Average Error: 18.4 → 1.4
Time: 3.2s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}
double f(double u, double v, double t1) {
        double r19890 = t1;
        double r19891 = -r19890;
        double r19892 = v;
        double r19893 = r19891 * r19892;
        double r19894 = u;
        double r19895 = r19890 + r19894;
        double r19896 = r19895 * r19895;
        double r19897 = r19893 / r19896;
        return r19897;
}
↓
double f(double u, double v, double t1) {
        double r19898 = t1;
        double r19899 = -r19898;
        double r19900 = v;
        double r19901 = u;
        double r19902 = r19898 + r19901;
        double r19903 = r19900 / r19902;
        double r19904 = r19899 * r19903;
        double r19905 = r19904 / r19902;
        return r19905;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.4

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied times-frac1.4

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  4. Using strategy rm

  5. Applied associate-*r/1.3

    \[\leadsto \color{blue}{\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}}\]

  6. Simplified1.4

    \[\leadsto \frac{\color{blue}{\left(-t1\right) \cdot \frac{v}{t1 + u}}}{t1 + u}\]

  7. Final simplification1.4

    \[\leadsto \frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}\]

Reproduce

herbie shell --seed 2019353 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))