Average Error: 17.7 → 1.2
Time: 17.0s
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 r19926 = t1;
        double r19927 = -r19926;
        double r19928 = v;
        double r19929 = r19927 * r19928;
        double r19930 = u;
        double r19931 = r19926 + r19930;
        double r19932 = r19931 * r19931;
        double r19933 = r19929 / r19932;
        return r19933;
}
↓
double f(double u, double v, double t1) {
        double r19934 = t1;
        double r19935 = -r19934;
        double r19936 = u;
        double r19937 = r19934 + r19936;
        double r19938 = r19935 / r19937;
        double r19939 = v;
        double r19940 = r19939 / r19937;
        double r19941 = r19938 * r19940;
        return r19941;
}

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 17.7

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

  3. Applied times-frac1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019325 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))