Average Error: 18.1 → 1.2
Time: 21.8s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}
double f(double u, double v, double t1) {
        double r21731 = t1;
        double r21732 = -r21731;
        double r21733 = v;
        double r21734 = r21732 * r21733;
        double r21735 = u;
        double r21736 = r21731 + r21735;
        double r21737 = r21736 * r21736;
        double r21738 = r21734 / r21737;
        return r21738;
}
↓
double f(double u, double v, double t1) {
        double r21739 = t1;
        double r21740 = -r21739;
        double r21741 = u;
        double r21742 = r21739 + r21741;
        double r21743 = r21740 / r21742;
        double r21744 = v;
        double r21745 = r21743 * r21744;
        double r21746 = r21745 / r21742;
        return r21746;
}

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. Final simplification1.2

    \[\leadsto \frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}\]

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))