Details

Time bar (total: 38.5s)

sample104.0ms

Algorithm
intervals
Results
38.0ms59×body1280valid
16.0ms137×body80valid
15.0ms207×body80nan
14.0ms33×body640valid
5.0ms19×body320valid
1.0ms8×body160valid

simplify34.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
34.0ms
(- (log (+ N 1)) (log N))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize8.0ms

Local error

Found 1 expressions with local error:

1.5b
(- (log1p N) (log N))

rewrite7.0ms

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))

series55.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
55.0ms
(- (log1p N) (log N))

simplify2.6s

Counts
38 → 40
Calls
38 calls:
Slowest
590.0ms
(fma (* (cbrt (log1p N)) (cbrt (log1p N))) (cbrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
191.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
191.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
174.0ms
(fma 1 (log1p N) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
158.0ms
(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))

prune278.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

1.8b
(log (/ (+ 1 N) N))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
16×log-prod
15×*-un-lft-identity
12×times-frac
9×add-sqr-sqrt add-cube-cbrt
4×add-exp-log
3×distribute-lft-out
2×pow1 rem-log-exp
1×expm1-log1p-u log-div add-cbrt-cube div-exp log-pow insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 30
Calls
1 calls:
Slowest
4.0ms
(log (/ (+ 1 N) N))

series65.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
65.0ms
(log (/ (+ 1 N) N))

simplify1.2s

Counts
22 → 33
Calls
22 calls:
Slowest
203.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
200.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
165.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
163.0ms
(log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (* (cbrt N) (cbrt N))))
78.0ms
(log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) 1))

prune210.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

15.4b
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
0.2b
(/ -1/2 (* N N))
0.2b
(/ -1/3 (* (* N N) N))
0.1b
(* (* N N) N)

rewrite285.0ms

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
226.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
28.0ms
(* (* N N) N)
20.0ms
(/ -1/3 (* (* N N) N))
6.0ms
(/ -1/2 (* N N))

series189.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
72.0ms
(/ -1/3 (* (* N N) N))
63.0ms
(* (* N N) N)
27.0ms
(/ -1/2 (* N N))
26.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))

simplify24.3s

Counts
140 → 158
Calls
140 calls:
Slowest
680.0ms
(* (+ (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ 1 N)))) (* (* N N) N))
548.0ms
(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)))))
541.0ms
(fma (- (/ -1/3 N)) (/ 1 (* N N)) (* (/ -1/3 N) (/ 1 (* N N))))
493.0ms
(* (* (* (* N N) (* N N)) (* N N)) (* (* N N) N))
478.0ms
(fma (- (/ -1/3 N)) (/ 1 (* N N)) (* (/ -1/3 N) (/ 1 (* N N))))

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (sqrt (+ (/ -1/2 (* N N)) (/ 1 N))) (sqrt (+ (/ -1/2 (* N N)) (/ 1 N))) (- (/ -1/3 (* (* N N) N))))
0.2b
(/ -1/2 (* N N))
0.2b
(/ -1/2 (* N N))
0.2b
(/ -1/3 (* (* N N) N))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
23×add-cbrt-cube add-exp-log
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac associate-/l*
7×cbrt-undiv div-exp
5×prod-exp cbrt-unprod
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num associate-/r* frac-2neg div-inv
1×fma-udef
Counts
4 → 85
Calls
4 calls:
Slowest
29.0ms
(/ -1/3 (* (* N N) N))
13.0ms
(/ -1/2 (* N N))
13.0ms
(/ -1/2 (* N N))
0.0ms
(fma (sqrt (+ (/ -1/2 (* N N)) (/ 1 N))) (sqrt (+ (/ -1/2 (* N N)) (/ 1 N))) (- (/ -1/3 (* (* N N) N))))

series326.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
191.0ms
(fma (sqrt (+ (/ -1/2 (* N N)) (/ 1 N))) (sqrt (+ (/ -1/2 (* N N)) (/ 1 N))) (- (/ -1/3 (* (* N N) N))))
52.0ms
(/ -1/2 (* N N))
47.0ms
(/ -1/3 (* (* N N) N))
37.0ms
(/ -1/2 (* N N))

simplify2.9s

Counts
50 → 97
Calls
50 calls:
Slowest
381.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) N) (* (* N N) N)))
380.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) N) (* (* N N) N)))
329.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) (* N N)) (* N N)))
328.0ms
(/ (* (* -1/2 -1/2) -1/2) (* (* (* N N) (* N N)) (* N N)))
209.0ms
(+ (/ (pow (sqrt -1/2) 2) (pow N 2)) (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3)))))

prune983.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch52.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
907.0ms1728×body1280valid
574.0ms588×body320valid
515.0ms7816×body80nan
502.0ms1321×body640valid
435.0ms4073×body80valid
69.0ms290×body160valid