Average Error: 17.6 → 1.5
Time: 3.7s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[-\frac{\frac{t1}{t1 + u}}{\frac{t1 + u}{v}}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
-\frac{\frac{t1}{t1 + u}}{\frac{t1 + u}{v}}
double f(double u, double v, double t1) {
        double r27869 = t1;
        double r27870 = -r27869;
        double r27871 = v;
        double r27872 = r27870 * r27871;
        double r27873 = u;
        double r27874 = r27869 + r27873;
        double r27875 = r27874 * r27874;
        double r27876 = r27872 / r27875;
        return r27876;
}
↓
double f(double u, double v, double t1) {
        double r27877 = t1;
        double r27878 = u;
        double r27879 = r27877 + r27878;
        double r27880 = r27877 / r27879;
        double r27881 = v;
        double r27882 = r27879 / r27881;
        double r27883 = r27880 / r27882;
        double r27884 = -r27883;
        return r27884;
}

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 17.6

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied times-frac1.2

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  4. Using strategy rm

  5. Applied clear-num1.6

    \[\leadsto \frac{-t1}{t1 + u} \cdot \color{blue}{\frac{1}{\frac{t1 + u}{v}}}\]
  6. Using strategy rm

  7. Applied distribute-frac-neg1.6

    \[\leadsto \color{blue}{\left(-\frac{t1}{t1 + u}\right)} \cdot \frac{1}{\frac{t1 + u}{v}}\]

  8. Applied distribute-lft-neg-out1.6

    \[\leadsto \color{blue}{-\frac{t1}{t1 + u} \cdot \frac{1}{\frac{t1 + u}{v}}}\]

  9. Simplified1.5

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

  10. Final simplification1.5

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

Reproduce

herbie shell --seed 2020021 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))