Average Error: 18.1 → 1.3
Time: 44.4s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{t1 \cdot \left(\frac{-1}{t1 + u} \cdot v\right)}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{t1 \cdot \left(\frac{-1}{t1 + u} \cdot v\right)}{t1 + u}
double f(double u, double v, double t1) {
        double r2526944 = t1;
        double r2526945 = -r2526944;
        double r2526946 = v;
        double r2526947 = r2526945 * r2526946;
        double r2526948 = u;
        double r2526949 = r2526944 + r2526948;
        double r2526950 = r2526949 * r2526949;
        double r2526951 = r2526947 / r2526950;
        return r2526951;
}
↓
double f(double u, double v, double t1) {
        double r2526952 = t1;
        double r2526953 = -1.0;
        double r2526954 = u;
        double r2526955 = r2526952 + r2526954;
        double r2526956 = r2526953 / r2526955;
        double r2526957 = v;
        double r2526958 = r2526956 * r2526957;
        double r2526959 = r2526952 * r2526958;
        double r2526960 = r2526959 / r2526955;
        return r2526960;
}

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 18.1

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

  3. Applied times-frac1.3

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

  5. Applied associate-*l/1.2

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

  7. Applied div-inv1.3

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

  8. Final simplification1.3

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

Reproduce

herbie shell --seed 2019119 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))