Average Error: 17.8 → 1.4
Time: 14.4s
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 r459221 = t1;
        double r459222 = -r459221;
        double r459223 = v;
        double r459224 = r459222 * r459223;
        double r459225 = u;
        double r459226 = r459221 + r459225;
        double r459227 = r459226 * r459226;
        double r459228 = r459224 / r459227;
        return r459228;
}
↓
double f(double u, double v, double t1) {
        double r459229 = v;
        double r459230 = t1;
        double r459231 = u;
        double r459232 = r459230 + r459231;
        double r459233 = r459229 / r459232;
        double r459234 = -r459230;
        double r459235 = r459234 / r459232;
        double r459236 = r459233 * r459235;
        return r459236;
}

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 17.8

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

  3. Applied times-frac1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))