Average Error: 18.2 → 1.3
Time: 18.0s
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 r1257343 = t1;
        double r1257344 = -r1257343;
        double r1257345 = v;
        double r1257346 = r1257344 * r1257345;
        double r1257347 = u;
        double r1257348 = r1257343 + r1257347;
        double r1257349 = r1257348 * r1257348;
        double r1257350 = r1257346 / r1257349;
        return r1257350;
}
↓
double f(double u, double v, double t1) {
        double r1257351 = v;
        double r1257352 = t1;
        double r1257353 = u;
        double r1257354 = r1257352 + r1257353;
        double r1257355 = r1257351 / r1257354;
        double r1257356 = -r1257352;
        double r1257357 = r1257356 / r1257354;
        double r1257358 = r1257355 * r1257357;
        return r1257358;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

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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-frac1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019169 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))