Average Error: 28.7 → 28.8
Time: 12.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61072 = x;
        double r61073 = y;
        double r61074 = r61072 * r61073;
        double r61075 = z;
        double r61076 = r61074 + r61075;
        double r61077 = r61076 * r61073;
        double r61078 = 27464.7644705;
        double r61079 = r61077 + r61078;
        double r61080 = r61079 * r61073;
        double r61081 = 230661.510616;
        double r61082 = r61080 + r61081;
        double r61083 = r61082 * r61073;
        double r61084 = t;
        double r61085 = r61083 + r61084;
        double r61086 = a;
        double r61087 = r61073 + r61086;
        double r61088 = r61087 * r61073;
        double r61089 = b;
        double r61090 = r61088 + r61089;
        double r61091 = r61090 * r61073;
        double r61092 = c;
        double r61093 = r61091 + r61092;
        double r61094 = r61093 * r61073;
        double r61095 = i;
        double r61096 = r61094 + r61095;
        double r61097 = r61085 / r61096;
        return r61097;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61098 = x;
        double r61099 = y;
        double r61100 = r61098 * r61099;
        double r61101 = z;
        double r61102 = r61100 + r61101;
        double r61103 = r61102 * r61099;
        double r61104 = 27464.7644705;
        double r61105 = r61103 + r61104;
        double r61106 = r61105 * r61099;
        double r61107 = 230661.510616;
        double r61108 = r61106 + r61107;
        double r61109 = r61108 * r61099;
        double r61110 = t;
        double r61111 = r61109 + r61110;
        double r61112 = 1.0;
        double r61113 = a;
        double r61114 = r61099 + r61113;
        double r61115 = b;
        double r61116 = fma(r61114, r61099, r61115);
        double r61117 = c;
        double r61118 = fma(r61116, r61099, r61117);
        double r61119 = i;
        double r61120 = fma(r61118, r61099, r61119);
        double r61121 = r61120 * r61112;
        double r61122 = r61112 / r61121;
        double r61123 = r61111 * r61122;
        return r61123;
}

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 28.7

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied div-inv28.8

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Simplified28.8

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \color{blue}{\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}}\]

  5. Final simplification28.8

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}\]

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))