Average Error: 18.5 → 1.6
Time: 24.3s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\left(\left(\frac{\sqrt[3]{-t1}}{\sqrt[3]{t1 + u}} \cdot \frac{\sqrt[3]{-t1}}{\sqrt[3]{t1 + u}}\right) \cdot \sqrt[3]{-t1}\right) \cdot \frac{v}{t1 + u}}{\sqrt[3]{t1 + u}}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\left(\left(\frac{\sqrt[3]{-t1}}{\sqrt[3]{t1 + u}} \cdot \frac{\sqrt[3]{-t1}}{\sqrt[3]{t1 + u}}\right) \cdot \sqrt[3]{-t1}\right) \cdot \frac{v}{t1 + u}}{\sqrt[3]{t1 + u}}
double f(double u, double v, double t1) {
        double r3169625 = t1;
        double r3169626 = -r3169625;
        double r3169627 = v;
        double r3169628 = r3169626 * r3169627;
        double r3169629 = u;
        double r3169630 = r3169625 + r3169629;
        double r3169631 = r3169630 * r3169630;
        double r3169632 = r3169628 / r3169631;
        return r3169632;
}
↓
double f(double u, double v, double t1) {
        double r3169633 = t1;
        double r3169634 = -r3169633;
        double r3169635 = cbrt(r3169634);
        double r3169636 = u;
        double r3169637 = r3169633 + r3169636;
        double r3169638 = cbrt(r3169637);
        double r3169639 = r3169635 / r3169638;
        double r3169640 = r3169639 * r3169639;
        double r3169641 = r3169640 * r3169635;
        double r3169642 = v;
        double r3169643 = r3169642 / r3169637;
        double r3169644 = r3169641 * r3169643;
        double r3169645 = r3169644 / r3169638;
        return r3169645;
}

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-frac1.5

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

  5. Applied add-cube-cbrt2.2

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

  6. Applied add-cube-cbrt1.8

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

  7. Applied times-frac1.8

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

  8. Simplified1.8

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

  10. Applied associate-*r/1.8

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

  11. Applied associate-*l/1.6

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

  12. Final simplification1.6

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

Reproduce

herbie shell --seed 2019173 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))