Details

Time bar (total: 10.6s)

sample85.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify69.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
068
1138
2168
3208
4268
5308
6328
done328

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite82.0ms

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:
69.0ms
(/ (- (+ f n)) (- f n))

series127.0ms

Counts
1 → 3
Calls
1 calls:
127.0ms
(/ (- (+ f n)) (- f n))

simplify763.0ms

Counts
100 → 100
Iterations

Useful iterations: done (757.0ms)

IterNodesCost
01351469
13161395
210801367
done50011358

prune186.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ -1 (- f n))
0.2b
(* (/ -1 (- f n)) (+ f n))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
38×*-un-lft-identity
31×times-frac
22×add-cube-cbrt
21×associate-*l*
9×add-exp-log add-cbrt-cube
7×distribute-lft-out-- difference-of-squares
5×associate-/r*
4×pow1 associate-*r* associate-/r/
3×associate-/l*
2×cbrt-undiv expm1-log1p-u frac-times flip3-- flip3-+ associate-*r/ div-exp prod-exp flip-- cbrt-unprod flip-+ log1p-expm1-u div-inv add-log-exp unswap-sqr
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num *-commutative distribute-lft-out
Counts
2 → 88
Calls
2 calls:
12.0ms
(/ -1 (- f n))
89.0ms
(* (/ -1 (- f n)) (+ f n))

series146.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(/ -1 (- f n))
78.0ms
(* (/ -1 (- f n)) (+ f n))

simplify1.2s

Counts
94 → 94
Iterations

Useful iterations: 2 (293.0ms)

IterNodesCost
01311006
1457964
21745867
done5002867

prune231.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ n f) (+ n f))
0.9b
(/ -1 (- (* f f) (* n n)))
4.8b
(- (* f f) (* n n))
29.9b
(* (/ -1 (- (* f f) (* n n))) (* (+ n f) (+ n f)))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
30×add-sqr-sqrt
25×add-cube-cbrt times-frac
22×associate-*l*
20×add-exp-log frac-times add-cbrt-cube
18×flip3-+ flip-+
16×pow1
14×associate-*r/
8×difference-of-squares
7×associate-*l/ prod-exp cbrt-unprod
6×swap-sqr distribute-lft-out add-log-exp
5×distribute-rgt-in distribute-lft-in associate-*r*
4×expm1-log1p-u pow-prod-down associate-/r* associate-/r/ log1p-expm1-u
3×cbrt-undiv flip3-- div-exp flip-- associate-/l* unswap-sqr
2×*-commutative div-inv
1×pow2 sub-neg frac-2neg pow-plus fma-neg diff-log prod-diff clear-num pow-sqr pow-prod-up
Counts
4 → 156
Calls
4 calls:
40.0ms
(* (+ n f) (+ n f))
25.0ms
(/ -1 (- (* f f) (* n n)))
19.0ms
(- (* f f) (* n n))
107.0ms
(* (/ -1 (- (* f f) (* n n))) (* (+ n f) (+ n f)))

series263.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (+ n f) (+ n f))
60.0ms
(/ -1 (- (* f f) (* n n)))
58.0ms
(- (* f f) (* n n))
116.0ms
(* (/ -1 (- (* f f) (* n n))) (* (+ n f) (+ n f)))

simplify599.0ms

Counts
168 → 168
Iterations

Useful iterations: done (591.0ms)

IterNodesCost
02152797
17442652
done50002352

prune534.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite525.0ms

Algorithm
rewrite-expression-head
Rules
880×*-un-lft-identity
587×times-frac
504×sqrt-prod
473×add-sqr-sqrt
238×add-cube-cbrt
220×distribute-rgt-neg-in
192×distribute-lft-neg-in
151×swap-sqr
142×distribute-lft-out--
124×distribute-lft-out
102×difference-of-squares
69×associate-*r* associate-*l*
41×neg-mul-1
24×associate-/l*
20×pow1
14×associate-/r/
10×add-exp-log associate-/r* add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-- flip-- div-inv
5×sqrt-div pow-prod-up
4×expm1-log1p-u log1p-expm1-u associate-/l/ distribute-neg-frac add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv neg-sub0 rem-sqrt-square frac-2neg flip3-+ div-sub distribute-frac-neg div-exp clear-num flip-+
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 602
Calls
4 calls:
32.0ms
(sqrt (/ (- (+ f n)) (- f n)))
318.0ms
(* (sqrt (/ (- (+ f n)) (- f n))) (sqrt (/ (- (+ f n)) (- f n))))
45.0ms
(/ (- (+ f n)) (- f n))
39.0ms
(/ (- (+ f n)) (- f n))

series835.0ms

Counts
4 → 12
Calls
4 calls:
437.0ms
(sqrt (/ (- (+ f n)) (- f n)))
190.0ms
(* (sqrt (/ (- (+ f n)) (- f n))) (sqrt (/ (- (+ f n)) (- f n))))
92.0ms
(/ (- (+ f n)) (- f n))
116.0ms
(/ (- (+ f n)) (- f n))

simplify2.3s

Counts
614 → 614
Iterations

Useful iterations: done (2.2s)

IterNodesCost
040213749
17379524
236389270
done50009211

prune1.5s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes96.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1128
2138
done138

end0.0ms

sample728.0ms

Algorithm
intervals
Results
432.0ms8000×body80valid