Average Error: 18.2 → 1.3
Time: 10.7s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\left(-t1\right) \cdot \frac{1}{t1 + u}\right) \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\left(\left(-t1\right) \cdot \frac{1}{t1 + u}\right) \cdot \frac{v}{t1 + u}
double f(double u, double v, double t1) {
        double r29896 = t1;
        double r29897 = -r29896;
        double r29898 = v;
        double r29899 = r29897 * r29898;
        double r29900 = u;
        double r29901 = r29896 + r29900;
        double r29902 = r29901 * r29901;
        double r29903 = r29899 / r29902;
        return r29903;
}
↓
double f(double u, double v, double t1) {
        double r29904 = t1;
        double r29905 = -r29904;
        double r29906 = 1.0;
        double r29907 = u;
        double r29908 = r29904 + r29907;
        double r29909 = r29906 / r29908;
        double r29910 = r29905 * r29909;
        double r29911 = v;
        double r29912 = r29911 / r29908;
        double r29913 = r29910 * r29912;
        return r29913;
}

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 18.2

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

  3. Applied times-frac1.2

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

  5. Applied div-inv1.3

    \[\leadsto \color{blue}{\left(\left(-t1\right) \cdot \frac{1}{t1 + u}\right)} \cdot \frac{v}{t1 + u}\]

  6. Final simplification1.3

    \[\leadsto \left(\left(-t1\right) \cdot \frac{1}{t1 + u}\right) \cdot \frac{v}{t1 + u}\]

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))