Average Error: 18.3 → 1.4
Time: 3.1s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}
double f(double u, double v, double t1) {
        double r23673 = t1;
        double r23674 = -r23673;
        double r23675 = v;
        double r23676 = r23674 * r23675;
        double r23677 = u;
        double r23678 = r23673 + r23677;
        double r23679 = r23678 * r23678;
        double r23680 = r23676 / r23679;
        return r23680;
}
↓
double f(double u, double v, double t1) {
        double r23681 = t1;
        double r23682 = -r23681;
        double r23683 = u;
        double r23684 = r23681 + r23683;
        double r23685 = r23682 / r23684;
        double r23686 = v;
        double r23687 = r23686 / r23684;
        double r23688 = r23685 * r23687;
        return r23688;
}

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 18.3

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

  3. Applied times-frac1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2020060 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))