Details

Time bar (total: 59.4s)

sample316.0ms

Algorithm
intervals
Results
103.0ms101×body1280valid
39.0ms51×body640valid
30.0ms35×body10240exit
21.0ms136×body80valid
20.0ms162×body80nan
19.0ms17×body1280nan
19.0ms13×body160valid
17.0ms23×body640nan
14.0ms28×body320valid
8.0ms15×body320nan
1.0ms5×body160nan

simplify262.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
261.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize23.0ms

Local error

Found 3 expressions with local error:

1.7b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.2b
(pow (+ x 1) (/ 1 n))
0.0b
(pow x (/ 1 n))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
28×*-un-lft-identity
26×pow-unpow
19×add-cube-cbrt
18×times-frac
17×unpow-prod-down
9×difference-of-squares
8×sqr-pow
5×pow1 add-exp-log add-log-exp
3×add-cbrt-cube insert-posit16 distribute-lft-out--
2×pow-to-exp pow-pow pow-exp div-inv distribute-lft-out
1×sub-neg flip3-- diff-log flip--
Counts
3 → 82
Calls
3 calls:
Slowest
59.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
7.0ms
(pow (+ x 1) (/ 1 n))
4.0ms
(pow x (/ 1 n))

series462.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
288.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
106.0ms
(pow (+ x 1) (/ 1 n))
68.0ms
(pow x (/ 1 n))

simplify10.0s

Counts
69 → 91
Calls
69 calls:
Slowest
652.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
612.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
555.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))
508.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
506.0ms
(+ (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))

prune970.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.9b

localize35.0ms

Local error

Found 4 expressions with local error:

3.2b
(- (pow (+ x 1) (/ 1 n)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
1.2b
(pow (+ x 1) (/ 1 n))
0.0b
(pow x (/ (/ 1 n) 2))
0.0b
(pow x (/ (/ 1 n) 2))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
99×pow-unpow
86×add-sqr-sqrt *-un-lft-identity
84×add-cube-cbrt
11×unpow-prod-down
9×div-inv
7×pow1 add-exp-log
6×add-log-exp
4×add-cbrt-cube insert-posit16 sqr-pow
3×pow-to-exp pow-pow pow-exp difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out
Counts
4 → 161
Calls
4 calls:
Slowest
93.0ms
(- (pow (+ x 1) (/ 1 n)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
7.0ms
(pow (+ x 1) (/ 1 n))
6.0ms
(pow x (/ (/ 1 n) 2))
5.0ms
(pow x (/ (/ 1 n) 2))

series598.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
341.0ms
(- (pow (+ x 1) (/ 1 n)) (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2))))
103.0ms
(pow (+ x 1) (/ 1 n))
88.0ms
(pow x (/ (/ 1 n) 2))
66.0ms
(pow x (/ (/ 1 n) 2))

simplify7.6s

Counts
132 → 173
Calls
132 calls:
Slowest
402.0ms
(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
389.0ms
(- (pow (sqrt (+ x 1)) (/ 1 n)) (pow x (/ (/ 1 n) 2)))
303.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
303.0ms
(- (+ (* 1/2 (/ (log -1) n)) (+ (* 1/8 (/ (pow (log -1) 2) (pow n 2))) (+ (* 1/8 (/ (pow (log (/ -1 x)) 2) (pow n 2))) 1))) (+ (* 1/2 (/ (log (/ -1 x)) n)) (* 1/4 (/ (* (log (/ -1 x)) (log -1)) (pow n 2)))))
291.0ms
(- (+ (* 1/2 (/ (log -1) n)) (+ (* 1/8 (/ (pow (log -1) 2) (pow n 2))) (+ (* 1/8 (/ (pow (log (/ -1 x)) 2) (pow n 2))) 1))) (+ (* 1/2 (/ (log (/ -1 x)) n)) (* 1/4 (/ (* (log (/ -1 x)) (log -1)) (pow n 2)))))

prune2.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 22.9b

localize33.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.2b
(pow (+ x 1) (/ 1 n))
0.1b
(exp (log (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
0.0b
(pow x (/ 1 n))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
38×*-un-lft-identity
27×unpow-prod-down
26×pow-unpow
22×add-cube-cbrt
18×times-frac difference-of-squares
15×log-prod exp-sum
14×sqr-pow
7×pow1
6×add-exp-log distribute-lft-out-- add-log-exp
4×exp-prod add-cbrt-cube insert-posit16
3×distribute-lft-out
2×pow-to-exp log-div pow-pow flip3-- exp-diff pow-exp div-inv flip--
1×sub-neg diff-log log-pow rem-exp-log
Counts
4 → 112
Calls
4 calls:
Slowest
57.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
25.0ms
(exp (log (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
8.0ms
(pow (+ x 1) (/ 1 n))
3.0ms
(pow x (/ 1 n))

series795.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
327.0ms
(exp (log (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
250.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
121.0ms
(pow (+ x 1) (/ 1 n))
97.0ms
(pow x (/ 1 n))

simplify14.8s

Counts
94 → 124
Calls
94 calls:
Slowest
571.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
525.0ms
(exp (log (+ (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))))
503.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
496.0ms
(- (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))
492.0ms
(exp (log (+ (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))))

prune1.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 22.9b

localize57.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (/ 1 (* n x)) (/ (- (log x)) (* n (* n x))))
1.1b
(/ -1/2 (* (* n x) x))
0.6b
(/ (- (log x)) (* n (* n x)))
0.5b
(/ 1 (* n x))

rewrite477.0ms

Algorithm
rewrite-expression-head
Rules
33×add-exp-log
27×add-cbrt-cube
24×times-frac
22×*-un-lft-identity
18×associate-/l*
16×add-sqr-sqrt
14×add-cube-cbrt
12×pow1
10×distribute-rgt-neg-in div-exp
9×prod-exp
8×distribute-lft-neg-in cbrt-undiv
7×cbrt-unprod
6×add-log-exp
5×log-pow distribute-lft-out--
4×insert-posit16 div-inv
3×clear-num associate-/r* frac-2neg
2×neg-sub0 rec-exp neg-mul-1 1-exp div-sub pow-flip
1×sub-neg flip3-- diff-log pow-prod-down distribute-frac-neg frac-sub flip-- inv-pow associate--r- difference-of-squares
Counts
4 → 118
Calls
4 calls:
Slowest
421.0ms
(- (/ 1 (* n x)) (/ (- (log x)) (* n (* n x))))
27.0ms
(/ -1/2 (* (* n x) x))
17.0ms
(/ (- (log x)) (* n (* n x)))
11.0ms
(/ 1 (* n x))

series246.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
103.0ms
(/ (- (log x)) (* n (* n x)))
76.0ms
(- (/ 1 (* n x)) (/ (- (log x)) (* n (* n x))))
45.0ms
(/ -1/2 (* (* n x) x))
21.0ms
(/ 1 (* n x))

simplify6.2s

Counts
97 → 130
Calls
97 calls:
Slowest
471.0ms
(/ (* (* (- (log x)) (- (log x))) (- (log x))) (* (* (* n (* n x)) (* n (* n x))) (* n (* n x))))
455.0ms
(/ (* (* (- (log x)) (- (log x))) (- (log x))) (* (* (* n n) n) (* (* (* n x) (* n x)) (* n x))))
372.0ms
(/ (* (* (- (log x)) (- (log x))) (- (log x))) (* (* (* n n) n) (* (* (* n n) n) (* (* x x) x))))
371.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (/ (log (/ -1 x)) (* x (pow n 2))))
267.0ms
(- (* 1 (* n (* n x))) (* (* n x) (- (log x))))

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 22.4b

regimes481.0ms

Accuracy

84.7% (1.4b remaining)

Error of 22.2b against oracle of 20.8b and baseline of 29.7b

bsearch8.0ms

end0.0ms

sample10.5s

Algorithm
intervals
Results
3.2s3194×body1280valid
1.3s1140×body10240exit
1.2s1617×body640valid
1.0s5126×body80nan
916.0ms668×body640nan
768.0ms4761×body80valid
737.0ms651×body1280nan
440.0ms851×body320valid
219.0ms437×body160valid
179.0ms395×body320nan
45.0ms159×body160nan