Average Error: 17.9 → 1.0
Time: 48.4s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\sqrt[3]{v}}{t1 + u} \cdot \left(\frac{t1}{\frac{t1 + u}{\sqrt[3]{v}}} \cdot \left(-\sqrt[3]{v}\right)\right)\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\sqrt[3]{v}}{t1 + u} \cdot \left(\frac{t1}{\frac{t1 + u}{\sqrt[3]{v}}} \cdot \left(-\sqrt[3]{v}\right)\right)
double f(double u, double v, double t1) {
        double r1299532 = t1;
        double r1299533 = -r1299532;
        double r1299534 = v;
        double r1299535 = r1299533 * r1299534;
        double r1299536 = u;
        double r1299537 = r1299532 + r1299536;
        double r1299538 = r1299537 * r1299537;
        double r1299539 = r1299535 / r1299538;
        return r1299539;
}
↓
double f(double u, double v, double t1) {
        double r1299540 = v;
        double r1299541 = cbrt(r1299540);
        double r1299542 = t1;
        double r1299543 = u;
        double r1299544 = r1299542 + r1299543;
        double r1299545 = r1299541 / r1299544;
        double r1299546 = r1299544 / r1299541;
        double r1299547 = r1299542 / r1299546;
        double r1299548 = -r1299541;
        double r1299549 = r1299547 * r1299548;
        double r1299550 = r1299545 * r1299549;
        return r1299550;
}

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 17.9

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 *-un-lft-identity1.3

    \[\leadsto \frac{-t1}{t1 + u} \cdot \frac{v}{\color{blue}{1 \cdot \left(t1 + u\right)}}\]

  6. Applied add-cube-cbrt2.0

    \[\leadsto \frac{-t1}{t1 + u} \cdot \frac{\color{blue}{\left(\sqrt[3]{v} \cdot \sqrt[3]{v}\right) \cdot \sqrt[3]{v}}}{1 \cdot \left(t1 + u\right)}\]

  7. Applied times-frac2.0

    \[\leadsto \frac{-t1}{t1 + u} \cdot \color{blue}{\left(\frac{\sqrt[3]{v} \cdot \sqrt[3]{v}}{1} \cdot \frac{\sqrt[3]{v}}{t1 + u}\right)}\]

  8. Applied associate-*r*1.4

    \[\leadsto \color{blue}{\left(\frac{-t1}{t1 + u} \cdot \frac{\sqrt[3]{v} \cdot \sqrt[3]{v}}{1}\right) \cdot \frac{\sqrt[3]{v}}{t1 + u}}\]

  9. Simplified1.0

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

  11. Applied *-un-lft-identity1.0

    \[\leadsto \frac{-t1}{\frac{\color{blue}{1 \cdot \left(t1 + u\right)}}{\sqrt[3]{v} \cdot \sqrt[3]{v}}} \cdot \frac{\sqrt[3]{v}}{t1 + u}\]

  12. Applied times-frac1.0

    \[\leadsto \frac{-t1}{\color{blue}{\frac{1}{\sqrt[3]{v}} \cdot \frac{t1 + u}{\sqrt[3]{v}}}} \cdot \frac{\sqrt[3]{v}}{t1 + u}\]

  13. Applied *-un-lft-identity1.0

    \[\leadsto \frac{\color{blue}{1 \cdot \left(-t1\right)}}{\frac{1}{\sqrt[3]{v}} \cdot \frac{t1 + u}{\sqrt[3]{v}}} \cdot \frac{\sqrt[3]{v}}{t1 + u}\]

  14. Applied times-frac1.0

    \[\leadsto \color{blue}{\left(\frac{1}{\frac{1}{\sqrt[3]{v}}} \cdot \frac{-t1}{\frac{t1 + u}{\sqrt[3]{v}}}\right)} \cdot \frac{\sqrt[3]{v}}{t1 + u}\]

  15. Simplified1.0

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

  16. Final simplification1.0

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

Reproduce

herbie shell --seed 2019165 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))