Average Error: 0.1 → 0.1
Time: 12.7s
Precision: binary64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\log c \cdot \left(b \cdot \frac{2}{3}\right) - 0.333333333333333315 \cdot \log c\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right) + y \cdot i\]
\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(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\log c \cdot \left(b \cdot \frac{2}{3}\right) - 0.333333333333333315 \cdot \log c\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\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) (((double) (x * ((double) log(y)))) + z)) + t)) + a)) + ((double) (((double) (((double) log(c)) * ((double) (b * 0.6666666666666666)))) - ((double) (0.3333333333333333 * ((double) log(c)))))))) + ((double) (((double) (b - 0.5)) * ((double) log(((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 0.1

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

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate-+r+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  10. Applied pow1/30.1

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

  11. Applied pow-prod-up0.1

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

  12. Simplified0.1

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

  13. Taylor expanded around 0 0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\left(\frac{2}{3} \cdot \left(\log c \cdot b\right) + \frac{2}{3} \cdot \left(\log 1 \cdot b\right)\right) - \left(0.333333333333333315 \cdot \log 1 + 0.333333333333333315 \cdot \log c\right)\right)}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right) + y \cdot i\]

  14. Simplified0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\log c \cdot \left(b \cdot \frac{2}{3}\right) - 0.333333333333333315 \cdot \log c\right)}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right) + y \cdot i\]

  15. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\log c \cdot \left(b \cdot \frac{2}{3}\right) - 0.333333333333333315 \cdot \log c\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right) + y \cdot i\]

Reproduce

herbie shell --seed 2020157 
(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)))