Average Error: 17.7 → 1.4
Time: 33.0s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\frac{t1}{t1 + u} \cdot v\right) \cdot \frac{-1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\left(\frac{t1}{t1 + u} \cdot v\right) \cdot \frac{-1}{t1 + u}
double f(double u, double v, double t1) {
        double r634996 = t1;
        double r634997 = -r634996;
        double r634998 = v;
        double r634999 = r634997 * r634998;
        double r635000 = u;
        double r635001 = r634996 + r635000;
        double r635002 = r635001 * r635001;
        double r635003 = r634999 / r635002;
        return r635003;
}
↓
double f(double u, double v, double t1) {
        double r635004 = t1;
        double r635005 = u;
        double r635006 = r635004 + r635005;
        double r635007 = r635004 / r635006;
        double r635008 = v;
        double r635009 = r635007 * r635008;
        double r635010 = -1.0;
        double r635011 = r635010 / r635006;
        double r635012 = r635009 * r635011;
        return r635012;
}

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 17.7

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 div-inv1.5

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

  6. Applied associate-*r*1.4

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

  7. Final simplification1.4

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

Reproduce

herbie shell --seed 2019129 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))