Average Error: 17.6 → 1.2
Time: 17.8s
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 r1158996 = t1;
        double r1158997 = -r1158996;
        double r1158998 = v;
        double r1158999 = r1158997 * r1158998;
        double r1159000 = u;
        double r1159001 = r1158996 + r1159000;
        double r1159002 = r1159001 * r1159001;
        double r1159003 = r1158999 / r1159002;
        return r1159003;
}
↓
double f(double u, double v, double t1) {
        double r1159004 = t1;
        double r1159005 = -r1159004;
        double r1159006 = u;
        double r1159007 = r1159004 + r1159006;
        double r1159008 = r1159005 / r1159007;
        double r1159009 = v;
        double r1159010 = r1159008 * r1159009;
        double r1159011 = r1159010 / r1159007;
        return r1159011;
}

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 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))