Average Error: 17.6 → 1.2
Time: 15.2s
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 r1138823 = t1;
        double r1138824 = -r1138823;
        double r1138825 = v;
        double r1138826 = r1138824 * r1138825;
        double r1138827 = u;
        double r1138828 = r1138823 + r1138827;
        double r1138829 = r1138828 * r1138828;
        double r1138830 = r1138826 / r1138829;
        return r1138830;
}
↓
double f(double u, double v, double t1) {
        double r1138831 = v;
        double r1138832 = u;
        double r1138833 = t1;
        double r1138834 = r1138832 + r1138833;
        double r1138835 = r1138831 / r1138834;
        double r1138836 = -r1138833;
        double r1138837 = r1138835 * r1138836;
        double r1138838 = r1138837 / r1138834;
        return r1138838;
}

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 17.6

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

  3. Applied times-frac1.2

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

  5. Applied associate-*l/1.2

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

  6. Final simplification1.2

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

Reproduce

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