Details

Time bar (total: 12.5s)

sample92.0ms

Algorithm
intervals
Results
27.0ms54×body1280valid
17.0ms293×body80nan
13.0ms42×body640valid
10.0ms115×body80valid
7.0ms34×body320valid
1.0ms11×body160valid

simplify12.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize12.0ms

Local error

Found 1 expressions with local error:

3.6b
(- (log1p N) (log N))

rewrite14.0ms

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
Counts
1 → 37
Calls
1 calls:
Slowest
13.0ms
(- (log1p N) (log N))

series91.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
91.0ms
(- (log1p N) (log N))

simplify1.5s

Counts
40 → 40

prune266.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ 1/3 N)
0.1b
(/ (/ 1 N) N)
0.1b
(fma (/ (/ 1 N) N) (+ (/ 1/3 N) -1/2) (/ 1 N))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
14×add-exp-log
10×add-cbrt-cube
7×div-exp
6×pow1 associate-/r* div-inv
4×cbrt-undiv
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg pow-div
1×rec-exp 1-exp fma-udef pow-flip inv-pow associate-/l/
Counts
3 → 118
Calls
3 calls:
Slowest
9.0ms
(/ (/ 1 N) N)
4.0ms
(/ 1/3 N)
0.0ms
(fma (/ (/ 1 N) N) (+ (/ 1/3 N) -1/2) (/ 1 N))

series94.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
38.0ms
(/ (/ 1 N) N)
37.0ms
(fma (/ (/ 1 N) N) (+ (/ 1/3 N) -1/2) (/ 1 N))
18.0ms
(/ 1/3 N)

simplify1.1s

Counts
127 → 127

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

8.2b
(sqrt (fma (/ (/ 1 N) N) (+ (/ 1/3 N) -1/2) (/ 1 N)))
8.2b
(sqrt (fma (/ (/ 1 N) N) (+ (/ 1/3 N) -1/2) (/ 1 N)))
0.4b
(/ 1/3 N)
0.4b
(/ 1/3 N)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
18×times-frac
8×add-cbrt-cube add-exp-log
6×pow1 associate-/r* sqrt-prod associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 92
Calls
4 calls:
Slowest
7.0ms
(/ 1/3 N)
7.0ms
(/ 1/3 N)
3.0ms
(sqrt (fma (/ (/ 1 N) N) (+ (/ 1/3 N) -1/2) (/ 1 N)))
2.0ms
(sqrt (fma (/ (/ 1 N) N) (+ (/ 1/3 N) -1/2) (/ 1 N)))

series179.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
88.0ms
(sqrt (fma (/ (/ 1 N) N) (+ (/ 1/3 N) -1/2) (/ 1 N)))
49.0ms
(sqrt (fma (/ (/ 1 N) N) (+ (/ 1/3 N) -1/2) (/ 1 N)))
23.0ms
(/ 1/3 N)
19.0ms
(/ 1/3 N)

simplify1.0s

Counts
104 → 104

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 2 expressions with local error:

4.2b
(log (/ (+ 1 N) N))
0.0b
(/ (+ 1 N) N)

rewrite41.0ms

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-+
Counts
2 → 66
Calls
2 calls:
Slowest
32.0ms
(/ (+ 1 N) N)
8.0ms
(log (/ (+ 1 N) N))

series119.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
66.0ms
(/ (+ 1 N) N)
53.0ms
(log (/ (+ 1 N) N))

simplify1.6s

Counts
72 → 72

prune520.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes49.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.6b

bsearch60.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.0s1826×body1280valid
963.0ms1237×body640valid
521.0ms7822×body80nan
476.0ms4050×body80valid
140.0ms577×body320valid
86.0ms310×body160valid