Details

Time bar (total: 19.3s)

sample141.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify105.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
068
1138
2168
3208
4268
5298
6318
done318

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 1 expressions with local error:

0.1b
(/ (- (+ f n)) (- f n))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
82×*-un-lft-identity
60×times-frac
58×add-sqr-sqrt
32×add-cube-cbrt
24×distribute-lft-neg-in distribute-rgt-neg-in
13×distribute-lft-out-- difference-of-squares
12×distribute-lft-out associate-/l*
6×neg-mul-1
5×associate-/r*
3×add-exp-log add-cbrt-cube
2×associate-/r/ associate-/l/ distribute-neg-frac
1×pow1 cbrt-undiv neg-sub0 expm1-log1p-u flip3-- frac-2neg flip3-+ div-sub distribute-frac-neg div-exp clear-num flip-- flip-+ log1p-expm1-u div-inv add-log-exp
Counts
1 → 97
Calls
1 calls:
68.0ms
(/ (- (+ f n)) (- f n))

series101.0ms

Counts
1 → 3
Calls
1 calls:
101.0ms
(/ (- (+ f n)) (- f n))

simplify2.8s

Counts
100 → 100
Iterations

Useful iterations: 3 (584.0ms)

IterNodesCost
01351469
12921395
27021365
319071357
done50001357

prune236.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1 (/ (- f n) (- (+ f n))))
0.1b
(/ (- f n) (- (+ f n)))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
498×times-frac
438×*-un-lft-identity
334×add-sqr-sqrt
212×add-cube-cbrt
104×distribute-lft-neg-in distribute-rgt-neg-in
78×associate-/r*
61×distribute-lft-out-- difference-of-squares
52×distribute-lft-out
26×neg-mul-1
15×add-exp-log
11×associate-/r/
10×distribute-neg-frac
9×add-cbrt-cube
8×div-exp associate-/l*
6×div-inv
5×flip3-+ flip-+
4×cbrt-undiv
3×pow1
2×expm1-log1p-u rec-exp frac-2neg 1-exp clear-num log1p-expm1-u associate-/l/ add-log-exp
1×flip3-- pow-flip div-sub flip-- inv-pow
Counts
2 → 386
Calls
2 calls:
56.0ms
(/ 1 (/ (- f n) (- (+ f n))))
55.0ms
(/ (- f n) (- (+ f n)))

series218.0ms

Counts
2 → 6
Calls
2 calls:
120.0ms
(/ 1 (/ (- f n) (- (+ f n))))
98.0ms
(/ (- f n) (- (+ f n)))

simplify2.1s

Counts
392 → 392
Iterations

Useful iterations: done (2.1s)

IterNodesCost
03937392
19186305
219825702
done50015585

prune609.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (expm1 (/ (- f n) (- (+ f n)))))
0.0b
(/ 1 (log1p (expm1 (/ (- f n) (- (+ f n))))))
0.1b
(/ (- f n) (- (+ f n)))
0.5b
(expm1 (/ (- f n) (- (+ f n))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
93×*-un-lft-identity
69×add-sqr-sqrt times-frac
43×add-cube-cbrt
24×distribute-lft-neg-in distribute-rgt-neg-in
15×associate-/r*
13×distribute-lft-out-- difference-of-squares
12×distribute-lft-out
10×add-exp-log
8×add-cbrt-cube associate-/l*
6×neg-mul-1
5×pow1 log1p-expm1-u
4×expm1-log1p-u add-log-exp
3×div-exp
2×cbrt-undiv frac-2neg clear-num associate-/r/ div-inv associate-/l/ distribute-neg-frac
1×rec-exp log1p-udef expm1-log1p flip3-- pow-flip flip3-+ 1-exp div-sub log1p-expm1 flip-- flip-+ inv-pow expm1-udef
Counts
4 → 151
Calls
4 calls:
0.0ms
(log1p (expm1 (/ (- f n) (- (+ f n)))))
5.0ms
(/ 1 (log1p (expm1 (/ (- f n) (- (+ f n))))))
70.0ms
(/ (- f n) (- (+ f n)))
1.0ms
(expm1 (/ (- f n) (- (+ f n))))

series615.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(log1p (expm1 (/ (- f n) (- (+ f n)))))
204.0ms
(/ 1 (log1p (expm1 (/ (- f n) (- (+ f n))))))
119.0ms
(/ (- f n) (- (+ f n)))
138.0ms
(expm1 (/ (- f n) (- (+ f n))))

simplify2.5s

Counts
163 → 163
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01992365
14212128
29792028
323801996
done50001995

prune486.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (log1p (expm1 (- (/ f (- (+ f n))) (/ n (- (+ n f)))))))
0.0b
(/ n (- (+ n f)))
0.0b
(- (/ f (- (+ f n))) (/ n (- (+ n f))))
0.5b
(expm1 (- (/ f (- (+ f n))) (/ n (- (+ n f)))))

rewrite811.0ms

Algorithm
rewrite-expression-head
Rules
3137×times-frac
3009×*-un-lft-identity
1919×add-sqr-sqrt
1907×add-cube-cbrt
1764×prod-diff
1048×distribute-rgt-neg-in
1044×distribute-lft-neg-in
528×distribute-lft-out
261×neg-mul-1
172×associate-/r/ distribute-neg-frac
87×div-inv
86×flip3-+ flip-+
42×fma-neg
15×associate-/r* distribute-lft-out--
10×add-exp-log
8×add-cbrt-cube
6×associate-/l* add-log-exp
5×pow1 log1p-expm1-u
4×expm1-log1p-u difference-of-squares
3×div-exp
2×cbrt-undiv frac-2neg clear-num
1×sub-neg rec-exp expm1-log1p flip3-- pow-flip diff-log 1-exp frac-sub flip-- inv-pow expm1-udef
Counts
4 → 1951
Calls
4 calls:
5.0ms
(/ 1 (log1p (expm1 (- (/ f (- (+ f n))) (/ n (- (+ n f)))))))
40.0ms
(/ n (- (+ n f)))
386.0ms
(- (/ f (- (+ f n))) (/ n (- (+ n f))))
1.0ms
(expm1 (- (/ f (- (+ f n))) (/ n (- (+ n f)))))

series507.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ 1 (log1p (expm1 (- (/ f (- (+ f n))) (/ n (- (+ n f)))))))
56.0ms
(/ n (- (+ n f)))
115.0ms
(- (/ f (- (+ f n))) (/ n (- (+ n f))))
169.0ms
(expm1 (- (/ f (- (+ f n))) (/ n (- (+ n f)))))

simplify2.8s

Counts
1963 → 1963
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01492116654
13129107033
done500082121

prune4.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01114
11714
21814
done1814

end0.0ms

sample719.0ms

Algorithm
intervals
Results
435.0ms8000×body80valid