Average Error: 18.6 → 1.3
Time: 8.6s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}
double f(double u, double v, double t1) {
        double r23937 = t1;
        double r23938 = -r23937;
        double r23939 = v;
        double r23940 = r23938 * r23939;
        double r23941 = u;
        double r23942 = r23937 + r23941;
        double r23943 = r23942 * r23942;
        double r23944 = r23940 / r23943;
        return r23944;
}
↓
double f(double u, double v, double t1) {
        double r23945 = t1;
        double r23946 = -r23945;
        double r23947 = u;
        double r23948 = r23945 + r23947;
        double r23949 = r23946 / r23948;
        double r23950 = v;
        double r23951 = r23949 * r23950;
        double r23952 = r23951 / r23948;
        return r23952;
}

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 18.6

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

  3. Applied times-frac1.4

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  4. Using strategy rm

  5. Applied associate-*r/1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2020042 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))