Average Error: 18.5 → 1.4
Time: 47.2s
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 r2547642 = t1;
        double r2547643 = -r2547642;
        double r2547644 = v;
        double r2547645 = r2547643 * r2547644;
        double r2547646 = u;
        double r2547647 = r2547642 + r2547646;
        double r2547648 = r2547647 * r2547647;
        double r2547649 = r2547645 / r2547648;
        return r2547649;
}
↓
double f(double u, double v, double t1) {
        double r2547650 = v;
        double r2547651 = t1;
        double r2547652 = u;
        double r2547653 = r2547651 + r2547652;
        double r2547654 = r2547650 / r2547653;
        double r2547655 = -r2547651;
        double r2547656 = r2547655 / r2547653;
        double r2547657 = r2547654 * r2547656;
        return r2547657;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.5

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

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

Reproduce

herbie shell --seed 2019104 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))