Average Error: 0.1 → 0.1
Time: 8.7s
Precision: binary64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[x \cdot \log y + \left(z + \left(t + \left(a + \left(\left(\left(b - 0.5\right) \cdot \left(\log \left(\sqrt[3]{c}\right) \cdot 2\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right) + y \cdot i\right)\right)\right)\right)\]
\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
↓
x \cdot \log y + \left(z + \left(t + \left(a + \left(\left(\left(b - 0.5\right) \cdot \left(\log \left(\sqrt[3]{c}\right) \cdot 2\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right) + y \cdot i\right)\right)\right)\right)
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) (x * ((double) log(y)))) + ((double) (z + ((double) (t + ((double) (a + ((double) (((double) (((double) (((double) (b - 0.5)) * ((double) (((double) log(((double) cbrt(c)))) * 2.0)))) + ((double) (((double) (b - 0.5)) * ((double) log(((double) pow(c, 0.3333333333333333)))))))) + ((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. Simplified0.1

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

  4. Applied add-cube-cbrt0.1

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

  5. Applied log-prod0.1

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

  6. Applied distribute-lft-in0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020184 
(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)))