Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	67×	body	1280	valid
6.0ms	44×	body	640	valid
4.0ms	120×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	8×	body	160	valid

simplify11.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

11.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize22.0ms

Local error

Found 3 expressions with local error:

2.7b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite74.0ms

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

66.0ms	(- (cbrt (+ x 1)) (cbrt x))
5.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series441.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

232.0ms	(cbrt x)
147.0ms	(- (cbrt (+ x 1)) (cbrt x))
62.0ms	(cbrt (+ x 1))

simplify1.8s

Counts

32 → 56

Calls

32 calls:

Slowest

320.0ms	(- (+ (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)))))
287.0ms	(- (+ (* 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)))
230.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
197.0ms	(- (+ (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))))
193.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune542.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.3b	(/ -1/9 x)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`cbrt-prod`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `insert-posit16` `add-log-exp`
3×	`distribute-lft-neg-in` `associate-/r` `distribute-rgt-neg-in` `pow1/3` `associate-/l`
1×	`cbrt-undiv` `clear-num` `neg-mul-1` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 71

Calls

4 calls:

Slowest

7.0ms	(/ -1/9 x)
3.0ms	(cbrt (- x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series816.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

295.0ms	(cbrt (- x))
249.0ms	(cbrt x)
243.0ms	(cbrt x)
28.0ms	(/ -1/9 x)

simplify978.0ms

Counts

52 → 83

Calls

52 calls:

Slowest

283.0ms	(/ (* (* -1/9 -1/9) -1/9) (* (* x x) x))
113.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
102.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
47.0ms	(/ (* (cbrt -1/9) (cbrt -1/9)) (* (cbrt x) (cbrt x)))
35.0ms	(* (pow x 1/3) (cbrt -1))

prune776.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize80.0ms

Local error

Found 4 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

19×	`cbrt-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
1×	`neg-mul-1`

Counts

4 → 55

Calls

4 calls:

Slowest

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

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

318.0ms	(cbrt (- x))
279.0ms	(cbrt x)
279.0ms	(cbrt x)
278.0ms	(cbrt x)

simplify653.0ms

Counts

31 → 67

Calls

31 calls:

Slowest

141.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
116.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
109.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
31.0ms	(pow (/ 1 x) -1/3)
28.0ms	(pow (/ 1 x) -1/3)

prune719.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.2b

localize71.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (* (cbrt x) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (cbrt x)))
0.6b	(cbrt (- x))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

17×	`cbrt-prod`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
1×	`neg-mul-1`

Counts

4 → 53

Calls

4 calls:

Slowest

62.0ms	(cbrt (* (* (cbrt x) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (cbrt x)))
3.0ms	(cbrt (- x))
2.0ms	(cbrt x)
2.0ms	(cbrt x)

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

334.0ms	(cbrt x)
310.0ms	(cbrt x)
296.0ms	(cbrt (- x))
270.0ms	(cbrt (* (* (cbrt x) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (cbrt x)))

simplify633.0ms

Counts

29 → 65

Calls

29 calls:

Slowest

133.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
115.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
98.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
31.0ms	(pow (/ 1 x) -1/3)
30.0ms	(pow (/ 1 x) -1/3)

prune872.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 0.2b

regimes272.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 31.6b

bsearch10.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

755.0ms	1305×	body	640	valid
461.0ms	1646×	body	1280	valid
240.0ms	4061×	body	80	valid
182.0ms	636×	body	320	valid
33.0ms	352×	body	160	valid