Average Error: 18.1 → 1.5
Time: 21.2s
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 r1181146 = t1;
        double r1181147 = -r1181146;
        double r1181148 = v;
        double r1181149 = r1181147 * r1181148;
        double r1181150 = u;
        double r1181151 = r1181146 + r1181150;
        double r1181152 = r1181151 * r1181151;
        double r1181153 = r1181149 / r1181152;
        return r1181153;
}
↓
double f(double u, double v, double t1) {
        double r1181154 = v;
        double r1181155 = t1;
        double r1181156 = u;
        double r1181157 = r1181155 + r1181156;
        double r1181158 = r1181154 / r1181157;
        double r1181159 = -r1181155;
        double r1181160 = r1181159 / r1181157;
        double r1181161 = r1181158 * r1181160;
        return r1181161;
}

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-frac1.5

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

  4. Final simplification1.5

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))