Average Error: 18.4 → 1.5
Time: 15.6s
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 r27056 = t1;
        double r27057 = -r27056;
        double r27058 = v;
        double r27059 = r27057 * r27058;
        double r27060 = u;
        double r27061 = r27056 + r27060;
        double r27062 = r27061 * r27061;
        double r27063 = r27059 / r27062;
        return r27063;
}
↓
double f(double u, double v, double t1) {
        double r27064 = t1;
        double r27065 = -r27064;
        double r27066 = u;
        double r27067 = r27064 + r27066;
        double r27068 = r27065 / r27067;
        double r27069 = v;
        double r27070 = r27069 / r27067;
        double r27071 = r27068 * r27070;
        return r27071;
}

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-frac1.5

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

  4. Final simplification1.5

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

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))