Average Error: 0.1 → 0.1
Time: 23.3s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\mathsf{fma}\left(y, i, \log c \cdot \left(b - 0.5\right) + \left(a + \left(\mathsf{fma}\left(x, \log y, z\right) + t\right)\right)\right)\]
\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
↓
\mathsf{fma}\left(y, i, \log c \cdot \left(b - 0.5\right) + \left(a + \left(\mathsf{fma}\left(x, \log y, z\right) + t\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62979 = x;
        double r62980 = y;
        double r62981 = log(r62980);
        double r62982 = r62979 * r62981;
        double r62983 = z;
        double r62984 = r62982 + r62983;
        double r62985 = t;
        double r62986 = r62984 + r62985;
        double r62987 = a;
        double r62988 = r62986 + r62987;
        double r62989 = b;
        double r62990 = 0.5;
        double r62991 = r62989 - r62990;
        double r62992 = c;
        double r62993 = log(r62992);
        double r62994 = r62991 * r62993;
        double r62995 = r62988 + r62994;
        double r62996 = i;
        double r62997 = r62980 * r62996;
        double r62998 = r62995 + r62997;
        return r62998;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62999 = y;
        double r63000 = i;
        double r63001 = c;
        double r63002 = log(r63001);
        double r63003 = b;
        double r63004 = 0.5;
        double r63005 = r63003 - r63004;
        double r63006 = r63002 * r63005;
        double r63007 = a;
        double r63008 = x;
        double r63009 = log(r62999);
        double r63010 = z;
        double r63011 = fma(r63008, r63009, r63010);
        double r63012 = t;
        double r63013 = r63011 + r63012;
        double r63014 = r63007 + r63013;
        double r63015 = r63006 + r63014;
        double r63016 = fma(r62999, r63000, r63015);
        return r63016;
}

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

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. Simplified0.1

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

  4. Applied fma-udef0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(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)))