Average Error: 28.7 → 28.8
Time: 23.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right)\]
\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}
↓
\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59206 = x;
        double r59207 = y;
        double r59208 = r59206 * r59207;
        double r59209 = z;
        double r59210 = r59208 + r59209;
        double r59211 = r59210 * r59207;
        double r59212 = 27464.7644705;
        double r59213 = r59211 + r59212;
        double r59214 = r59213 * r59207;
        double r59215 = 230661.510616;
        double r59216 = r59214 + r59215;
        double r59217 = r59216 * r59207;
        double r59218 = t;
        double r59219 = r59217 + r59218;
        double r59220 = a;
        double r59221 = r59207 + r59220;
        double r59222 = r59221 * r59207;
        double r59223 = b;
        double r59224 = r59222 + r59223;
        double r59225 = r59224 * r59207;
        double r59226 = c;
        double r59227 = r59225 + r59226;
        double r59228 = r59227 * r59207;
        double r59229 = i;
        double r59230 = r59228 + r59229;
        double r59231 = r59219 / r59230;
        return r59231;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59232 = 1.0;
        double r59233 = y;
        double r59234 = a;
        double r59235 = r59233 + r59234;
        double r59236 = r59235 * r59233;
        double r59237 = b;
        double r59238 = r59236 + r59237;
        double r59239 = r59238 * r59233;
        double r59240 = c;
        double r59241 = r59239 + r59240;
        double r59242 = r59241 * r59233;
        double r59243 = i;
        double r59244 = r59242 + r59243;
        double r59245 = r59232 / r59244;
        double r59246 = x;
        double r59247 = r59246 * r59233;
        double r59248 = z;
        double r59249 = r59247 + r59248;
        double r59250 = r59249 * r59233;
        double r59251 = 27464.7644705;
        double r59252 = r59250 + r59251;
        double r59253 = r59252 * r59233;
        double r59254 = 230661.510616;
        double r59255 = r59253 + r59254;
        double r59256 = r59255 * r59233;
        double r59257 = t;
        double r59258 = r59256 + r59257;
        double r59259 = r59245 * r59258;
        return r59259;
}

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 28.7

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

  3. Applied clear-num28.9

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

  5. Applied div-inv28.9

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

  6. Applied add-cube-cbrt28.9

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}\]

  7. Applied times-frac28.8

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}}\]

  8. Simplified28.8

    \[\leadsto \color{blue}{\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}\]

  9. Simplified28.8

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

  10. Final simplification28.8

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

Reproduce

herbie shell --seed 2019212 
(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)))