Average Error: 17.7 → 1.1
Time: 24.6s
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 r1105144 = t1;
        double r1105145 = -r1105144;
        double r1105146 = v;
        double r1105147 = r1105145 * r1105146;
        double r1105148 = u;
        double r1105149 = r1105144 + r1105148;
        double r1105150 = r1105149 * r1105149;
        double r1105151 = r1105147 / r1105150;
        return r1105151;
}
↓
double f(double u, double v, double t1) {
        double r1105152 = t1;
        double r1105153 = u;
        double r1105154 = r1105152 + r1105153;
        double r1105155 = r1105152 / r1105154;
        double r1105156 = v;
        double r1105157 = r1105155 * r1105156;
        double r1105158 = r1105157 / r1105154;
        double r1105159 = -r1105158;
        return r1105159;
}

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 17.7

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

  3. Applied times-frac1.2

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  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 2019139 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))