Details

Time bar (total: 59.0s)

sample307.0ms

Algorithm
intervals
Results
114.0ms111×body1280valid
33.0ms25×body320valid
33.0ms50×body640valid
29.0ms31×body10240exit
19.0ms139×body80valid
18.0ms22×body640nan
16.0ms15×body1280nan
15.0ms137×body80nan
4.0ms9×body320nan
3.0ms13×body160valid
2.0ms9×body160nan

simplify703.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
703.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize16.0ms

Local error

Found 3 expressions with local error:

2.5b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.2b
(pow (+ x 1) (/ 1 n))
0.8b
(pow x (/ 1 n))

rewrite89.0ms

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
68.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
14.0ms
(pow (+ x 1) (/ 1 n))
5.0ms
(pow x (/ 1 n))

series477.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
282.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
110.0ms
(pow (+ x 1) (/ 1 n))
85.0ms
(pow x (/ 1 n))

simplify9.7s

Counts
69 → 91
Calls
69 calls:
Slowest
569.0ms
(+ (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
565.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
540.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))
511.0ms
(+ (sqrt (pow (+ x 1) (/ 1 n))) (pow (sqrt x) (/ 1 n)))
498.0ms
(- (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.9b

localize42.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (pow (+ x 1) (/ 1 n)) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))
1.2b
(pow (+ x 1) (/ 1 n))
0.8b
(pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))
0.6b
(cbrt (/ 1 n))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
24×unpow-prod-down *-un-lft-identity
20×add-cube-cbrt
18×times-frac
15×difference-of-squares
14×pow-unpow
13×cbrt-prod sqr-pow
6×pow1 add-exp-log add-log-exp
4×add-cbrt-cube insert-posit16
2×pow-to-exp pow-pow pow-exp div-inv
1×cbrt-div sub-neg flip3-- pow1/3 diff-log flip-- distribute-lft-out distribute-lft-out--
Counts
4 → 97
Calls
4 calls:
Slowest
93.0ms
(- (pow (+ x 1) (/ 1 n)) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))
10.0ms
(pow (+ x 1) (/ 1 n))
3.0ms
(pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))
3.0ms
(cbrt (/ 1 n))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
444.0ms
(- (pow (+ x 1) (/ 1 n)) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))
257.0ms
(cbrt (/ 1 n))
225.0ms
(pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))
94.0ms
(pow (+ x 1) (/ 1 n))

simplify14.8s

Counts
82 → 109
Calls
82 calls:
Slowest
550.0ms
(- (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))) (cbrt (/ 1 n))))
514.0ms
(- (pow (sqrt (+ x 1)) (/ 1 n)) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (/ (cbrt (/ 1 n)) 2)))
493.0ms
(- (pow (sqrt (+ x 1)) (/ 1 n)) (pow (pow x (/ (* (cbrt (/ 1 n)) (cbrt (/ 1 n))) 2)) (cbrt (/ 1 n))))
474.0ms
(- (pow (sqrt (+ x 1)) (/ 1 n)) (pow (pow (sqrt x) (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))
464.0ms
(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow (pow (sqrt x) (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.9b

localize63.0ms

Local error

Found 4 expressions with local error:

3.5b
(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
1.2b
(pow (+ x 1) (/ 1 n))
0.8b
(pow (cbrt x) (/ 1 n))
0.6b
(cbrt x)

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
26×pow-unpow
24×*-un-lft-identity
22×add-sqr-sqrt add-cube-cbrt
18×times-frac
10×unpow-prod-down
6×cbrt-prod pow1 add-exp-log add-log-exp
4×add-cbrt-cube insert-posit16
3×pow-pow
2×pow-to-exp pow1/3 pow-exp div-inv sqr-pow
1×sub-neg flip3-- diff-log flip-- distribute-lft-out
Counts
4 → 86
Calls
4 calls:
Slowest
66.0ms
(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
14.0ms
(pow (+ x 1) (/ 1 n))
4.0ms
(pow (cbrt x) (/ 1 n))
1.0ms
(cbrt x)

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
667.0ms
(cbrt x)
464.0ms
(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
136.0ms
(pow (+ x 1) (/ 1 n))
110.0ms
(pow (cbrt x) (/ 1 n))

simplify4.4s

Counts
56 → 98
Calls
56 calls:
Slowest
745.0ms
(- (+ (/ 1 (* x n)) (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2)))) (+ (/ (log (pow (/ 1 x) -1/3)) n) (+ (/ (log (/ 1 x)) n) (+ (/ (log (pow (/ 1 x) -2/3)) n) (+ (* 1/2 (/ (pow (log (pow (/ 1 x) -1/3)) 2) (pow n 2))) (+ (/ (* (log (pow (/ 1 x) -1/3)) (log (pow (/ 1 x) -2/3))) (pow n 2)) (* 1/2 (/ (pow (log (pow (/ 1 x) -2/3)) 2) (pow n 2)))))))))
434.0ms
(/ (exp (pow (+ x 1) (/ 1 n))) (exp (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n)))))
419.0ms
(- 1 (* (exp (/ (log (pow x 2/3)) n)) (exp (/ (log (pow x 1/3)) n))))
386.0ms
(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
367.0ms
(+ (/ (log (pow (/ 1 x) -1/3)) n) (+ (* 1/2 (/ (pow (log (pow (/ 1 x) -1/3)) 2) (pow n 2))) 1))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.5b

localize46.0ms

Local error

Found 4 expressions with local error:

3.5b
(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
3.4b
(log (exp (- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))))
1.2b
(pow (+ x 1) (/ 1 n))
0.8b
(pow (cbrt x) (/ 1 n))

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
26×pow-unpow
25×*-un-lft-identity
23×add-sqr-sqrt add-cube-cbrt
18×times-frac
10×unpow-prod-down
7×pow1
6×add-exp-log add-log-exp
5×log-prod
4×add-cbrt-cube log-pow insert-posit16
3×cbrt-prod exp-prod pow-pow
2×pow-to-exp sub-neg exp-sum pow-exp div-inv sqr-pow
1×log-div flip3-- exp-diff pow1/3 diff-log rem-log-exp flip-- distribute-lft-out
Counts
4 → 93
Calls
4 calls:
Slowest
121.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))))
82.0ms
(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
11.0ms
(pow (+ x 1) (/ 1 n))
7.0ms
(pow (cbrt x) (/ 1 n))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
494.0ms
(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
473.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))))
127.0ms
(pow (cbrt x) (/ 1 n))
122.0ms
(pow (+ x 1) (/ 1 n))

simplify7.6s

Counts
63 → 105
Calls
63 calls:
Slowest
788.0ms
(- (+ (/ 1 (* x n)) (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2)))) (+ (/ (log (pow (/ 1 x) -1/3)) n) (+ (/ (log (/ 1 x)) n) (+ (/ (log (pow (/ 1 x) -2/3)) n) (+ (* 1/2 (/ (pow (log (pow (/ 1 x) -1/3)) 2) (pow n 2))) (+ (/ (* (log (pow (/ 1 x) -1/3)) (log (pow (/ 1 x) -2/3))) (pow n 2)) (* 1/2 (/ (pow (log (pow (/ 1 x) -2/3)) 2) (pow n 2)))))))))
703.0ms
(- (+ (/ 1 (* x n)) (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2)))) (+ (/ (log (pow (/ 1 x) -1/3)) n) (+ (/ (log (/ 1 x)) n) (+ (/ (log (pow (/ 1 x) -2/3)) n) (+ (* 1/2 (/ (pow (log (pow (/ 1 x) -1/3)) 2) (pow n 2))) (+ (/ (* (log (pow (/ 1 x) -1/3)) (log (pow (/ 1 x) -2/3))) (pow n 2)) (* 1/2 (/ (pow (log (pow (/ 1 x) -2/3)) 2) (pow n 2)))))))))
462.0ms
(- 1 (* (exp (/ (log (pow x 2/3)) n)) (exp (/ (log (pow x 1/3)) n))))
414.0ms
(- 1 (* (exp (/ (log (pow x 2/3)) n)) (exp (/ (log (pow x 1/3)) n))))
395.0ms
(log (* (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n)))))) (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))))))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.5b

regimes377.0ms

Accuracy

78.1% (2.0b remaining)

Error of 22.5b against oracle of 20.5b and baseline of 29.5b

bsearch18.0ms

end0.0ms

sample10.9s

Algorithm
intervals
Results
3.5s3236×body1280valid
1.4s1139×body10240exit
1.2s1530×body640valid
1.1s5018×body80nan
881.0ms636×body640nan
750.0ms4624×body80valid
694.0ms616×body1280nan
488.0ms909×body320valid
205.0ms360×body320nan
129.0ms408×body160valid
69.0ms183×body160nan