Details

Time bar (total: 2.8m)

sample292.0ms

Algorithm
intervals
Results
107.0ms111×body1280valid
40.0ms50×body640valid
29.0ms31×body10240exit
19.0ms139×body80valid
18.0ms22×body640nan
16.0ms15×body1280nan
14.0ms137×body80nan
14.0ms25×body320valid
5.0ms13×body160valid
5.0ms9×body320nan
2.0ms9×body160nan

simplify328.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
328.0ms
(- (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))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
73×unpow-prod-down
63×add-sqr-sqrt
56×prod-diff
51×add-cube-cbrt
26×pow-unpow
24×sqr-pow
18×times-frac
10×distribute-lft-out
9×difference-of-squares
8×fma-neg
5×pow1 add-exp-log add-log-exp
3×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u distribute-lft-out--
2×pow-to-exp pow-pow pow-exp div-inv
1×sub-neg flip3-- diff-log flip--
Counts
3 → 152
Calls
3 calls:
Slowest
69.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
8.0ms
(pow (+ x 1) (/ 1 n))
3.0ms
(pow x (/ 1 n))

series433.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
240.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
108.0ms
(pow (+ x 1) (/ 1 n))
84.0ms
(pow x (/ 1 n))

simplify40.6s

Counts
188 → 161
Calls
188 calls:
Slowest
606.0ms
(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n))))))
554.0ms
(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
538.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
535.0ms
(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
532.0ms
(- (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.0b

localize35.0ms

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))

rewrite547.0ms

Algorithm
rewrite-expression-head
Rules
152×unpow-prod-down
96×*-un-lft-identity
88×prod-diff
87×add-sqr-sqrt
68×add-cube-cbrt
41×sqr-pow
18×times-frac
15×difference-of-squares
14×pow-unpow
13×cbrt-prod distribute-lft-out
8×fma-neg
6×pow1 add-exp-log add-log-exp
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
2×pow-to-exp pow-pow pow-exp div-inv
1×cbrt-div sub-neg flip3-- pow1/3 diff-log flip-- distribute-lft-out--
Counts
4 → 201
Calls
4 calls:
Slowest
406.0ms
(pow (+ x 1) (/ 1 n))
133.0ms
(- (pow (+ x 1) (/ 1 n)) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))
3.0ms
(pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))
1.0ms
(cbrt (/ 1 n))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
447.0ms
(- (pow (+ x 1) (/ 1 n)) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))
274.0ms
(cbrt (/ 1 n))
221.0ms
(pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))
140.0ms
(pow (+ x 1) (/ 1 n))

simplify1.0m

Counts
265 → 213
Calls
265 calls:
Slowest
876.0ms
(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))) 1)))
696.0ms
(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
608.0ms
(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))) (cbrt (/ 1 n))) (pow (* (cbrt (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))) (cbrt (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))))) (cbrt (/ 1 n))))))
593.0ms
(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (pow (cbrt x) (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))) (pow (pow (* (cbrt x) (cbrt x)) (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))))
538.0ms
(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))) (cbrt (/ 1 n))) (pow (* (cbrt (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))) (cbrt (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))))) (cbrt (/ 1 n))))))

prune2.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.0b

localize50.0ms

Local error

Found 4 expressions with local error:

4.4b
(- (* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2))) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))
1.2b
(pow (+ x 1) (/ (/ 1 n) 2))
1.2b
(pow (+ x 1) (/ (/ 1 n) 2))
0.8b
(pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
87×pow-unpow
84×*-un-lft-identity
83×add-sqr-sqrt
80×add-cube-cbrt
25×unpow-prod-down
11×prod-diff
8×div-inv
7×pow1 add-exp-log sqr-pow
6×add-log-exp
5×difference-of-squares
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×pow-to-exp pow-pow pow-exp
2×distribute-lft-out
1×sub-neg flip3-- fma-neg diff-log flip--
Counts
4 → 172
Calls
4 calls:
Slowest
59.0ms
(- (* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2))) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))
16.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
16.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
5.0ms
(pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
605.0ms
(- (* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2))) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))
210.0ms
(pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))
137.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
133.0ms
(pow (+ x 1) (/ (/ 1 n) 2))

simplify16.7s

Counts
149 → 184
Calls
149 calls:
Slowest
751.0ms
(- (pow (+ x 1) (/ (/ 1 n) 2)) (sqrt (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n)))))
518.0ms
(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (/ 1 n) 2))
505.0ms
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (pow (cbrt x) (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))) (pow (pow (* (cbrt x) (cbrt x)) (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))))
483.0ms
(- (+ (* 1/2 (/ (log -1) n)) (+ 1 (* 1/2 (/ 1 (* x n))))) (* 1/2 (/ (log (/ -1 x)) n)))
435.0ms
(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (/ 1 n) 2))

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.0b

localize42.0ms

Local error

Found 4 expressions with local error:

4.4b
(- (* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2))) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))
4.4b
(log (exp (- (* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2))) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))))
1.2b
(pow (+ x 1) (/ (/ 1 n) 2))
1.2b
(pow (+ x 1) (/ (/ 1 n) 2))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
90×add-sqr-sqrt
88×*-un-lft-identity
86×pow-unpow
84×add-cube-cbrt
36×unpow-prod-down
22×prod-diff
16×log-prod
13×exp-sum
10×difference-of-squares sqr-pow
9×log-pow
8×exp-prod div-inv
7×pow1
6×add-exp-log add-log-exp
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
2×pow-to-exp sub-neg pow-pow pow-exp distribute-lft-out
1×log-div flip3-- exp-diff fma-neg diff-log rem-log-exp flip--
Counts
4 → 191
Calls
4 calls:
Slowest
116.0ms
(log (exp (- (* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2))) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))))
58.0ms
(- (* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2))) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))
16.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
16.0ms
(pow (+ x 1) (/ (/ 1 n) 2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
568.0ms
(log (exp (- (* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2))) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))))
565.0ms
(- (* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2))) (pow (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))
113.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
98.0ms
(pow (+ x 1) (/ (/ 1 n) 2))

simplify23.8s

Counts
170 → 203
Calls
170 calls:
Slowest
830.0ms
(log (exp (* (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)))))
600.0ms
(log (exp (fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (cbrt (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))) (cbrt (/ 1 n))) (pow (* (cbrt (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))) (cbrt (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))))) (cbrt (/ 1 n))))))))
574.0ms
(log (exp (fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (pow (cbrt x) (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))) (pow (pow (* (cbrt x) (cbrt x)) (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))))))
566.0ms
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (pow (cbrt x) (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))) (pow (pow (* (cbrt x) (cbrt x)) (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))))))
525.0ms
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (cbrt (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))) (cbrt (/ 1 n))) (pow (* (cbrt (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n))))) (cbrt (pow x (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))))) (cbrt (/ 1 n))))))

prune3.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.0b

regimes413.0ms

Accuracy

89.1% (1.3b remaining)

Error of 19.2b against oracle of 17.9b and baseline of 29.6b

bsearch10.0ms

end0.0ms

sample10.7s

Algorithm
intervals
Results
3.4s3236×body1280valid
1.4s1530×body640valid
1.3s1139×body10240exit
1.0s616×body1280nan
940.0ms5018×body80nan
714.0ms4624×body80valid
623.0ms909×body320valid
507.0ms636×body640nan
171.0ms360×body320nan
129.0ms408×body160valid
51.0ms183×body160nan