Average Error: 18.4 → 1.3
Time: 26.8s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\sqrt[3]{t1}}{\sqrt[3]{t1 + u}} \cdot \left(\frac{-\sqrt[3]{t1}}{\sqrt[3]{t1 + u}} \cdot \left(\frac{v}{t1 + u} \cdot \frac{\sqrt[3]{t1}}{\sqrt[3]{t1 + u}}\right)\right)\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\sqrt[3]{t1}}{\sqrt[3]{t1 + u}} \cdot \left(\frac{-\sqrt[3]{t1}}{\sqrt[3]{t1 + u}} \cdot \left(\frac{v}{t1 + u} \cdot \frac{\sqrt[3]{t1}}{\sqrt[3]{t1 + u}}\right)\right)
double f(double u, double v, double t1) {
        double r29664 = t1;
        double r29665 = -r29664;
        double r29666 = v;
        double r29667 = r29665 * r29666;
        double r29668 = u;
        double r29669 = r29664 + r29668;
        double r29670 = r29669 * r29669;
        double r29671 = r29667 / r29670;
        return r29671;
}
↓
double f(double u, double v, double t1) {
        double r29672 = t1;
        double r29673 = cbrt(r29672);
        double r29674 = u;
        double r29675 = r29672 + r29674;
        double r29676 = cbrt(r29675);
        double r29677 = r29673 / r29676;
        double r29678 = -r29673;
        double r29679 = r29678 / r29676;
        double r29680 = v;
        double r29681 = r29680 / r29675;
        double r29682 = r29681 * r29677;
        double r29683 = r29679 * r29682;
        double r29684 = r29677 * r29683;
        return r29684;
}

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. Simplified1.5

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

  4. Applied add-cube-cbrt2.3

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

  5. Applied add-cube-cbrt1.9

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

  6. Applied times-frac1.9

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

  7. Applied associate-*r*1.3

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

  8. Simplified1.3

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

  9. Final simplification1.3

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

Reproduce

herbie shell --seed 2019195 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))