Average Error: 18.2 → 1.3
Time: 33.3s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[-\frac{\frac{t1}{t1 + u} \cdot v}{t1 + u}\]
double f(double u, double v, double t1) {
        double r1837122 = t1;
        double r1837123 = -r1837122;
        double r1837124 = v;
        double r1837125 = r1837123 * r1837124;
        double r1837126 = u;
        double r1837127 = r1837122 + r1837126;
        double r1837128 = r1837127 * r1837127;
        double r1837129 = r1837125 / r1837128;
        return r1837129;
}
↓
double f(double u, double v, double t1) {
        double r1837130 = t1;
        double r1837131 = u;
        double r1837132 = r1837130 + r1837131;
        double r1837133 = r1837130 / r1837132;
        double r1837134 = v;
        double r1837135 = r1837133 * r1837134;
        double r1837136 = r1837135 / r1837132;
        double r1837137 = -r1837136;
        return r1837137;
}


\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
-\frac{\frac{t1}{t1 + u} \cdot v}{t1 + u}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Derivation

  1. Initial program 18.2

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

  3. Applied times-frac1.5

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

  5. Applied associate-*r/1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019102 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))