Average Error: 18.2 → 1.2
Time: 45.7s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}
double f(double u, double v, double t1) {
        double r1408747 = t1;
        double r1408748 = -r1408747;
        double r1408749 = v;
        double r1408750 = r1408748 * r1408749;
        double r1408751 = u;
        double r1408752 = r1408747 + r1408751;
        double r1408753 = r1408752 * r1408752;
        double r1408754 = r1408750 / r1408753;
        return r1408754;
}
↓
double f(double u, double v, double t1) {
        double r1408755 = v;
        double r1408756 = t1;
        double r1408757 = u;
        double r1408758 = r1408756 + r1408757;
        double r1408759 = r1408755 / r1408758;
        double r1408760 = -r1408756;
        double r1408761 = r1408760 / r1408758;
        double r1408762 = r1408759 * r1408761;
        return r1408762;
}

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. Final simplification1.2

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

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))