Details

sample41.0ms

Algorithm

intervals

Results

12.0ms	51×	body	1280	valid
8.0ms	44×	body	640	valid
6.0ms	134×	body	80	valid
3.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
1.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite119.0ms

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:

8.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt x)
100.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series588.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(cbrt (+ x 1.0))
229.0ms	(cbrt x)
227.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.1s

Counts

108 → 108

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	194	2160
1	459	1790
2	1408	1468
done	5001	1288

prune387.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.8b	(- (cbrt (+ x 1.0)) (cbrt x))
1.8b	(- (cbrt (+ x 1.0)) (cbrt x))
1.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

174×	`cbrt-prod`
152×	`*-un-lft-identity`
126×	`prod-diff`
113×	`add-sqr-sqrt`
89×	`add-cube-cbrt`
24×	`distribute-lft-out`
21×	`fma-neg`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow1/3`

Counts

4 → 223

Calls

4 calls:

2.0ms	(cbrt x)
88.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
89.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
77.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series1.1s

Counts

4 → 12

Calls

4 calls:

320.0ms	(cbrt x)
251.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
222.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
260.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.0s

Counts

235 → 235

Iterations

Useful iterations: done (976.0ms)

Iter	Nodes	Cost
0	172	5645
1	399	4635
2	1182	3676
done	5000	3184

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
18.6b	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

6.0ms	(cbrt (cbrt x))
3.0ms	(cbrt (cbrt x))
3.0ms	(cbrt (cbrt x))
71.0ms	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

series1.5s

Counts

4 → 12

Calls

4 calls:

358.0ms	(cbrt (cbrt x))
414.0ms	(cbrt (cbrt x))
449.0ms	(cbrt (cbrt x))
257.0ms	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

simplify2.7s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	132	1236
1	307	881
2	978	689
3	4644	642
done	5000	642

prune368.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cbrt (+ x 1.0)))
0.3b	(cbrt (cbrt (+ x 1.0)))
0.6b	(cbrt x)
18.6b	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite126.0ms

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

5.0ms	(cbrt (cbrt (+ x 1.0)))
5.0ms	(cbrt (cbrt (+ x 1.0)))
2.0ms	(cbrt x)
112.0ms	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series792.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(cbrt (cbrt (+ x 1.0)))
133.0ms	(cbrt (cbrt (+ x 1.0)))
308.0ms	(cbrt x)
222.0ms	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify1.1s

Counts

84 → 84

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	202	1450
1	494	1348
2	1654	930
done	5000	869

prune359.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.7b

regimes109.0ms

Accuracy

98.3% (0.4b remaining)

Error of 8.9b against oracle of 8.5b and baseline of 29.6b

bsearch156.0ms

Steps

Iters	Range		Point
11	0.022891638200552334	5.118117448855024e+31	0.0283861619384399
10	-911936.9907706906	-4.3470241882695893e-07	-4127.440397266408

simplify9.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	50	74
1	60	72
2	62	72
done	62	72

end0.0ms

sample1.3s

Algorithm

intervals

Results

425.0ms	1721×	body	1280	valid
321.0ms	4127×	body	80	valid
230.0ms	1227×	body	640	valid
73.0ms	614×	body	320	valid
25.0ms	311×	body	160	valid