Average Error: 18.2 → 1.4
Time: 3.8s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}
double f(double u, double v, double t1) {
        double r29171 = t1;
        double r29172 = -r29171;
        double r29173 = v;
        double r29174 = r29172 * r29173;
        double r29175 = u;
        double r29176 = r29171 + r29175;
        double r29177 = r29176 * r29176;
        double r29178 = r29174 / r29177;
        return r29178;
}
↓
double f(double u, double v, double t1) {
        double r29179 = t1;
        double r29180 = -r29179;
        double r29181 = v;
        double r29182 = u;
        double r29183 = r29179 + r29182;
        double r29184 = r29181 / r29183;
        double r29185 = r29180 * r29184;
        double r29186 = r29185 / r29183;
        return r29186;
}

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 18.2

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

  3. Applied times-frac1.4

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  4. Using strategy rm

  5. Applied associate-*r/1.4

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

  6. Simplified1.4

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

  7. Final simplification1.4

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

Reproduce

herbie shell --seed 2019318 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))