Average Error: 18.3 → 1.5
Time: 3.8s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \left(v \cdot \frac{1}{t1 + u}\right)\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-t1}{t1 + u} \cdot \left(v \cdot \frac{1}{t1 + u}\right)
double f(double u, double v, double t1) {
        double r24654 = t1;
        double r24655 = -r24654;
        double r24656 = v;
        double r24657 = r24655 * r24656;
        double r24658 = u;
        double r24659 = r24654 + r24658;
        double r24660 = r24659 * r24659;
        double r24661 = r24657 / r24660;
        return r24661;
}
↓
double f(double u, double v, double t1) {
        double r24662 = t1;
        double r24663 = -r24662;
        double r24664 = u;
        double r24665 = r24662 + r24664;
        double r24666 = r24663 / r24665;
        double r24667 = v;
        double r24668 = 1.0;
        double r24669 = r24668 / r24665;
        double r24670 = r24667 * r24669;
        double r24671 = r24666 * r24670;
        return r24671;
}

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 18.3

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 div-inv1.5

    \[\leadsto \frac{-t1}{t1 + u} \cdot \color{blue}{\left(v \cdot \frac{1}{t1 + u}\right)}\]

  6. Final simplification1.5

    \[\leadsto \frac{-t1}{t1 + u} \cdot \left(v \cdot \frac{1}{t1 + u}\right)\]

Reproduce

herbie shell --seed 2020035 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))