Details

sample19.0ms

Algorithm

intervals

Results

6.0ms	62×	body	1280	valid
3.0ms	38×	body	640	valid
3.0ms	119×	body	80	valid
1.0ms	23×	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: 32.1b

localize5.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.8b	(- (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)
7.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series412.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(cbrt (+ x 1.0))
174.0ms	(cbrt x)
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify157.0ms

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

prune152.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.3b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
3.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite23.0ms

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:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
9.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
8.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series564.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (+ x 1.0))
175.0ms	(cbrt x)
152.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
150.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify35.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

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

prune243.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.0b

localize12.0ms

Local error

Found 4 expressions with local error:

3.4b	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
3.4b	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
3.8b	(- (cbrt (+ x 1.0)) (cbrt x))
3.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
32×	`cbrt-prod`
26×	`log-pow`
22×	`sqrt-pow1`
20×	`exp-prod`
16×	`log-prod` `difference-of-squares`
12×	`distribute-lft-out--`
10×	`add-cube-cbrt` `sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`sub-neg` `exp-sum` `add-cbrt-cube` `distribute-lft-out`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 98

Calls

4 calls:

9.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
9.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
8.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
8.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series817.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
259.0ms	(log (sqrt (exp (- (cbrt (+ x 1.0)) (cbrt x)))))
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify38.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	360	1078
1	1059	1004
2	5001	982

prune444.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 14.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
3.3b	(log (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x)))))
3.7b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
31×	`log-pow`
30×	`exp-prod`
24×	`times-frac`
22×	`cbrt-prod`
18×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`distribute-lft-out`
7×	`difference-of-squares`
6×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`log-prod`
2×	`pow1/3` `associate-/r/`
1×	`sub-neg` `log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `div-sub` `rem-log-exp` `flip--` `flip-+` `div-inv`

Counts

4 → 78

Calls

4 calls:

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

series925.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt x)
175.0ms	(cbrt x)
396.0ms	(log (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x)))))
179.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify93.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	750	1315
1	3389	1203
2	5001	1200

prune282.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 14.0b

regimes172.0ms

Accuracy

99.2% (0.2b remaining)

Error of 11.8b against oracle of 11.6b and baseline of 30.0b

bsearch84.0ms

Steps

Iters	Range		Point
10	9.598072339636849e-08	814.2255113159289	0.008973416440535552
9	-4.331403552570957e+63	-1.0403327671093588e+58	-4.469039200229726e+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

sample500.0ms

Algorithm

intervals

Results

170.0ms	1682×	body	1280	valid
98.0ms	1267×	body	640	valid
91.0ms	4063×	body	80	valid
37.0ms	664×	body	320	valid
12.0ms	324×	body	160	valid