Average Error: 18.5 → 1.0
Time: 33.0s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{-\sqrt[3]{t1} \cdot \sqrt[3]{t1}}{\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}} \cdot \left(\frac{\sqrt[3]{t1}}{\sqrt[3]{t1 + u}} \cdot v\right)}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\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 v\right)}{t1 + u}
double f(double u, double v, double t1) {
        double r23685 = t1;
        double r23686 = -r23685;
        double r23687 = v;
        double r23688 = r23686 * r23687;
        double r23689 = u;
        double r23690 = r23685 + r23689;
        double r23691 = r23690 * r23690;
        double r23692 = r23688 / r23691;
        return r23692;
}
↓
double f(double u, double v, double t1) {
        double r23693 = t1;
        double r23694 = cbrt(r23693);
        double r23695 = r23694 * r23694;
        double r23696 = -r23695;
        double r23697 = u;
        double r23698 = r23693 + r23697;
        double r23699 = cbrt(r23698);
        double r23700 = r23699 * r23699;
        double r23701 = r23696 / r23700;
        double r23702 = r23694 / r23699;
        double r23703 = v;
        double r23704 = r23702 * r23703;
        double r23705 = r23701 * r23704;
        double r23706 = r23705 / r23698;
        return r23706;
}

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 18.5

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 associate-*r/1.3

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

  7. Applied add-cube-cbrt2.0

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

  8. Applied add-cube-cbrt1.6

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

  9. Applied distribute-lft-neg-in1.6

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

  10. Applied times-frac1.6

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

  11. Applied associate-*l*1.0

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

  12. Final simplification1.0

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))