Average Error: 18.4 → 1.3
Time: 18.2s
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 r24700 = t1;
        double r24701 = -r24700;
        double r24702 = v;
        double r24703 = r24701 * r24702;
        double r24704 = u;
        double r24705 = r24700 + r24704;
        double r24706 = r24705 * r24705;
        double r24707 = r24703 / r24706;
        return r24707;
}
↓
double f(double u, double v, double t1) {
        double r24708 = t1;
        double r24709 = -r24708;
        double r24710 = u;
        double r24711 = r24708 + r24710;
        double r24712 = r24709 / r24711;
        double r24713 = v;
        double r24714 = r24713 / r24711;
        double r24715 = r24712 * r24714;
        return r24715;
}

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 18.4

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 2019322 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))