Details

Time bar (total: 13.1s)

sample35.0ms

Algorithm
intervals
Results
11.0ms51×body1280valid
7.0ms45×body640valid
6.0ms136×body80valid
2.0ms16×body320valid
1.0ms8×body160valid

simplify13.0ms

Calls
1 calls:
Slowest
13.0ms
(- (cbrt (+ x 1)) (cbrt x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite44.0ms

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--
Calls
3 calls:
Slowest
40.0ms
(- (cbrt (+ x 1)) (cbrt x))
2.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)

series438.0ms

Calls
3 calls:
Slowest
241.0ms
(cbrt x)
139.0ms
(- (cbrt (+ x 1)) (cbrt x))
58.0ms
(cbrt (+ x 1))

simplify2.0s

Calls
32 calls:
Slowest
291.0ms
(- (+ (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)))))
272.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
267.0ms
(- (+ (* 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
(- (+ (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))))
227.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune474.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite54.0ms

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--
Calls
3 calls:
Slowest
47.0ms
(- (cbrt (+ x 1)) (cbrt x))
5.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)

series478.0ms

Calls
3 calls:
Slowest
276.0ms
(cbrt x)
137.0ms
(- (cbrt (+ x 1)) (cbrt x))
66.0ms
(cbrt (+ x 1))

simplify1.8s

Calls
32 calls:
Slowest
294.0ms
(- (+ (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)))))
288.0ms
(- (+ (* 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)))
240.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
213.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
163.0ms
(- (+ (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))))

prune509.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite40.0ms

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--
Calls
3 calls:
Slowest
33.0ms
(- (cbrt (+ x 1)) (cbrt x))
5.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)

series437.0ms

Calls
3 calls:
Slowest
287.0ms
(cbrt x)
107.0ms
(- (cbrt (+ x 1)) (cbrt x))
43.0ms
(cbrt (+ x 1))

simplify1.9s

Calls
32 calls:
Slowest
315.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
299.0ms
(- (+ (* 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)))
294.0ms
(- (+ (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)))))
216.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
156.0ms
(- (+ (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))))

prune420.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.4b
(* 1/9 x)
0.2b
(* x (- (* 1/9 x) 1/3))
0.0b
(- (* 1/9 x) 1/3)

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l* add-log-exp
4×insert-posit16
3×cbrt-prod sub-neg
2×distribute-rgt-in distribute-lft-in flip3-- pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod flip-- unswap-sqr
1×pow1/3 diff-log
Calls
4 calls:
Slowest
30.0ms
(* x (- (* 1/9 x) 1/3))
7.0ms
(- (* 1/9 x) 1/3)
6.0ms
(* 1/9 x)
1.0ms
(cbrt x)

series372.0ms

Calls
4 calls:
Slowest
224.0ms
(cbrt x)
70.0ms
(* x (- (* 1/9 x) 1/3))
50.0ms
(- (* 1/9 x) 1/3)
27.0ms
(* 1/9 x)

simplify1.6s

Calls
41 calls:
Slowest
548.0ms
(* (* (* x x) x) (* (* (- (* 1/9 x) 1/3) (- (* 1/9 x) 1/3)) (- (* 1/9 x) 1/3)))
139.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
139.0ms
(* (* (* 1/9 1/9) 1/9) (* (* x x) x))
117.0ms
(+ (* (* 1/9 x) (* 1/9 x)) (+ (* 1/3 1/3) (* (* 1/9 x) 1/3)))
107.0ms
(/ (exp (* 1/9 x)) (exp 1/3))

prune613.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes81.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 29.6b

bsearch5.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
697.0ms1285×body640valid
481.0ms1650×body1280valid
190.0ms4109×body80valid
130.0ms612×body320valid
31.0ms344×body160valid