Average Error: 18.2 → 1.5
Time: 3.1s
Precision: binary64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{1}{\frac{-1 - \frac{u}{t1}}{v}}}{u + t1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{1}{\frac{-1 - \frac{u}{t1}}{v}}}{u + t1}
(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))
↓
(FPCore (u v t1)
 :precision binary64
 (/ (/ 1.0 (/ (- -1.0 (/ u t1)) v)) (+ u t1)))
double code(double u, double v, double t1) {
	return (-t1 * v) / ((t1 + u) * (t1 + u));
}
↓
double code(double u, double v, double t1) {
	return (1.0 / ((-1.0 - (u / t1)) / v)) / (u + t1);
}

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. Simplified1.5

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

  4. Applied div-inv_binary641.5

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

  6. Applied associate-*l/_binary641.4

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

  7. Simplified1.4

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

  9. Applied clear-num_binary641.5

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

  10. Final simplification1.5

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

Reproduce

herbie shell --seed 2020232 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))