Average Error: 0.0 → 0.0
Time: 8.0s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)
double f(double f, double n) {
        double r40004 = f;
        double r40005 = n;
        double r40006 = r40004 + r40005;
        double r40007 = -r40006;
        double r40008 = r40004 - r40005;
        double r40009 = r40007 / r40008;
        return r40009;
}
↓
double f(double f, double n) {
        double r40010 = f;
        double r40011 = n;
        double r40012 = r40010 + r40011;
        double r40013 = -r40012;
        double r40014 = r40010 - r40011;
        double r40015 = r40013 / r40014;
        double r40016 = exp(r40015);
        double r40017 = log(r40016);
        return r40017;
}

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. Using strategy rm

  3. Applied add-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)}\]

  4. Final simplification0.0

    \[\leadsto \log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)\]

Reproduce

herbie shell --seed 2020033 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))