Average Error: 0.1 → 0.1
Time: 12.1s
Precision: binary64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(x \cdot \log y + z\right) + t\right) + \left(\left(b - 0.5\right) \cdot \log c + a\right)\right) + y \cdot i\]
\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(x \cdot \log y + z\right) + t\right) + \left(\left(b - 0.5\right) \cdot \log c + a\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) (+ (* (- b 0.5) (log c)) a)) (* 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) + (((b - 0.5) * log(c)) + a)) + (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 associate-+l+_binary64_17160.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020344 
(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)))