Average Error: 18.3 → 1.2
Time: 39.1s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\sqrt[3]{t1} \cdot \sqrt[3]{t1}}{\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}} \cdot \left(\left(-\frac{v}{t1 + u}\right) \cdot \frac{\sqrt[3]{t1}}{\sqrt[3]{t1 + u}}\right)\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\sqrt[3]{t1} \cdot \sqrt[3]{t1}}{\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}} \cdot \left(\left(-\frac{v}{t1 + u}\right) \cdot \frac{\sqrt[3]{t1}}{\sqrt[3]{t1 + u}}\right)
double f(double u, double v, double t1) {
        double r1356319 = t1;
        double r1356320 = -r1356319;
        double r1356321 = v;
        double r1356322 = r1356320 * r1356321;
        double r1356323 = u;
        double r1356324 = r1356319 + r1356323;
        double r1356325 = r1356324 * r1356324;
        double r1356326 = r1356322 / r1356325;
        return r1356326;
}
↓
double f(double u, double v, double t1) {
        double r1356327 = t1;
        double r1356328 = cbrt(r1356327);
        double r1356329 = r1356328 * r1356328;
        double r1356330 = u;
        double r1356331 = r1356327 + r1356330;
        double r1356332 = cbrt(r1356331);
        double r1356333 = r1356332 * r1356332;
        double r1356334 = r1356329 / r1356333;
        double r1356335 = v;
        double r1356336 = r1356335 / r1356331;
        double r1356337 = -r1356336;
        double r1356338 = r1356328 / r1356332;
        double r1356339 = r1356337 * r1356338;
        double r1356340 = r1356334 * r1356339;
        return r1356340;
}

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-frac1.4

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  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-cbrt1.7

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

  7. Applied distribute-lft-neg-in1.7

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

  8. Applied times-frac1.7

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

  9. Applied associate-*l*1.2

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

  10. Final simplification1.2

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

Reproduce

herbie shell --seed 2019143 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))