Average Error: 18.2 → 1.3
Time: 20.9s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}
double f(double u, double v, double t1) {
        double r1140948 = t1;
        double r1140949 = -r1140948;
        double r1140950 = v;
        double r1140951 = r1140949 * r1140950;
        double r1140952 = u;
        double r1140953 = r1140948 + r1140952;
        double r1140954 = r1140953 * r1140953;
        double r1140955 = r1140951 / r1140954;
        return r1140955;
}
↓
double f(double u, double v, double t1) {
        double r1140956 = v;
        double r1140957 = t1;
        double r1140958 = u;
        double r1140959 = r1140957 + r1140958;
        double r1140960 = r1140956 / r1140959;
        double r1140961 = -r1140957;
        double r1140962 = r1140961 / r1140959;
        double r1140963 = r1140960 * r1140962;
        return r1140963;
}

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 18.2

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

  3. Applied times-frac1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))