Average Error: 18.0 → 1.5
Time: 33.1s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{t1}{\frac{u + t1}{-v}}}{u + t1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{t1}{\frac{u + t1}{-v}}}{u + t1}
double f(double u, double v, double t1) {
        double r1488870 = t1;
        double r1488871 = -r1488870;
        double r1488872 = v;
        double r1488873 = r1488871 * r1488872;
        double r1488874 = u;
        double r1488875 = r1488870 + r1488874;
        double r1488876 = r1488875 * r1488875;
        double r1488877 = r1488873 / r1488876;
        return r1488877;
}
↓
double f(double u, double v, double t1) {
        double r1488878 = t1;
        double r1488879 = u;
        double r1488880 = r1488879 + r1488878;
        double r1488881 = v;
        double r1488882 = -r1488881;
        double r1488883 = r1488880 / r1488882;
        double r1488884 = r1488878 / r1488883;
        double r1488885 = r1488884 / r1488880;
        return r1488885;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.0

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 associate-*l/1.3

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

  7. Applied *-un-lft-identity1.3

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

  8. Applied *-un-lft-identity1.3

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

  9. Applied distribute-lft-out1.3

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

  10. Applied associate-/r*1.3

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

  11. Simplified1.5

    \[\leadsto \frac{\color{blue}{\frac{t1}{\frac{u + t1}{-v}}}}{t1 + u}\]

  12. Final simplification1.5

    \[\leadsto \frac{\frac{t1}{\frac{u + t1}{-v}}}{u + t1}\]

Reproduce

herbie shell --seed 2019141 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))