Average Error: 17.9 → 1.3
Time: 19.0s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}
double f(double u, double v, double t1) {
        double r25183 = t1;
        double r25184 = -r25183;
        double r25185 = v;
        double r25186 = r25184 * r25185;
        double r25187 = u;
        double r25188 = r25183 + r25187;
        double r25189 = r25188 * r25188;
        double r25190 = r25186 / r25189;
        return r25190;
}
↓
double f(double u, double v, double t1) {
        double r25191 = t1;
        double r25192 = -r25191;
        double r25193 = u;
        double r25194 = r25191 + r25193;
        double r25195 = r25192 / r25194;
        double r25196 = v;
        double r25197 = r25196 / r25194;
        double r25198 = r25195 * r25197;
        return r25198;
}

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 17.9

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

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

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))