Average Error: 0.1 → 0.1
Time: 13.9s
Precision: binary64
Cost: 27328
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log y \cdot \left(x \cdot 0.3333333333333333\right)\right)\right)\right)\right)\right)\]
\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
↓
y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + \left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log y \cdot \left(x \cdot 0.3333333333333333\right)\right)\right)\right)\right)\right)
(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
 (+
  (* y i)
  (+
   (* (log c) (- b 0.5))
   (+
    a
    (+
     t
     (+
      z
      (+
       (* x (* 2.0 (log (cbrt y))))
       (* (log y) (* x 0.3333333333333333)))))))))
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 (y * i) + ((log(c) * (b - 0.5)) + (a + (t + (z + ((x * (2.0 * log(cbrt(y)))) + (log(y) * (x * 0.3333333333333333)))))));
}

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

Alternatives

Alternative 1
Error0.1
Cost14016
\[y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\right)\]
Alternative 2
Error0.3
Cost14216
\[\begin{array}{l} \mathbf{if}\;x \leq -2.8878632339575142 \cdot 10^{+38} \lor \neg \left(x \leq 1.5082297105666514 \cdot 10^{-62}\right):\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + z\right)\right)\right)\\ \end{array}\]
Alternative 3
Error9.3
Cost7681
\[\begin{array}{l} \mathbf{if}\;x \leq 3.602273834251848 \cdot 10^{+193}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \end{array}\]
Alternative 4
Error37.0
Cost8132
\[\begin{array}{l} \mathbf{if}\;a \leq -9.839083460723915 \cdot 10^{+148}:\\ \;\;\;\;y \cdot i + a\\ \mathbf{elif}\;a \leq 8.271293034847638 \cdot 10^{-263}:\\ \;\;\;\;y \cdot i + \log c \cdot b\\ \mathbf{elif}\;a \leq 1.0450086183394857 \cdot 10^{-153}:\\ \;\;\;\;y \cdot i + z\\ \mathbf{elif}\;a \leq 3.7550542520952592 \cdot 10^{-124}:\\ \;\;\;\;y \cdot i + \log c \cdot b\\ \mathbf{elif}\;a \leq 8.734193249816575 \cdot 10^{+110}:\\ \;\;\;\;y \cdot i + t\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a\\ \end{array}\]
Alternative 5
Error37.4
Cost1925
\[\begin{array}{l} \mathbf{if}\;z \leq -2.9790999939101416 \cdot 10^{+165}:\\ \;\;\;\;y \cdot i + z\\ \mathbf{elif}\;z \leq -4.412835249230618 \cdot 10^{-68}:\\ \;\;\;\;y \cdot i + t\\ \mathbf{elif}\;z \leq 4.121521196919986 \cdot 10^{-291}:\\ \;\;\;\;y \cdot i + a\\ \mathbf{elif}\;z \leq 5.8665729733122296 \cdot 10^{-198}:\\ \;\;\;\;y \cdot i + t\\ \mathbf{elif}\;z \leq 4.736248621264831 \cdot 10^{+143}:\\ \;\;\;\;y \cdot i + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + z\\ \end{array}\]
Alternative 6
Error37.4
Cost648
\[\begin{array}{l} \mathbf{if}\;t \leq -5.9626233229406005 \cdot 10^{+53} \lor \neg \left(t \leq 1.4327759250740434 \cdot 10^{+133}\right):\\ \;\;\;\;y \cdot i + t\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a\\ \end{array}\]
Alternative 7
Error44.8
Cost320
\[y \cdot i + a\]
Alternative 8
Error62.4
Cost64
\[1\]

Error

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_25000.1

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

  4. Applied log-prod_binary64_25510.1

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

  5. Applied distribute-rgt-in_binary64_24150.1

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

  6. Simplified0.1

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

  7. Simplified0.1

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

  9. Applied pow1/3_binary64_25470.1

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

  10. Applied log-pow_binary64_25540.1

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

  11. Applied associate-*r*_binary64_24050.1

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2021044 
(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)))