Average Error: 18.5 → 1.3
Time: 4.4s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}
double f(double u, double v, double t1) {
        double r24242 = t1;
        double r24243 = -r24242;
        double r24244 = v;
        double r24245 = r24243 * r24244;
        double r24246 = u;
        double r24247 = r24242 + r24246;
        double r24248 = r24247 * r24247;
        double r24249 = r24245 / r24248;
        return r24249;
}
↓
double f(double u, double v, double t1) {
        double r24250 = t1;
        double r24251 = -r24250;
        double r24252 = u;
        double r24253 = r24250 + r24252;
        double r24254 = r24251 / r24253;
        double r24255 = v;
        double r24256 = r24255 / r24253;
        double r24257 = r24254 * r24256;
        return r24257;
}

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 18.5

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

  3. Applied times-frac1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020081 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))