Average Error: 17.9 → 1.1
Time: 15.3s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\sqrt[3]{t1} \cdot \sqrt[3]{t1}}{\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}} \cdot \left(\left(-\frac{v}{t1 + u}\right) \cdot \frac{\sqrt[3]{t1}}{\sqrt[3]{t1 + u}}\right)\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\sqrt[3]{t1} \cdot \sqrt[3]{t1}}{\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}} \cdot \left(\left(-\frac{v}{t1 + u}\right) \cdot \frac{\sqrt[3]{t1}}{\sqrt[3]{t1 + u}}\right)
double f(double u, double v, double t1) {
        double r1120736 = t1;
        double r1120737 = -r1120736;
        double r1120738 = v;
        double r1120739 = r1120737 * r1120738;
        double r1120740 = u;
        double r1120741 = r1120736 + r1120740;
        double r1120742 = r1120741 * r1120741;
        double r1120743 = r1120739 / r1120742;
        return r1120743;
}
↓
double f(double u, double v, double t1) {
        double r1120744 = t1;
        double r1120745 = cbrt(r1120744);
        double r1120746 = r1120745 * r1120745;
        double r1120747 = u;
        double r1120748 = r1120744 + r1120747;
        double r1120749 = cbrt(r1120748);
        double r1120750 = r1120749 * r1120749;
        double r1120751 = r1120746 / r1120750;
        double r1120752 = v;
        double r1120753 = r1120752 / r1120748;
        double r1120754 = -r1120753;
        double r1120755 = r1120745 / r1120749;
        double r1120756 = r1120754 * r1120755;
        double r1120757 = r1120751 * r1120756;
        return r1120757;
}

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-frac1.4

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

  5. Applied add-cube-cbrt2.1

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

  6. Applied add-cube-cbrt1.7

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

  7. Applied distribute-lft-neg-in1.7

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

  8. Applied times-frac1.7

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

  9. Applied associate-*l*1.1

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

  10. Final simplification1.1

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

Reproduce

herbie shell --seed 2019192 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))