Average Error: 17.9 → 1.2
Time: 3.3s
Precision: binary64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{-v}{\frac{u}{t1} - -1}}{u + t1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{-v}{\frac{u}{t1} - -1}}{u + t1}
(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))
↓
(FPCore (u v t1) :precision binary64 (/ (/ (- v) (- (/ u t1) -1.0)) (+ 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 (-v / ((u / t1) - -1.0)) / (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 17.9

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

  2. Simplified1.3

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

  4. Applied div-inv_binary641.4

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

  5. Simplified1.4

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

  7. Applied associate-*l/_binary641.2

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

  8. Simplified1.2

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

  9. Final simplification1.2

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

Reproduce

herbie shell --seed 2020224 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))