Average Error: 18.2 → 1.2
Time: 19.1s
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 r450549 = t1;
        double r450550 = -r450549;
        double r450551 = v;
        double r450552 = r450550 * r450551;
        double r450553 = u;
        double r450554 = r450549 + r450553;
        double r450555 = r450554 * r450554;
        double r450556 = r450552 / r450555;
        return r450556;
}
↓
double f(double u, double v, double t1) {
        double r450557 = v;
        double r450558 = t1;
        double r450559 = u;
        double r450560 = r450558 + r450559;
        double r450561 = r450557 / r450560;
        double r450562 = -r450558;
        double r450563 = r450562 / r450560;
        double r450564 = r450561 * r450563;
        return r450564;
}

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 18.2

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied times-frac1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))