Details

sample31.0ms

Algorithm

intervals

Results

10.0ms	57×	body	1280	valid
6.0ms	40×	body	640	valid
5.0ms	131×	body	80	valid
1.0ms	14×	body	320	valid
1.0ms	14×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.5b	(cbrt x)
3.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite26.0ms

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)
21.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series420.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(cbrt (+ x 1.0))
182.0ms	(cbrt x)
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify162.0ms

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

prune167.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.5b	(cbrt x)
2.6b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
3.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
50.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
26.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series572.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (+ x 1.0))
179.0ms	(cbrt x)
152.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
147.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify43.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	336	568
1	1025	536
2	5001	505

prune278.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
3.4b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite13.0ms

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:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
11.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series728.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt x)
181.0ms	(cbrt x)
189.0ms	(cbrt x)
182.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify134.0ms

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

prune392.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
0.3b	(cbrt (+ x 1.0))
0.5b	(cbrt x)
3.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
31×	`cbrt-prod`
12×	`difference-of-squares`
10×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `distribute-lft-out--`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`distribute-lft-out`
3×	`pow-unpow`
2×	`cube-div` `cbrt-div` `flip3--` `pow1/3` `flip--`
1×	`cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `flip3-+` `diff-log` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

28.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
22.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series609.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
85.0ms	(cbrt (+ x 1.0))
174.0ms	(cbrt x)
143.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify76.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	694	859
1	3138	808
2	5001	804

prune272.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.5b

regimes50.0ms

Accuracy

98.2% (0.4b remaining)

Error of 8.6b against oracle of 8.2b and baseline of 30.5b

bsearch75.0ms

Steps

Iters	Range		Point
10	4.555257425893614e-05	47183757994.54101	0.15097238251788841
9	-13600.963204601821	-0.00047371797307045637	-4084.891149633814

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	32
1	54	32
2	54	32

end0.0ms

sample542.0ms

Algorithm

intervals

Results

185.0ms	1743×	body	1280	valid
107.0ms	1305×	body	640	valid
87.0ms	4004×	body	80	valid
41.0ms	656×	body	320	valid
12.0ms	292×	body	160	valid