Average Error: 0.1 → 0.1
Time: 11.1s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)\right)\right)\]
\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(i, y, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69145 = x;
        double r69146 = y;
        double r69147 = log(r69146);
        double r69148 = r69145 * r69147;
        double r69149 = z;
        double r69150 = r69148 + r69149;
        double r69151 = t;
        double r69152 = r69150 + r69151;
        double r69153 = a;
        double r69154 = r69152 + r69153;
        double r69155 = b;
        double r69156 = 0.5;
        double r69157 = r69155 - r69156;
        double r69158 = c;
        double r69159 = log(r69158);
        double r69160 = r69157 * r69159;
        double r69161 = r69154 + r69160;
        double r69162 = i;
        double r69163 = r69146 * r69162;
        double r69164 = r69161 + r69163;
        return r69164;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69165 = i;
        double r69166 = y;
        double r69167 = c;
        double r69168 = log(r69167);
        double r69169 = b;
        double r69170 = 0.5;
        double r69171 = r69169 - r69170;
        double r69172 = x;
        double r69173 = log(r69166);
        double r69174 = z;
        double r69175 = fma(r69172, r69173, r69174);
        double r69176 = t;
        double r69177 = a;
        double r69178 = r69176 + r69177;
        double r69179 = r69175 + r69178;
        double r69180 = fma(r69168, r69171, r69179);
        double r69181 = fma(r69165, r69166, r69180);
        return r69181;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020002 +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)))