Average Error: 18.2 → 1.4
Time: 52.9s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}
double f(double u, double v, double t1) {
        double r1002600 = t1;
        double r1002601 = -r1002600;
        double r1002602 = v;
        double r1002603 = r1002601 * r1002602;
        double r1002604 = u;
        double r1002605 = r1002600 + r1002604;
        double r1002606 = r1002605 * r1002605;
        double r1002607 = r1002603 / r1002606;
        return r1002607;
}
↓
double f(double u, double v, double t1) {
        double r1002608 = v;
        double r1002609 = u;
        double r1002610 = t1;
        double r1002611 = r1002609 + r1002610;
        double r1002612 = r1002608 / r1002611;
        double r1002613 = -r1002610;
        double r1002614 = r1002612 * r1002613;
        double r1002615 = r1002614 / r1002611;
        return r1002615;
}

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-frac1.5

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

  5. Applied associate-*l/1.4

    \[\leadsto \color{blue}{\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}}\]

  6. Final simplification1.4

    \[\leadsto \frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}\]

Reproduce

herbie shell --seed 2019142 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))