Details

Time bar (total: 22.9s)

sample129.0ms

Algorithm
intervals
Results
73.0ms74×body1280valid
25.0ms51×body640valid
8.0ms28×body320valid
5.0ms89×body80valid
5.0ms100×body80nan
2.0ms14×body160valid

simplify7.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
6.0ms
(log (+ 1 x))

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize5.0ms

Local error

Found 1 expressions with local error:

3.3b
(log (+ 1 x))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×log-prod *-un-lft-identity
2×add-sqr-sqrt pow1 log-div add-exp-log add-cube-cbrt
1×flip3-+ add-cbrt-cube rem-log-exp log-pow flip-+ insert-posit16 distribute-lft-out add-log-exp
Counts
1 → 16
Calls
1 calls:
Slowest
3.0ms
(log (+ 1 x))

series34.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
34.0ms
(log (+ 1 x))

simplify894.0ms

Counts
10 → 19
Calls
10 calls:
Slowest
356.0ms
(- (+ (/ 1 x) (log -1)) (+ (log (/ -1 x)) (* 1/2 (/ 1 (pow x 2)))))
229.0ms
(- (+ x (* 1/3 (pow x 3))) (* 1/2 (pow x 2)))
209.0ms
(- (/ 1 x) (+ (log (/ 1 x)) (* 1/2 (/ 1 (pow x 2)))))
56.0ms
(log (+ (pow 1 3) (pow x 3)))
15.0ms
(log (* (cbrt (+ 1 x)) (cbrt (+ 1 x))))

prune163.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b
(* x 1/3)
0.0b
(* x (* x (+ -1/2 (* x 1/3))))
0.0b
(* x (+ -1/2 (* x 1/3)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
9×associate-*l*
8×*-un-lft-identity add-cube-cbrt
7×associate-*r*
6×associate-*r/
5×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod
3×*-commutative insert-posit16 add-log-exp
2×flip3-+ flip-+ unswap-sqr
Counts
3 → 67
Calls
3 calls:
Slowest
30.0ms
(* x (* x (+ -1/2 (* x 1/3))))
14.0ms
(* x (+ -1/2 (* x 1/3)))
10.0ms
(* x 1/3)

series227.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
125.0ms
(* x (* x (+ -1/2 (* x 1/3))))
86.0ms
(* x (+ -1/2 (* x 1/3)))
16.0ms
(* x 1/3)

simplify2.8s

Counts
47 → 76
Calls
47 calls:
Slowest
332.0ms
(* (* (* x x) x) (* (* (* x x) x) (* (* (+ -1/2 (* x 1/3)) (+ -1/2 (* x 1/3))) (+ -1/2 (* x 1/3)))))
315.0ms
(* (* (* x x) x) (* (* (* x (+ -1/2 (* x 1/3))) (* x (+ -1/2 (* x 1/3)))) (* x (+ -1/2 (* x 1/3)))))
209.0ms
(+ (* -1/2 -1/2) (- (* (* x 1/3) (* x 1/3)) (* -1/2 (* x 1/3))))
201.0ms
(* (* (* x x) x) (* (* (+ -1/2 (* x 1/3)) (+ -1/2 (* x 1/3))) (+ -1/2 (* x 1/3))))
191.0ms
(+ (* -1/2 -1/2) (- (* (* x 1/3) (* x 1/3)) (* -1/2 (* x 1/3))))

prune600.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

3.4b
(log (cbrt (+ 1 x)))
3.3b
(log (* (cbrt (+ 1 x)) (cbrt (+ 1 x))))
0.2b
(cbrt (+ 1 x))
0.2b
(cbrt (+ 1 x))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
14×*-un-lft-identity
13×pow1
12×cbrt-prod
11×log-pow
10×log-div
9×flip3-+ pow1/3 flip-+
8×add-sqr-sqrt log-prod add-exp-log add-cube-cbrt
4×frac-times add-cbrt-cube insert-posit16 add-log-exp
3×rem-log-exp distribute-lft-out
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp
Counts
4 → 78
Calls
4 calls:
Slowest
11.0ms
(log (* (cbrt (+ 1 x)) (cbrt (+ 1 x))))
11.0ms
(cbrt (+ 1 x))
4.0ms
(cbrt (+ 1 x))
3.0ms
(log (cbrt (+ 1 x)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
90.0ms
(log (cbrt (+ 1 x)))
81.0ms
(log (* (cbrt (+ 1 x)) (cbrt (+ 1 x))))
43.0ms
(cbrt (+ 1 x))
34.0ms
(cbrt (+ 1 x))

simplify4.7s

Counts
50 → 90
Calls
50 calls:
Slowest
563.0ms
(log (* (cbrt (+ 1 x)) (cbrt (+ (pow 1 3) (pow x 3)))))
318.0ms
(- (+ (* 1/3 (/ 1 x)) (* 1/3 (log -1))) (+ (* 1/3 (log (/ -1 x))) (* 1/6 (/ 1 (pow x 2)))))
284.0ms
(- (+ (* 2/3 x) (* 2/9 (pow x 3))) (* 1/3 (pow x 2)))
275.0ms
(- (+ (* 1/3 x) (* 1/9 (pow x 3))) (* 1/6 (pow x 2)))
259.0ms
(- (+ (* 2/3 (/ 1 x)) (log (pow (/ -1 x) -2/3))) (* 1/3 (/ 1 (pow x 2))))

prune836.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

10.4b
(cbrt (- 1 (* x x)))
10.4b
(cbrt (- 1 (* x x)))
6.7b
(log (* (cbrt (- 1 (* x x))) (cbrt (- 1 (* x x)))))
3.4b
(log (cbrt (+ 1 x)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
14×cbrt-prod
13×pow1
12×*-un-lft-identity
11×log-pow
10×add-sqr-sqrt log-div
9×pow1/3
8×log-prod flip3-- add-exp-log add-cube-cbrt flip--
4×frac-times add-cbrt-cube insert-posit16 add-log-exp difference-of-squares
3×rem-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 flip3-+ pow-plus prod-exp flip-+ distribute-lft-out
Counts
4 → 80
Calls
4 calls:
Slowest
12.0ms
(log (* (cbrt (- 1 (* x x))) (cbrt (- 1 (* x x)))))
4.0ms
(cbrt (- 1 (* x x)))
3.0ms
(log (cbrt (+ 1 x)))
2.0ms
(cbrt (- 1 (* x x)))

series655.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
283.0ms
(log (* (cbrt (- 1 (* x x))) (cbrt (- 1 (* x x)))))
155.0ms
(cbrt (- 1 (* x x)))
150.0ms
(cbrt (- 1 (* x x)))
66.0ms
(log (cbrt (+ 1 x)))

simplify7.0s

Counts
52 → 92
Calls
52 calls:
Slowest
446.0ms
(- (+ (* 2/3 (pow x 2)) (+ (* 1/3 (pow x 4)) (* 2/9 (pow x 6)))))
394.0ms
(log (* (cbrt (- 1 (* x x))) (cbrt (- (pow 1 3) (pow (* x x) 3)))))
390.0ms
(- (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))) (+ (* 1/9 (/ (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 4))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 2)))))
351.0ms
(- (log (pow (/ -1 x) -4/3)) (+ (* 1/3 (/ 1 (pow x 4))) (* 2/3 (/ 1 (pow x 2)))))
349.0ms
(log (* (cbrt (- (pow 1 3) (pow (* x x) 3))) (cbrt (- (pow 1 3) (pow (* x x) 3)))))

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes85.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 20.9b

bsearch59.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.7s2240×body1280valid
682.0ms1705×body640valid
176.0ms787×body320valid
172.0ms2830×body80valid
95.0ms2714×body80nan
82.0ms438×body160valid