Average Error: 29.0 → 29.0
Time: 1.7m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right)\right) \cdot \sqrt[3]{y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\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{\left(\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right)\right) \cdot \sqrt[3]{y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\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 r64049 = x;
        double r64050 = y;
        double r64051 = r64049 * r64050;
        double r64052 = z;
        double r64053 = r64051 + r64052;
        double r64054 = r64053 * r64050;
        double r64055 = 27464.7644705;
        double r64056 = r64054 + r64055;
        double r64057 = r64056 * r64050;
        double r64058 = 230661.510616;
        double r64059 = r64057 + r64058;
        double r64060 = r64059 * r64050;
        double r64061 = t;
        double r64062 = r64060 + r64061;
        double r64063 = a;
        double r64064 = r64050 + r64063;
        double r64065 = r64064 * r64050;
        double r64066 = b;
        double r64067 = r64065 + r64066;
        double r64068 = r64067 * r64050;
        double r64069 = c;
        double r64070 = r64068 + r64069;
        double r64071 = r64070 * r64050;
        double r64072 = i;
        double r64073 = r64071 + r64072;
        double r64074 = r64062 / r64073;
        return r64074;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r64075 = y;
        double r64076 = cbrt(r64075);
        double r64077 = r64076 * r64076;
        double r64078 = x;
        double r64079 = r64078 * r64075;
        double r64080 = z;
        double r64081 = r64079 + r64080;
        double r64082 = r64081 * r64075;
        double r64083 = 27464.7644705;
        double r64084 = r64082 + r64083;
        double r64085 = r64077 * r64084;
        double r64086 = r64085 * r64076;
        double r64087 = 230661.510616;
        double r64088 = r64086 + r64087;
        double r64089 = r64088 * r64075;
        double r64090 = t;
        double r64091 = r64089 + r64090;
        double r64092 = a;
        double r64093 = r64075 + r64092;
        double r64094 = r64093 * r64075;
        double r64095 = b;
        double r64096 = r64094 + r64095;
        double r64097 = r64096 * r64075;
        double r64098 = c;
        double r64099 = r64097 + r64098;
        double r64100 = r64099 * r64075;
        double r64101 = i;
        double r64102 = r64100 + r64101;
        double r64103 = r64091 / r64102;
        return r64103;
}

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. Using strategy rm

  3. Applied add-cube-cbrt29.0

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

  4. Applied associate-*r*29.0

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

  5. Simplified29.0

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

  6. Final simplification29.0

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))