Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	52×	body	1280	valid
4.0ms	45×	body	640	valid
3.0ms	132×	body	80	valid
1.0ms	16×	body	320	valid
0.0ms	11×	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: 29.7b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.2b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite15.0ms

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))

series427.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(cbrt (+ x 1.0))
184.0ms	(cbrt x)
152.0ms	(- (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

prune143.0ms

Filtered

53 candidates to 45 candidates (84.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	43	10	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	10	54

Merged error: 11.4b

Counts

54 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.2b	(- (cbrt (+ x 1.0)) (cbrt x))
9.5b	(log (- (cbrt (+ x 1.0)) (cbrt x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
10×	`log-prod`
8×	`difference-of-squares`
7×	`add-cube-cbrt`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`log-div` `cbrt-div` `flip3--` `pow1/3` `flip--`
1×	`sub-neg` `flip3-+` `diff-log` `rem-log-exp` `log-pow` `flip-+`

Counts

4 → 65

Calls

4 calls:

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

series630.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (+ x 1.0))
186.0ms	(cbrt x)
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
203.0ms	(log (- (cbrt (+ x 1.0)) (cbrt x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	467	711
1	1623	676
2	5002	672

prune239.0ms

Filtered

77 candidates to 64 candidates (83.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	70	7	77
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	75	12	87

Merged error: 11.3b

Counts

87 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt x) 3)
2.4b	(- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3))
4.6b	(log (- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3)))
9.5b	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

131×	`add-sqr-sqrt`
86×	`cbrt-prod`
78×	`unpow-prod-down` `cube-prod`
72×	`difference-of-squares`
71×	`*-un-lft-identity`
56×	`log-prod`
26×	`distribute-lft-out--`
25×	`sqr-pow`
24×	`cbrt-div`
21×	`flip3-+` `flip-+`
20×	`log-div`
16×	`frac-add`
11×	`add-cube-cbrt`
8×	`frac-times` `distribute-lft-out`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`associate-r/` `associate-l/` `add-cbrt-cube`
3×	`pow-unpow`
2×	`difference-cubes` `flip3--` `pow-pow` `rem-log-exp` `log-pow` `flip--`
1×	`cube-mult` `pow-to-exp` `sub-neg` `pow1/3` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt`

Counts

4 → 186

Calls

4 calls:

3.0ms	(pow (cbrt x) 3)
26.0ms	(- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3))
23.0ms	(log (- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3)))
14.0ms	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

series813.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(pow (cbrt x) 3)
65.0ms	(- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3))
180.0ms	(log (- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3)))
343.0ms	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1209	3634
1	5001	3450

prune485.0ms

Filtered

198 candidates to 88 candidates (44.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	195	3	198
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	205	5	210

Merged error: 2.4b

Counts

210 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.6b	(exp (- (log 1.0) (log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))))
9.5b	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

48×	`cbrt-div`
42×	`flip3-+` `flip-+`
36×	`log-div`
32×	`frac-add`
23×	`exp-sum`
18×	`associate--r-`
16×	`frac-times`
13×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt`
8×	`exp-prod` `associate-r/` `associate-l/`
6×	`cbrt-prod` `log-prod`
5×	`add-exp-log` `log-pow` `add-log-exp`
4×	`add-cbrt-cube` `distribute-lft-out--`
3×	`associate--l+`
2×	`pow1/3` `rem-exp-log`
1×	`sub-neg` `exp-diff` `diff-log` `rem-log-exp` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(exp (- (log 1.0) (log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))))
19.0ms	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt x)
183.0ms	(cbrt x)
507.0ms	(exp (- (log 1.0) (log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))))
341.0ms	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1432	4496
1	5001	4331

prune628.0ms

Filtered

105 candidates to 81 candidates (77.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	104	6	110

Merged error: 0.5b

Counts

110 → 6

regimes41.0ms

Accuracy

0% (0.1b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15

end0.0ms

sample486.0ms

Algorithm

intervals

Results

164.0ms	1676×	body	1280	valid
98.0ms	1236×	body	640	valid
84.0ms	4135×	body	80	valid
37.0ms	624×	body	320	valid
12.0ms	329×	body	160	valid