Average Error: 28.6 → 28.7
Time: 33.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(c + \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \mathsf{fma}\left(y + a, y, b\right)\right) \cdot \sqrt[3]{y}\right)}\]
\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{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(c + \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \mathsf{fma}\left(y + a, y, b\right)\right) \cdot \sqrt[3]{y}\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3296920 = x;
        double r3296921 = y;
        double r3296922 = r3296920 * r3296921;
        double r3296923 = z;
        double r3296924 = r3296922 + r3296923;
        double r3296925 = r3296924 * r3296921;
        double r3296926 = 27464.7644705;
        double r3296927 = r3296925 + r3296926;
        double r3296928 = r3296927 * r3296921;
        double r3296929 = 230661.510616;
        double r3296930 = r3296928 + r3296929;
        double r3296931 = r3296930 * r3296921;
        double r3296932 = t;
        double r3296933 = r3296931 + r3296932;
        double r3296934 = a;
        double r3296935 = r3296921 + r3296934;
        double r3296936 = r3296935 * r3296921;
        double r3296937 = b;
        double r3296938 = r3296936 + r3296937;
        double r3296939 = r3296938 * r3296921;
        double r3296940 = c;
        double r3296941 = r3296939 + r3296940;
        double r3296942 = r3296941 * r3296921;
        double r3296943 = i;
        double r3296944 = r3296942 + r3296943;
        double r3296945 = r3296933 / r3296944;
        return r3296945;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3296946 = t;
        double r3296947 = y;
        double r3296948 = z;
        double r3296949 = x;
        double r3296950 = r3296949 * r3296947;
        double r3296951 = r3296948 + r3296950;
        double r3296952 = r3296947 * r3296951;
        double r3296953 = 27464.7644705;
        double r3296954 = r3296952 + r3296953;
        double r3296955 = r3296947 * r3296954;
        double r3296956 = 230661.510616;
        double r3296957 = r3296955 + r3296956;
        double r3296958 = r3296957 * r3296947;
        double r3296959 = r3296946 + r3296958;
        double r3296960 = i;
        double r3296961 = c;
        double r3296962 = cbrt(r3296947);
        double r3296963 = r3296962 * r3296962;
        double r3296964 = a;
        double r3296965 = r3296947 + r3296964;
        double r3296966 = b;
        double r3296967 = fma(r3296965, r3296947, r3296966);
        double r3296968 = r3296963 * r3296967;
        double r3296969 = r3296968 * r3296962;
        double r3296970 = r3296961 + r3296969;
        double r3296971 = r3296947 * r3296970;
        double r3296972 = r3296960 + r3296971;
        double r3296973 = r3296959 / r3296972;
        return r3296973;
}

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 28.6

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

  3. Applied add-cube-cbrt28.7

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} + c\right) \cdot y + i}\]

  4. Applied associate-*r*28.7

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}} + c\right) \cdot y + i}\]

  5. Simplified28.7

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

  6. Final simplification28.7

    \[\leadsto \frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(c + \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \mathsf{fma}\left(y + a, y, b\right)\right) \cdot \sqrt[3]{y}\right)}\]

Reproduce

herbie shell --seed 2019163 +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)))