Average Error: 17.8 → 1.2
Time: 1.6m
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 r4837285 = t1;
        double r4837286 = -r4837285;
        double r4837287 = v;
        double r4837288 = r4837286 * r4837287;
        double r4837289 = u;
        double r4837290 = r4837285 + r4837289;
        double r4837291 = r4837290 * r4837290;
        double r4837292 = r4837288 / r4837291;
        return r4837292;
}
↓
double f(double u, double v, double t1) {
        double r4837293 = v;
        double r4837294 = u;
        double r4837295 = t1;
        double r4837296 = r4837294 + r4837295;
        double r4837297 = r4837293 / r4837296;
        double r4837298 = -r4837295;
        double r4837299 = r4837297 * r4837298;
        double r4837300 = r4837299 / r4837296;
        return r4837300;
}

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-frac1.2

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

  5. Applied associate-*l/1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2019125 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))