Average Error: 17.6 → 1.2
Time: 16.4s
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 r1135003 = t1;
        double r1135004 = -r1135003;
        double r1135005 = v;
        double r1135006 = r1135004 * r1135005;
        double r1135007 = u;
        double r1135008 = r1135003 + r1135007;
        double r1135009 = r1135008 * r1135008;
        double r1135010 = r1135006 / r1135009;
        return r1135010;
}
↓
double f(double u, double v, double t1) {
        double r1135011 = t1;
        double r1135012 = u;
        double r1135013 = r1135011 + r1135012;
        double r1135014 = r1135011 / r1135013;
        double r1135015 = v;
        double r1135016 = r1135014 * r1135015;
        double r1135017 = r1135016 / r1135013;
        double r1135018 = -r1135017;
        return r1135018;
}

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-frac1.3

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  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 2019163 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))