Average Error: 28.8 → 28.9
Time: 2.2m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r762016 = x;
        double r762017 = y;
        double r762018 = r762016 * r762017;
        double r762019 = z;
        double r762020 = r762018 + r762019;
        double r762021 = r762020 * r762017;
        double r762022 = 27464.7644705;
        double r762023 = r762021 + r762022;
        double r762024 = r762023 * r762017;
        double r762025 = 230661.510616;
        double r762026 = r762024 + r762025;
        double r762027 = r762026 * r762017;
        double r762028 = t;
        double r762029 = r762027 + r762028;
        double r762030 = a;
        double r762031 = r762017 + r762030;
        double r762032 = r762031 * r762017;
        double r762033 = b;
        double r762034 = r762032 + r762033;
        double r762035 = r762034 * r762017;
        double r762036 = c;
        double r762037 = r762035 + r762036;
        double r762038 = r762037 * r762017;
        double r762039 = i;
        double r762040 = r762038 + r762039;
        double r762041 = r762029 / r762040;
        return r762041;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r762042 = x;
        double r762043 = y;
        double r762044 = r762042 * r762043;
        double r762045 = z;
        double r762046 = r762044 + r762045;
        double r762047 = r762046 * r762043;
        double r762048 = 27464.7644705;
        double r762049 = r762047 + r762048;
        double r762050 = r762049 * r762043;
        double r762051 = 230661.510616;
        double r762052 = r762050 + r762051;
        double r762053 = r762052 * r762043;
        double r762054 = t;
        double r762055 = r762053 + r762054;
        double r762056 = 1.0;
        double r762057 = a;
        double r762058 = r762043 + r762057;
        double r762059 = r762058 * r762043;
        double r762060 = b;
        double r762061 = r762059 + r762060;
        double r762062 = r762061 * r762043;
        double r762063 = c;
        double r762064 = r762062 + r762063;
        double r762065 = r762064 * r762043;
        double r762066 = i;
        double r762067 = r762065 + r762066;
        double r762068 = r762056 / r762067;
        double r762069 = r762055 * r762068;
        return r762069;
}

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 28.8

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

  3. Applied div-inv28.9

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

  4. Final simplification28.9

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

Reproduce

herbie shell --seed 2019303 
(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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))