Average Error: 18.4 → 1.4
Time: 5.3s
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 r40409 = t1;
        double r40410 = -r40409;
        double r40411 = v;
        double r40412 = r40410 * r40411;
        double r40413 = u;
        double r40414 = r40409 + r40413;
        double r40415 = r40414 * r40414;
        double r40416 = r40412 / r40415;
        return r40416;
}
↓
double f(double u, double v, double t1) {
        double r40417 = t1;
        double r40418 = -r40417;
        double r40419 = u;
        double r40420 = r40417 + r40419;
        double r40421 = r40418 / r40420;
        double r40422 = v;
        double r40423 = r40422 / r40420;
        double r40424 = r40421 * r40423;
        return r40424;
}

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 2020083 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))