Average Error: 27.7 → 27.8
Time: 25.1s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)} \cdot \left(y \cdot \left(230661.510616 + \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right) \cdot y\right) + t\right)\]
\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{1}{i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)} \cdot \left(y \cdot \left(230661.510616 + \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right) \cdot y\right) + t\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1324052 = x;
        double r1324053 = y;
        double r1324054 = r1324052 * r1324053;
        double r1324055 = z;
        double r1324056 = r1324054 + r1324055;
        double r1324057 = r1324056 * r1324053;
        double r1324058 = 27464.7644705;
        double r1324059 = r1324057 + r1324058;
        double r1324060 = r1324059 * r1324053;
        double r1324061 = 230661.510616;
        double r1324062 = r1324060 + r1324061;
        double r1324063 = r1324062 * r1324053;
        double r1324064 = t;
        double r1324065 = r1324063 + r1324064;
        double r1324066 = a;
        double r1324067 = r1324053 + r1324066;
        double r1324068 = r1324067 * r1324053;
        double r1324069 = b;
        double r1324070 = r1324068 + r1324069;
        double r1324071 = r1324070 * r1324053;
        double r1324072 = c;
        double r1324073 = r1324071 + r1324072;
        double r1324074 = r1324073 * r1324053;
        double r1324075 = i;
        double r1324076 = r1324074 + r1324075;
        double r1324077 = r1324065 / r1324076;
        return r1324077;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1324078 = 1.0;
        double r1324079 = i;
        double r1324080 = y;
        double r1324081 = b;
        double r1324082 = a;
        double r1324083 = r1324080 + r1324082;
        double r1324084 = r1324083 * r1324080;
        double r1324085 = r1324081 + r1324084;
        double r1324086 = r1324085 * r1324080;
        double r1324087 = c;
        double r1324088 = r1324086 + r1324087;
        double r1324089 = r1324080 * r1324088;
        double r1324090 = r1324079 + r1324089;
        double r1324091 = r1324078 / r1324090;
        double r1324092 = 230661.510616;
        double r1324093 = 27464.7644705;
        double r1324094 = z;
        double r1324095 = x;
        double r1324096 = r1324095 * r1324080;
        double r1324097 = r1324094 + r1324096;
        double r1324098 = r1324080 * r1324097;
        double r1324099 = r1324093 + r1324098;
        double r1324100 = r1324099 * r1324080;
        double r1324101 = r1324092 + r1324100;
        double r1324102 = r1324080 * r1324101;
        double r1324103 = t;
        double r1324104 = r1324102 + r1324103;
        double r1324105 = r1324091 * r1324104;
        return r1324105;
}

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 27.7

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

  3. Applied clear-num28.0

    \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]
  4. Using strategy rm

  5. Applied div-inv28.0

    \[\leadsto \frac{1}{\color{blue}{\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]

  6. Applied *-un-lft-identity28.0

    \[\leadsto \frac{\color{blue}{1 \cdot 1}}{\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}\]

  7. Applied times-frac27.9

    \[\leadsto \color{blue}{\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \frac{1}{\frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]

  8. Simplified27.8

    \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(t + y \cdot \left(y \cdot \left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) + 230661.510616\right)\right)}\]

  9. Final simplification27.8

    \[\leadsto \frac{1}{i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)} \cdot \left(y \cdot \left(230661.510616 + \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right) \cdot y\right) + t\right)\]

Reproduce

herbie shell --seed 2019156 
(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)))