Average Error: 18.5 → 1.3
Time: 4.6s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}
double f(double u, double v, double t1) {
        double r34899 = t1;
        double r34900 = -r34899;
        double r34901 = v;
        double r34902 = r34900 * r34901;
        double r34903 = u;
        double r34904 = r34899 + r34903;
        double r34905 = r34904 * r34904;
        double r34906 = r34902 / r34905;
        return r34906;
}
↓
double f(double u, double v, double t1) {
        double r34907 = t1;
        double r34908 = -r34907;
        double r34909 = u;
        double r34910 = r34907 + r34909;
        double r34911 = r34908 / r34910;
        double r34912 = v;
        double r34913 = r34912 / r34910;
        double r34914 = r34911 * r34913;
        return r34914;
}

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 18.5

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

  3. Applied times-frac1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))