Average Error: 18.2 → 1.4
Time: 3.7s
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 r25224 = t1;
        double r25225 = -r25224;
        double r25226 = v;
        double r25227 = r25225 * r25226;
        double r25228 = u;
        double r25229 = r25224 + r25228;
        double r25230 = r25229 * r25229;
        double r25231 = r25227 / r25230;
        return r25231;
}
↓
double f(double u, double v, double t1) {
        double r25232 = t1;
        double r25233 = -r25232;
        double r25234 = u;
        double r25235 = r25232 + r25234;
        double r25236 = r25233 / r25235;
        double r25237 = v;
        double r25238 = r25237 / r25235;
        double r25239 = r25236 * r25238;
        return r25239;
}

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 18.2

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 2020027 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))