Average Error: 18.4 → 1.1
Time: 19.1s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\frac{v}{t1 + u} \cdot \frac{\sqrt[3]{-t1}}{\sqrt[3]{t1 + u}}\right) \cdot \frac{\sqrt[3]{-t1} \cdot \sqrt[3]{-t1}}{\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\left(\frac{v}{t1 + u} \cdot \frac{\sqrt[3]{-t1}}{\sqrt[3]{t1 + u}}\right) \cdot \frac{\sqrt[3]{-t1} \cdot \sqrt[3]{-t1}}{\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}}
double f(double u, double v, double t1) {
        double r1330745 = t1;
        double r1330746 = -r1330745;
        double r1330747 = v;
        double r1330748 = r1330746 * r1330747;
        double r1330749 = u;
        double r1330750 = r1330745 + r1330749;
        double r1330751 = r1330750 * r1330750;
        double r1330752 = r1330748 / r1330751;
        return r1330752;
}
↓
double f(double u, double v, double t1) {
        double r1330753 = v;
        double r1330754 = t1;
        double r1330755 = u;
        double r1330756 = r1330754 + r1330755;
        double r1330757 = r1330753 / r1330756;
        double r1330758 = -r1330754;
        double r1330759 = cbrt(r1330758);
        double r1330760 = cbrt(r1330756);
        double r1330761 = r1330759 / r1330760;
        double r1330762 = r1330757 * r1330761;
        double r1330763 = r1330759 * r1330759;
        double r1330764 = r1330760 * r1330760;
        double r1330765 = r1330763 / r1330764;
        double r1330766 = r1330762 * r1330765;
        return r1330766;
}

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-frac1.3

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  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 times-frac1.6

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

  8. Applied associate-*l*1.1

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

  9. Final simplification1.1

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

Reproduce

herbie shell --seed 2019162 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))