Details

Time bar (total: 48.4s)

sample106.0ms

Algorithm
intervals
Results
28.0ms46×body1280valid
25.0ms42×body640valid
19.0ms278×body80nan
15.0ms139×body80valid
6.0ms22×body320valid
1.0ms7×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: 27.4b

localize9.0ms

Local error

Found 1 expressions with local error:

2.2b
(- (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))

series99.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
99.0ms
(- (log1p N) (log N))

simplify2.3s

Counts
38 → 40
Calls
38 calls:
Slowest
212.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
199.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
173.0ms
(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
169.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
155.0ms
(fma 1 (log1p N) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))

prune270.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (- (log1p N) (log (sqrt N))) (log (sqrt N)))
0.0b
(- (log1p N) (log (sqrt N)))
0.0b
(log (sqrt N))
0.0b
(log (sqrt N))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
79×*-un-lft-identity
72×prod-diff
62×add-sqr-sqrt
55×log-pow
45×pow1
44×add-cube-cbrt
26×distribute-lft-out--
24×log-prod
20×associate--l+
14×sqrt-pow1 pow1/2
12×sqrt-prod associate--r+
9×fma-neg difference-of-squares
7×diff-log add-log-exp
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×sub-neg
2×log1p-udef flip3-- rem-log-exp flip--
1×associate--l-
Counts
4 → 179
Calls
4 calls:
Slowest
58.0ms
(- (- (log1p N) (log (sqrt N))) (log (sqrt N)))
10.0ms
(- (log1p N) (log (sqrt N)))
2.0ms
(log (sqrt N))
2.0ms
(log (sqrt N))

series431.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(- (log1p N) (log (sqrt N)))
133.0ms
(- (- (log1p N) (log (sqrt N))) (log (sqrt N)))
89.0ms
(log (sqrt N))
74.0ms
(log (sqrt N))

simplify14.0s

Counts
191 → 191
Calls
191 calls:
Slowest
532.0ms
(fma (+ (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (* (log N) 1/2)))
522.0ms
(fma (+ (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (* (sqrt (log (sqrt N))) (sqrt (log (sqrt N))))))
471.0ms
(fma (+ (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (* (log (sqrt N)) 1)))
470.0ms
(fma (+ (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (* (log (sqrt N)) 1)))
413.0ms
(fma (sqrt (- (log1p N) (log (sqrt N)))) (sqrt (- (log1p N) (log (sqrt N)))) (- (* (cbrt (log (sqrt N))) (* (cbrt (log (sqrt N))) (cbrt (log (sqrt N)))))))

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

27.7b
(fma (sqrt (- (log1p N) (log (sqrt N)))) (sqrt (- (log1p N) (log (sqrt N)))) (- (log (sqrt N))))
0.1b
(sqrt (- (log1p N) (log (sqrt N))))
0.1b
(sqrt (- (log1p N) (log (sqrt N))))
0.0b
(- (log1p N) (log (sqrt N)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
26×add-sqr-sqrt
18×prod-diff add-cube-cbrt
15×pow1 sqrt-prod
12×log-pow
6×log-prod associate--r+ distribute-lft-out--
5×sqrt-pow1 pow1/2 add-log-exp
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×flip3-- fma-neg flip-- difference-of-squares
2×rem-sqrt-square diff-log
1×log1p-udef sub-neg fma-udef
Counts
4 → 99
Calls
4 calls:
Slowest
13.0ms
(sqrt (- (log1p N) (log (sqrt N))))
9.0ms
(sqrt (- (log1p N) (log (sqrt N))))
7.0ms
(- (log1p N) (log (sqrt N)))
0.0ms
(fma (sqrt (- (log1p N) (log (sqrt N)))) (sqrt (- (log1p N) (log (sqrt N)))) (- (log (sqrt N))))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
461.0ms
(fma (sqrt (- (log1p N) (log (sqrt N)))) (sqrt (- (log1p N) (log (sqrt N)))) (- (log (sqrt N))))
209.0ms
(sqrt (- (log1p N) (log (sqrt N))))
209.0ms
(sqrt (- (log1p N) (log (sqrt N))))
125.0ms
(- (log1p N) (log (sqrt N)))

simplify3.5s

Counts
82 → 111
Calls
82 calls:
Slowest
260.0ms
(sqrt (- (pow (log1p N) 3) (pow (log (sqrt N)) 3)))
240.0ms
(sqrt (- (pow (log1p N) 3) (pow (log (sqrt N)) 3)))
204.0ms
(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (* (cbrt (log (sqrt N))) (* (cbrt (log (sqrt N))) (cbrt (log (sqrt N)))))))
188.0ms
(sqrt (- (* (log1p N) (log1p N)) (* (log (sqrt N)) (log (sqrt N)))))
172.0ms
(fma (* (cbrt (log1p N)) (cbrt (log1p N))) (cbrt (log1p N)) (- (* (cbrt (log (sqrt N))) (* (cbrt (log (sqrt N))) (cbrt (log (sqrt N)))))))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (- (log1p N) (log (sqrt N))) (log (sqrt N)))
0.7b
(exp (log (- (- (log1p N) (log (sqrt N))) (log (sqrt N)))))
0.0b
(log (- (- (log1p N) (log (sqrt N))) (log (sqrt N))))
0.0b
(- (log1p N) (log (sqrt N)))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
100×*-un-lft-identity
72×prod-diff
65×add-sqr-sqrt
61×log-pow
53×pow1
46×distribute-lft-out--
43×add-cube-cbrt
32×log-prod
20×associate--l+
12×sqrt-pow1 pow1/2 associate--r+
11×difference-of-squares
10×exp-sum
9×fma-neg
7×diff-log add-log-exp
6×sqrt-prod
5×add-exp-log
4×expm1-log1p-u log-div exp-prod flip3-- add-cbrt-cube insert-posit16 log1p-expm1-u flip--
3×sub-neg
2×log1p-udef exp-diff
1×associate--l- rem-log-exp rem-exp-log
Counts
4 → 190
Calls
4 calls:
Slowest
78.0ms
(- (- (log1p N) (log (sqrt N))) (log (sqrt N)))
45.0ms
(log (- (- (log1p N) (log (sqrt N))) (log (sqrt N))))
39.0ms
(exp (log (- (- (log1p N) (log (sqrt N))) (log (sqrt N)))))
6.0ms
(- (log1p N) (log (sqrt N)))

series635.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(log (- (- (log1p N) (log (sqrt N))) (log (sqrt N))))
143.0ms
(exp (log (- (- (log1p N) (log (sqrt N))) (log (sqrt N)))))
138.0ms
(- (- (log1p N) (log (sqrt N))) (log (sqrt N)))
136.0ms
(- (log1p N) (log (sqrt N)))

simplify17.5s

Counts
205 → 202
Calls
205 calls:
Slowest
946.0ms
(exp (log (- (* (- (log1p N) (log (sqrt N))) (- (log1p N) (log (sqrt N)))) (* (log (sqrt N)) (log (sqrt N))))))
937.0ms
(log (- (* (- (log1p N) (log (sqrt N))) (- (log1p N) (log (sqrt N)))) (* (log (sqrt N)) (log (sqrt N)))))
576.0ms
(fma (+ (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (* (log N) (/ 1 2))))
493.0ms
(fma (+ (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (* (log N) 1/2)))
484.0ms
(fma (+ (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (sqrt (log1p N)) (sqrt (log (sqrt N)))) (- (* (sqrt (log (sqrt N))) (sqrt (log (sqrt N))))))

prune2.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

100% (0.0b remaining)

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

bsearch60.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.0s1190×body640valid
987.0ms1710×body1280valid
625.0ms8344×body80nan
438.0ms4162×body80valid
160.0ms628×body320valid
50.0ms310×body160valid