Details

sample43.0ms

Algorithm

intervals

Results

20.0ms	51×	body	1280	valid
7.0ms	45×	body	640	valid
6.0ms	137×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid

simplify21.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

21.0ms

(- (cbrt (+ x 1)) (cbrt x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize13.0ms

Local error

Found 3 expressions with local error:

2.3b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite38.0ms

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-cbrt-cube` `add-exp-log` `insert-posit16` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3` `distribute-lft-out`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

3 → 47

Calls

3 calls:

Slowest

30.0ms	(- (cbrt (+ x 1)) (cbrt x))
5.0ms	(cbrt (+ x 1))
2.0ms	(cbrt x)

series425.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

268.0ms	(cbrt x)
122.0ms	(- (cbrt (+ x 1)) (cbrt x))
35.0ms	(cbrt (+ x 1))

simplify2.0s

Counts

32 → 56

Calls

32 calls:

Slowest

309.0ms	(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2)))))
266.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (* 5/81 (pow (/ 1 (pow x 8)) 1/3))) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
262.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
253.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
221.0ms	(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))

prune600.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize85.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (pow (cbrt (+ x 1)) 3) (pow (cbrt x) 3))
0.7b	(pow (cbrt x) 3)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
52×	`cbrt-prod`
42×	`unpow-prod-down` `cube-prod`
41×	`*-un-lft-identity`
36×	`difference-of-squares`
13×	`distribute-lft-out--` `sqr-pow`
11×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `distribute-lft-out`
3×	`pow-unpow` `pow1/3`
2×	`pow-pow`
1×	`cube-mult` `pow-to-exp` `difference-cubes` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `flip--` `rem-cube-cbrt`

Counts

4 → 118

Calls

4 calls:

Slowest

75.0ms	(- (pow (cbrt (+ x 1)) 3) (pow (cbrt x) 3))
4.0ms	(pow (cbrt x) 3)
3.0ms	(cbrt x)
1.0ms	(cbrt x)

series967.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

352.0ms	(pow (cbrt x) 3)
290.0ms	(cbrt x)
250.0ms	(cbrt x)
76.0ms	(- (pow (cbrt (+ x 1)) 3) (pow (cbrt x) 3))

simplify24.4s

Counts

134 → 130

Calls

134 calls:

Slowest

682.0ms	(+ (pow (sqrt (cbrt (+ x 1))) 3) (pow (cbrt (sqrt x)) 3))
439.0ms	(+ (pow (cbrt (+ x 1)) (/ 3 2)) (pow (cbrt x) (/ 3 2)))
438.0ms	(+ (pow (cbrt (+ x 1)) (/ 3 2)) (pow (sqrt (cbrt x)) 3))
409.0ms	(+ (pow (cbrt (sqrt (+ x 1))) 3) (pow (cbrt (sqrt x)) 3))
392.0ms	(+ (pow (cbrt (+ x 1)) (/ 3 2)) (pow (cbrt (sqrt x)) 3))

prune1.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.5b	(* (cbrt x) (cbrt x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 77

Calls

4 calls:

Slowest

16.0ms	(* (cbrt x) (cbrt x))
2.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

368.0ms	(* (cbrt x) (cbrt x))
333.0ms	(cbrt x)
291.0ms	(cbrt x)
263.0ms	(cbrt x)

simplify926.0ms

Counts

63 → 89

Calls

63 calls:

Slowest

166.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
140.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
126.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
115.0ms	(* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))
59.0ms	(* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt x)) (cbrt (cbrt x))))

prune950.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `add-log-exp`

Counts

4 → 48

Calls

4 calls:

Slowest

2.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

308.0ms	(cbrt x)
267.0ms	(cbrt x)
260.0ms	(cbrt x)
245.0ms	(cbrt x)

simplify817.0ms

Counts

24 → 60

Calls

24 calls:

Slowest

179.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
178.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
138.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
136.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
32.0ms	(pow (/ 1 x) -1/3)

prune702.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes62.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch5.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

607.0ms	4038×	body	80	valid
516.0ms	1716×	body	1280	valid
246.0ms	1311×	body	640	valid
126.0ms	611×	body	320	valid
29.0ms	324×	body	160	valid