Details

Time bar (total: 3.5m)

sample49.0ms

Algorithm
intervals
Results
17.0ms53×body1280valid
9.0ms38×body640valid
8.0ms142×body80valid
3.0ms18×body320valid
1.0ms5×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: 27.4b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite54.0ms

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
46.0ms
(- (cbrt (+ x 1)) (cbrt x))
5.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)

series456.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
288.0ms
(cbrt x)
107.0ms
(- (cbrt (+ x 1)) (cbrt x))
61.0ms
(cbrt (+ x 1))

simplify7.7s

Counts
122 → 111
Calls
122 calls:
Slowest
497.0ms
(fma (- (cbrt (cbrt x))) (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt x)) (* (cbrt (cbrt x)) (cbrt (cbrt x)))))
343.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
337.0ms
(- (+ (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)))))
273.0ms
(- (+ (* 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)))
255.0ms
(fma (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (cbrt x)) (* (cbrt (cbrt x)) (cbrt (cbrt x))))))

prune891.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.8b

localize47.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (pow (cbrt (+ x 1)) 3) (pow (cbrt x) 3))
0.7b
(pow (cbrt x) 3)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite137.0ms

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
112.0ms
(- (pow (cbrt (+ x 1)) 3) (pow (cbrt x) 3))
2.0ms
(pow (cbrt x) 3)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
383.0ms
(pow (cbrt x) 3)
304.0ms
(cbrt x)
272.0ms
(cbrt x)
96.0ms
(- (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)))
933.0ms
(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)))
925.0ms
(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)))
721.0ms
(fma 1 (pow (cbrt (+ x 1)) 3) (- (* (pow (cbrt x) 3) (pow 1 3))))
718.0ms
(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)))

prune5.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
0.4b
(* (cbrt x) (cbrt x))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
8.0ms
(* (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
313.0ms
(* (cbrt x) (cbrt x))
276.0ms
(cbrt x)
229.0ms
(cbrt x)
221.0ms
(cbrt x)

simplify984.0ms

Counts
63 → 97
Calls
63 calls:
Slowest
177.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
139.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
121.0ms
(* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))
117.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
83.0ms
(* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt x)) (cbrt (cbrt x))))

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt x))
0.6b
(cbrt (cbrt x))
0.6b
(cbrt (cbrt x))
0.6b
(cbrt x)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
30×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 65
Calls
4 calls:
Slowest
1.0ms
(cbrt (cbrt x))
1.0ms
(cbrt (cbrt x))
1.0ms
(cbrt (cbrt x))
1.0ms
(cbrt x)

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
406.0ms
(cbrt (cbrt x))
392.0ms
(cbrt (cbrt x))
379.0ms
(cbrt (cbrt x))
236.0ms
(cbrt x)

simplify2.4s

Counts
33 → 77
Calls
33 calls:
Slowest
701.0ms
(* (pow (* x -1) 1/9) (pow (cbrt -1) 1/3))
686.0ms
(* (pow (* x -1) 1/9) (pow (cbrt -1) 1/3))
663.0ms
(* (pow (* x -1) 1/9) (pow (cbrt -1) 1/3))
129.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
23.0ms
(pow (/ 1 x) -1/9)

prune964.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

regimes172.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch5.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
644.0ms4123×body80valid
560.0ms1693×body1280valid
340.0ms1255×body640valid
87.0ms597×body320valid
33.0ms332×body160valid