Details

Time bar (total: 56.3s)

sample40.0ms

Algorithm
intervals
Results
17.0ms62×body1280valid
6.0ms36×body640valid
5.0ms132×body80valid
2.0ms15×body320valid
1.0ms11×body160valid

simplify20.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
20.0ms
(- (cbrt (+ x 1)) (cbrt x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize23.0ms

Local error

Found 3 expressions with local error:

2.7b
(- (cbrt (+ x 1)) (cbrt x))
0.6b
(cbrt x)
0.2b
(cbrt (+ x 1))

rewrite32.0ms

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
28.0ms
(- (cbrt (+ x 1)) (cbrt x))
2.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)

series451.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
289.0ms
(cbrt x)
120.0ms
(- (cbrt (+ x 1)) (cbrt x))
42.0ms
(cbrt (+ x 1))

simplify1.9s

Counts
32 → 56
Calls
32 calls:
Slowest
287.0ms
(- (+ (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)))))
284.0ms
(- (+ (* 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)))
237.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
171.0ms
(- (+ (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))))

prune575.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

8.8b
(- (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (cbrt x))
0.6b
(cbrt x)
0.3b
(cbrt (cbrt (+ x 1)))
0.3b
(cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-div
15×cbrt-prod
9×*-un-lft-identity
7×add-sqr-sqrt flip3-+ add-cube-cbrt flip-+
6×add-log-exp
4×frac-times pow1 add-cbrt-cube add-exp-log insert-posit16
3×pow1/3
2×associate-*l/ associate-*r/
1×sub-neg flip3-- diff-log flip-- distribute-lft-out
Counts
4 → 61
Calls
4 calls:
Slowest
29.0ms
(- (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (cbrt x))
13.0ms
(cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))
3.0ms
(cbrt (cbrt (+ x 1)))
1.0ms
(cbrt x)

series509.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
288.0ms
(cbrt x)
122.0ms
(- (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (cbrt x))
51.0ms
(cbrt (cbrt (+ x 1)))
48.0ms
(cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))

simplify4.0s

Counts
34 → 73
Calls
34 calls:
Slowest
348.0ms
(- (+ (* 2/9 (pow (/ 1 (pow x 7)) 1/9)) (pow (/ -1 x) -2/9)) (* 7/81 (pow (/ 1 (pow x 16)) 1/9)))
316.0ms
(- (+ (* 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)))
315.0ms
(- (+ (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)))))
307.0ms
(- (+ (* 2/9 (pow (/ 1 (pow x 7)) 1/9)) (pow (/ 1 x) -2/9)) (* 7/81 (pow (/ 1 (pow x 16)) 1/9)))
270.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))

prune912.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize62.0ms

Local error

Found 4 expressions with local error:

8.8b
(- (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x)))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite200.0ms

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
197.0ms
(- (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x)))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series948.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
333.0ms
(cbrt x)
261.0ms
(cbrt x)
246.0ms
(cbrt x)
109.0ms
(- (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x)))

simplify1.8s

Counts
24 → 62
Calls
24 calls:
Slowest
488.0ms
(/ (exp (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (exp (* (cbrt x) (cbrt x))))
286.0ms
(- (+ (* 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)))
232.0ms
(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
161.0ms
(- (+ (* 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))))
145.0ms
(* (pow (* x -1) 1/3) (cbrt -1))

prune778.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize144.0ms

Local error

Found 4 expressions with local error:

16.3b
(- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))))
0.8b
(/ (- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x)))) (+ (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x))))
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite26.6s

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×times-frac
6×cbrt-prod add-cbrt-cube add-exp-log add-log-exp
5×difference-of-squares
4×pow1 insert-posit16 associate-/l*
3×associate-/r*
2×flip3-- pow1/3 associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Counts
4 → 75
Calls
4 calls:
Slowest
14.1s
(- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))))
12.6s
(/ (- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x)))) (+ (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x))))
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
340.0ms
(/ (- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x)))) (+ (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x))))
281.0ms
(cbrt x)
259.0ms
(cbrt x)
168.0ms
(- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))))

simplify13.2s

Counts
58 → 87
Calls
58 calls:
Slowest
1.3s
(/ (* (* (- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x)))) (- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))))) (- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))))) (* (* (+ (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x))) (+ (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x)))) (+ (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x)))))
496.0ms
(/ (- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x)))) (sqrt (+ (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x)))))
484.0ms
(/ (- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x)))) (cbrt (+ (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x)))))
472.0ms
(/ (- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x)))) (+ (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x))))
450.0ms
(/ (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (+ (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x))))

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

regimes87.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.4b

bsearch245.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
531.0ms1747×body1280valid
319.0ms1269×body640valid
225.0ms4078×body80valid
157.0ms607×body320valid
29.0ms299×body160valid