Average Error: 17.8 → 1.3
Time: 6.0s
Precision: binary64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
↓
\[\frac{\frac{v}{-1 - \frac{u}{t1}}}{u + t1} \]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{-1 - \frac{u}{t1}}}{u + t1}

(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))
↓
(FPCore (u v t1) :precision binary64 (/ (/ v (- -1.0 (/ u t1))) (+ 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 / (-1.0 - (u / t1))) / (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 17.8

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

  2. Simplified1.5

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

  3. Applied div-inv_binary641.7

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

  4. Applied associate-/l*_binary643.6

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

  5. Applied associate-/r/_binary643.5

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

  6. Applied associate-/r*_binary641.3

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

  7. Simplified1.3

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

  8. Final simplification1.3

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

Reproduce

herbie shell --seed 2022068 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))