Details

Time bar (total: 15.0s)

sample52.0ms

Algorithm
intervals
Results
18.0ms54×body1280valid
11.0ms41×body640valid
9.0ms130×body80valid
4.0ms19×body320valid
1.0ms12×body160valid

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: 29.8b

localize34.0ms

Local error

Found 3 expressions with local error:

3.5b
(- (cbrt (+ x 1)) (cbrt x))
0.6b
(cbrt x)
0.2b
(cbrt (+ x 1))

rewrite55.0ms

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
48.0ms
(- (cbrt (+ x 1)) (cbrt x))
5.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)

series437.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
269.0ms
(cbrt x)
119.0ms
(- (cbrt (+ x 1)) (cbrt x))
48.0ms
(cbrt (+ x 1))

simplify1.9s

Counts
32 → 56
Calls
32 calls:
Slowest
312.0ms
(- (+ (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)))))
278.0ms
(- (+ (* 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)))
248.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
211.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
196.0ms
(- (+ (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))))

prune501.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

3.5b
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite19.0ms

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
17.0ms
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
347.0ms
(cbrt x)
278.0ms
(cbrt x)
265.0ms
(cbrt x)
135.0ms
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))

simplify1.4s

Counts
24 → 62
Calls
24 calls:
Slowest
307.0ms
(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
256.0ms
(- (+ (* 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)))
194.0ms
(/ (exp (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (exp (* (cbrt x) (cbrt x))))
155.0ms
(- (+ (* 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))))
121.0ms
(* (pow (* x -1) 1/3) (cbrt -1))

prune565.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

9.4b
(- (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (cbrt x))
0.6b
(cbrt x)
0.3b
(cbrt (cbrt (+ x 1)))
0.2b
(cbrt (+ x 1))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
12×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×pow1/3
2×flip3-+ flip-+ distribute-lft-out
1×sub-neg flip3-- diff-log flip--
Counts
4 → 58
Calls
4 calls:
Slowest
33.0ms
(- (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (cbrt x))
6.0ms
(cbrt (cbrt (+ x 1)))
5.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)

series510.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
302.0ms
(cbrt x)
112.0ms
(- (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (cbrt x))
55.0ms
(cbrt (cbrt (+ x 1)))
41.0ms
(cbrt (+ x 1))

simplify2.9s

Counts
31 → 70
Calls
31 calls:
Slowest
316.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
291.0ms
(- (+ (* 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)))
272.0ms
(- (+ (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)))))
262.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
240.0ms
(- (+ (exp (* 1/9 (- (log -1) (log (/ -1 x))))) (* 1/9 (/ (exp (* 1/9 (- (log -1) (log (/ -1 x))))) x))) (* 4/81 (/ (exp (* 1/9 (- (log -1) (log (/ -1 x))))) (pow x 2))))

prune776.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize38.0ms

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)

rewrite10.0ms

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
6.0ms
(/ -1/9 x)
1.0ms
(cbrt (- x))
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series905.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
324.0ms
(cbrt (- x))
319.0ms
(cbrt x)
245.0ms
(cbrt x)
17.0ms
(/ -1/9 x)

simplify1.1s

Counts
52 → 83
Calls
52 calls:
Slowest
317.0ms
(/ (* (* -1/9 -1/9) -1/9) (* (* x x) x))
169.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
164.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
39.0ms
(pow (/ 1 x) -1/3)
36.0ms
(/ (* (cbrt -1/9) (cbrt -1/9)) (* (cbrt x) (cbrt x)))

prune701.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.1b

regimes78.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 30.0b

bsearch123.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
520.0ms645×body320valid
513.0ms1747×body1280valid
368.0ms1230×body640valid
240.0ms4064×body80valid
31.0ms314×body160valid