Average Error: 18.2 → 1.4
Time: 3.7s
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 r29786 = t1;
        double r29787 = -r29786;
        double r29788 = v;
        double r29789 = r29787 * r29788;
        double r29790 = u;
        double r29791 = r29786 + r29790;
        double r29792 = r29791 * r29791;
        double r29793 = r29789 / r29792;
        return r29793;
}
↓
double f(double u, double v, double t1) {
        double r29794 = t1;
        double r29795 = -r29794;
        double r29796 = u;
        double r29797 = r29794 + r29796;
        double r29798 = r29795 / r29797;
        double r29799 = v;
        double r29800 = r29799 / r29797;
        double r29801 = r29798 * r29800;
        return r29801;
}

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-frac1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))