Details

Time bar (total: 33.9s)

sample32.0ms

Algorithm
intervals
Results
10.0ms57×body1280valid
6.0ms44×body640valid
5.0ms132×body80valid
2.0ms17×body320valid
0.0ms6×body160valid

simplify11.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
11.0ms
(- (cbrt (+ x 1)) (cbrt x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize19.0ms

Local error

Found 3 expressions with local error:

1.8b
(- (cbrt (+ x 1)) (cbrt x))
0.6b
(cbrt x)
0.3b
(cbrt (+ x 1))

rewrite47.0ms

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
40.0ms
(- (cbrt (+ x 1)) (cbrt x))
5.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)

series456.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
312.0ms
(cbrt x)
102.0ms
(- (cbrt (+ x 1)) (cbrt x))
41.0ms
(cbrt (+ x 1))

simplify1.9s

Counts
32 → 56
Calls
32 calls:
Slowest
293.0ms
(- (+ (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 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
258.0ms
(- (+ (* 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)))
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)))
190.0ms
(- (+ (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))))

prune595.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))
0.6b
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×cbrt-prod *-un-lft-identity
6×add-cube-cbrt add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×pow1/3
2×difference-of-squares
1×sub-neg flip3-- diff-log pow3 rem-cbrt-cube flip-- distribute-lft-out--
Counts
4 → 51
Calls
4 calls:
Slowest
47.0ms
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))
18.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series893.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
284.0ms
(cbrt x)
272.0ms
(cbrt x)
235.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
102.0ms
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))

simplify1.7s

Counts
25 → 63
Calls
25 calls:
Slowest
330.0ms
(- (+ (* 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)))
317.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
301.0ms
(- (+ (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)))))
151.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
147.0ms
(* (pow (* x -1) 1/3) (cbrt -1))

prune631.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

6.5b
(log (- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))
1.8b
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))
0.6b
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
0.6b
(cbrt x)

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
6×cbrt-prod log-prod add-cube-cbrt add-log-exp
5×pow1 add-exp-log
4×add-cbrt-cube insert-posit16 difference-of-squares
2×log-div flip3-- pow1/3 flip-- distribute-lft-out--
1×sub-neg diff-log rem-log-exp pow3 log-pow rem-cbrt-cube
Counts
4 → 57
Calls
4 calls:
Slowest
57.0ms
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))
36.0ms
(log (- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))
14.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
1.0ms
(cbrt x)

series682.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
229.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
217.0ms
(cbrt x)
122.0ms
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))
114.0ms
(log (- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))

simplify3.2s

Counts
31 → 69
Calls
31 calls:
Slowest
424.0ms
(- (+ (* 1/3 (/ x (- 1 (pow x 1/3)))) (log (- 1 (pow x 1/3)))) (+ (* 1/9 (/ (pow x 2) (- 1 (pow x 1/3)))) (* 1/18 (/ (pow x 2) (pow (- 1 (pow x 1/3)) 2)))))
374.0ms
(- (+ (log (- (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1)))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* x (- (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1))))))) (+ (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow x 2) (- (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1)))))) (* 1/18 (/ (pow (exp (* 1/3 (- (log -1) (log (/ -1 x))))) 2) (* (pow x 2) (pow (- (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1))) 2))))))
348.0ms
(- (+ (log (* 1/3 (pow x 1/3))) (+ (log (/ 1 x)) (* 7/54 (/ 1 (pow x 2))))) (* 1/3 (/ 1 x)))
324.0ms
(- (+ (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)))))
274.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))

prune861.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize74.0ms

Local error

Found 4 expressions with local error:

6.5b
(log (+ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (+ (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))))
2.5b
(exp (- 0 (log (+ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (+ (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))))))
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
48×cbrt-div
42×flip3-+ flip-+
36×log-div
32×frac-add
20×exp-sum
18×associate--r-
16×frac-times
11×*-un-lft-identity
10×add-sqr-sqrt
8×associate-*l/ associate-*r/ add-cube-cbrt
6×cbrt-prod pow1 exp-prod add-log-exp
5×add-exp-log
4×add-cbrt-cube insert-posit16
3×log-prod
2×pow1/3 log-pow distribute-lft-out-- rem-exp-log
1×exp-neg sub-neg exp-diff diff-log rem-log-exp difference-of-squares sub0-neg
Counts
4 → 93
Calls
4 calls:
Slowest
79.0ms
(log (+ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (+ (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))))
51.0ms
(exp (- 0 (log (+ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (+ (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))))))
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
395.0ms
(exp (- 0 (log (+ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (+ (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))))))
285.0ms
(cbrt x)
269.0ms
(log (+ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (+ (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))))
268.0ms
(cbrt x)

simplify17.8s

Counts
69 → 105
Calls
69 calls:
Slowest
978.0ms
(exp (- 0 (log (- (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (+ (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))) (+ (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))))))))
668.0ms
(- (+ (* 1/9 (/ (* (exp (- (log (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))))))) (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))))) (* (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)))) (pow x 2)))) (+ (exp (- (log (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))))))) (+ (* 1/9 (* (/ (exp (- (log (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))))))) (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))))) (pow (/ 1 (pow x 4)) 1/3))) (+ (* 4/9 (* (/ (exp (- (log (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))))))) (pow (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)))) 2)) (pow (/ 1 (pow x 2)) 1/3))) (+ (* 4/9 (* (/ (* (exp (- (log (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))))))) (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))))) (pow (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)))) 2)) (pow (/ 1 (pow x 4)) 1/3))) (* 1/9 (/ (* (exp (- (log (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))))))) (* (pow (cbrt -1) 2) (pow (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))) 2))) (* (pow (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)))) 2) (pow x 2))))))))) (+ (* 1/3 (/ (* (exp (- (log (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))))))) (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))))) (* (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)))) x))) (* 2/3 (* (/ (exp (- (log (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))))))) (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))))) (pow (/ 1 x) 1/3)))))
647.0ms
(exp (- 0 (log (+ (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) 3) (pow (+ (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))) 3)))))
599.0ms
(- (+ (* 2/3 (* (pow (/ 1 x) 1/3) (/ 1 (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))))))) (+ (log (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))))) (* 1/3 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)))) x))))) (+ (* 1/18 (/ (* (pow (cbrt -1) 2) (pow (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))) 2)) (* (pow (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)))) 2) (pow x 2)))) (+ (* 1/9 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)))) (pow x 2)))) (+ (* 2/9 (* (pow (/ 1 (pow x 4)) 1/3) (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (pow (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)))) 2)))) (+ (* 1/9 (* (pow (/ 1 (pow x 4)) 1/3) (/ 1 (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))))))) (* 2/9 (* (pow (/ 1 (pow x 2)) 1/3) (/ 1 (pow (+ (pow (/ -1 x) -2/3) (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x))))))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)))) 2)))))))))
562.0ms
(log (+ (* (* (cbrt (+ (pow x 3) (pow 1 3))) (cbrt (- (* x x) (* 1 1)))) (+ (* (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))) (- (* (* (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))) (* (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))))) (* (* (cbrt (+ (* x x) (- (* 1 1) (* x 1)))) (cbrt (- x 1))) (+ (pow (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) 3) (pow (* (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) 3)))))

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes76.0ms

Accuracy

0% (0.4b remaining)

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

bsearch6.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
500.0ms1700×body1280valid
263.0ms1194×body640valid
201.0ms4155×body80valid
117.0ms624×body320valid
97.0ms327×body160valid