Average Error: 18.2 → 1.0
Time: 47.6s
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 r2208144 = t1;
        double r2208145 = -r2208144;
        double r2208146 = v;
        double r2208147 = r2208145 * r2208146;
        double r2208148 = u;
        double r2208149 = r2208144 + r2208148;
        double r2208150 = r2208149 * r2208149;
        double r2208151 = r2208147 / r2208150;
        return r2208151;
}
↓
double f(double u, double v, double t1) {
        double r2208152 = t1;
        double r2208153 = cbrt(r2208152);
        double r2208154 = -r2208153;
        double r2208155 = r2208154 * r2208153;
        double r2208156 = u;
        double r2208157 = r2208156 + r2208152;
        double r2208158 = cbrt(r2208157);
        double r2208159 = r2208158 * r2208158;
        double r2208160 = r2208155 / r2208159;
        double r2208161 = r2208153 / r2208158;
        double r2208162 = v;
        double r2208163 = r2208162 / r2208157;
        double r2208164 = r2208161 * r2208163;
        double r2208165 = r2208160 * r2208164;
        return r2208165;
}

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 18.2

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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*1.0

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

  10. Final simplification1.0

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

Reproduce

herbie shell --seed 2019121 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))