Details

Time bar (total: 1.2m)

sample67.0ms

Algorithm
intervals
Results
20.0ms54×body1280valid
12.0ms273×body80nan
11.0ms47×body640valid
10.0ms130×body80valid
2.0ms15×body320valid
1.0ms10×body160valid

simplify39.0ms

Calls
1 calls:
Slowest
39.0ms
(- (log (+ N 1)) (log N))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize18.0ms

Local error

Found 1 expressions with local error:

2.6b
(- (log1p N) (log N))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×add-sqr-sqrt prod-diff
10×add-cube-cbrt
5×pow1
4×log-pow
3×log-prod fma-neg associate--r+
2×diff-log distribute-lft-out-- add-log-exp
1×expm1-log1p-u log1p-udef sub-neg flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
Calls
1 calls:
Slowest
12.0ms
(- (log1p N) (log N))

series82.0ms

Calls
1 calls:
Slowest
82.0ms
(- (log1p N) (log N))

simplify2.3s

Calls
38 calls:
Slowest
215.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
194.0ms
(fma (* (cbrt (log1p N)) (cbrt (log1p N))) (cbrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
194.0ms
(fma 1 (log1p N) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
182.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
166.0ms
(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))

prune326.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

2.8b
(log (/ (+ 1 N) N))
0.0b
(/ (+ 1 N) N)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
24×times-frac
19×add-sqr-sqrt add-cube-cbrt
16×log-prod
7×add-exp-log distribute-lft-out
4×add-cbrt-cube associate-/l*
3×pow1 associate-/r*
2×expm1-log1p-u div-exp rem-log-exp insert-posit16 log1p-expm1-u div-inv add-log-exp associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg flip3-+ log-pow flip-+
Calls
2 calls:
Slowest
28.0ms
(/ (+ 1 N) N)
8.0ms
(log (/ (+ 1 N) N))

series129.0ms

Calls
2 calls:
Slowest
74.0ms
(/ (+ 1 N) N)
55.0ms
(log (/ (+ 1 N) N))

simplify2.0s

Calls
57 calls:
Slowest
379.0ms
(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
189.0ms
(log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (* (cbrt N) (cbrt N))))
181.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
178.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
119.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))

prune567.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

13.4b
(log (/ (/ (+ 1 N) (sqrt N)) (sqrt N)))
0.4b
(/ (+ 1 N) (sqrt N))
0.2b
(/ (/ (+ 1 N) (sqrt N)) (sqrt N))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
672×times-frac
500×*-un-lft-identity
342×sqrt-prod
330×add-sqr-sqrt add-cube-cbrt
172×log-prod
85×distribute-lft-out
32×associate-/l*
16×add-exp-log div-inv
12×associate-/r*
10×add-cbrt-cube
7×div-exp
4×pow1 cbrt-undiv
3×expm1-log1p-u rem-log-exp insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×clear-num frac-2neg
1×log-div flip3-+ log-pow flip-+
Calls
3 calls:
Slowest
38.0ms
(/ (/ (+ 1 N) (sqrt N)) (sqrt N))
20.0ms
(/ (+ 1 N) (sqrt N))
6.0ms
(log (/ (/ (+ 1 N) (sqrt N)) (sqrt N)))

series238.0ms

Calls
3 calls:
Slowest
91.0ms
(log (/ (/ (+ 1 N) (sqrt N)) (sqrt N)))
77.0ms
(/ (+ 1 N) (sqrt N))
70.0ms
(/ (/ (+ 1 N) (sqrt N)) (sqrt N))

simplify30.3s

Calls
619 calls:
Slowest
435.0ms
(/ (* (* (/ (+ 1 N) (sqrt N)) (/ (+ 1 N) (sqrt N))) (/ (+ 1 N) (sqrt N))) (* (* (sqrt N) (sqrt N)) (sqrt N)))
360.0ms
(log (/ (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) 1) (* (cbrt (sqrt N)) (cbrt (sqrt N)))))
337.0ms
(log (/ (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (* (cbrt (sqrt N)) (cbrt (sqrt N)))) (* (cbrt (sqrt N)) (cbrt (sqrt N)))))
331.0ms
(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* (sqrt N) (sqrt N)) (sqrt N)))
315.0ms
(log (/ (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (* (cbrt (sqrt N)) (cbrt (sqrt N)))) (sqrt (* (cbrt N) (cbrt N)))))

prune4.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

14.2b
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
0.6b
(/ -1/3 (* (* N N) N))
0.1b
(/ -1/2 (* N N))
0.1b
(* (* N N) N)

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
35×prod-diff
30×add-sqr-sqrt
27×add-cube-cbrt
23×pow1 add-cbrt-cube add-exp-log
21×times-frac
18×distribute-lft-out
16×div-inv
9×add-log-exp
7×prod-exp cbrt-unprod
6×pow-plus pow-prod-up associate-/l*
5×cbrt-undiv fma-neg div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*r* pow-prod-down frac-sub distribute-lft-out--
2×pow2 clear-num associate-/r* frac-2neg diff-log frac-add pow-sqr
1×sum-log sub-neg flip3-+ flip3-- associate-*l* pow3 associate--l+ *-commutative flip-+ flip-- sub-div difference-of-squares unswap-sqr
Calls
4 calls:
Slowest
192.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
29.0ms
(* (* N N) N)
27.0ms
(/ -1/3 (* (* N N) N))
12.0ms
(/ -1/2 (* N N))

series192.0ms

Calls
4 calls:
Slowest
79.0ms
(/ -1/3 (* (* N N) N))
40.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
36.0ms
(* (* N N) N)
36.0ms
(/ -1/2 (* N N))

simplify23.8s

Calls
140 calls:
Slowest
694.0ms
(* (+ (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ 1 N)))) (* (* N N) N))
638.0ms
(fma 1 (+ (/ -1/2 (* N N)) (/ 1 N)) (- (* (/ -1/3 N) (/ 1 (* N N)))))
613.0ms
(fma (* (cbrt (+ (/ -1/2 (* N N)) (/ 1 N))) (cbrt (+ (/ -1/2 (* N N)) (/ 1 N)))) (cbrt (+ (/ -1/2 (* N N)) (/ 1 N))) (- (* (/ -1/3 N) (/ 1 (* N N)))))
437.0ms
(fma (sqrt (+ (/ -1/2 (* N N)) (/ 1 N))) (sqrt (+ (/ -1/2 (* N N)) (/ 1 N))) (- (* (/ (cbrt -1/3) N) (/ (* (cbrt -1/3) (cbrt -1/3)) (* N N)))))
428.0ms
(fma (- (/ -1/3 N)) (/ 1 (* N N)) (* (/ -1/3 N) (/ 1 (* N N))))

prune1.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes22.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.8b

bsearch51.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
894.0ms1702×body1280valid
770.0ms4043×body80valid
589.0ms8046×body80nan
573.0ms1320×body640valid
172.0ms616×body320valid
46.0ms319×body160valid