Average Error: 17.9 → 1.3
Time: 2.9s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \left(v \cdot \frac{1}{t1 + u}\right)\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-t1}{t1 + u} \cdot \left(v \cdot \frac{1}{t1 + u}\right)
double f(double u, double v, double t1) {
        double r20876 = t1;
        double r20877 = -r20876;
        double r20878 = v;
        double r20879 = r20877 * r20878;
        double r20880 = u;
        double r20881 = r20876 + r20880;
        double r20882 = r20881 * r20881;
        double r20883 = r20879 / r20882;
        return r20883;
}
↓
double f(double u, double v, double t1) {
        double r20884 = t1;
        double r20885 = -r20884;
        double r20886 = u;
        double r20887 = r20884 + r20886;
        double r20888 = r20885 / r20887;
        double r20889 = v;
        double r20890 = 1.0;
        double r20891 = r20890 / r20887;
        double r20892 = r20889 * r20891;
        double r20893 = r20888 * r20892;
        return r20893;
}

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 17.9

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

  3. Applied times-frac1.2

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

  5. Applied div-inv1.3

    \[\leadsto \frac{-t1}{t1 + u} \cdot \color{blue}{\left(v \cdot \frac{1}{t1 + u}\right)}\]

  6. Final simplification1.3

    \[\leadsto \frac{-t1}{t1 + u} \cdot \left(v \cdot \frac{1}{t1 + u}\right)\]

Reproduce

herbie shell --seed 2019354 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))