Average Error: 18.4 → 1.1
Time: 25.8s
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 r3092367 = t1;
        double r3092368 = -r3092367;
        double r3092369 = v;
        double r3092370 = r3092368 * r3092369;
        double r3092371 = u;
        double r3092372 = r3092367 + r3092371;
        double r3092373 = r3092372 * r3092372;
        double r3092374 = r3092370 / r3092373;
        return r3092374;
}
↓
double f(double u, double v, double t1) {
        double r3092375 = t1;
        double r3092376 = -r3092375;
        double r3092377 = u;
        double r3092378 = r3092375 + r3092377;
        double r3092379 = r3092376 / r3092378;
        double r3092380 = v;
        double r3092381 = r3092379 * r3092380;
        double r3092382 = r3092381 / r3092378;
        return r3092382;
}

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 18.4

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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/1.1

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

  6. Final simplification1.1

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))