Details

Time bar (total: 19.2s)

sample78.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify138.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
068
1138
2168
3208
4268
5298
6318
done318

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 1 expressions with local error:

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

rewrite157.0ms

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:
145.0ms
(/ (- (+ f n)) (- f n))

series172.0ms

Counts
1 → 3
Calls
1 calls:
172.0ms
(/ (- (+ f n)) (- f n))

simplify2.9s

Counts
100 → 100
Iterations

Useful iterations: 3 (995.0ms)

IterNodesCost
01351469
12921395
27021365
319071357
done50001357

prune266.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
500×times-frac
424×*-un-lft-identity
302×add-sqr-sqrt
204×add-cube-cbrt
81×distribute-lft-neg-in distribute-rgt-neg-in
61×distribute-lft-out
49×distribute-lft-out-- difference-of-squares
30×associate-/r*
27×neg-mul-1
25×associate-/r/
15×associate-/l*
13×div-inv
12×flip3-+ flip-+
9×add-exp-log add-cbrt-cube
4×cbrt-undiv div-exp
2×pow1 expm1-log1p-u frac-2neg div-sub clear-num log1p-expm1-u associate-/l/ add-log-exp
1×neg-sub0 flip3-- distribute-frac-neg flip--
Counts
2 → 363
Calls
2 calls:
31.0ms
(/ (- 1) (/ (- f n) (+ f n)))
36.0ms
(/ (- f n) (+ f n))

series200.0ms

Counts
2 → 6
Calls
2 calls:
102.0ms
(/ (- 1) (/ (- f n) (+ f n)))
98.0ms
(/ (- f n) (+ f n))

simplify1.9s

Counts
369 → 369
Iterations

Useful iterations: done (1.9s)

IterNodesCost
04027547
19856221
224405842
done50015762

prune532.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite358.0ms

Algorithm
rewrite-expression-head
Rules
3124×times-frac
2165×*-un-lft-identity
1651×add-sqr-sqrt
1250×sqrt-prod
1151×add-cube-cbrt
257×distribute-lft-out
250×distribute-lft-out-- difference-of-squares
145×associate-/r/
82×sqrt-div
73×div-inv
50×associate-/r*
41×flip3-- flip-- associate-/l*
32×flip3-+ flip-+
19×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
3×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
Counts
3 → 1343
Calls
3 calls:
100.0ms
(/ (/ -1 (sqrt (- f n))) (/ (sqrt (- f n)) (+ f n)))
16.0ms
(/ -1 (sqrt (- f n)))
33.0ms
(/ (sqrt (- f n)) (+ f n))

series333.0ms

Counts
3 → 9
Calls
3 calls:
90.0ms
(/ (/ -1 (sqrt (- f n))) (/ (sqrt (- f n)) (+ f n)))
106.0ms
(/ -1 (sqrt (- f n)))
136.0ms
(/ (sqrt (- f n)) (+ f n))

simplify3.0s

Counts
1352 → 1352
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0121545313
1351539949
done500039115

prune3.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* n n) (* f n))
3.9b
(+ (pow f 3) (pow n 3))
8.2b
(/ (+ (pow f 3) (pow n 3)) (- f n))
33.2b
(/ (- (/ (+ (pow f 3) (pow n 3)) (- f n))) (+ (* f f) (- (* n n) (* f n))))

rewrite429.0ms

Algorithm
rewrite-expression-head
Rules
888×*-un-lft-identity
723×times-frac
418×add-sqr-sqrt
254×add-cube-cbrt
235×distribute-lft-out
204×distribute-lft-neg-in distribute-rgt-neg-in
191×unpow-prod-down cube-prod
115×associate-/l*
82×distribute-lft-out-- difference-of-squares
47×sum-cubes
20×associate-/r/
12×fma-def
10×flip3-- flip-- div-inv
8×add-exp-log associate-/r* add-cbrt-cube add-log-exp
4×pow1 expm1-log1p-u neg-mul-1 log1p-expm1-u
3×flip3-+ flip-+ associate-/l/
2×cbrt-undiv frac-2neg div-exp clear-num
1×+-commutative neg-sub0 cube-mult sub-neg distribute-rgt-out-- fma-neg diff-log unpow3 div-sub distribute-frac-neg prod-diff sum-log distribute-neg-frac sqr-pow
Counts
4 → 571
Calls
4 calls:
9.0ms
(- (* n n) (* f n))
27.0ms
(+ (pow f 3) (pow n 3))
100.0ms
(/ (+ (pow f 3) (pow n 3)) (- f n))
221.0ms
(/ (- (/ (+ (pow f 3) (pow n 3)) (- f n))) (+ (* f f) (- (* n n) (* f n))))

series347.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (* n n) (* f n))
71.0ms
(+ (pow f 3) (pow n 3))
61.0ms
(/ (+ (pow f 3) (pow n 3)) (- f n))
147.0ms
(/ (- (/ (+ (pow f 3) (pow n 3)) (- f n))) (+ (* f f) (- (* n n) (* f n))))

simplify2.3s

Counts
583 → 583
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
056320822
1120317413
2340817184
done500217184

prune2.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes68.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1128
2138
done138

end0.0ms

sample559.0ms

Algorithm
intervals
Results
271.0ms8000×body80valid