Average Error: 28.5 → 28.6
Time: 2.1m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(230661.510616 + \left(\left(\sqrt[3]{y \cdot \left(z + x \cdot y\right)} \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)}\right) \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)} + 27464.7644705\right) \cdot y\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]
\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 + \left(\left(\sqrt[3]{y \cdot \left(z + x \cdot y\right)} \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)}\right) \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)} + 27464.7644705\right) \cdot y\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 r12506054 = x;
        double r12506055 = y;
        double r12506056 = r12506054 * r12506055;
        double r12506057 = z;
        double r12506058 = r12506056 + r12506057;
        double r12506059 = r12506058 * r12506055;
        double r12506060 = 27464.7644705;
        double r12506061 = r12506059 + r12506060;
        double r12506062 = r12506061 * r12506055;
        double r12506063 = 230661.510616;
        double r12506064 = r12506062 + r12506063;
        double r12506065 = r12506064 * r12506055;
        double r12506066 = t;
        double r12506067 = r12506065 + r12506066;
        double r12506068 = a;
        double r12506069 = r12506055 + r12506068;
        double r12506070 = r12506069 * r12506055;
        double r12506071 = b;
        double r12506072 = r12506070 + r12506071;
        double r12506073 = r12506072 * r12506055;
        double r12506074 = c;
        double r12506075 = r12506073 + r12506074;
        double r12506076 = r12506075 * r12506055;
        double r12506077 = i;
        double r12506078 = r12506076 + r12506077;
        double r12506079 = r12506067 / r12506078;
        return r12506079;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r12506080 = y;
        double r12506081 = 230661.510616;
        double r12506082 = z;
        double r12506083 = x;
        double r12506084 = r12506083 * r12506080;
        double r12506085 = r12506082 + r12506084;
        double r12506086 = r12506080 * r12506085;
        double r12506087 = cbrt(r12506086);
        double r12506088 = r12506087 * r12506087;
        double r12506089 = r12506088 * r12506087;
        double r12506090 = 27464.7644705;
        double r12506091 = r12506089 + r12506090;
        double r12506092 = r12506091 * r12506080;
        double r12506093 = r12506081 + r12506092;
        double r12506094 = r12506080 * r12506093;
        double r12506095 = t;
        double r12506096 = r12506094 + r12506095;
        double r12506097 = c;
        double r12506098 = b;
        double r12506099 = a;
        double r12506100 = r12506080 + r12506099;
        double r12506101 = r12506080 * r12506100;
        double r12506102 = r12506098 + r12506101;
        double r12506103 = r12506102 * r12506080;
        double r12506104 = r12506097 + r12506103;
        double r12506105 = r12506080 * r12506104;
        double r12506106 = i;
        double r12506107 = r12506105 + r12506106;
        double r12506108 = r12506096 / r12506107;
        return r12506108;
}

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 28.5

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

  3. Applied add-cube-cbrt28.6

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

  4. Final simplification28.6

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

Reproduce

herbie shell --seed 2019119 
(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)))