Average Error: 17.6 → 1.2
Time: 20.3s
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 r1042268 = t1;
        double r1042269 = -r1042268;
        double r1042270 = v;
        double r1042271 = r1042269 * r1042270;
        double r1042272 = u;
        double r1042273 = r1042268 + r1042272;
        double r1042274 = r1042273 * r1042273;
        double r1042275 = r1042271 / r1042274;
        return r1042275;
}
↓
double f(double u, double v, double t1) {
        double r1042276 = t1;
        double r1042277 = -r1042276;
        double r1042278 = u;
        double r1042279 = r1042276 + r1042278;
        double r1042280 = r1042277 / r1042279;
        double r1042281 = v;
        double r1042282 = r1042280 * r1042281;
        double r1042283 = r1042282 / r1042279;
        return r1042283;
}

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 17.6

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 2019163 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))