Average Error: 17.8 → 1.2
Time: 41.2s
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 r2442980 = t1;
        double r2442981 = -r2442980;
        double r2442982 = v;
        double r2442983 = r2442981 * r2442982;
        double r2442984 = u;
        double r2442985 = r2442980 + r2442984;
        double r2442986 = r2442985 * r2442985;
        double r2442987 = r2442983 / r2442986;
        return r2442987;
}
↓
double f(double u, double v, double t1) {
        double r2442988 = v;
        double r2442989 = u;
        double r2442990 = t1;
        double r2442991 = r2442989 + r2442990;
        double r2442992 = r2442988 / r2442991;
        double r2442993 = -r2442990;
        double r2442994 = r2442992 * r2442993;
        double r2442995 = r2442994 / r2442991;
        return r2442995;
}

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 17.8

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

  3. Applied times-frac1.1

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  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 2019124 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))