Average Error: 0.0 → 0.0
Time: 13.3s
Precision: 64
Internal Precision: 128
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[-\frac{n + f}{f - n}\]

Error

Bits error versus f

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]

  2. Final simplification0.0

    \[\leadsto -\frac{n + f}{f - n}\]

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))

Details

Time bar (total: 12.9s)Debug log

sample144.0ms

Algorithm
intervals

simplify257.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

256.0ms
(/ (- (+ f n)) (- f n))

prune49.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 1 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
1 → 63
Calls

1 calls. Slowest were:

10.0ms
(/ (- (+ f n)) (- f n))

series44.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

44.0ms
(/ (- (+ f n)) (- f n))

simplify1.0s

Counts
81 → 66
Calls

81 calls. Slowest were:

226.0ms
(- (- (* f f) (* n n)))
82.0ms
(/ (* (* (- (+ f n)) (- (+ f n))) (- (+ f n))) (* (* (- f n) (- f n)) (- f n)))
56.0ms
(/ (- (* (cbrt (+ f n)) (cbrt (+ f n)))) (* (cbrt (- f n)) (cbrt (- f n))))

prune484.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (- (+ f n))) (cbrt (- (+ f n))))
0.5b
(* (cbrt (- f n)) (cbrt (- f n)))
0.5b
(cbrt (- (+ f n)))
0.5b
(cbrt (- (+ f n)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Counts
4 → 134
Calls

4 calls. Slowest were:

15.0ms
(* (cbrt (- (+ f n))) (cbrt (- (+ f n))))
9.0ms
(* (cbrt (- f n)) (cbrt (- f n)))
1.0ms
(cbrt (- (+ f n)))

series657.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

236.0ms
(* (cbrt (- (+ f n))) (cbrt (- (+ f n))))
175.0ms
(cbrt (- (+ f n)))
146.0ms
(cbrt (- (+ f n)))
100.0ms
(* (cbrt (- f n)) (cbrt (- f n)))

simplify5.3s

Counts
114 → 146
Calls

114 calls. Slowest were:

537.0ms
(* (cbrt (- (+ (pow f 3) (pow n 3)))) (cbrt (- (- (* f f) (* n n)))))
445.0ms
(* (- (+ f n)) (- (+ f n)))
440.0ms
(* (- (+ f n)) (- (+ f n)))

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
2 → 57
Calls

2 calls. Slowest were:

7.0ms
(* (- (+ f n)) (/ 1 (- f n)))
1.0ms
(/ 1 (- f n))

series65.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

39.0ms
(* (- (+ f n)) (/ 1 (- f n)))
26.0ms
(/ 1 (- f n))

simplify1.8s

Counts
38 → 63
Calls

38 calls. Slowest were:

480.0ms
(* (- (- (* f f) (* n n))) 1)
400.0ms
(* (- (+ f n)) (/ 1 (- f n)))
152.0ms
(* (- (- (* f f) (* n n))) (/ 1 (- f n)))

prune503.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes112.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample847.0ms

Algorithm
intervals