Details

Time bar (total: 47.4s)

sample102.0ms

Algorithm
intervals
Results
31.0ms56×body1280valid
20.0ms131×body80valid
16.0ms267×body80nan
14.0ms40×body640valid
5.0ms22×body320valid
1.0ms7×body160valid

simplify21.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
21.0ms
(- (log (+ N 1)) (log N))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize18.0ms

Local error

Found 1 expressions with local error:

1.7b
(- (log1p N) (log N))

rewrite10.0ms

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
9.0ms
(- (log1p N) (log N))

series71.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
71.0ms
(- (log1p N) (log N))

simplify2.1s

Counts
38 → 40
Calls
38 calls:
Slowest
182.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
164.0ms
(fma (* (cbrt (log1p N)) (cbrt (log1p N))) (cbrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
156.0ms
(fma 1 (log1p N) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
152.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
147.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune248.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

2.1b
(log (/ (+ 1 N) N))
0.0b
(/ (+ 1 N) N)

rewrite26.0ms

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
20.0ms
(/ (+ 1 N) N)
4.0ms
(log (/ (+ 1 N) N))

series142.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
74.0ms
(log (/ (+ 1 N) N))
69.0ms
(/ (+ 1 N) N)

simplify2.0s

Counts
57 → 72
Calls
57 calls:
Slowest
366.0ms
(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
203.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
185.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
177.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
172.0ms
(log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (* (cbrt N) (cbrt N))))

prune500.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (* (log1p N) (log1p N)) (* (log N) (log N)))
0.5b
(* (log N) (log N))
0.3b
(* (log1p N) (log1p N))
0.2b
(/ (- (* (log1p N) (log1p N)) (* (log N) (log N))) (+ (log1p N) (log N)))

rewrite75.0ms

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
Counts
4 → 140
Calls
4 calls:
Slowest
43.0ms
(/ (- (* (log1p N) (log1p N)) (* (log N) (log N))) (+ (log1p N) (log N)))
14.0ms
(- (* (log1p N) (log1p N)) (* (log N) (log N)))
8.0ms
(* (log N) (log N))
7.0ms
(* (log1p N) (log1p N))

series646.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
247.0ms
(* (log N) (log N))
212.0ms
(/ (- (* (log1p N) (log1p N)) (* (log N) (log N))) (+ (log1p N) (log N)))
124.0ms
(- (* (log1p N) (log1p N)) (* (log N) (log N)))
63.0ms
(* (log1p N) (log1p N))

simplify11.1s

Counts
134 → 152
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))))))))))))
492.0ms
(- (+ (* 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))))))
352.0ms
(- (+ (* 2 (/ (log -1) N)) (+ (/ 1 (pow N 2)) (+ (/ (log (/ -1 N)) (pow N 2)) (+ (pow (log (/ -1 N)) 2) (pow (log -1) 2))))) (+ (* 2 (* (log (/ -1 N)) (log -1))) (+ (* 2 (/ (log (/ -1 N)) N)) (/ (log -1) (pow N 2)))))
333.0ms
(- (+ (/ 1 (pow N 2)) (+ (/ (log (/ 1 N)) (pow N 2)) (pow (log (/ 1 N)) 2))) (* 2 (/ (log (/ 1 N)) N)))
322.0ms
(- (* (* (log1p N) (log1p N)) (* (log1p N) (log1p N))) (* (* (log N) (log N)) (* (log N) (log N))))

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

10.6b
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
0.5b
(/ -1/2 (* N N))
0.3b
(/ -1/3 (* (* N N) N))
0.1b
(* (* N N) N)

rewrite293.0ms

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
Counts
4 → 146
Calls
4 calls:
Slowest
217.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
30.0ms
(* (* N N) N)
29.0ms
(/ -1/3 (* (* N N) N))
13.0ms
(/ -1/2 (* N N))

series161.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
44.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
42.0ms
(* (* N N) N)
39.0ms
(/ -1/3 (* (* N N) N))
35.0ms
(/ -1/2 (* N N))

simplify24.0s

Counts
140 → 158
Calls
140 calls:
Slowest
724.0ms
(* (+ (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ 1 N)))) (* (* N N) N))
693.0ms
(fma (- (/ (cbrt -1/3) N)) (/ (* (cbrt -1/3) (cbrt -1/3)) (* N N)) (* (/ (cbrt -1/3) N) (/ (* (cbrt -1/3) (cbrt -1/3)) (* N N))))
483.0ms
(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 (- (/ -1/3 N)) (/ 1 (* N N)) (* (/ -1/3 N) (/ 1 (* N N))))
453.0ms
(fma (- (/ -1/3 N)) (/ 1 (* N N)) (* (/ -1/3 N) (/ 1 (* N N))))

prune1.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes67.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.3b

bsearch64.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.0s1782×body1280valid
561.0ms7847×body80nan
516.0ms620×body320valid
489.0ms4087×body80valid
462.0ms1209×body640valid
47.0ms302×body160valid