Average Error: 0.0 → 0.0
Time: 11.7s
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 r22570 = f;
        double r22571 = n;
        double r22572 = r22570 + r22571;
        double r22573 = -r22572;
        double r22574 = r22570 - r22571;
        double r22575 = r22573 / r22574;
        return r22575;
}
↓
double f(double f, double n) {
        double r22576 = f;
        double r22577 = n;
        double r22578 = r22576 + r22577;
        double r22579 = -r22578;
        double r22580 = r22576 - r22577;
        double r22581 = r22579 / r22580;
        double r22582 = exp(r22581);
        double r22583 = log(r22582);
        return r22583;
}

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 2020042 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))