Details

sample23.0ms

Algorithm

intervals

Results

8.0ms	49×	body	1280	valid
4.0ms	52×	body	640	valid
3.0ms	133×	body	80	valid
1.0ms	13×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite27.0ms

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:

2.0ms	(cbrt (+ x 1.0))
0.0ms	(cbrt x)
23.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series424.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(cbrt (+ x 1.0))
178.0ms	(cbrt x)
154.0ms	(- (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

prune155.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.0b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite85.0ms

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:

2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
57.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
23.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series581.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (+ x 1.0))
181.0ms	(cbrt x)
154.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
153.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify36.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

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

prune238.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.4b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite61.0ms

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)
27.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series651.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
92.0ms	(cbrt (+ x 1.0))
180.0ms	(cbrt x)
156.0ms	(- (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	861
1	3138	808
2	5002	804

prune268.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt (cbrt x))
0.6b	(cbrt (* (cbrt x) (cbrt x)))
7.7b	(- (cbrt (+ x 1.0)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`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 → 46

Calls

4 calls:

0.0ms	(cbrt x)
1.0ms	(cbrt (cbrt x))
3.0ms	(cbrt (* (cbrt x) (cbrt x)))
23.0ms	(- (cbrt (+ x 1.0)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))

series1.0s

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt x)
423.0ms	(cbrt (cbrt x))
276.0ms	(cbrt (* (cbrt x) (cbrt x)))
152.0ms	(- (cbrt (+ x 1.0)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))

simplify95.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	295	442
1	815	391
2	3015	376
3	5002	364

prune169.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.4b

regimes55.0ms

Accuracy

98.1% (0.4b remaining)

Error of 8.8b against oracle of 8.4b and baseline of 29.0b

bsearch85.0ms

Steps

Iters	Range		Point
10	5.968040026638966e-05	117627206.70733242	0.000879034653916002
10	-64880754058.88788	-2.651420353119469e-05	-3761.124489091299

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	39
1	58	39
2	58	39

end0.0ms

sample516.0ms

Algorithm

intervals

Results

180.0ms	1735×	body	1280	valid
102.0ms	1222×	body	640	valid
86.0ms	4115×	body	80	valid
40.0ms	615×	body	320	valid
12.0ms	313×	body	160	valid