Average Error: 27.9 → 28.0
Time: 2.2m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(230661.510616 + \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)}\right)\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]
\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{y \cdot \left(230661.510616 + \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)}\right)\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3178932 = x;
        double r3178933 = y;
        double r3178934 = r3178932 * r3178933;
        double r3178935 = z;
        double r3178936 = r3178934 + r3178935;
        double r3178937 = r3178936 * r3178933;
        double r3178938 = 27464.7644705;
        double r3178939 = r3178937 + r3178938;
        double r3178940 = r3178939 * r3178933;
        double r3178941 = 230661.510616;
        double r3178942 = r3178940 + r3178941;
        double r3178943 = r3178942 * r3178933;
        double r3178944 = t;
        double r3178945 = r3178943 + r3178944;
        double r3178946 = a;
        double r3178947 = r3178933 + r3178946;
        double r3178948 = r3178947 * r3178933;
        double r3178949 = b;
        double r3178950 = r3178948 + r3178949;
        double r3178951 = r3178950 * r3178933;
        double r3178952 = c;
        double r3178953 = r3178951 + r3178952;
        double r3178954 = r3178953 * r3178933;
        double r3178955 = i;
        double r3178956 = r3178954 + r3178955;
        double r3178957 = r3178945 / r3178956;
        return r3178957;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3178958 = y;
        double r3178959 = 230661.510616;
        double r3178960 = z;
        double r3178961 = x;
        double r3178962 = r3178961 * r3178958;
        double r3178963 = r3178960 + r3178962;
        double r3178964 = r3178958 * r3178963;
        double r3178965 = 27464.7644705;
        double r3178966 = r3178964 + r3178965;
        double r3178967 = r3178958 * r3178966;
        double r3178968 = cbrt(r3178967);
        double r3178969 = r3178968 * r3178968;
        double r3178970 = r3178968 * r3178969;
        double r3178971 = r3178959 + r3178970;
        double r3178972 = r3178958 * r3178971;
        double r3178973 = t;
        double r3178974 = r3178972 + r3178973;
        double r3178975 = c;
        double r3178976 = b;
        double r3178977 = a;
        double r3178978 = r3178958 + r3178977;
        double r3178979 = r3178958 * r3178978;
        double r3178980 = r3178976 + r3178979;
        double r3178981 = r3178980 * r3178958;
        double r3178982 = r3178975 + r3178981;
        double r3178983 = r3178958 * r3178982;
        double r3178984 = i;
        double r3178985 = r3178983 + r3178984;
        double r3178986 = r3178974 / r3178985;
        return r3178986;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 27.9

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

  3. Applied add-cube-cbrt28.0

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

  4. Final simplification28.0

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

Reproduce

herbie shell --seed 2019158 
(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)))