Average Error: 18.0 → 1.2
Time: 15.5s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}
double f(double u, double v, double t1) {
        double r25235 = t1;
        double r25236 = -r25235;
        double r25237 = v;
        double r25238 = r25236 * r25237;
        double r25239 = u;
        double r25240 = r25235 + r25239;
        double r25241 = r25240 * r25240;
        double r25242 = r25238 / r25241;
        return r25242;
}
↓
double f(double u, double v, double t1) {
        double r25243 = t1;
        double r25244 = -r25243;
        double r25245 = v;
        double r25246 = u;
        double r25247 = r25243 + r25246;
        double r25248 = r25245 / r25247;
        double r25249 = r25244 * r25248;
        double r25250 = r25249 / r25247;
        return r25250;
}

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 18.0

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 associate-*l/1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2019209 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))