Details

Time bar (total: 3.9m)

sample37.0ms

Algorithm
intervals
Results
14.0ms60×body1280valid
8.0ms49×body640valid
5.0ms114×body80valid
2.0ms21×body320valid
1.0ms12×body160valid

simplify11.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
11.0ms
(- (cbrt (+ x 1)) (cbrt x))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite34.0ms

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

series462.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
295.0ms
(cbrt x)
104.0ms
(- (cbrt (+ x 1)) (cbrt x))
62.0ms
(cbrt (+ x 1))

simplify7.4s

Counts
122 → 111
Calls
122 calls:
Slowest
347.0ms
(- (+ (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)))))
335.0ms
(- (+ (* 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)))
324.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
251.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
225.0ms
(- (+ (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))))

prune946.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.7b

localize25.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (cbrt (+ 1 x)) (cbrt x))
2.2b
(log (exp (- (cbrt (+ 1 x)) (cbrt x))))
0.6b
(cbrt x)
0.3b
(cbrt (+ 1 x))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
117×cbrt-prod
104×*-un-lft-identity
84×prod-diff
78×add-sqr-sqrt
62×add-cube-cbrt
47×log-prod
44×exp-sum
16×distribute-lft-out
11×log-pow
10×exp-prod
8×difference-of-squares
7×fma-neg
6×distribute-lft-out-- add-log-exp
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×cbrt-div sub-neg pow1/3
1×log-div flip3-+ flip3-- exp-diff diff-log rem-log-exp flip-+ flip--
Counts
4 → 172
Calls
4 calls:
Slowest
97.0ms
(log (exp (- (cbrt (+ 1 x)) (cbrt x))))
34.0ms
(- (cbrt (+ 1 x)) (cbrt x))
3.0ms
(cbrt (+ 1 x))
1.0ms
(cbrt x)

series546.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
280.0ms
(cbrt x)
103.0ms
(log (exp (- (cbrt (+ 1 x)) (cbrt x))))
98.0ms
(- (cbrt (+ 1 x)) (cbrt x))
65.0ms
(cbrt (+ 1 x))

simplify20.0s

Counts
184 → 184
Calls
184 calls:
Slowest
683.0ms
(- (+ (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)))))
573.0ms
(log (exp (fma (cbrt (sqrt (+ 1 x))) (cbrt (sqrt (+ 1 x))) (- (* (cbrt (cbrt x)) (* (cbrt (cbrt x)) (cbrt (cbrt x))))))))
487.0ms
(log (exp (fma 1 (cbrt (+ 1 x)) (- (* (cbrt (cbrt x)) (* (cbrt (cbrt x)) (cbrt (cbrt x))))))))
439.0ms
(log (exp (fma (* (cbrt (cbrt (+ 1 x))) (cbrt (cbrt (+ 1 x)))) (cbrt (cbrt (+ 1 x))) (- (* (cbrt (cbrt x)) (cbrt (* (cbrt x) (cbrt x))))))))
404.0ms
(log (exp (fma (cbrt 1) (cbrt (+ 1 x)) (- (* (cbrt (cbrt x)) (* (cbrt (cbrt x)) (cbrt (cbrt x))))))))

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.7b

localize47.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (* (cbrt (+ 1 x)) (cbrt (+ 1 x))) (* (cbrt x) (cbrt x)))
2.2b
(log (exp (/ (- (* (cbrt (+ 1 x)) (cbrt (+ 1 x))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ 1 x)) (cbrt x)))))
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
31×log-pow
30×exp-prod
24×times-frac
22×cbrt-prod
18×add-sqr-sqrt add-cube-cbrt
16×distribute-lft-out
7×difference-of-squares
6×add-log-exp
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×log-prod
2×pow1/3 associate-/r/
1×log-div sub-neg flip3-+ flip3-- exp-diff fma-neg diff-log div-sub rem-log-exp prod-diff flip-+ div-inv flip--
Counts
4 → 92
Calls
4 calls:
Slowest
93.0ms
(log (exp (/ (- (* (cbrt (+ 1 x)) (cbrt (+ 1 x))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ 1 x)) (cbrt x)))))
37.0ms
(- (* (cbrt (+ 1 x)) (cbrt (+ 1 x))) (* (cbrt x) (cbrt x)))
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series953.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
278.0ms
(cbrt x)
273.0ms
(log (exp (/ (- (* (cbrt (+ 1 x)) (cbrt (+ 1 x))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ 1 x)) (cbrt x)))))
272.0ms
(cbrt x)
129.0ms
(- (* (cbrt (+ 1 x)) (cbrt (+ 1 x))) (* (cbrt x) (cbrt x)))

simplify8.5s

Counts
59 → 104
Calls
59 calls:
Slowest
860.0ms
(- (+ (* 1/3 (* (/ (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow (cbrt -1) 2)) (pow (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1))) 2)) (pow (/ 1 x) 1/3))) (+ (* 2/3 (* (pow (/ 1 x) 1/3) (/ 1 (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1)))))) (+ (* 1/9 (* (pow (/ 1 (pow x 4)) 1/3) (/ (pow (exp (* 1/3 (- (log -1) (log (/ -1 x))))) 2) (pow (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1))) 3)))) (* (pow (pow x 2) 1/3) (/ 1 (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1)))))))) (+ (* 1/9 (* (pow (/ 1 (pow x 4)) 1/3) (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1))) 2)))) (+ (* 1/9 (* (/ (* (pow (cbrt -1) 2) (exp (* 1/3 (- (log -1) (log (/ -1 x)))))) (pow (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1))) 2)) (pow (/ 1 (pow x 4)) 1/3))) (+ (* 1/9 (* (pow (/ 1 (pow x 4)) 1/3) (/ 1 (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1)))))) (+ (* 1/3 (* (pow (/ 1 x) 1/3) (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1))) 2)))) (+ (* 1/9 (* (/ (* (pow (cbrt -1) 2) (pow (exp (* 1/3 (- (log -1) (log (/ -1 x))))) 2)) (pow (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1))) 3)) (pow (/ 1 (pow x 4)) 1/3))) (* (pow (pow x 2) 1/3) (/ (pow (cbrt -1) 2) (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* (pow (* x -1) 1/3) (cbrt -1)))))))))))
339.0ms
(log (* (cbrt (exp (/ (- (* (cbrt (+ 1 x)) (cbrt (+ 1 x))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ 1 x)) (cbrt x))))) (cbrt (exp (/ (- (* (cbrt (+ 1 x)) (cbrt (+ 1 x))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ 1 x)) (cbrt x)))))))
331.0ms
(- (+ (* 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)))
314.0ms
(/ (- (* (cbrt (+ 1 x)) (cbrt (+ 1 x))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ 1 x)) (cbrt x)))
295.0ms
(log (sqrt (exp (/ (- (* (cbrt (+ 1 x)) (cbrt (+ 1 x))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ 1 x)) (cbrt x))))))

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.7b

localize38.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (pow (cbrt (+ x 1)) 3) (pow (cbrt x) 3))
0.8b
(pow (cbrt x) 3)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
360×prod-diff
324×cbrt-prod
312×*-un-lft-identity
295×unpow-prod-down cube-prod
266×add-sqr-sqrt
206×add-cube-cbrt
52×sqr-pow
42×distribute-lft-out
40×cube-mult unpow3
36×difference-of-squares
20×fma-neg
13×distribute-lft-out--
6×add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×pow-unpow pow1/3
2×pow-pow
1×pow-to-exp difference-cubes sub-neg flip3-- diff-log pow-exp flip-- rem-cube-cbrt
Counts
4 → 506
Calls
4 calls:
Slowest
100.0ms
(- (pow (cbrt (+ x 1)) 3) (pow (cbrt x) 3))
5.0ms
(pow (cbrt x) 3)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
349.0ms
(cbrt x)
344.0ms
(pow (cbrt x) 3)
322.0ms
(cbrt x)
104.0ms
(- (pow (cbrt (+ x 1)) 3) (pow (cbrt x) 3))

simplify3.1m

Counts
873 → 518
Calls
873 calls:
Slowest
1.0s
(fma (- (pow (cbrt (cbrt x)) 3)) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3) (* (pow (cbrt (cbrt x)) 3) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3)))
1.0s
(fma (- (pow (cbrt (cbrt x)) 3)) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3) (* (pow (cbrt (cbrt x)) 3) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3)))
981.0ms
(fma (- (pow (cbrt (cbrt x)) 3)) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3) (* (pow (cbrt (cbrt x)) 3) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3)))
773.0ms
(fma (* (cbrt (pow (cbrt (+ x 1)) 3)) (cbrt (pow (cbrt (+ x 1)) 3))) (cbrt (pow (cbrt (+ x 1)) 3)) (- (* (pow (cbrt x) 3) (pow 1 3))))
739.0ms
(fma (- (pow (cbrt (cbrt x)) 3)) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3) (* (pow (cbrt (cbrt x)) 3) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3)))

prune5.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

regimes41.0ms

Accuracy

0% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 0.5b

bsearch4.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
549.0ms1762×body1280valid
417.0ms1235×body640valid
249.0ms4069×body80valid
103.0ms618×body320valid
73.0ms316×body160valid