Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	59×	body	1280	valid
3.0ms	139×	body	80	valid
2.0ms	26×	body	640	valid
1.0ms	23×	body	320	valid
0.0ms	9×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.1b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite13.0ms

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:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
8.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series423.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(cbrt (+ x 1.0))
177.0ms	(cbrt x)
157.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify158.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	287	358
1	934	344
2	4833	322
3	5001	322

prune151.0ms

Filtered

53 candidates to 45 candidates (84.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	44	9	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	9	54

Merged error: 10.6b

Counts

54 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
3.3b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite14.0ms

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)
10.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series714.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt x)
176.0ms	(cbrt x)
182.0ms	(cbrt x)
179.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify132.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	243	356
1	829	292
2	4198	276
3	5001	276

prune189.0ms

Filtered

58 candidates to 50 candidates (86.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	58	9	67

Merged error: 10.6b

Counts

67 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
20.1b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))

rewrite16.0ms

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--`

Counts

4 → 45

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))

series716.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt x)
182.0ms	(cbrt x)
176.0ms	(cbrt x)
179.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))

simplify144.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (139.0ms)

Iter	Nodes	Cost
0	248	481
1	888	407
2	4642	365
3	5002	350

prune202.0ms

Filtered

57 candidates to 46 candidates (80.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	57	9	66

Merged error: 10.6b

Counts

66 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
3.3b	(- (cbrt (+ x 1.0)) (cbrt x))
3.3b	(- (cbrt (+ x 1.0)) (cbrt x))
3.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`cbrt-prod`
26×	`*-un-lft-identity`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`pow1/3`

Counts

4 → 68

Calls

4 calls:

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

series625.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
144.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
150.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify129.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	234	664
1	748	628
2	3971	589
3	5002	589

prune256.0ms

Filtered

80 candidates to 66 candidates (82.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	80	9	89

Merged error: 10.6b

Counts

89 → 9

regimes54.0ms

Accuracy

99.3% (0.1b remaining)

Error of 12.0b against oracle of 11.9b and baseline of 30.1b

bsearch77.0ms

Steps

Iters	Range		Point
9	1.2497558356096057e-15	3.88064682879673e-06	2.5883840984013146e-14
8	-4.7170329246979447e+61	-3.6046192339311515e+58	-4.455930272966536e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	34
1	64	34
2	64	34

end0.0ms

sample705.0ms

Algorithm

intervals

Results

364.0ms	1749×	body	1280	valid
98.0ms	1253×	body	640	valid
90.0ms	4072×	body	80	valid
38.0ms	586×	body	320	valid
14.0ms	340×	body	160	valid