Average Error: 18.4 → 1.1
Time: 19.4s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}
double f(double u, double v, double t1) {
        double r1068548 = t1;
        double r1068549 = -r1068548;
        double r1068550 = v;
        double r1068551 = r1068549 * r1068550;
        double r1068552 = u;
        double r1068553 = r1068548 + r1068552;
        double r1068554 = r1068553 * r1068553;
        double r1068555 = r1068551 / r1068554;
        return r1068555;
}
↓
double f(double u, double v, double t1) {
        double r1068556 = t1;
        double r1068557 = -r1068556;
        double r1068558 = u;
        double r1068559 = r1068556 + r1068558;
        double r1068560 = r1068557 / r1068559;
        double r1068561 = v;
        double r1068562 = r1068560 * r1068561;
        double r1068563 = r1068562 / r1068559;
        return r1068563;
}

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-frac1.4

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  4. Using strategy rm

  5. Applied associate-*r/1.1

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

  6. Final simplification1.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))