Average Error: 18.4 → 1.1
Time: 16.5s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{t1}{t1 + u} \cdot \left(-v\right)}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{t1}{t1 + u} \cdot \left(-v\right)}{t1 + u}
double f(double u, double v, double t1) {
        double r18907 = t1;
        double r18908 = -r18907;
        double r18909 = v;
        double r18910 = r18908 * r18909;
        double r18911 = u;
        double r18912 = r18907 + r18911;
        double r18913 = r18912 * r18912;
        double r18914 = r18910 / r18913;
        return r18914;
}
↓
double f(double u, double v, double t1) {
        double r18915 = t1;
        double r18916 = u;
        double r18917 = r18915 + r18916;
        double r18918 = r18915 / r18917;
        double r18919 = v;
        double r18920 = -r18919;
        double r18921 = r18918 * r18920;
        double r18922 = r18921 / r18917;
        return r18922;
}

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 18.4

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

  2. Simplified1.4

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

  4. Applied *-un-lft-identity1.4

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

  5. Applied associate-*l*1.4

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

  6. Simplified1.1

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

  7. Final simplification1.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))