Average Error: 18.4 → 1.4
Time: 3.3s
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 r28776 = t1;
        double r28777 = -r28776;
        double r28778 = v;
        double r28779 = r28777 * r28778;
        double r28780 = u;
        double r28781 = r28776 + r28780;
        double r28782 = r28781 * r28781;
        double r28783 = r28779 / r28782;
        return r28783;
}
↓
double f(double u, double v, double t1) {
        double r28784 = t1;
        double r28785 = -r28784;
        double r28786 = u;
        double r28787 = r28784 + r28786;
        double r28788 = r28785 / r28787;
        double r28789 = v;
        double r28790 = r28789 / r28787;
        double r28791 = r28788 * r28790;
        return r28791;
}

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. Final simplification1.4

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))