Average Error: 18.3 → 1.4
Time: 39.5s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\frac{t1}{t1 + u} \cdot v\right) \cdot \frac{-1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\left(\frac{t1}{t1 + u} \cdot v\right) \cdot \frac{-1}{t1 + u}
double f(double u, double v, double t1) {
        double r918080 = t1;
        double r918081 = -r918080;
        double r918082 = v;
        double r918083 = r918081 * r918082;
        double r918084 = u;
        double r918085 = r918080 + r918084;
        double r918086 = r918085 * r918085;
        double r918087 = r918083 / r918086;
        return r918087;
}
↓
double f(double u, double v, double t1) {
        double r918088 = t1;
        double r918089 = u;
        double r918090 = r918088 + r918089;
        double r918091 = r918088 / r918090;
        double r918092 = v;
        double r918093 = r918091 * r918092;
        double r918094 = -1.0;
        double r918095 = r918094 / r918090;
        double r918096 = r918093 * r918095;
        return r918096;
}

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 18.3

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 div-inv1.3

    \[\leadsto \frac{-t1}{t1 + u} \cdot \color{blue}{\left(v \cdot \frac{1}{t1 + u}\right)}\]

  6. Applied associate-*r*1.4

    \[\leadsto \color{blue}{\left(\frac{-t1}{t1 + u} \cdot v\right) \cdot \frac{1}{t1 + u}}\]

  7. Final simplification1.4

    \[\leadsto \left(\frac{t1}{t1 + u} \cdot v\right) \cdot \frac{-1}{t1 + u}\]

Reproduce

herbie shell --seed 2019138 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))