Average Error: 18.1 → 1.1
Time: 52.7s
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 r2758636 = t1;
        double r2758637 = -r2758636;
        double r2758638 = v;
        double r2758639 = r2758637 * r2758638;
        double r2758640 = u;
        double r2758641 = r2758636 + r2758640;
        double r2758642 = r2758641 * r2758641;
        double r2758643 = r2758639 / r2758642;
        return r2758643;
}
↓
double f(double u, double v, double t1) {
        double r2758644 = t1;
        double r2758645 = cbrt(r2758644);
        double r2758646 = -r2758645;
        double r2758647 = r2758646 * r2758645;
        double r2758648 = u;
        double r2758649 = r2758648 + r2758644;
        double r2758650 = cbrt(r2758649);
        double r2758651 = r2758650 * r2758650;
        double r2758652 = r2758647 / r2758651;
        double r2758653 = r2758645 / r2758650;
        double r2758654 = v;
        double r2758655 = r2758654 / r2758649;
        double r2758656 = r2758653 * r2758655;
        double r2758657 = r2758652 * r2758656;
        return r2758657;
}

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 18.1

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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*1.1

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

  10. Final simplification1.1

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

Reproduce

herbie shell --seed 2019107 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))