Details

Time bar (total: 5.1m)

sample285.0ms

Algorithm
intervals
Results
87.0ms99×body1280valid
38.0ms144×body80valid
36.0ms53×body640valid
31.0ms31×body10240exit
25.0ms27×body1280nan
14.0ms140×body80nan
12.0ms17×body640nan
11.0ms25×body320valid
7.0ms14×body320nan
4.0ms11×body160valid
1.0ms6×body160nan

simplify251.0ms

Calls
1 calls:
Slowest
251.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize23.0ms

Local error

Found 3 expressions with local error:

1.5b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.5b
(pow x (/ 1 n))
0.5b
(pow (+ x 1) (/ 1 n))

rewrite107.0ms

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--
Calls
3 calls:
Slowest
85.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
14.0ms
(pow (+ x 1) (/ 1 n))
5.0ms
(pow x (/ 1 n))

series452.0ms

Calls
3 calls:
Slowest
244.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
129.0ms
(pow (+ x 1) (/ 1 n))
78.0ms
(pow x (/ 1 n))

simplify40.0s

Calls
188 calls:
Slowest
725.0ms
(fma (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt (+ x 1)) (/ 1 n)) (- (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n))))))
678.0ms
(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
574.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
526.0ms
(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
503.0ms
(+ (sqrt (pow (+ x 1) (/ 1 n))) (pow (sqrt x) (/ 1 n)))

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.8b

localize25.0ms

Local error

Found 4 expressions with local error:

1.5b
(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
1.5b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.5b
(pow x (/ 1 n))
0.5b
(pow (+ x 1) (/ 1 n))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
135×unpow-prod-down
130×*-un-lft-identity
112×prod-diff
108×add-sqr-sqrt
84×add-cube-cbrt
61×log-prod
58×exp-sum
45×sqr-pow
26×pow-unpow
18×times-frac distribute-lft-out difference-of-squares
16×log-pow
15×exp-prod
8×fma-neg
7×pow1
6×add-exp-log distribute-lft-out-- 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 div-inv
1×log-div flip3-- exp-diff diff-log rem-log-exp flip--
Calls
4 calls:
Slowest
107.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
104.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
14.0ms
(pow (+ x 1) (/ 1 n))
5.0ms
(pow x (/ 1 n))

series767.0ms

Calls
4 calls:
Slowest
288.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
244.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
137.0ms
(pow (+ x 1) (/ 1 n))
98.0ms
(pow x (/ 1 n))

simplify1.1m

Calls
269 calls:
Slowest
818.0ms
(log (exp (fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))))
746.0ms
(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
569.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
541.0ms
(log (exp (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)))))))
537.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))

prune3.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.8b

localize34.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.5b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.5b
(pow x (/ 1 n))
0.5b
(pow x (/ 1 n))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
138×unpow-prod-down
130×*-un-lft-identity
112×prod-diff
108×add-sqr-sqrt
84×add-cube-cbrt
46×sqr-pow
26×pow-unpow
18×times-frac distribute-lft-out difference-of-squares
16×fma-neg
8×add-log-exp
6×pow1 add-exp-log distribute-lft-out--
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
2×pow-to-exp sub-neg pow-pow flip3-- diff-log pow-exp div-inv flip--
Calls
4 calls:
Slowest
101.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
87.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.0ms
(pow x (/ 1 n))
3.0ms
(pow x (/ 1 n))

series630.0ms

Calls
4 calls:
Slowest
246.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
234.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
80.0ms
(pow x (/ 1 n))
70.0ms
(pow x (/ 1 n))

simplify1.3m

Calls
332 calls:
Slowest
912.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
734.0ms
(fma (- (pow (sqrt x) (/ 1 n))) (pow (sqrt x) (/ 1 n)) (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n))))
622.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
533.0ms
(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
512.0ms
(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)))))

prune4.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.8b

localize38.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n)))))
1.5b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.6b
(log (exp (sqrt (- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n))))))))
0.5b
(pow x (/ 1 n))

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
149×*-un-lft-identity
144×prod-diff
143×unpow-prod-down
118×add-sqr-sqrt
96×add-cube-cbrt
78×log-pow
67×exp-prod
45×sqr-pow
21×distribute-lft-out
16×pow1 fma-neg
15×difference-of-squares
13×pow-unpow
9×times-frac
8×sqrt-prod
7×distribute-lft-out-- add-log-exp
6×log-prod
5×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×associate--r+
2×sub-neg flip3-- diff-log flip--
1×pow-to-exp pow-pow rem-log-exp pow-exp div-inv
Calls
4 calls:
Slowest
156.0ms
(log (exp (sqrt (- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n))))))))
109.0ms
(- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n)))))
68.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
5.0ms
(pow x (/ 1 n))

series1.3s

Calls
4 calls:
Slowest
597.0ms
(log (exp (sqrt (- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n))))))))
281.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
280.0ms
(- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n)))))
100.0ms
(pow x (/ 1 n))

simplify1.6m

Calls
382 calls:
Slowest
723.0ms
(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
717.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
700.0ms
(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (log (exp (pow (* (cbrt x) (cbrt x)) (/ 1 n)))) (pow (cbrt x) (/ 1 n)))))
577.0ms
(fma (- (log (exp (pow x (/ 1 n))))) 1 (* (log (exp (pow x (/ 1 n)))) 1))
550.0ms
(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (log (exp (pow x (/ (/ 1 n) 2)))) (pow x (/ (/ 1 n) 2)))))

prune4.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.8b

regimes385.0ms

Accuracy

88.7% (1.3b remaining)

Error of 19.2b against oracle of 17.9b and baseline of 29.2b

bsearch11.0ms

end0.0ms

sample10.6s

Algorithm
intervals
Results
3.4s3158×body1280valid
1.6s1099×body10240exit
1.3s1631×body640valid
1.3s672×body1280nan
731.0ms4671×body80valid
586.0ms5011×body80nan
482.0ms844×body320valid
472.0ms608×body640nan
178.0ms333×body320nan
134.0ms425×body160valid
56.0ms170×body160nan