Average Error: 18.1 → 1.4
Time: 4.3s
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 r32492 = t1;
        double r32493 = -r32492;
        double r32494 = v;
        double r32495 = r32493 * r32494;
        double r32496 = u;
        double r32497 = r32492 + r32496;
        double r32498 = r32497 * r32497;
        double r32499 = r32495 / r32498;
        return r32499;
}
↓
double f(double u, double v, double t1) {
        double r32500 = t1;
        double r32501 = -r32500;
        double r32502 = u;
        double r32503 = r32500 + r32502;
        double r32504 = r32501 / r32503;
        double r32505 = v;
        double r32506 = r32505 / r32503;
        double r32507 = r32504 * r32506;
        return r32507;
}

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-frac1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019362 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))