Average Error: 0.1 → 0.1
Time: 8.1s
Precision: binary64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{-c} \cdot \sqrt[3]{-1}\right) \cdot \left(b \cdot 3 + -1.5\right)\right) + y \cdot i\]
\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) + \log \left(\sqrt[3]{-c} \cdot \sqrt[3]{-1}\right) \cdot \left(b \cdot 3 + -1.5\right)\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
 (+
  (+
   (+ (+ (+ (* x (log y)) z) t) a)
   (* (log (* (cbrt (- c)) (cbrt -1.0))) (+ (* b 3.0) -1.5)))
  (* 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 (((((x * log(y)) + z) + t) + a) + (log(cbrt(-c) * cbrt(-1.0)) * ((b * 3.0) + -1.5))) + (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_17940.1

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

  4. Applied log-prod_binary64_18450.1

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

  5. Applied distribute-rgt-in_binary64_17140.1

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

  6. Simplified0.1

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

  7. Simplified0.1

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

  8. Taylor expanded around -inf 64.0

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(3 \cdot \left(b \cdot \log \left({\left(-1 \cdot c\right)}^{0.3333333333333333} \cdot \sqrt[3]{-1}\right)\right) - 1.5 \cdot \log \left({\left(-1 \cdot c\right)}^{0.3333333333333333} \cdot \sqrt[3]{-1}\right)\right)}\right) + y \cdot i\]

  9. Simplified0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\log \left(\sqrt[3]{-c} \cdot \sqrt[3]{-1}\right) \cdot \left(b \cdot 3 + -1.5\right)}\right) + y \cdot i\]

  10. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{-c} \cdot \sqrt[3]{-1}\right) \cdot \left(b \cdot 3 + -1.5\right)\right) + y \cdot i\]

Reproduce

herbie shell --seed 2020281 
(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)))