Average Error: 0.1 → 0.1
Time: 29.7s
Precision: binary64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\log \left(\sqrt{c}\right) \cdot \left(b - 0.5\right) + \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt{c}\right) \cdot \left(b - 0.5\right)\right)\right) + y \cdot i\]
\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(\log \left(\sqrt{c}\right) \cdot \left(b - 0.5\right) + \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt{c}\right) \cdot \left(b - 0.5\right)\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
 (+
  (+
   (* (log (sqrt c)) (- b 0.5))
   (+ (+ (+ (+ (* x (log y)) z) t) a) (* (log (sqrt c)) (- b 0.5))))
  (* 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 ((log(sqrt(c)) * (b - 0.5)) + (((((x * log(y)) + z) + t) + a) + (log(sqrt(c)) * (b - 0.5)))) + (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-sqr-sqrt_binary64_24870.1

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

  4. Applied log-prod_binary64_25510.1

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

  5. Applied distribute-rgt-in_binary64_24150.1

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

  6. Applied associate-+r+_binary64_23970.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2021093 
(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)))