Average Error: 0.1 → 0.1
Time: 5.6s
Precision: binary64
Cost: 26496
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right) + x \cdot \log \left({y}^{0.3333333333333333}\right)\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right) + x \cdot \log \left({y}^{0.3333333333333333}\right)\right) - z\right) - y
(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))
↓
(FPCore (x y z)
 :precision binary64
 (-
  (- (+ (* x (* (log (cbrt y)) 2.0)) (* x (log (pow y 0.3333333333333333)))) z)
  y))
double code(double x, double y, double z) {
	return ((x * log(y)) - z) - y;
}
↓
double code(double x, double y, double z) {
	return (((x * (log(cbrt(y)) * 2.0)) + (x * log(pow(y, 0.3333333333333333)))) - 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

Alternatives

Alternative 1
Error0.1
Cost20160
\[\left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right) + \log y \cdot \left(x \cdot 0.3333333333333333\right)\right) - z\right) - y\]
Alternative 2
Error0.1
Cost6848
\[\left(x \cdot \log y - z\right) - y\]
Alternative 3
Error10.8
Cost7048
\[\begin{array}{l} \mathbf{if}\;z \leq -2.085724244926605 \cdot 10^{+149} \lor \neg \left(z \leq 4.8779414024382666 \cdot 10^{-51}\right):\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array}\]
Alternative 4
Error21.8
Cost256
\[\left(-y\right) - z\]
Alternative 5
Error61.6
Cost64
\[-1\]
Alternative 6
Error62.5
Cost64
\[0\]
Alternative 7
Error62.5
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.1

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

  3. Applied add-cube-cbrt_binary64_1130.1

    \[\leadsto \left(x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} - z\right) - y\]

  4. Applied log-prod_binary64_1640.1

    \[\leadsto \left(x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} - z\right) - y\]

  5. Applied distribute-rgt-in_binary64_280.1

    \[\leadsto \left(\color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right)} - z\right) - y\]

  6. Simplified0.1

    \[\leadsto \left(\left(\color{blue}{x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right)} + \log \left(\sqrt[3]{y}\right) \cdot x\right) - z\right) - y\]

  7. Simplified0.1

    \[\leadsto \left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right) + \color{blue}{x \cdot \log \left(\sqrt[3]{y}\right)}\right) - z\right) - y\]
  8. Using strategy rm

  9. Applied pow1/3_binary64_1600.1

    \[\leadsto \left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right) + x \cdot \log \color{blue}{\left({y}^{0.3333333333333333}\right)}\right) - z\right) - y\]

  10. Simplified0.1

    \[\leadsto \color{blue}{\left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right) + x \cdot \log \left({y}^{0.3333333333333333}\right)\right) - z\right) - y}\]

  11. Final simplification0.1

    \[\leadsto \left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right) + x \cdot \log \left({y}^{0.3333333333333333}\right)\right) - z\right) - y\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))