Average Error: 0.0 → 0.0
Time: 6.9s
Precision: binary64
Cost: 832
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{1}{\frac{n}{n + f} - \frac{f}{n + f}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{1}{\frac{n}{n + f} - \frac{f}{n + f}}
(FPCore (f n) :precision binary64 (/ (- (+ f n)) (- f n)))
↓
(FPCore (f n) :precision binary64 (/ 1.0 (- (/ n (+ n f)) (/ f (+ n f)))))
double code(double f, double n) {
	return -(f + n) / (f - n);
}
↓
double code(double f, double n) {
	return 1.0 / ((n / (n + f)) - (f / (n + f)));
}

Error

Bits error versus f

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error48.2
Cost26560
\[\frac{\sqrt{f + n}}{\sqrt{n - f}} \cdot \frac{\sqrt{f + n}}{\sqrt{n - f}}\]
Alternative 2
Error0.1
Cost20800
\[\frac{1}{\sqrt[3]{\frac{n - f}{f + n}} \cdot \left(\sqrt[3]{\frac{n - f}{f + n}} \cdot \sqrt[3]{\frac{n - f}{f + n}}\right)}\]
Alternative 3
Error1.3
Cost20160
\[\left(\sqrt[3]{f + n} \cdot \sqrt[3]{f + n}\right) \cdot \frac{\sqrt[3]{f + n}}{n - f}\]
Alternative 4
Error31.9
Cost13760
\[\sqrt{\frac{f + n}{n - f}} \cdot \sqrt{\frac{f + n}{n - f}}\]
Alternative 5
Error32.6
Cost13632
\[\frac{f + n}{\sqrt{n - f}} \cdot \frac{1}{\sqrt{n - f}}\]
Alternative 6
Error32.6
Cost13632
\[\frac{1}{\sqrt{n - f} \cdot \frac{\sqrt{n - f}}{f + n}}\]
Alternative 7
Error32.6
Cost13504
\[\frac{\frac{f + n}{\sqrt{n - f}}}{\sqrt{n - f}}\]
Alternative 8
Error32.4
Cost13504
\[\sqrt{f + n} \cdot \frac{\sqrt{f + n}}{n - f}\]
Alternative 9
Error0.0
Cost13312
\[\sqrt[3]{{\left(\frac{f + n}{n - f}\right)}^{3}}\]
Alternative 10
Error31.9
Cost832
\[1 + \frac{f}{n} \cdot \left(2 + \frac{f}{n} \cdot 2\right)\]
Alternative 11
Error0.0
Cost832
\[\frac{1}{\frac{n}{f + n} - \frac{f}{f + n}}\]
Alternative 12
Error0.2
Cost704
\[\frac{1}{\left(n - f\right) \cdot \frac{1}{f + n}}\]
Alternative 13
Error0.2
Cost576
\[\left(f + n\right) \cdot \frac{1}{n - f}\]
Alternative 14
Error0.0
Cost576
\[\frac{1}{\frac{n - f}{f + n}}\]
Alternative 15
Error0.0
Cost512
\[\frac{-\left(f + n\right)}{f - n}\]
Alternative 16
Error31.7
Cost448
\[-1 - 2 \cdot \frac{n}{f}\]
Alternative 17
Error0.0
Cost448
\[\frac{f + n}{n - f}\]
Alternative 18
Error31.4
Cost448
\[1 + \frac{f}{n} \cdot 2\]
Alternative 19
Error32.4
Cost64
\[-1\]
Alternative 20
Error32.1
Cost64
\[1\]
Alternative 21
Error62.0
Cost64
\[0\]

Error

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{f + n}{n - f}}\]
  3. Using strategy rm

  4. Applied clear-num_binary640.0

    \[\leadsto \color{blue}{\frac{1}{\frac{n - f}{f + n}}}\]
  5. Using strategy rm

  6. Applied div-sub_binary640.0

    \[\leadsto \frac{1}{\color{blue}{\frac{n}{f + n} - \frac{f}{f + n}}}\]

  7. Simplified0.0

    \[\leadsto \frac{1}{\color{blue}{\frac{n}{n + f}} - \frac{f}{f + n}}\]

  8. Simplified0.0

    \[\leadsto \frac{1}{\frac{n}{n + f} - \color{blue}{\frac{f}{n + f}}}\]

  9. Simplified0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{n}{f + n} - \frac{f}{f + n}}}\]

  10. Final simplification0.0

    \[\leadsto \frac{1}{\frac{n}{n + f} - \frac{f}{n + f}}\]

Reproduce

herbie shell --seed 2021042 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))