Average Error: 18.4 → 1.4
Time: 3.3s
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 r21954 = t1;
        double r21955 = -r21954;
        double r21956 = v;
        double r21957 = r21955 * r21956;
        double r21958 = u;
        double r21959 = r21954 + r21958;
        double r21960 = r21959 * r21959;
        double r21961 = r21957 / r21960;
        return r21961;
}
↓
double f(double u, double v, double t1) {
        double r21962 = t1;
        double r21963 = -r21962;
        double r21964 = u;
        double r21965 = r21962 + r21964;
        double r21966 = r21963 / r21965;
        double r21967 = v;
        double r21968 = r21967 / r21965;
        double r21969 = r21966 * r21968;
        return r21969;
}

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 18.4

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 2020002 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))