Average Error: 18.3 → 1.6
Time: 26.7s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{v \cdot \left(\frac{\sqrt[3]{t1}}{\sqrt[3]{u + t1}} \cdot \frac{\left(-\sqrt[3]{t1}\right) \cdot \sqrt[3]{t1}}{\sqrt[3]{u + t1} \cdot \sqrt[3]{u + t1}}\right)}{u + t1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{v \cdot \left(\frac{\sqrt[3]{t1}}{\sqrt[3]{u + t1}} \cdot \frac{\left(-\sqrt[3]{t1}\right) \cdot \sqrt[3]{t1}}{\sqrt[3]{u + t1} \cdot \sqrt[3]{u + t1}}\right)}{u + t1}
double f(double u, double v, double t1) {
        double r1335153 = t1;
        double r1335154 = -r1335153;
        double r1335155 = v;
        double r1335156 = r1335154 * r1335155;
        double r1335157 = u;
        double r1335158 = r1335153 + r1335157;
        double r1335159 = r1335158 * r1335158;
        double r1335160 = r1335156 / r1335159;
        return r1335160;
}
↓
double f(double u, double v, double t1) {
        double r1335161 = v;
        double r1335162 = t1;
        double r1335163 = cbrt(r1335162);
        double r1335164 = u;
        double r1335165 = r1335164 + r1335162;
        double r1335166 = cbrt(r1335165);
        double r1335167 = r1335163 / r1335166;
        double r1335168 = -r1335163;
        double r1335169 = r1335168 * r1335163;
        double r1335170 = r1335166 * r1335166;
        double r1335171 = r1335169 / r1335170;
        double r1335172 = r1335167 * r1335171;
        double r1335173 = r1335161 * r1335172;
        double r1335174 = r1335173 / r1335165;
        return r1335174;
}

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 18.3

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied times-frac1.1

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

  5. Applied associate-*r/1.2

    \[\leadsto \color{blue}{\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}}\]
  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-cbrt1.5

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

  9. Applied distribute-lft-neg-in1.5

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

  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. Final simplification1.6

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

Reproduce

herbie shell --seed 2019200 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))