Details

Time bar (total: 23.6s)

sample38.0ms

Algorithm
intervals
Results
12.0ms132×body80valid
10.0ms53×body1280valid
6.0ms40×body640valid
2.0ms20×body320valid
1.0ms11×body160valid

simplify12.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
12.0ms
(- (cbrt (+ x 1)) (cbrt x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

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
58.0ms
(- (cbrt (+ x 1)) (cbrt x))
2.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)

series429.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
284.0ms
(cbrt x)
105.0ms
(- (cbrt (+ x 1)) (cbrt x))
40.0ms
(cbrt (+ x 1))

simplify7.8s

Counts
122 → 111
Calls
122 calls:
Slowest
403.0ms
(- (+ (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)))))
363.0ms
(- (+ (* 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)))
269.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
250.0ms
(- (+ (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))))

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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
30.0ms
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (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
358.0ms
(cbrt x)
273.0ms
(cbrt x)
268.0ms
(cbrt x)
131.0ms
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))

simplify1.7s

Counts
27 → 72
Calls
27 calls:
Slowest
380.0ms
(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
309.0ms
(- (+ (* 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)))
173.0ms
(/ (exp (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (exp (* (cbrt x) (cbrt x))))
170.0ms
(- (+ (* 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))))
136.0ms
(* (pow (* x -1) 1/3) (cbrt -1))

prune794.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

16.4b
(fma (sqrt (cbrt (+ x 1))) (sqrt (cbrt (+ x 1))) (- (cbrt x)))
0.6b
(cbrt x)
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
11×cbrt-prod *-un-lft-identity
7×add-sqr-sqrt 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-+ distribute-lft-out
1×fma-udef
Counts
4 → 59
Calls
4 calls:
Slowest
2.0ms
(cbrt (+ x 1))
2.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)
0.0ms
(fma (sqrt (cbrt (+ x 1))) (sqrt (cbrt (+ x 1))) (- (cbrt x)))

series523.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
286.0ms
(cbrt x)
144.0ms
(fma (sqrt (cbrt (+ x 1))) (sqrt (cbrt (+ x 1))) (- (cbrt x)))
52.0ms
(cbrt (+ x 1))
41.0ms
(cbrt (+ x 1))

simplify2.6s

Counts
27 → 71
Calls
27 calls:
Slowest
409.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
395.0ms
(- (+ (* 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))))
276.0ms
(- (+ (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))))
258.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
222.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune878.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize64.0ms

Local error

Found 4 expressions with local error:

16.4b
(fma (sqrt (cbrt (+ x 1))) (sqrt (* (* (cbrt (cbrt (+ x 1))) (cbrt (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (cbrt x)))
0.6b
(cbrt x)
0.3b
(cbrt (cbrt (+ x 1)))
0.3b
(cbrt (cbrt (+ x 1)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
13×*-un-lft-identity
9×add-sqr-sqrt add-cube-cbrt
8×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
2×flip3-+ flip-+ distribute-lft-out
1×fma-udef
Counts
4 → 65
Calls
4 calls:
Slowest
4.0ms
(cbrt (cbrt (+ x 1)))
3.0ms
(cbrt (cbrt (+ x 1)))
1.0ms
(cbrt x)
0.0ms
(fma (sqrt (cbrt (+ x 1))) (sqrt (* (* (cbrt (cbrt (+ x 1))) (cbrt (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (cbrt x)))

series539.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
302.0ms
(cbrt x)
140.0ms
(fma (sqrt (cbrt (+ x 1))) (sqrt (* (* (cbrt (cbrt (+ x 1))) (cbrt (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (cbrt x)))
54.0ms
(cbrt (cbrt (+ x 1)))
44.0ms
(cbrt (cbrt (+ x 1)))

simplify3.1s

Counts
33 → 77
Calls
33 calls:
Slowest
399.0ms
(- (+ (* 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))))
372.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
296.0ms
(- (+ (pow (/ 1 x) -1/9) (* 1/9 (pow (/ 1 (pow x 8)) 1/9))) (* 4/81 (pow (/ 1 (pow x 17)) 1/9)))
265.0ms
(- (+ (pow (/ 1 x) -1/9) (* 1/9 (pow (/ 1 (pow x 8)) 1/9))) (* 4/81 (pow (/ 1 (pow x 17)) 1/9)))
261.0ms
(- (+ (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))))

prune942.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

regimes52.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 29.7b

bsearch187.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
538.0ms1658×body1280valid
524.0ms632×body320valid
295.0ms1231×body640valid
251.0ms4198×body80valid
27.0ms281×body160valid