Details

sample54.0ms

Algorithm

intervals

Results

15.0ms	45×	body	1280	valid
13.0ms	49×	body	640	valid
9.0ms	132×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	9×	body	160	valid

simplify22.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

22.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize10.0ms

Local error

Found 3 expressions with local error:

2.0b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite49.0ms

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

42.0ms	(- (cbrt (+ x 1)) (cbrt x))
5.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series419.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

253.0ms	(cbrt x)
109.0ms	(- (cbrt (+ x 1)) (cbrt x))
57.0ms	(cbrt (+ x 1))

simplify2.0s

Counts

32 → 56

Calls

32 calls:

Slowest

321.0ms	(- (+ (* 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)))
318.0ms	(- (+ (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)))))
317.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
211.0ms	(- (+ (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))))
209.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune562.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 50

Calls

4 calls:

Slowest

22.0ms	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series987.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

305.0ms	(cbrt x)
271.0ms	(cbrt x)
270.0ms	(cbrt x)
141.0ms	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))

simplify1.4s

Counts

24 → 62

Calls

24 calls:

Slowest

242.0ms	(- (+ (* 4/81 (pow (/ 1 (pow x 7)) 1/3)) (* 2/3 (pow (/ 1 x) 1/3))) (* 1/9 (pow (/ 1 (pow x 4)) 1/3)))
240.0ms	(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
204.0ms	(/ (exp (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (exp (* (cbrt x) (cbrt x))))
174.0ms	(- (+ (* 2/3 (pow (/ 1 x) 1/3)) (pow (/ -1 x) -2/3)) (+ (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)) (* 1/9 (pow (/ 1 (pow x 4)) 1/3))))
164.0ms	(* (pow (* x -1) 1/3) (cbrt -1))

prune651.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (cbrt (+ x 1)) (cbrt x))
2.0b	(- (cbrt (+ x 1)) (cbrt x))
2.0b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`cbrt-prod`
26×	`*-un-lft-identity`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
5×	`add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`pow1/3`

Counts

4 → 72

Calls

4 calls:

Slowest

42.0ms	(- (cbrt (+ x 1)) (cbrt x))
37.0ms	(- (cbrt (+ x 1)) (cbrt x))
28.0ms	(- (cbrt (+ x 1)) (cbrt x))
1.0ms	(cbrt x)

series598.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

257.0ms	(cbrt x)
125.0ms	(- (cbrt (+ x 1)) (cbrt x))
112.0ms	(- (cbrt (+ x 1)) (cbrt x))
104.0ms	(- (cbrt (+ x 1)) (cbrt x))

simplify3.5s

Counts

57 → 84

Calls

57 calls:

Slowest

344.0ms	(- (+ (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)))))
313.0ms	(- (+ (* 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)))
302.0ms	(- (+ (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)))))
298.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
283.0ms	(- (+ (* 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)))

prune843.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

16.9b	(- (/ (cbrt (+ -1 (* x x))) (cbrt (- x 1))) (cbrt x))
15.5b	(cbrt (+ -1 (* x x)))
0.6b	(cbrt x)
0.3b	(cbrt (- x 1))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
26×	`cbrt-prod`
12×	`*-un-lft-identity` `difference-of-squares`
8×	`times-frac`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `cbrt-div` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`pow1/3`
2×	`flip3--` `flip--` `distribute-lft-out--`
1×	`sub-neg` `flip3-+` `diff-log` `difference-of-sqr-1` `flip-+`

Counts

4 → 68

Calls

4 calls:

Slowest

57.0ms	(- (/ (cbrt (+ -1 (* x x))) (cbrt (- x 1))) (cbrt x))
2.0ms	(cbrt (- x 1))
2.0ms	(cbrt (+ -1 (* x x)))
1.0ms	(cbrt x)

series597.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

236.0ms	(cbrt x)
159.0ms	(cbrt (+ -1 (* x x)))
140.0ms	(- (/ (cbrt (+ -1 (* x x))) (cbrt (- x 1))) (cbrt x))
62.0ms	(cbrt (- x 1))

simplify5.6s

Counts

51 → 80

Calls

51 calls:

Slowest

388.0ms	(cbrt (- (* -1 -1) (* (* x x) (* x x))))
374.0ms	(- (* (pow (* x -1) 1/3) (cbrt -1)) (+ (* 1/9 (* (pow (/ -1 (pow x 5)) 1/3) (cbrt -1))) (* 1/3 (* (pow (/ -1 (pow x 2)) 1/3) (cbrt -1)))))
335.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
292.0ms	(- (+ (* 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)))
284.0ms	(cbrt (+ (pow -1 3) (pow (* x x) 3)))

prune628.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.2b

regimes101.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 29.8b

bsearch7.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

704.0ms	1267×	body	640	valid
460.0ms	1698×	body	1280	valid
194.0ms	4093×	body	80	valid
84.0ms	631×	body	320	valid
61.0ms	311×	body	160	valid