Average Error: 29.0 → 29.1
Time: 30.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(t + y \cdot \left(\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right)\right) \cdot \frac{1}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right)}\]
\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}
↓
\left(t + y \cdot \left(\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right)\right) \cdot \frac{1}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68023 = x;
        double r68024 = y;
        double r68025 = r68023 * r68024;
        double r68026 = z;
        double r68027 = r68025 + r68026;
        double r68028 = r68027 * r68024;
        double r68029 = 27464.7644705;
        double r68030 = r68028 + r68029;
        double r68031 = r68030 * r68024;
        double r68032 = 230661.510616;
        double r68033 = r68031 + r68032;
        double r68034 = r68033 * r68024;
        double r68035 = t;
        double r68036 = r68034 + r68035;
        double r68037 = a;
        double r68038 = r68024 + r68037;
        double r68039 = r68038 * r68024;
        double r68040 = b;
        double r68041 = r68039 + r68040;
        double r68042 = r68041 * r68024;
        double r68043 = c;
        double r68044 = r68042 + r68043;
        double r68045 = r68044 * r68024;
        double r68046 = i;
        double r68047 = r68045 + r68046;
        double r68048 = r68036 / r68047;
        return r68048;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68049 = t;
        double r68050 = y;
        double r68051 = z;
        double r68052 = x;
        double r68053 = r68050 * r68052;
        double r68054 = r68051 + r68053;
        double r68055 = r68054 * r68050;
        double r68056 = 27464.7644705;
        double r68057 = r68055 + r68056;
        double r68058 = r68057 * r68050;
        double r68059 = 230661.510616;
        double r68060 = r68058 + r68059;
        double r68061 = r68050 * r68060;
        double r68062 = r68049 + r68061;
        double r68063 = 1.0;
        double r68064 = i;
        double r68065 = b;
        double r68066 = a;
        double r68067 = r68066 + r68050;
        double r68068 = r68050 * r68067;
        double r68069 = r68065 + r68068;
        double r68070 = r68050 * r68069;
        double r68071 = c;
        double r68072 = r68070 + r68071;
        double r68073 = r68050 * r68072;
        double r68074 = r68064 + r68073;
        double r68075 = r68063 / r68074;
        double r68076 = r68062 * r68075;
        return r68076;
}

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 29.0

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

  2. Simplified29.0

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

  4. Applied div-inv29.1

    \[\leadsto \color{blue}{\left(y \cdot \left(\left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) + t\right) \cdot \frac{1}{i + y \cdot \left(y \cdot \left(\left(y + a\right) \cdot y + b\right) + c\right)}}\]

  5. Simplified29.1

    \[\leadsto \left(y \cdot \left(\left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) + t\right) \cdot \color{blue}{\frac{1}{y \cdot \left(c + y \cdot \left(b + \left(a + y\right) \cdot y\right)\right) + i}}\]

  6. Final simplification29.1

    \[\leadsto \left(t + y \cdot \left(\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right)\right) \cdot \frac{1}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right)}\]

Reproduce

herbie shell --seed 2019196 
(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)))