Average Error: 18.5 → 1.4
Time: 48.1s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}
double f(double u, double v, double t1) {
        double r2541440 = t1;
        double r2541441 = -r2541440;
        double r2541442 = v;
        double r2541443 = r2541441 * r2541442;
        double r2541444 = u;
        double r2541445 = r2541440 + r2541444;
        double r2541446 = r2541445 * r2541445;
        double r2541447 = r2541443 / r2541446;
        return r2541447;
}
↓
double f(double u, double v, double t1) {
        double r2541448 = v;
        double r2541449 = t1;
        double r2541450 = u;
        double r2541451 = r2541449 + r2541450;
        double r2541452 = r2541448 / r2541451;
        double r2541453 = -r2541449;
        double r2541454 = r2541453 / r2541451;
        double r2541455 = r2541452 * r2541454;
        return r2541455;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.5

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

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

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))