Details

Time bar (total: 38.6s)

sample82.0ms

Algorithm
intervals
Results
24.0ms277×body80nan
22.0ms52×body1280valid
14.0ms50×body640valid
9.0ms125×body80valid
4.0ms20×body320valid
1.0ms9×body160valid

simplify11.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
11.0ms
(- (log (+ N 1)) (log N))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize9.0ms

Local error

Found 1 expressions with local error:

3.0b
(- (log1p N) (log N))

rewrite6.0ms

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
6.0ms
(- (log1p N) (log N))

series105.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
105.0ms
(- (log1p N) (log N))

simplify2.4s

Counts
38 → 40
Calls
38 calls:
Slowest
205.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
204.0ms
(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
194.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
178.0ms
(fma (* (cbrt (log1p N)) (cbrt (log1p N))) (cbrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
171.0ms
(fma (- (cbrt (log N))) (* (cbrt (log N)) (cbrt (log N))) (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N)))))

prune379.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

10.8b
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
0.5b
(/ -1/3 (* (* N N) N))
0.3b
(/ -1/2 (* N N))
0.3b
(+ (/ -1/2 (* N N)) (/ 1 N))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity
35×prod-diff
30×add-sqr-sqrt
28×add-cube-cbrt
24×times-frac
20×distribute-lft-out
18×add-cbrt-cube add-exp-log div-inv
11×add-log-exp
7×fma-def
6×associate-/l*
5×cbrt-undiv fma-neg div-exp
4×expm1-log1p-u pow1 prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×frac-add frac-sub distribute-lft-out--
2×clear-num associate-/r* sum-log frac-2neg flip3-+ diff-log flip-+
1×+-commutative sub-neg flip3-- associate--l+ flip-- sub-div difference-of-squares
Counts
4 → 139
Calls
4 calls:
Slowest
178.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
20.0ms
(/ -1/3 (* (* N N) N))
20.0ms
(+ (/ -1/2 (* N N)) (/ 1 N))
6.0ms
(/ -1/2 (* N N))

series262.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
93.0ms
(+ (/ -1/2 (* N N)) (/ 1 N))
76.0ms
(/ -1/3 (* (* N N) N))
49.0ms
(/ -1/2 (* N N))
44.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))

simplify23.5s

Counts
136 → 151
Calls
136 calls:
Slowest
698.0ms
(* (+ (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ 1 N)))) (* (* N N) N))
554.0ms
(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)))))
459.0ms
(fma (* (cbrt (+ (/ -1/2 (* N N)) (/ 1 N))) (cbrt (+ (/ -1/2 (* N N)) (/ 1 N)))) (cbrt (+ (/ -1/2 (* N N)) (/ 1 N))) (- (* (/ (cbrt -1/3) N) (/ (* (cbrt -1/3) (cbrt -1/3)) (* N N)))))
442.0ms
(fma (- (/ -1/3 N)) (/ 1 (* N N)) (* (/ -1/3 N) (/ 1 (* N N))))
440.0ms
(fma (- (/ -1/3 N)) (/ 1 (* N N)) (* (/ -1/3 N) (/ 1 (* N N))))

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ -1/3 (* (* N N) N))
0.3b
(/ -1/2 (* N N))
0.3b
(/ -1/2 (* N N))
0.3b
(+ (/ -1/2 (* N N)) (/ 1 N))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
23×add-cbrt-cube add-exp-log
15×*-un-lft-identity
12×add-sqr-sqrt times-frac add-cube-cbrt
9×associate-/l*
7×cbrt-undiv fma-def div-exp
6×add-log-exp
5×prod-exp cbrt-unprod div-inv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×clear-num associate-/r* frac-2neg
2×distribute-lft-out
1×+-commutative sum-log flip3-+ frac-add flip-+
Counts
4 → 98
Calls
4 calls:
Slowest
29.0ms
(/ -1/3 (* (* N N) N))
26.0ms
(+ (/ -1/2 (* N N)) (/ 1 N))
7.0ms
(/ -1/2 (* N N))
6.0ms
(/ -1/2 (* N N))

series660.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
509.0ms
(+ (/ -1/2 (* N N)) (/ 1 N))
77.0ms
(/ -1/3 (* (* N N) N))
46.0ms
(/ -1/2 (* N N))
28.0ms
(/ -1/2 (* N N))

simplify3.0s

Counts
60 → 110
Calls
60 calls:
Slowest
380.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) (* N N)) (* N N)))
374.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) N) (* (* N N) N)))
339.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) N) (* (* N N) N)))
294.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) (* N N)) (* N N)))
135.0ms
(/ (* (* -1/3 -1/3) -1/3) (* (* (* (* N N) N) (* (* N N) N)) (* (* N N) N)))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 2 expressions with local error:

3.4b
(log (/ (+ 1 N) N))
0.0b
(/ (+ 1 N) N)

rewrite36.0ms

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
27.0ms
(/ (+ 1 N) N)
8.0ms
(log (/ (+ 1 N) N))

series161.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
81.0ms
(/ (+ 1 N) N)
80.0ms
(log (/ (+ 1 N) N))

simplify2.1s

Counts
57 → 72
Calls
57 calls:
Slowest
357.0ms
(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
215.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
206.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
166.0ms
(log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (* (cbrt N) (cbrt N))))
149.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))

prune506.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes23.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.0b

bsearch46.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
985.0ms1752×body1280valid
542.0ms1248×body640valid
464.0ms7931×body80nan
418.0ms4083×body80valid
139.0ms619×body320valid
42.0ms298×body160valid