Average Error: 18.5 → 1.4
Time: 16.5s
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 r19159 = t1;
        double r19160 = -r19159;
        double r19161 = v;
        double r19162 = r19160 * r19161;
        double r19163 = u;
        double r19164 = r19159 + r19163;
        double r19165 = r19164 * r19164;
        double r19166 = r19162 / r19165;
        return r19166;
}
↓
double f(double u, double v, double t1) {
        double r19167 = t1;
        double r19168 = -r19167;
        double r19169 = u;
        double r19170 = r19167 + r19169;
        double r19171 = r19168 / r19170;
        double r19172 = v;
        double r19173 = r19172 / r19170;
        double r19174 = r19171 * r19173;
        return r19174;
}

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 18.5

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

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))