Average Error: 17.8 → 1.1
Time: 39.4s
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 r2416187 = t1;
        double r2416188 = -r2416187;
        double r2416189 = v;
        double r2416190 = r2416188 * r2416189;
        double r2416191 = u;
        double r2416192 = r2416187 + r2416191;
        double r2416193 = r2416192 * r2416192;
        double r2416194 = r2416190 / r2416193;
        return r2416194;
}
↓
double f(double u, double v, double t1) {
        double r2416195 = v;
        double r2416196 = t1;
        double r2416197 = u;
        double r2416198 = r2416196 + r2416197;
        double r2416199 = r2416195 / r2416198;
        double r2416200 = -r2416196;
        double r2416201 = r2416200 / r2416198;
        double r2416202 = r2416199 * r2416201;
        return r2416202;
}

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 17.8

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied times-frac1.1

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

  4. Final simplification1.1

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

Reproduce

herbie shell --seed 2019124 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))