Average Error: 17.3 → 1.2
Time: 19.8s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\sqrt[3]{t1}}{\sqrt[3]{u + t1}} \cdot \frac{\left(\left(-\sqrt[3]{t1}\right) \cdot \sqrt[3]{t1}\right) \cdot \frac{v}{u + t1}}{\sqrt[3]{u + t1} \cdot \sqrt[3]{u + t1}}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\sqrt[3]{t1}}{\sqrt[3]{u + t1}} \cdot \frac{\left(\left(-\sqrt[3]{t1}\right) \cdot \sqrt[3]{t1}\right) \cdot \frac{v}{u + t1}}{\sqrt[3]{u + t1} \cdot \sqrt[3]{u + t1}}
double f(double u, double v, double t1) {
        double r34904 = t1;
        double r34905 = -r34904;
        double r34906 = v;
        double r34907 = r34905 * r34906;
        double r34908 = u;
        double r34909 = r34904 + r34908;
        double r34910 = r34909 * r34909;
        double r34911 = r34907 / r34910;
        return r34911;
}
↓
double f(double u, double v, double t1) {
        double r34912 = t1;
        double r34913 = cbrt(r34912);
        double r34914 = u;
        double r34915 = r34914 + r34912;
        double r34916 = cbrt(r34915);
        double r34917 = r34913 / r34916;
        double r34918 = -r34913;
        double r34919 = r34918 * r34913;
        double r34920 = v;
        double r34921 = r34920 / r34915;
        double r34922 = r34919 * r34921;
        double r34923 = r34916 * r34916;
        double r34924 = r34922 / r34923;
        double r34925 = r34917 * r34924;
        return r34925;
}

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 17.3

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

  2. Simplified1.4

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

  4. Applied add-cube-cbrt2.1

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

  5. Applied add-cube-cbrt1.7

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

  6. Applied times-frac1.7

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

  7. Applied associate-*r*1.1

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

  8. Simplified1.2

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

  9. Final simplification1.2

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

Reproduce

herbie shell --seed 2019194 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))