Average Error: 17.8 → 1.2
Time: 19.3s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[-\frac{\frac{t1}{t1 + u} \cdot v}{t1 + u}\]
\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 r1230962 = t1;
        double r1230963 = -r1230962;
        double r1230964 = v;
        double r1230965 = r1230963 * r1230964;
        double r1230966 = u;
        double r1230967 = r1230962 + r1230966;
        double r1230968 = r1230967 * r1230967;
        double r1230969 = r1230965 / r1230968;
        return r1230969;
}
↓
double f(double u, double v, double t1) {
        double r1230970 = t1;
        double r1230971 = u;
        double r1230972 = r1230970 + r1230971;
        double r1230973 = r1230970 / r1230972;
        double r1230974 = v;
        double r1230975 = r1230973 * r1230974;
        double r1230976 = r1230975 / r1230972;
        double r1230977 = -r1230976;
        return r1230977;
}

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 17.8

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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-*r/1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))