Average Error: 17.9 → 1.4
Time: 8.6s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\left(-t1\right) \cdot \left(v \cdot \frac{1}{t1 + u}\right)}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\left(-t1\right) \cdot \left(v \cdot \frac{1}{t1 + u}\right)}{t1 + u}
double f(double u, double v, double t1) {
        double r29030 = t1;
        double r29031 = -r29030;
        double r29032 = v;
        double r29033 = r29031 * r29032;
        double r29034 = u;
        double r29035 = r29030 + r29034;
        double r29036 = r29035 * r29035;
        double r29037 = r29033 / r29036;
        return r29037;
}
↓
double f(double u, double v, double t1) {
        double r29038 = t1;
        double r29039 = -r29038;
        double r29040 = v;
        double r29041 = 1.0;
        double r29042 = u;
        double r29043 = r29038 + r29042;
        double r29044 = r29041 / r29043;
        double r29045 = r29040 * r29044;
        double r29046 = r29039 * r29045;
        double r29047 = r29046 / r29043;
        return r29047;
}

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 17.9

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

  3. Applied associate-/r*11.2

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

  4. Simplified1.3

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

  6. Applied div-inv1.4

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

  7. Final simplification1.4

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

Reproduce

herbie shell --seed 2020045 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))