Average Error: 18.4 → 1.4
Time: 3.3s
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 r24716 = t1;
        double r24717 = -r24716;
        double r24718 = v;
        double r24719 = r24717 * r24718;
        double r24720 = u;
        double r24721 = r24716 + r24720;
        double r24722 = r24721 * r24721;
        double r24723 = r24719 / r24722;
        return r24723;
}
↓
double f(double u, double v, double t1) {
        double r24724 = t1;
        double r24725 = -r24724;
        double r24726 = u;
        double r24727 = r24724 + r24726;
        double r24728 = r24725 / r24727;
        double r24729 = v;
        double r24730 = r24729 / r24727;
        double r24731 = r24728 * r24730;
        return r24731;
}

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. Final simplification1.4

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

Reproduce

herbie shell --seed 2020001 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))