Details

Time bar (total: 25.1s)

sample45.0ms

Algorithm
intervals
Results
19.0ms63×body1280valid
8.0ms43×body640valid
6.0ms122×body80valid
3.0ms21×body320valid
1.0ms7×body160valid

simplify10.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize10.0ms

Local error

Found 3 expressions with local error:

2.5b
(- (cbrt (+ x 1)) (cbrt x))
0.6b
(cbrt x)
0.3b
(cbrt (+ x 1))

rewrite15.0ms

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
12.0ms
(- (cbrt (+ x 1)) (cbrt x))
1.0ms
(cbrt (+ x 1))
0.0ms
(cbrt x)

series444.0ms

Calls
3 calls:
Slowest
267.0ms
(cbrt x)
129.0ms
(- (cbrt (+ x 1)) (cbrt x))
49.0ms
(cbrt (+ x 1))

simplify3.1s

Calls
61 calls:
Slowest
419.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
336.0ms
(- (+ (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))))
215.0ms
(- (+ (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)))))
148.0ms
(- (+ (* 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)))
122.0ms
(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))

prune610.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.1b

localize13.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt x))
0.6b
(cbrt x)
0.3b
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
0.3b
(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
92×cbrt-div
33×flip3-+ flip-+
32×frac-times
18×add-sqr-sqrt *-un-lft-identity
16×associate-*l/ add-cube-cbrt
12×prod-diff
11×cbrt-prod
10×associate-*r/
9×pow1
6×pow1/3 associate-*r* associate-*l* add-exp-log add-log-exp
4×expm1-log1p-u add-cbrt-cube fma-neg insert-posit16 log1p-expm1-u
2×pow-prod-down pow-prod-up
1×pow2 sub-neg pow-plus flip3-- diff-log pow3 prod-exp *-commutative rem-cbrt-cube cbrt-unprod flip-- distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
26.0ms
(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt x))
15.0ms
(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))
12.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
0.0ms
(cbrt x)

series386.0ms

Calls
4 calls:
Slowest
232.0ms
(cbrt x)
91.0ms
(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt x))
32.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
31.0ms
(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))

simplify6.6s

Calls
103 calls:
Slowest
378.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
373.0ms
(- (+ (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))))
245.0ms
(- (+ (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)))))
204.0ms
(- (+ (* 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)))
147.0ms
(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.1b

localize30.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (cbrt (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (+ x 1)))) (cbrt x))
0.6b
(cbrt x)
0.3b
(cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))
0.3b
(cbrt (cbrt (+ x 1)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-div
16×add-sqr-sqrt *-un-lft-identity
14×cbrt-prod add-cube-cbrt
12×prod-diff
7×flip3-+ flip-+
6×add-log-exp
4×expm1-log1p-u frac-times pow1 add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u
3×pow1/3
2×associate-*l/ associate-*r/
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
106.0ms
(- (cbrt (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (+ x 1)))) (cbrt x))
8.0ms
(cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))
2.0ms
(cbrt (cbrt (+ x 1)))
0.0ms
(cbrt x)

series507.0ms

Calls
4 calls:
Slowest
308.0ms
(cbrt x)
108.0ms
(- (cbrt (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (+ x 1)))) (cbrt x))
46.0ms
(cbrt (cbrt (+ x 1)))
44.0ms
(cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))

simplify4.4s

Calls
60 calls:
Slowest
449.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
307.0ms
(- (+ (exp (* 1/9 (- (log -1) (log (/ -1 x))))) (* 1/9 (/ (exp (* 1/9 (- (log -1) (log (/ -1 x))))) x))) (* 4/81 (/ (exp (* 1/9 (- (log -1) (log (/ -1 x))))) (pow x 2))))
267.0ms
(- (+ (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)))))
166.0ms
(- (+ (* 2/9 (pow (/ 1 (pow x 7)) 1/9)) (pow (/ -1 x) -2/9)) (* 7/81 (pow (/ 1 (pow x 16)) 1/9)))
165.0ms
(- (+ (* 2/9 (pow (/ 1 (pow x 7)) 1/9)) (pow (/ 1 x) -2/9)) (* 7/81 (pow (/ 1 (pow x 16)) 1/9)))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.1b

localize27.0ms

Local error

Found 4 expressions with local error:

21.8b
(- (cbrt (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (+ x 1)))) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube fma-neg prod-diff add-exp-log insert-posit16 log1p-expm1-u
3×pow1/3
2×cbrt-prod
1×sub-neg flip3-- diff-log flip--
Calls
4 calls:
Slowest
96.0ms
(- (cbrt (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (+ x 1)))) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))
0.0ms
(cbrt x)
0.0ms
(cbrt x)
0.0ms
(cbrt x)

series926.0ms

Calls
4 calls:
Slowest
315.0ms
(cbrt x)
279.0ms
(cbrt x)
238.0ms
(cbrt x)
93.0ms
(- (cbrt (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (+ x 1)))) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

simplify1.7s

Calls
24 calls:
Slowest
429.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
223.0ms
(- (+ (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)))))
165.0ms
(- (+ (* 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)))
145.0ms
(/ (exp (cbrt (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (+ x 1))))) (exp (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))
121.0ms
(fma (* (cbrt (cbrt (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (+ x 1))))) (cbrt (cbrt (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (+ x 1)))))) (cbrt (cbrt (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (+ x 1))))) (- (* (cbrt (cbrt x)) (* (cbrt (cbrt x)) (cbrt (cbrt x))))))

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.1b

regimes116.0ms

Accuracy

99.6% (0.1b remaining)

Error of 15.2b against oracle of 15.2b and baseline of 29.4b

bsearch138.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
493.0ms1673×body1280valid
417.0ms287×body160valid
273.0ms4164×body80valid
255.0ms1242×body640valid
216.0ms634×body320valid