Average Error: 18.4 → 1.4
Time: 6.1s
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 r21875 = t1;
        double r21876 = -r21875;
        double r21877 = v;
        double r21878 = r21876 * r21877;
        double r21879 = u;
        double r21880 = r21875 + r21879;
        double r21881 = r21880 * r21880;
        double r21882 = r21878 / r21881;
        return r21882;
}
↓
double f(double u, double v, double t1) {
        double r21883 = t1;
        double r21884 = -r21883;
        double r21885 = u;
        double r21886 = r21883 + r21885;
        double r21887 = r21884 / r21886;
        double r21888 = v;
        double r21889 = r21888 / r21886;
        double r21890 = r21887 * r21889;
        return r21890;
}

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. Using strategy rm

  5. Applied add-cube-cbrt2.1

    \[\leadsto \frac{-t1}{t1 + u} \cdot \frac{v}{\color{blue}{\left(\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}\right) \cdot \sqrt[3]{t1 + u}}}\]

  6. Applied add-cube-cbrt2.3

    \[\leadsto \frac{-t1}{t1 + u} \cdot \frac{\color{blue}{\left(\sqrt[3]{v} \cdot \sqrt[3]{v}\right) \cdot \sqrt[3]{v}}}{\left(\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}\right) \cdot \sqrt[3]{t1 + u}}\]

  7. Applied times-frac2.3

    \[\leadsto \frac{-t1}{t1 + u} \cdot \color{blue}{\left(\frac{\sqrt[3]{v} \cdot \sqrt[3]{v}}{\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}} \cdot \frac{\sqrt[3]{v}}{\sqrt[3]{t1 + u}}\right)}\]

  8. Applied associate-*r*1.6

    \[\leadsto \color{blue}{\left(\frac{-t1}{t1 + u} \cdot \frac{\sqrt[3]{v} \cdot \sqrt[3]{v}}{\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}}\right) \cdot \frac{\sqrt[3]{v}}{\sqrt[3]{t1 + u}}}\]

  9. Final simplification1.4

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

Reproduce

herbie shell --seed 2019308 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))