Average Error: 17.7 → 1.1
Time: 7.2s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{-t1}{u + t1} \cdot v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{-t1}{u + t1} \cdot v}{t1 + u}
double f(double u, double v, double t1) {
        double r23144 = t1;
        double r23145 = -r23144;
        double r23146 = v;
        double r23147 = r23145 * r23146;
        double r23148 = u;
        double r23149 = r23144 + r23148;
        double r23150 = r23149 * r23149;
        double r23151 = r23147 / r23150;
        return r23151;
}
↓
double f(double u, double v, double t1) {
        double r23152 = t1;
        double r23153 = -r23152;
        double r23154 = u;
        double r23155 = r23154 + r23152;
        double r23156 = r23153 / r23155;
        double r23157 = v;
        double r23158 = r23156 * r23157;
        double r23159 = r23152 + r23154;
        double r23160 = r23158 / r23159;
        return r23160;
}

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 17.7

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

  3. Applied associate-/r*11.1

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

  4. Simplified1.3

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

  6. Applied clear-num1.7

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

  8. Applied associate-/r/1.4

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

  9. Applied associate-*r*1.2

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

  10. Simplified1.1

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

  11. Final simplification1.1

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

Reproduce

herbie shell --seed 2020046 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))