Average Error: 17.8 → 1.2
Time: 18.3s
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 r1298161 = t1;
        double r1298162 = -r1298161;
        double r1298163 = v;
        double r1298164 = r1298162 * r1298163;
        double r1298165 = u;
        double r1298166 = r1298161 + r1298165;
        double r1298167 = r1298166 * r1298166;
        double r1298168 = r1298164 / r1298167;
        return r1298168;
}
↓
double f(double u, double v, double t1) {
        double r1298169 = t1;
        double r1298170 = u;
        double r1298171 = r1298169 + r1298170;
        double r1298172 = r1298169 / r1298171;
        double r1298173 = v;
        double r1298174 = r1298172 * r1298173;
        double r1298175 = r1298174 / r1298171;
        double r1298176 = -r1298175;
        return r1298176;
}

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 17.8

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 2019172 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))