Details

Time bar (total: 40.7s)

sample53.0ms

Algorithm
intervals
Results
20.0ms62×body1280valid
9.0ms36×body640valid
9.0ms132×body80valid
3.0ms15×body320valid
1.0ms11×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: 29.4b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
64×cbrt-prod
56×*-un-lft-identity
42×prod-diff
41×add-sqr-sqrt
33×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
5×add-log-exp
4×difference-of-squares
3×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u distribute-lft-out--
2×cbrt-div pow1/3
1×sub-neg flip3-+ flip3-- diff-log flip-+ flip--
Counts
3 → 102
Calls
3 calls:
Slowest
34.0ms
(- (cbrt (+ x 1)) (cbrt x))
2.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)

series430.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
273.0ms
(cbrt x)
96.0ms
(- (cbrt (+ x 1)) (cbrt x))
60.0ms
(cbrt (+ x 1))

simplify7.4s

Counts
122 → 111
Calls
122 calls:
Slowest
382.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
361.0ms
(- (+ (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)))))
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)))
247.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
224.0ms
(fma (sqrt (cbrt (+ x 1))) (sqrt (cbrt (+ x 1))) (- (* (cbrt (cbrt x)) (* (cbrt (cbrt x)) (cbrt (cbrt x))))))

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.5b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
120×cbrt-prod
104×*-un-lft-identity
84×prod-diff
78×add-sqr-sqrt
62×add-cube-cbrt
16×distribute-lft-out
14×fma-neg
8×add-log-exp difference-of-squares
6×distribute-lft-out--
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×sub-neg flip3-- pow1/3 diff-log flip--
Counts
4 → 170
Calls
4 calls:
Slowest
39.0ms
(- (cbrt (+ x 1)) (cbrt x))
38.0ms
(- (cbrt (+ x 1)) (cbrt x))
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series765.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
277.0ms
(cbrt x)
259.0ms
(cbrt x)
117.0ms
(- (cbrt (+ x 1)) (cbrt x))
112.0ms
(- (cbrt (+ x 1)) (cbrt x))

simplify13.2s

Counts
226 → 182
Calls
226 calls:
Slowest
363.0ms
(- (+ (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)))))
345.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
336.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
320.0ms
(- (+ (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)))))
259.0ms
(- (+ (* 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)))

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.5b

localize30.0ms

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))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-div
18×cbrt-prod
11×*-un-lft-identity
9×add-sqr-sqrt add-cube-cbrt
7×flip3-+ flip-+
6×prod-diff add-log-exp
4×expm1-log1p-u frac-times pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×pow1/3
2×associate-*l/ associate-*r/
1×sub-neg flip3-- fma-neg diff-log flip-- distribute-lft-out
Counts
4 → 76
Calls
4 calls:
Slowest
49.0ms
(- (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (cbrt x))
8.0ms
(cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))
3.0ms
(cbrt (cbrt (+ x 1)))
1.0ms
(cbrt x)

series466.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
267.0ms
(cbrt x)
102.0ms
(- (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (cbrt x))
48.0ms
(cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))
48.0ms
(cbrt (cbrt (+ x 1)))

simplify5.5s

Counts
47 → 88
Calls
47 calls:
Slowest
693.0ms
(- (+ (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)))))
384.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
353.0ms
(- (+ (* 2/9 (pow (/ 1 (pow x 7)) 1/9)) (pow (/ 1 x) -2/9)) (* 7/81 (pow (/ 1 (pow x 16)) 1/9)))
339.0ms
(- (+ (* 2/9 (pow (/ 1 (pow x 7)) 1/9)) (pow (/ -1 x) -2/9)) (* 7/81 (pow (/ 1 (pow x 16)) 1/9)))
290.0ms
(cbrt (* (cbrt (- (* x x) (* 1 1))) (cbrt (+ (pow x 3) (pow 1 3)))))

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.4b

localize63.0ms

Local error

Found 4 expressions with local error:

14.1b
(- (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (cbrt (cbrt (+ x 1)))))) (cbrt x))
0.6b
(cbrt x)
0.3b
(cbrt (cbrt (cbrt (+ x 1))))
0.3b
(cbrt (cbrt (+ x 1)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
38×cbrt-prod
16×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt
10×cbrt-div
6×prod-diff add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×pow1/3
2×flip3-+ flip-+ distribute-lft-out
1×sub-neg flip3-- fma-neg diff-log flip--
Counts
4 → 79
Calls
4 calls:
Slowest
142.0ms
(- (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (cbrt (cbrt (+ x 1)))))) (cbrt x))
3.0ms
(cbrt (cbrt (cbrt (+ x 1))))
3.0ms
(cbrt (cbrt (+ x 1)))
1.0ms
(cbrt x)

series427.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
237.0ms
(cbrt x)
90.0ms
(- (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (cbrt (cbrt (+ x 1)))))) (cbrt x))
53.0ms
(cbrt (cbrt (+ x 1)))
48.0ms
(cbrt (cbrt (cbrt (+ x 1))))

simplify4.5s

Counts
50 → 91
Calls
50 calls:
Slowest
628.0ms
(/ (exp (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (cbrt (cbrt (+ x 1))))))) (exp (cbrt x)))
380.0ms
(- (+ (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)))))
359.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
285.0ms
(- (+ (pow (/ 1 x) -1/27) (* 1/27 (pow (/ 1 (pow x 26)) 1/27))) (* 13/729 (pow (/ 1 (pow x 53)) 1/27)))
264.0ms
(- (+ (pow (/ 1 x) -1/9) (* 1/9 (pow (/ 1 (pow x 8)) 1/9))) (* 4/81 (pow (/ 1 (pow x 17)) 1/9)))

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.4b

regimes180.0ms

Accuracy

99.6% (0.1b remaining)

Error of 15.7b against oracle of 15.6b and baseline of 29.9b

bsearch158.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
530.0ms1747×body1280valid
332.0ms1269×body640valid
246.0ms4078×body80valid
137.0ms607×body320valid
30.0ms299×body160valid