Average Error: 18.8 → 1.3
Time: 1.3m
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}
double f(double u, double v, double t1) {
        double r4362864 = t1;
        double r4362865 = -r4362864;
        double r4362866 = v;
        double r4362867 = r4362865 * r4362866;
        double r4362868 = u;
        double r4362869 = r4362864 + r4362868;
        double r4362870 = r4362869 * r4362869;
        double r4362871 = r4362867 / r4362870;
        return r4362871;
}
↓
double f(double u, double v, double t1) {
        double r4362872 = v;
        double r4362873 = u;
        double r4362874 = t1;
        double r4362875 = r4362873 + r4362874;
        double r4362876 = r4362872 / r4362875;
        double r4362877 = -r4362874;
        double r4362878 = r4362876 * r4362877;
        double r4362879 = r4362878 / r4362875;
        return r4362879;
}

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 18.8

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 associate-*l/1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019128 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))