Average Error: 18.1 → 1.3
Time: 16.1s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}
double f(double u, double v, double t1) {
        double r18970 = t1;
        double r18971 = -r18970;
        double r18972 = v;
        double r18973 = r18971 * r18972;
        double r18974 = u;
        double r18975 = r18970 + r18974;
        double r18976 = r18975 * r18975;
        double r18977 = r18973 / r18976;
        return r18977;
}
↓
double f(double u, double v, double t1) {
        double r18978 = t1;
        double r18979 = -r18978;
        double r18980 = v;
        double r18981 = u;
        double r18982 = r18978 + r18981;
        double r18983 = r18980 / r18982;
        double r18984 = r18979 * r18983;
        double r18985 = r18984 / r18982;
        return r18985;
}

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 18.1

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 associate-*r/1.2

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

  7. Applied div-inv1.2

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

  8. Applied associate-*l*1.4

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

  9. Simplified1.3

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

  10. Final simplification1.3

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

Reproduce

herbie shell --seed 2019303 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))