Details

Time bar (total: 27.8s)

sample38.0ms

Algorithm
intervals
Results
12.0ms51×body1280valid
7.0ms143×body80valid
6.0ms31×body640valid
3.0ms19×body320valid
1.0ms12×body160valid

simplify30.0ms

Calls
1 calls:
Slowest
30.0ms
(- (cbrt (+ x 1)) (cbrt x))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize11.0ms

Local error

Found 3 expressions with local error:

2.6b
(- (cbrt (+ x 1)) (cbrt x))
0.6b
(cbrt x)
0.3b
(cbrt (+ x 1))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
20×*-un-lft-identity
18×prod-diff add-cube-cbrt
16×cbrt-prod
6×fma-neg
5×add-log-exp
3×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×cbrt-div pow1/3 difference-of-squares
1×sub-neg flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out--
Calls
3 calls:
Slowest
9.0ms
(- (cbrt (+ x 1)) (cbrt x))
1.0ms
(cbrt (+ x 1))
0.0ms
(cbrt x)

series459.0ms

Calls
3 calls:
Slowest
314.0ms
(cbrt x)
112.0ms
(- (cbrt (+ x 1)) (cbrt x))
33.0ms
(cbrt (+ x 1))

simplify3.1s

Calls
61 calls:
Slowest
360.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
289.0ms
(- (+ (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))))
228.0ms
(- (+ (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)))))
159.0ms
(- (+ (* 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)))
124.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune725.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.8b

localize14.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (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)

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt prod-diff
23×cbrt-prod
22×*-un-lft-identity
20×add-cube-cbrt
6×fma-neg add-log-exp
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--
Calls
4 calls:
Slowest
32.0ms
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))
16.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
0.0ms
(cbrt x)
0.0ms
(cbrt x)

series893.0ms

Calls
4 calls:
Slowest
271.0ms
(cbrt x)
268.0ms
(cbrt x)
259.0ms
(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
96.0ms
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))

simplify4.0s

Calls
72 calls:
Slowest
411.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
256.0ms
(- (+ (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)))))
176.0ms
(- (+ (* 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)))
129.0ms
(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))))))))
110.0ms
(fma (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ 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))))))))

prune978.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.8b

localize31.0ms

Local error

Found 4 expressions with local error:

26.6b
(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))
0.6b
(cbrt x)
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 cbrt-div add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
2×flip3-+ flip-+
1×fma-udef
Calls
4 calls:
Slowest
1.0ms
(cbrt (+ x 1))
1.0ms
(cbrt (+ x 1))
0.0ms
(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))
0.0ms
(cbrt x)

series495.0ms

Calls
4 calls:
Slowest
272.0ms
(cbrt x)
130.0ms
(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))
54.0ms
(cbrt (+ x 1))
39.0ms
(cbrt (+ x 1))

simplify2.5s

Calls
22 calls:
Slowest
378.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
367.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow x 1/3)) (+ (pow (/ 1 x) -1/3) (* 1/9 (pow (/ 1 (pow x 5)) 1/3))))
353.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow x 7)) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x))))))) (* (pow (pow x 2) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x))))))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (* (pow (/ 1 (pow x 16)) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x)))))))))
309.0ms
(- (+ (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))))
288.0ms
(- (+ (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))))

prune920.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.8b

localize20.0ms

Local error

Found 4 expressions with local error:

6.7b
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x))))
0.6b
(cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt prod-diff
23×cbrt-prod
22×*-un-lft-identity
20×add-cube-cbrt
6×fma-neg add-log-exp
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 flip-- distribute-lft-out--
Calls
4 calls:
Slowest
69.0ms
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x))))
67.0ms
(cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))
0.0ms
(cbrt x)
0.0ms
(cbrt x)

series939.0ms

Calls
4 calls:
Slowest
292.0ms
(cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))
275.0ms
(cbrt x)
269.0ms
(cbrt x)
104.0ms
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x))))

simplify9.7s

Calls
72 calls:
Slowest
545.0ms
(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (* (sqrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))) (sqrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))))))
428.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
328.0ms
(fma (- (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x))))) (* (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))) (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x))))) (* (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))) (* (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))) (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))))))
312.0ms
(fma (- (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x))))) (* (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))) (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x))))) (* (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))) (* (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))) (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))))))
310.0ms
(fma (- (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x))))) (* (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))) (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x))))) (* (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))) (* (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))) (cbrt (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))))))

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.8b

regimes111.0ms

Accuracy

99.6% (0.1b remaining)

Error of 15.6b against oracle of 15.5b and baseline of 30.1b

bsearch180.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
469.0ms1737×body1280valid
357.0ms4092×body80valid
307.0ms1199×body640valid
132.0ms646×body320valid
33.0ms326×body160valid