Details

Time bar (total: 2.5m)

sample348.0ms

Algorithm
intervals
Results
102.0ms99×body1280valid
63.0ms44×body10240exit
38.0ms50×body640valid
33.0ms18×body640nan
26.0ms26×body1280nan
23.0ms154×body80valid
17.0ms164×body80nan
12.0ms26×body320valid
5.0ms10×body320nan
3.0ms10×body160valid
2.0ms6×body160nan

simplify323.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
323.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize32.0ms

Local error

Found 3 expressions with local error:

2.0b
(pow (+ x 1) (/ 1 n))
1.8b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.3b
(pow x (/ 1 n))

rewrite132.0ms

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
112.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
15.0ms
(pow (+ x 1) (/ 1 n))
3.0ms
(pow x (/ 1 n))

series409.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
224.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
109.0ms
(pow (+ x 1) (/ 1 n))
75.0ms
(pow x (/ 1 n))

simplify40.8s

Counts
188 → 161
Calls
188 calls:
Slowest
827.0ms
(fma (- (pow (sqrt x) (/ 1 n))) (pow (sqrt x) (/ 1 n)) (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n))))
603.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
587.0ms
(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
479.0ms
(+ (sqrt (pow (+ x 1) (/ 1 n))) (pow (sqrt x) (/ 1 n)))
475.0ms
(- (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.0b

localize36.0ms

Local error

Found 4 expressions with local error:

2.6b
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))
2.0b
(pow (+ x 1) (/ (/ 1 n) 2))
2.0b
(pow (+ x 1) (/ (/ 1 n) 2))
1.3b
(pow x (/ (/ 1 n) 2))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
198×times-frac
129×pow-unpow
116×*-un-lft-identity
112×add-sqr-sqrt add-cube-cbrt
12×div-inv
11×unpow-prod-down
7×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow pow-exp sqr-pow
2×distribute-lft-out
1×fma-udef
Counts
4 → 193
Calls
4 calls:
Slowest
14.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
14.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
6.0ms
(pow x (/ (/ 1 n) 2))
1.0ms
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))

series744.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
430.0ms
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))
126.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
120.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
68.0ms
(pow x (/ (/ 1 n) 2))

simplify8.3s

Counts
157 → 205
Calls
157 calls:
Slowest
828.0ms
(- (+ (* 1/2 (/ (log -1) n)) (+ 1 (* 1/2 (/ 1 (* x n))))) (* 1/2 (/ (log (/ -1 x)) n)))
520.0ms
(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (/ 1 n) 2))
472.0ms
(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (/ 1 n) 2))
466.0ms
(- (+ (* 1/2 (/ (log -1) n)) (+ 1 (* 1/2 (/ 1 (* x n))))) (* 1/2 (/ (log (/ -1 x)) n)))
357.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))

prune3.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.0b

localize21.0ms

Local error

Found 4 expressions with local error:

2.0b
(pow (+ x 1) (/ 1 n))
1.8b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.8b
(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
1.3b
(pow x (/ 1 n))

rewrite273.0ms

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--
Counts
4 → 241
Calls
4 calls:
Slowest
142.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
116.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
8.0ms
(pow (+ x 1) (/ 1 n))
3.0ms
(pow x (/ 1 n))

series757.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
302.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
254.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
133.0ms
(pow (+ x 1) (/ 1 n))
68.0ms
(pow x (/ 1 n))

simplify1.1m

Counts
269 → 253
Calls
269 calls:
Slowest
728.0ms
(log (exp (fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))))
722.0ms
(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)))))))
630.0ms
(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n))))))
592.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
574.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))

prune3.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.0b

localize52.0ms

Local error

Found 4 expressions with local error:

2.0b
(pow (+ x 1) (/ 1 n))
2.0b
(pow (+ x 1) (/ 1 n))
2.0b
(pow (+ x 1) (/ 1 n))
1.9b
(log (* (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))))

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
39×pow-unpow
34×*-un-lft-identity
28×add-sqr-sqrt add-cube-cbrt
27×times-frac
15×pow1
12×unpow-prod-down
10×add-exp-log
9×log-pow
6×pow1/3
4×expm1-log1p-u cbrt-div add-cbrt-cube exp-diff insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp log-div pow-pow pow-exp div-inv distribute-lft-out sqr-pow
2×rem-log-exp pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times log-prod pow-plus associate-*l/ prod-exp associate-*r/
Counts
4 → 118
Calls
4 calls:
Slowest
202.0ms
(log (* (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))))
7.0ms
(pow (+ x 1) (/ 1 n))
7.0ms
(pow (+ x 1) (/ 1 n))
7.0ms
(pow (+ x 1) (/ 1 n))

series764.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
447.0ms
(log (* (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))))
111.0ms
(pow (+ x 1) (/ 1 n))
105.0ms
(pow (+ x 1) (/ 1 n))
102.0ms
(pow (+ x 1) (/ 1 n))

simplify6.8s

Counts
80 → 130
Calls
80 calls:
Slowest
860.0ms
(* (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))))
554.0ms
(log (* (cbrt (exp (pow (+ x 1) (/ 1 n)))) (cbrt (exp (pow (+ x 1) (/ 1 n))))))
495.0ms
(log (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))))
461.0ms
(log (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))))
444.0ms
(log (* (cbrt (exp (pow (+ x 1) (/ 1 n)))) (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))))

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.0b

regimes331.0ms

Accuracy

88.4% (1.4b remaining)

Error of 19.2b against oracle of 17.8b and baseline of 29.7b

bsearch504.0ms

end0.0ms

sample11.7s

Algorithm
intervals
Results
3.5s3145×body1280valid
2.0s1168×body10240exit
1.4s1625×body640valid
1.2s621×body1280nan
722.0ms4727×body80valid
669.0ms5047×body80nan
620.0ms691×body640nan
482.0ms840×body320valid
206.0ms351×body320nan
199.0ms432×body160valid
87.0ms170×body160nan