Average Error: 18.5 → 1.6
Time: 3.2s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{-t1}{\frac{t1 + u}{v}}}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{-t1}{\frac{t1 + u}{v}}}{t1 + u}
double f(double u, double v, double t1) {
        double r20416 = t1;
        double r20417 = -r20416;
        double r20418 = v;
        double r20419 = r20417 * r20418;
        double r20420 = u;
        double r20421 = r20416 + r20420;
        double r20422 = r20421 * r20421;
        double r20423 = r20419 / r20422;
        return r20423;
}
↓
double f(double u, double v, double t1) {
        double r20424 = t1;
        double r20425 = -r20424;
        double r20426 = u;
        double r20427 = r20424 + r20426;
        double r20428 = v;
        double r20429 = r20427 / r20428;
        double r20430 = r20425 / r20429;
        double r20431 = r20430 / r20427;
        return r20431;
}

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 18.5

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

  3. Applied times-frac1.3

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

  5. Applied clear-num1.7

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

  7. Applied associate-*l/1.8

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

  8. Simplified1.6

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

  9. Final simplification1.6

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

Reproduce

herbie shell --seed 2020047 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))