Average Error: 18.4 → 1.4
Time: 17.5s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}
double f(double u, double v, double t1) {
        double r1024908 = t1;
        double r1024909 = -r1024908;
        double r1024910 = v;
        double r1024911 = r1024909 * r1024910;
        double r1024912 = u;
        double r1024913 = r1024908 + r1024912;
        double r1024914 = r1024913 * r1024913;
        double r1024915 = r1024911 / r1024914;
        return r1024915;
}
↓
double f(double u, double v, double t1) {
        double r1024916 = v;
        double r1024917 = u;
        double r1024918 = t1;
        double r1024919 = r1024917 + r1024918;
        double r1024920 = r1024916 / r1024919;
        double r1024921 = -r1024918;
        double r1024922 = r1024920 * r1024921;
        double r1024923 = r1024922 / r1024919;
        return r1024923;
}

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. 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/1.4

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

  6. Final simplification1.4

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

Reproduce

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