Average Error: 17.7 → 1.2
Time: 15.9s
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 r19961 = t1;
        double r19962 = -r19961;
        double r19963 = v;
        double r19964 = r19962 * r19963;
        double r19965 = u;
        double r19966 = r19961 + r19965;
        double r19967 = r19966 * r19966;
        double r19968 = r19964 / r19967;
        return r19968;
}
↓
double f(double u, double v, double t1) {
        double r19969 = t1;
        double r19970 = -r19969;
        double r19971 = u;
        double r19972 = r19969 + r19971;
        double r19973 = r19970 / r19972;
        double r19974 = v;
        double r19975 = r19974 / r19972;
        double r19976 = r19973 * r19975;
        return r19976;
}

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))))