Average Error: 29.1 → 29.2
Time: 1.2m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)} \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)} \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3091938 = x;
        double r3091939 = y;
        double r3091940 = r3091938 * r3091939;
        double r3091941 = z;
        double r3091942 = r3091940 + r3091941;
        double r3091943 = r3091942 * r3091939;
        double r3091944 = 27464.7644705;
        double r3091945 = r3091943 + r3091944;
        double r3091946 = r3091945 * r3091939;
        double r3091947 = 230661.510616;
        double r3091948 = r3091946 + r3091947;
        double r3091949 = r3091948 * r3091939;
        double r3091950 = t;
        double r3091951 = r3091949 + r3091950;
        double r3091952 = a;
        double r3091953 = r3091939 + r3091952;
        double r3091954 = r3091953 * r3091939;
        double r3091955 = b;
        double r3091956 = r3091954 + r3091955;
        double r3091957 = r3091956 * r3091939;
        double r3091958 = c;
        double r3091959 = r3091957 + r3091958;
        double r3091960 = r3091959 * r3091939;
        double r3091961 = i;
        double r3091962 = r3091960 + r3091961;
        double r3091963 = r3091951 / r3091962;
        return r3091963;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3091964 = 1.0;
        double r3091965 = y;
        double r3091966 = a;
        double r3091967 = r3091965 + r3091966;
        double r3091968 = b;
        double r3091969 = fma(r3091967, r3091965, r3091968);
        double r3091970 = c;
        double r3091971 = fma(r3091965, r3091969, r3091970);
        double r3091972 = i;
        double r3091973 = fma(r3091971, r3091965, r3091972);
        double r3091974 = r3091964 / r3091973;
        double r3091975 = x;
        double r3091976 = z;
        double r3091977 = fma(r3091965, r3091975, r3091976);
        double r3091978 = 27464.7644705;
        double r3091979 = fma(r3091965, r3091977, r3091978);
        double r3091980 = 230661.510616;
        double r3091981 = fma(r3091965, r3091979, r3091980);
        double r3091982 = t;
        double r3091983 = fma(r3091965, r3091981, r3091982);
        double r3091984 = r3091974 * r3091983;
        return r3091984;
}

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 29.1

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Simplified29.1

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}}\]
  3. Using strategy rm

  4. Applied div-inv29.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}}\]

  5. Final simplification29.2

    \[\leadsto \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)} \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))