Average Error: 18.5 → 1.5
Time: 8.2s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\left(-t1\right) \cdot \frac{v}{t1 + u}\right) \cdot \frac{1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\left(\left(-t1\right) \cdot \frac{v}{t1 + u}\right) \cdot \frac{1}{t1 + u}
double f(double u, double v, double t1) {
        double r22031 = t1;
        double r22032 = -r22031;
        double r22033 = v;
        double r22034 = r22032 * r22033;
        double r22035 = u;
        double r22036 = r22031 + r22035;
        double r22037 = r22036 * r22036;
        double r22038 = r22034 / r22037;
        return r22038;
}
↓
double f(double u, double v, double t1) {
        double r22039 = t1;
        double r22040 = -r22039;
        double r22041 = v;
        double r22042 = u;
        double r22043 = r22039 + r22042;
        double r22044 = r22041 / r22043;
        double r22045 = r22040 * r22044;
        double r22046 = 1.0;
        double r22047 = r22046 / r22043;
        double r22048 = r22045 * r22047;
        return r22048;
}

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 18.5

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

  3. Applied associate-/r*11.7

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

  4. Simplified1.4

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

  6. Applied div-inv1.5

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

  7. Final simplification1.5

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))