Average Error: 18.2 → 1.4
Time: 3.2s
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 r27125 = t1;
        double r27126 = -r27125;
        double r27127 = v;
        double r27128 = r27126 * r27127;
        double r27129 = u;
        double r27130 = r27125 + r27129;
        double r27131 = r27130 * r27130;
        double r27132 = r27128 / r27131;
        return r27132;
}
↓
double f(double u, double v, double t1) {
        double r27133 = t1;
        double r27134 = -r27133;
        double r27135 = u;
        double r27136 = r27133 + r27135;
        double r27137 = r27134 / r27136;
        double r27138 = v;
        double r27139 = r27138 / r27136;
        double r27140 = r27137 * r27139;
        return r27140;
}

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 2020062 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))