Average Error: 17.8 → 1.2
Time: 19.2s
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 r1092244 = t1;
        double r1092245 = -r1092244;
        double r1092246 = v;
        double r1092247 = r1092245 * r1092246;
        double r1092248 = u;
        double r1092249 = r1092244 + r1092248;
        double r1092250 = r1092249 * r1092249;
        double r1092251 = r1092247 / r1092250;
        return r1092251;
}
↓
double f(double u, double v, double t1) {
        double r1092252 = t1;
        double r1092253 = u;
        double r1092254 = r1092252 + r1092253;
        double r1092255 = r1092252 / r1092254;
        double r1092256 = v;
        double r1092257 = r1092255 * r1092256;
        double r1092258 = r1092257 / r1092254;
        double r1092259 = -r1092258;
        return r1092259;
}

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 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))