Average Error: 18.1 → 1.4
Time: 21.4s
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 r38700 = t1;
        double r38701 = -r38700;
        double r38702 = v;
        double r38703 = r38701 * r38702;
        double r38704 = u;
        double r38705 = r38700 + r38704;
        double r38706 = r38705 * r38705;
        double r38707 = r38703 / r38706;
        return r38707;
}
↓
double f(double u, double v, double t1) {
        double r38708 = t1;
        double r38709 = -r38708;
        double r38710 = u;
        double r38711 = r38708 + r38710;
        double r38712 = r38709 / r38711;
        double r38713 = v;
        double r38714 = r38713 / r38711;
        double r38715 = r38712 * r38714;
        return r38715;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

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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-frac1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019198 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))