Average Error: 18.1 → 1.3
Time: 17.7s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}
double f(double u, double v, double t1) {
        double r1058170 = t1;
        double r1058171 = -r1058170;
        double r1058172 = v;
        double r1058173 = r1058171 * r1058172;
        double r1058174 = u;
        double r1058175 = r1058170 + r1058174;
        double r1058176 = r1058175 * r1058175;
        double r1058177 = r1058173 / r1058176;
        return r1058177;
}
↓
double f(double u, double v, double t1) {
        double r1058178 = v;
        double r1058179 = u;
        double r1058180 = t1;
        double r1058181 = r1058179 + r1058180;
        double r1058182 = r1058178 / r1058181;
        double r1058183 = -r1058180;
        double r1058184 = r1058182 * r1058183;
        double r1058185 = r1058184 / r1058181;
        return r1058185;
}

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 18.1

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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-*l/1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019179 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))