Average Error: 0.1 → 0.1
Time: 2.8s
Precision: binary64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[x \cdot \log \left(\sqrt{y}\right) + \left(x \cdot \log \left(\sqrt{y}\right) - \left(y + z\right)\right)\]
\left(x \cdot \log y - z\right) - y
↓
x \cdot \log \left(\sqrt{y}\right) + \left(x \cdot \log \left(\sqrt{y}\right) - \left(y + z\right)\right)
(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))
↓
(FPCore (x y z)
 :precision binary64
 (+ (* x (log (sqrt y))) (- (* x (log (sqrt y))) (+ y z))))
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (x * ((double) log(y)))) - z)) - y));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) log(((double) sqrt(y)))))) + ((double) (((double) (x * ((double) log(((double) sqrt(y)))))) - ((double) (y + z))))));
}

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 Error: 0.1 bits

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

  3. Applied add-sqr-sqrtError: 0.1 bits

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

  4. Applied log-prodError: 0.1 bits

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

  5. Applied distribute-lft-inError: 0.1 bits

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

  6. Applied associate--l+Error: 0.1 bits

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

  7. Applied associate--l+Error: 0.1 bits

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

  8. SimplifiedError: 0.1 bits

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

  9. Final simplificationError: 0.1 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))