Details

Time bar (total: 26.9s)

sample48.0ms

Algorithm
intervals
Results
19.0ms47×body1280valid
10.0ms48×body640valid
7.0ms133×body80valid
2.0ms16×body320valid
1.0ms12×body160valid

simplify10.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(- (cbrt (+ x 1)) (cbrt x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize10.0ms

Local error

Found 3 expressions with local error:

3.0b
(- (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
30.0ms
(- (cbrt (+ x 1)) (cbrt x))
3.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)

series382.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
265.0ms
(cbrt x)
79.0ms
(- (cbrt (+ x 1)) (cbrt x))
36.0ms
(cbrt (+ x 1))

simplify6.9s

Counts
122 → 111
Calls
122 calls:
Slowest
343.0ms
(- (+ (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)))))
325.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
281.0ms
(- (+ (* 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)))
266.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
226.0ms
(fma (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (cbrt x)) (* (cbrt (cbrt x)) (cbrt (cbrt x))))))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize39.0ms

Local error

Found 4 expressions with local error:

3.0b
(- (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)

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
35×cbrt-prod *-un-lft-identity
28×prod-diff
27×add-sqr-sqrt
23×add-cube-cbrt
7×fma-neg
6×add-log-exp
5×distribute-lft-out
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×pow1/3
2×difference-of-squares
1×sub-neg flip3-- diff-log pow3 rem-cbrt-cube flip-- distribute-lft-out--
Counts
4 → 94
Calls
4 calls:
Slowest
55.0ms
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))
14.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series944.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
291.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
284.0ms
(cbrt x)
251.0ms
(cbrt x)
116.0ms
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))

simplify6.4s

Counts
87 → 106
Calls
87 calls:
Slowest
378.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
310.0ms
(- (+ (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)))))
247.0ms
(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (* (cbrt (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (cbrt (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))))))
227.0ms
(- (+ (* 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)))
226.0ms
(fma (cbrt 1) (cbrt (+ x 1)) (- (* (cbrt (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (cbrt (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))))))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize69.0ms

Local error

Found 4 expressions with local error:

3.0b
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×pow1/3
1×sub-neg flip3-- fma-neg diff-log prod-diff flip-- difference-of-squares
Counts
4 → 60
Calls
4 calls:
Slowest
90.0ms
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (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
327.0ms
(cbrt x)
305.0ms
(cbrt x)
272.0ms
(cbrt x)
131.0ms
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))

simplify1.8s

Counts
27 → 72
Calls
27 calls:
Slowest
339.0ms
(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
322.0ms
(- (+ (* 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)))
197.0ms
(/ (exp (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (exp (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))))
164.0ms
(- (+ (* 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))))
162.0ms
(* (pow (* x -1) 1/3) (cbrt -1))

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize89.0ms

Local error

Found 4 expressions with local error:

3.0b
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))
0.6b
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
0.6b
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
0.6b
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u
3×cbrt-prod pow1/3 pow3 rem-cbrt-cube
1×sub-neg flip3-- fma-neg diff-log prod-diff flip-- difference-of-squares
Counts
4 → 57
Calls
4 calls:
Slowest
104.0ms
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))
22.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
18.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
14.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
308.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
300.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
277.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
145.0ms
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))

simplify1.7s

Counts
21 → 69
Calls
21 calls:
Slowest
363.0ms
(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
280.0ms
(- (+ (* 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)))
203.0ms
(/ (exp (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (exp (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))))
168.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
148.0ms
(* (pow (* x -1) 1/3) (cbrt -1))

prune965.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

regimes92.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 30.3b

bsearch192.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
856.0ms1733×body1280valid
295.0ms1262×body640valid
210.0ms4058×body80valid
121.0ms611×body320valid
29.0ms336×body160valid