.2b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-div`
8×	`cbrt-prod` `*-un-lft-identity`
7×	`flip3-+` `flip-+`
6×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`associate-r/` `associate-l/`
1×	`fma-udef` `distribute-lft-out`

Counts

4 → 58

Calls

4 calls:

2.0ms	(cbrt (+ x 1.0))
7.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
1.0ms	(cbrt x)
0.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series648.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (+ x 1.0))
107.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
188.0ms	(cbrt x)
260.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify1.4s

Counts

70 → 70

Iterations

Useful iterations: 3 (613.0ms)

Iter	Nodes	Cost
0	210	1162
1	454	1112
2	1255	1030
3	3811	971
done	5000	971

prune253.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.7b

regimes115.0ms

Accuracy

98.3% (0.4b remaining)

Error of 8.6b against oracle of 8.2b and baseline of 29.8b

bsearch81.0ms

Steps

Iters	Range		Point
8	8.116859208030337e-08	6.379368274952145e-05	3.485900037587471e-06
10	-155084744.97222546	-0.0009113054925467739	-3699.6791529658512

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	46	74
1	54	72
done	54	72

end0.0ms

sample494.0ms

Algorithm

intervals

Results

172.0ms	1666×	body	1280	valid
93.0ms	1210×	body	640	valid
84.0ms	4089×	body	80	valid
37.0ms	669×	body	320	valid
14.0ms	366×	body	160	valid