Average Error: 0.1 → 0.1
Time: 11.6s
Precision: binary64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\log \left({y}^{0.6666666666666666}\right) \cdot x + \left(x \cdot \log \left(\sqrt[3]{y}\right) + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(\left(\left(\log \left({y}^{0.6666666666666666}\right) \cdot x + \left(x \cdot \log \left(\sqrt[3]{y}\right) + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))
↓
(FPCore (x y z t a b c i)
 :precision binary64
 (+
  (+
   (+
    (+ (+ (* (log (pow y 0.6666666666666666)) x) (+ (* x (log (cbrt y))) z)) t)
    a)
   (* (- b 0.5) (log c)))
  (* y i)))
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((log(pow(y, 0.6666666666666666)) * x) + ((x * log(cbrt(y))) + z)) + t) + a) + ((b - 0.5) * log(c))) + (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-cbrt_binary64_11870.1

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

  4. Applied log-prod_binary64_11340.1

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

  5. Applied distribute-rgt-in_binary64_12590.1

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

  6. Applied associate-+l+_binary64_12680.1

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

  7. Simplified0.1

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

  9. Applied pow1/3_binary64_11540.1

    \[\leadsto \left(\left(\left(\left(\log \left(\sqrt[3]{y} \cdot \color{blue}{{y}^{0.3333333333333333}}\right) \cdot x + \left(x \cdot \log \left(\sqrt[3]{y}\right) + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  10. Applied pow1/3_binary64_11540.1

    \[\leadsto \left(\left(\left(\left(\log \left(\color{blue}{{y}^{0.3333333333333333}} \cdot {y}^{0.3333333333333333}\right) \cdot x + \left(x \cdot \log \left(\sqrt[3]{y}\right) + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  11. Applied pow-sqr_binary64_12490.1

    \[\leadsto \left(\left(\left(\left(\log \color{blue}{\left({y}^{\left(2 \cdot 0.3333333333333333\right)}\right)} \cdot x + \left(x \cdot \log \left(\sqrt[3]{y}\right) + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  12. Simplified0.1

    \[\leadsto \left(\left(\left(\left(\log \left({y}^{\color{blue}{0.6666666666666666}}\right) \cdot x + \left(x \cdot \log \left(\sqrt[3]{y}\right) + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  13. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(\log \left({y}^{0.6666666666666666}\right) \cdot x + \left(x \cdot \log \left(\sqrt[3]{y}\right) + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

Reproduce

herbie shell --seed 2020231 
(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)))