Average Error: 18.3 → 1.4
Time: 3.4s
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 r25266 = t1;
        double r25267 = -r25266;
        double r25268 = v;
        double r25269 = r25267 * r25268;
        double r25270 = u;
        double r25271 = r25266 + r25270;
        double r25272 = r25271 * r25271;
        double r25273 = r25269 / r25272;
        return r25273;
}
↓
double f(double u, double v, double t1) {
        double r25274 = t1;
        double r25275 = -r25274;
        double r25276 = u;
        double r25277 = r25274 + r25276;
        double r25278 = r25275 / r25277;
        double r25279 = v;
        double r25280 = r25279 / r25277;
        double r25281 = r25278 * r25280;
        return r25281;
}

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. Final simplification1.4

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

Reproduce

herbie shell --seed 2020060 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))