Average Error: 0.1 → 0.1
Time: 7.8s
Precision: binary64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(\log \left(\sqrt[3]{c}\right) \cdot 2 + \log \left({c}^{0.2222222222222222}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{c}}\right)\right)\right) + y \cdot i\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(\log \left(\sqrt[3]{c}\right) \cdot 2 + \log \left({c}^{0.2222222222222222}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{c}}\right)\right)\right) + y \cdot i
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (x * ((double) log(y)))) + z)) + t)) + a)) + ((double) (((double) (b - 0.5)) * ((double) log(c)))))) + ((double) (y * i))));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (x * ((double) log(y)))) + z)) + t)) + a)) + ((double) (((double) (((double) (b - 0.5)) * ((double) (((double) (((double) log(((double) cbrt(c)))) * 2.0)) + ((double) log(((double) pow(c, 0.2222222222222222)))))))) + ((double) (((double) (b - 0.5)) * ((double) log(((double) cbrt(((double) cbrt(c)))))))))))) + ((double) (y * i))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 0.1 bits

    \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  2. Using strategy rm

  3. Applied add-cube-cbrtError: 0.1 bits

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) \cdot \sqrt[3]{c}\right)}\right) + y \cdot i\]

  4. Applied log-prodError: 0.1 bits

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) + \log \left(\sqrt[3]{c}\right)\right)}\right) + y \cdot i\]

  5. Applied distribute-lft-inError: 0.1 bits

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)}\right) + y \cdot i\]

  6. SimplifiedError: 0.1 bits

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\color{blue}{\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right)} + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + y \cdot i\]
  7. Using strategy rm

  8. Applied add-cube-cbrtError: 0.1 bits

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) \cdot \sqrt[3]{c}}}\right)\right)\right) + y \cdot i\]

  9. Applied cbrt-prodError: 0.1 bits

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \color{blue}{\left(\sqrt[3]{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \sqrt[3]{\sqrt[3]{c}}\right)}\right)\right) + y \cdot i\]

  10. Applied log-prodError: 0.1 bits

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{c} \cdot \sqrt[3]{c}}\right) + \log \left(\sqrt[3]{\sqrt[3]{c}}\right)\right)}\right)\right) + y \cdot i\]

  11. Applied distribute-lft-inError: 0.1 bits

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \color{blue}{\left(\left(b - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{c} \cdot \sqrt[3]{c}}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{c}}\right)\right)}\right)\right) + y \cdot i\]

  12. Applied associate-+r+Error: 0.1 bits

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{c} \cdot \sqrt[3]{c}}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{c}}\right)\right)}\right) + y \cdot i\]

  13. SimplifiedError: 0.1 bits

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\color{blue}{\left(b - 0.5\right) \cdot \left(\log \left(\sqrt[3]{c}\right) \cdot 2 + \log \left(\sqrt[3]{{\left(\sqrt[3]{c}\right)}^{2}}\right)\right)} + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{c}}\right)\right)\right) + y \cdot i\]

  14. Taylor expanded around 0 Error: 0.1 bits

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(\log \left(\sqrt[3]{c}\right) \cdot 2 + \log \color{blue}{\left(e^{0.1111111111111111 \cdot \left(\log 1 + 2 \cdot \log c\right)}\right)}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{c}}\right)\right)\right) + y \cdot i\]

  15. SimplifiedError: 0.1 bits

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(\log \left(\sqrt[3]{c}\right) \cdot 2 + \log \color{blue}{\left({c}^{0.2222222222222222}\right)}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{c}}\right)\right)\right) + y \cdot i\]

  16. Final simplificationError: 0.1 bits

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(\log \left(\sqrt[3]{c}\right) \cdot 2 + \log \left({c}^{0.2222222222222222}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{c}}\right)\right)\right) + y \cdot i\]

Reproduce

herbie shell --seed 2020200 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))