Average Error: 29.1 → 29.5
Time: 8.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\left(\left(i + y \cdot c\right) + y \cdot {\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right)}^{3}\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}\]
\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}
↓
\frac{1}{\left(\left(i + y \cdot c\right) + y \cdot {\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right)}^{3}\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r57061 = x;
        double r57062 = y;
        double r57063 = r57061 * r57062;
        double r57064 = z;
        double r57065 = r57063 + r57064;
        double r57066 = r57065 * r57062;
        double r57067 = 27464.7644705;
        double r57068 = r57066 + r57067;
        double r57069 = r57068 * r57062;
        double r57070 = 230661.510616;
        double r57071 = r57069 + r57070;
        double r57072 = r57071 * r57062;
        double r57073 = t;
        double r57074 = r57072 + r57073;
        double r57075 = a;
        double r57076 = r57062 + r57075;
        double r57077 = r57076 * r57062;
        double r57078 = b;
        double r57079 = r57077 + r57078;
        double r57080 = r57079 * r57062;
        double r57081 = c;
        double r57082 = r57080 + r57081;
        double r57083 = r57082 * r57062;
        double r57084 = i;
        double r57085 = r57083 + r57084;
        double r57086 = r57074 / r57085;
        return r57086;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r57087 = 1.0;
        double r57088 = i;
        double r57089 = y;
        double r57090 = c;
        double r57091 = r57089 * r57090;
        double r57092 = r57088 + r57091;
        double r57093 = a;
        double r57094 = r57089 + r57093;
        double r57095 = r57094 * r57089;
        double r57096 = b;
        double r57097 = r57095 + r57096;
        double r57098 = r57097 * r57089;
        double r57099 = cbrt(r57098);
        double r57100 = 3.0;
        double r57101 = pow(r57099, r57100);
        double r57102 = r57089 * r57101;
        double r57103 = r57092 + r57102;
        double r57104 = x;
        double r57105 = r57104 * r57089;
        double r57106 = z;
        double r57107 = r57105 + r57106;
        double r57108 = r57107 * r57089;
        double r57109 = 27464.7644705;
        double r57110 = r57108 + r57109;
        double r57111 = r57110 * r57089;
        double r57112 = 230661.510616;
        double r57113 = r57111 + r57112;
        double r57114 = r57113 * r57089;
        double r57115 = t;
        double r57116 = r57114 + r57115;
        double r57117 = r57087 / r57116;
        double r57118 = r57103 * r57117;
        double r57119 = r57087 / r57118;
        return r57119;
}

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 29.1

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

  3. Applied add-cube-cbrt29.2

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}} + c\right) \cdot y + i}\]
  4. Using strategy rm

  5. Applied clear-num29.4

    \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}}\]

  6. Simplified29.5

    \[\leadsto \frac{1}{\color{blue}{\left(\left(i + y \cdot c\right) + y \cdot {\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right)}^{3}\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}}\]

  7. Final simplification29.5

    \[\leadsto \frac{1}{\left(\left(i + y \cdot c\right) + y \cdot {\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right)}^{3}\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}\]

Reproduce

herbie shell --seed 2020083 
(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)))