Details

Time bar (total: 46.2s)

sample80.0ms

Algorithm
intervals
Results
26.0ms54×body1280valid
15.0ms271×body80nan
12.0ms37×body640valid
12.0ms141×body80valid
4.0ms14×body320valid
1.0ms10×body160valid

simplify11.0ms

Calls
1 calls:
Slowest
10.0ms
(- (log (+ N 1)) (log N))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize13.0ms

Local error

Found 1 expressions with local error:

2.7b
(- (log1p N) (log N))

rewrite34.0ms

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
33.0ms
(- (log1p N) (log N))

series76.0ms

Calls
1 calls:
Slowest
75.0ms
(- (log1p N) (log N))

simplify2.3s

Calls
38 calls:
Slowest
214.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
198.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
198.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
148.0ms
(fma (- (cbrt (log N))) (* (cbrt (log N)) (cbrt (log N))) (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N)))))
148.0ms
(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))

prune261.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

2.7b
(log (/ (+ 1 N) N))
0.0b
(/ (+ 1 N) N)

rewrite17.0ms

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
13.0ms
(/ (+ 1 N) N)
4.0ms
(log (/ (+ 1 N) N))

series120.0ms

Calls
2 calls:
Slowest
61.0ms
(log (/ (+ 1 N) N))
58.0ms
(/ (+ 1 N) N)

simplify1.9s

Calls
57 calls:
Slowest
327.0ms
(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
200.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
190.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
170.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
155.0ms
(log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (* (cbrt N) (cbrt N))))

prune455.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (* (log1p N) (log1p N)) (* (log N) (log N)))
0.6b
(* (log N) (log N))
0.3b
(/ (- (* (log1p N) (log1p N)) (* (log N) (log N))) (+ (log1p N) (log N)))
0.3b
(* (log1p N) (log1p N))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity
31×add-sqr-sqrt
29×pow1
27×add-cube-cbrt
20×times-frac
12×log-prod
11×log-pow
10×add-cbrt-cube add-exp-log distribute-lft-out
9×swap-sqr
7×associate-*r* associate-*l* difference-of-squares
6×distribute-rgt-in distribute-lft-in associate--r+ add-log-exp
5×associate-/r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l*
2×pow2 pow-plus flip3-- pow-prod-down prod-exp associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod flip-- unswap-sqr associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ fma-neg diff-log div-sub div-exp prod-diff flip-+ div-inv
Calls
4 calls:
Slowest
32.0ms
(/ (- (* (log1p N) (log1p N)) (* (log N) (log N))) (+ (log1p N) (log N)))
16.0ms
(- (* (log1p N) (log1p N)) (* (log N) (log N)))
15.0ms
(* (log N) (log N))
5.0ms
(* (log1p N) (log1p N))

series645.0ms

Calls
4 calls:
Slowest
248.0ms
(* (log N) (log N))
238.0ms
(/ (- (* (log1p N) (log1p N)) (* (log N) (log N))) (+ (log1p N) (log N)))
124.0ms
(- (* (log1p N) (log1p N)) (* (log N) (log N)))
34.0ms
(* (log1p N) (log1p N))

simplify10.6s

Calls
134 calls:
Slowest
1.1s
(- (+ (/ 1 (* (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) (pow N 2))) (+ (* 2 (/ (log -1) (* (pow (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) 3) (pow N 3)))) (+ (* 2 (/ (log -1) (* (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) N))) (+ (/ (log (/ -1 N)) (* (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) (pow N 2))) (+ (* 2/3 (/ (log -1) (* (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) (pow N 3)))) (+ (* 2 (/ (log -1) (* (pow (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) 2) (pow N 3)))) (* 2 (/ (log (/ -1 N)) (* (pow (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) 2) (pow N 2)))))))))) (+ (* 2 (/ (log -1) (* (pow (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) 2) (pow N 2)))) (+ (* 2 (/ (log (/ -1 N)) (* (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) N))) (+ (/ 1 (* (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) (pow N 3))) (+ (* 2/3 (/ (log (/ -1 N)) (* (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) (pow N 3)))) (+ (/ 1 (* (pow (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) 2) (pow N 3))) (+ (* 2 (/ (log (/ -1 N)) (* (pow (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) 3) (pow N 3)))) (+ (/ (log -1) (* (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) (pow N 2))) (* 2 (/ (log (/ -1 N)) (* (pow (- (* 2 (log -1)) (* 2 (log (/ -1 N)))) 2) (pow N 3))))))))))))
519.0ms
(- (+ (* 2 (/ (log -1) N)) (+ (/ 1 (pow N 2)) (+ (/ (log (/ -1 N)) (pow N 2)) (* 2/3 (/ (log -1) (pow N 3)))))) (+ (/ 1 (pow N 3)) (+ (* 2/3 (/ (log (/ -1 N)) (pow N 3))) (+ (* 2 (/ (log (/ -1 N)) N)) (/ (log -1) (pow N 2))))))
335.0ms
(- (+ (/ 1 (pow N 2)) (+ (/ (log (/ 1 N)) (pow N 2)) (pow (log (/ 1 N)) 2))) (* 2 (/ (log (/ 1 N)) N)))
319.0ms
(- (* (* (log1p N) (log1p N)) (* (log1p N) (log1p N))) (* (* (log N) (log N)) (* (log N) (log N))))
288.0ms
(/ (- (* (log1p N) (log1p N)) (* (log N) (log N))) (+ (log1p N) (log N)))

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

14.0b
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
0.7b
(/ -1/2 (* N N))
0.3b
(/ -1/3 (* (* N N) N))
0.1b
(* (* N N) N)

rewrite328.0ms

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
254.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
29.0ms
(* (* N N) N)
28.0ms
(/ -1/3 (* (* N N) N))
13.0ms
(/ -1/2 (* N N))

series198.0ms

Calls
4 calls:
Slowest
56.0ms
(/ -1/3 (* (* N N) N))
50.0ms
(* (* N N) N)
49.0ms
(/ -1/2 (* N N))
42.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))

simplify23.2s

Calls
140 calls:
Slowest
647.0ms
(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 N) N)) 1)))
552.0ms
(* (+ (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ 1 N)))) (* (* N N) N))
538.0ms
(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)))))
498.0ms
(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)))))
413.0ms
(fma 1 (+ (/ -1/2 (* N N)) (/ 1 N)) (- (* (/ -1/3 (* (* N N) N)) 1)))

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.8b

bsearch52.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.5s1762×body1280valid
638.0ms8072×body80nan
486.0ms1279×body640valid
405.0ms4021×body80valid
153.0ms628×body320valid
50.0ms310×body160valid