Average Error: 18.5 → 1.3
Time: 3.5s
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 r24879 = t1;
        double r24880 = -r24879;
        double r24881 = v;
        double r24882 = r24880 * r24881;
        double r24883 = u;
        double r24884 = r24879 + r24883;
        double r24885 = r24884 * r24884;
        double r24886 = r24882 / r24885;
        return r24886;
}
↓
double f(double u, double v, double t1) {
        double r24887 = t1;
        double r24888 = -r24887;
        double r24889 = u;
        double r24890 = r24887 + r24889;
        double r24891 = r24888 / r24890;
        double r24892 = v;
        double r24893 = r24892 / r24890;
        double r24894 = r24891 * r24893;
        return r24894;
}

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-frac1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020039 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))