Average Error: 0.1 → 0.1
Time: 2.9s
Precision: binary64
\[\left(x \cdot \log y - z\right) - y \]
↓
\[\begin{array}{l} t_0 := \log \left(\sqrt{y}\right) \cdot x\\ \left(t_0 + \left(t_0 - z\right)\right) - y \end{array} \]
\left(x \cdot \log y - z\right) - y
↓
\begin{array}{l}
t_0 := \log \left(\sqrt{y}\right) \cdot x\\
\left(t_0 + \left(t_0 - z\right)\right) - y
\end{array}

(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))
↓
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log (sqrt y)) x))) (- (+ t_0 (- t_0 z)) y)))
double code(double x, double y, double z) {
	return ((x * log(y)) - z) - y;
}
↓
double code(double x, double y, double z) {
	double t_0 = log(sqrt(y)) * x;
	return (t_0 + (t_0 - z)) - y;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(x \cdot \log y - z\right) - y \]
  2. Using strategy rm

  3. Applied add-sqr-sqrt_binary640.1

    \[\leadsto \left(x \cdot \log \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} - z\right) - y \]

  4. Applied log-prod_binary640.1

    \[\leadsto \left(x \cdot \color{blue}{\left(\log \left(\sqrt{y}\right) + \log \left(\sqrt{y}\right)\right)} - z\right) - y \]

  5. Applied distribute-rgt-in_binary640.1

    \[\leadsto \left(\color{blue}{\left(\log \left(\sqrt{y}\right) \cdot x + \log \left(\sqrt{y}\right) \cdot x\right)} - z\right) - y \]

  6. Applied associate--l+_binary640.1

    \[\leadsto \color{blue}{\left(\log \left(\sqrt{y}\right) \cdot x + \left(\log \left(\sqrt{y}\right) \cdot x - z\right)\right)} - y \]

  7. Simplified0.1

    \[\leadsto \left(\log \left(\sqrt{y}\right) \cdot x + \color{blue}{\left(x \cdot \log \left(\sqrt{y}\right) - z\right)}\right) - y \]

  8. Final simplification0.1

    \[\leadsto \left(\log \left(\sqrt{y}\right) \cdot x + \left(\log \left(\sqrt{y}\right) \cdot x - z\right)\right) - y \]

Reproduce

herbie shell --seed 2021204 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))