Average Error: 29.1 → 29.2
Time: 27.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + y \cdot \left(\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right)}{y \cdot \left(c + \left(\sqrt[3]{y} \cdot \left(b + y \cdot \left(a + y\right)\right)\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{t + y \cdot \left(\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right)}{y \cdot \left(c + \left(\sqrt[3]{y} \cdot \left(b + y \cdot \left(a + y\right)\right)\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62027 = x;
        double r62028 = y;
        double r62029 = r62027 * r62028;
        double r62030 = z;
        double r62031 = r62029 + r62030;
        double r62032 = r62031 * r62028;
        double r62033 = 27464.7644705;
        double r62034 = r62032 + r62033;
        double r62035 = r62034 * r62028;
        double r62036 = 230661.510616;
        double r62037 = r62035 + r62036;
        double r62038 = r62037 * r62028;
        double r62039 = t;
        double r62040 = r62038 + r62039;
        double r62041 = a;
        double r62042 = r62028 + r62041;
        double r62043 = r62042 * r62028;
        double r62044 = b;
        double r62045 = r62043 + r62044;
        double r62046 = r62045 * r62028;
        double r62047 = c;
        double r62048 = r62046 + r62047;
        double r62049 = r62048 * r62028;
        double r62050 = i;
        double r62051 = r62049 + r62050;
        double r62052 = r62040 / r62051;
        return r62052;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62053 = t;
        double r62054 = y;
        double r62055 = z;
        double r62056 = x;
        double r62057 = r62054 * r62056;
        double r62058 = r62055 + r62057;
        double r62059 = r62058 * r62054;
        double r62060 = 27464.7644705;
        double r62061 = r62059 + r62060;
        double r62062 = r62061 * r62054;
        double r62063 = 230661.510616;
        double r62064 = r62062 + r62063;
        double r62065 = r62054 * r62064;
        double r62066 = r62053 + r62065;
        double r62067 = c;
        double r62068 = cbrt(r62054);
        double r62069 = b;
        double r62070 = a;
        double r62071 = r62070 + r62054;
        double r62072 = r62054 * r62071;
        double r62073 = r62069 + r62072;
        double r62074 = r62068 * r62073;
        double r62075 = r62068 * r62068;
        double r62076 = r62074 * r62075;
        double r62077 = r62067 + r62076;
        double r62078 = r62054 * r62077;
        double r62079 = i;
        double r62080 = r62078 + r62079;
        double r62081 = r62066 / r62080;
        return r62081;
}

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

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Simplified29.1

    \[\leadsto \color{blue}{\frac{y \cdot \left(\left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) + t}{i + y \cdot \left(y \cdot \left(\left(y + a\right) \cdot y + b\right) + c\right)}}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt29.2

    \[\leadsto \frac{y \cdot \left(\left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) + t}{i + y \cdot \left(\color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} \cdot \left(\left(y + a\right) \cdot y + b\right) + c\right)}\]

  5. Applied associate-*l*29.2

    \[\leadsto \frac{y \cdot \left(\left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) + t}{i + y \cdot \left(\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + c\right)}\]

  6. Simplified29.2

    \[\leadsto \frac{y \cdot \left(\left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) + t}{i + y \cdot \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \color{blue}{\left(\left(b + \left(a + y\right) \cdot y\right) \cdot \sqrt[3]{y}\right)} + c\right)}\]

  7. Final simplification29.2

    \[\leadsto \frac{t + y \cdot \left(\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right)}{y \cdot \left(c + \left(\sqrt[3]{y} \cdot \left(b + y \cdot \left(a + y\right)\right)\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) + i}\]

Reproduce

herbie shell --seed 2019179 
(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)))