Details

Time bar (total: 36.4s)

sample66.0ms

Algorithm
intervals
Results
19.0ms46×body1280valid
13.0ms278×body80nan
11.0ms42×body640valid
10.0ms139×body80valid
4.0ms22×body320valid
1.0ms7×body160valid

simplify11.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize30.0ms

Local error

Found 2 expressions with local error:

3.3b
(log (+ N 1))
2.2b
(- (log (+ N 1)) (log N))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×log-prod
7×add-sqr-sqrt pow1
5×log-pow add-cube-cbrt
4×log-div associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- flip3-+ add-cbrt-cube flip-+ insert-posit16 distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 43
Calls
2 calls:
Slowest
8.0ms
(- (log (+ N 1)) (log N))
4.0ms
(log (+ N 1))

series88.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
65.0ms
(- (log (+ N 1)) (log N))
23.0ms
(log (+ N 1))

simplify1.5s

Counts
29 → 49
Calls
29 calls:
Slowest
345.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
216.0ms
(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))
199.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
194.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
186.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune471.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

3.3b
(log (+ N 1))
2.2b
(- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt N)))
0.0b
(- (log (+ N 1)) (log (sqrt N)))
0.0b
(log (sqrt N))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
30×log-prod
24×pow1
22×distribute-lft-out--
21×log-pow
17×add-sqr-sqrt
14×associate--l+
13×add-cube-cbrt
12×associate--r+
9×sqrt-prod
6×add-exp-log
5×add-log-exp
4×log-div add-cbrt-cube diff-log insert-posit16
3×associate--l- sub-neg distribute-lft-out
2×flip3-+ flip3-- rem-log-exp flip-+ flip-- difference-of-squares
1×sqrt-pow1 pow1/2
Counts
4 → 102
Calls
4 calls:
Slowest
57.0ms
(- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt N)))
21.0ms
(- (log (+ N 1)) (log (sqrt N)))
7.0ms
(log (+ N 1))
3.0ms
(log (sqrt N))

series424.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(- (log (+ N 1)) (log (sqrt N)))
130.0ms
(- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt N)))
113.0ms
(log (sqrt N))
25.0ms
(log (+ N 1))

simplify2.1s

Counts
73 → 114
Calls
73 calls:
Slowest
383.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
209.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
179.0ms
(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))
82.0ms
(/ (exp (- (log (+ N 1)) (log (sqrt N)))) (sqrt N))
80.0ms
(- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt N)))

prune950.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

23.1b
(- (- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt (* (cbrt N) (cbrt N))))) (log (sqrt (cbrt N))))
3.3b
(log (+ N 1))
0.6b
(cbrt N)
0.6b
(cbrt N)

rewrite404.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity distribute-lft-out--
42×pow1
38×log-pow
18×associate--l+
17×log-prod
13×add-sqr-sqrt
11×add-cube-cbrt
9×cbrt-prod associate--r+
6×diff-log sqrt-prod add-log-exp
5×add-exp-log
4×add-cbrt-cube insert-posit16
3×sub-neg
2×log-div pow1/3 distribute-lft-out
1×associate--l- flip3-+ flip3-- rem-log-exp flip-+ flip-- difference-of-squares
Counts
4 → 96
Calls
4 calls:
Slowest
392.0ms
(- (- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt (* (cbrt N) (cbrt N))))) (log (sqrt (cbrt N))))
6.0ms
(log (+ N 1))
2.0ms
(cbrt N)
1.0ms
(cbrt N)

series848.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
288.0ms
(- (- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt (* (cbrt N) (cbrt N))))) (log (sqrt (cbrt N))))
262.0ms
(cbrt N)
260.0ms
(cbrt N)
38.0ms
(log (+ N 1))

simplify9.3s

Counts
70 → 108
Calls
70 calls:
Slowest
378.0ms
(- (- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt (* (cbrt N) (cbrt N))))) (log (sqrt (cbrt N))))
373.0ms
(- (- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt (* (cbrt N) (cbrt N))))) (log (sqrt (cbrt N))))
369.0ms
(- (- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt (* (cbrt N) (cbrt N))))) (log (sqrt (cbrt N))))
367.0ms
(- (- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt (* (cbrt N) (cbrt N))))) (log (sqrt (cbrt N))))
358.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

22.2b
(- (- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt (* (cbrt N) (cbrt N))))) (log (sqrt (pow N 1/3))))
5.1b
(pow N 1/3)
3.3b
(log (+ N 1))
0.6b
(cbrt N)

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
59×*-un-lft-identity
58×distribute-lft-out--
43×pow1
38×log-pow
18×log-prod associate--l+
14×add-sqr-sqrt
12×add-cube-cbrt
10×associate--r+
7×sqrt-prod
6×unpow-prod-down diff-log add-exp-log add-log-exp
4×add-cbrt-cube insert-posit16
3×cbrt-prod pow-unpow sub-neg
2×log-div distribute-lft-out sqr-pow
1×associate--l- pow-to-exp pow-pow flip3-+ flip3-- unpow1/3 pow1/3 rem-log-exp pow-exp flip-+ flip-- difference-of-squares
Counts
4 → 104
Calls
4 calls:
Slowest
332.0ms
(- (- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt (* (cbrt N) (cbrt N))))) (log (sqrt (pow N 1/3))))
3.0ms
(log (+ N 1))
2.0ms
(pow N 1/3)
1.0ms
(cbrt N)

series773.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
303.0ms
(cbrt N)
250.0ms
(- (- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt (* (cbrt N) (cbrt N))))) (log (sqrt (pow N 1/3))))
199.0ms
(pow N 1/3)
22.0ms
(log (+ N 1))

simplify11.9s

Counts
74 → 116
Calls
74 calls:
Slowest
587.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 N)))))
456.0ms
(- (- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt (* (cbrt N) (cbrt N))))) (log (sqrt (pow N 1/3))))
446.0ms
(- (- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt (* (cbrt N) (cbrt N))))) (log (sqrt (pow N 1/3))))
421.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
416.0ms
(- (- (- (log (+ N 1)) (log (sqrt N))) (log (sqrt (* (cbrt N) (cbrt N))))) (log (sqrt (pow N 1/3))))

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes426.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 28.8b

bsearch54.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
962.0ms1710×body1280valid
687.0ms8344×body80nan
490.0ms4162×body80valid
484.0ms1190×body640valid
194.0ms628×body320valid
84.0ms310×body160valid