Average Error: 18.2 → 1.0
Time: 32.4s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\left(-\sqrt[3]{t1}\right) \cdot \sqrt[3]{t1}}{\sqrt[3]{u + t1} \cdot \sqrt[3]{u + t1}} \cdot \left(\frac{\sqrt[3]{t1}}{\sqrt[3]{u + t1}} \cdot \frac{v}{u + t1}\right)\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\left(-\sqrt[3]{t1}\right) \cdot \sqrt[3]{t1}}{\sqrt[3]{u + t1} \cdot \sqrt[3]{u + t1}} \cdot \left(\frac{\sqrt[3]{t1}}{\sqrt[3]{u + t1}} \cdot \frac{v}{u + t1}\right)
double f(double u, double v, double t1) {
        double r1572779 = t1;
        double r1572780 = -r1572779;
        double r1572781 = v;
        double r1572782 = r1572780 * r1572781;
        double r1572783 = u;
        double r1572784 = r1572779 + r1572783;
        double r1572785 = r1572784 * r1572784;
        double r1572786 = r1572782 / r1572785;
        return r1572786;
}
↓
double f(double u, double v, double t1) {
        double r1572787 = t1;
        double r1572788 = cbrt(r1572787);
        double r1572789 = -r1572788;
        double r1572790 = r1572789 * r1572788;
        double r1572791 = u;
        double r1572792 = r1572791 + r1572787;
        double r1572793 = cbrt(r1572792);
        double r1572794 = r1572793 * r1572793;
        double r1572795 = r1572790 / r1572794;
        double r1572796 = r1572788 / r1572793;
        double r1572797 = v;
        double r1572798 = r1572797 / r1572792;
        double r1572799 = r1572796 * r1572798;
        double r1572800 = r1572795 * r1572799;
        return r1572800;
}

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 18.2

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

  3. Applied times-frac1.3

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

  5. Applied add-cube-cbrt2.1

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

  6. Applied add-cube-cbrt1.6

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

  7. Applied distribute-rgt-neg-in1.6

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

  8. Applied times-frac1.6

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

  9. Applied associate-*l*1.0

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

  10. Final simplification1.0

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

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))