Average Error: 29.1 → 29.2
Time: 1.3m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y\right) \cdot \frac{1}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}\]
\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}
↓
\left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y\right) \cdot \frac{1}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4117227 = x;
        double r4117228 = y;
        double r4117229 = r4117227 * r4117228;
        double r4117230 = z;
        double r4117231 = r4117229 + r4117230;
        double r4117232 = r4117231 * r4117228;
        double r4117233 = 27464.7644705;
        double r4117234 = r4117232 + r4117233;
        double r4117235 = r4117234 * r4117228;
        double r4117236 = 230661.510616;
        double r4117237 = r4117235 + r4117236;
        double r4117238 = r4117237 * r4117228;
        double r4117239 = t;
        double r4117240 = r4117238 + r4117239;
        double r4117241 = a;
        double r4117242 = r4117228 + r4117241;
        double r4117243 = r4117242 * r4117228;
        double r4117244 = b;
        double r4117245 = r4117243 + r4117244;
        double r4117246 = r4117245 * r4117228;
        double r4117247 = c;
        double r4117248 = r4117246 + r4117247;
        double r4117249 = r4117248 * r4117228;
        double r4117250 = i;
        double r4117251 = r4117249 + r4117250;
        double r4117252 = r4117240 / r4117251;
        return r4117252;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4117253 = t;
        double r4117254 = y;
        double r4117255 = z;
        double r4117256 = x;
        double r4117257 = r4117256 * r4117254;
        double r4117258 = r4117255 + r4117257;
        double r4117259 = r4117254 * r4117258;
        double r4117260 = 27464.7644705;
        double r4117261 = r4117259 + r4117260;
        double r4117262 = r4117254 * r4117261;
        double r4117263 = 230661.510616;
        double r4117264 = r4117262 + r4117263;
        double r4117265 = r4117264 * r4117254;
        double r4117266 = r4117253 + r4117265;
        double r4117267 = 1.0;
        double r4117268 = i;
        double r4117269 = a;
        double r4117270 = r4117269 + r4117254;
        double r4117271 = r4117270 * r4117254;
        double r4117272 = b;
        double r4117273 = r4117271 + r4117272;
        double r4117274 = r4117273 * r4117254;
        double r4117275 = c;
        double r4117276 = r4117274 + r4117275;
        double r4117277 = r4117254 * r4117276;
        double r4117278 = r4117268 + r4117277;
        double r4117279 = r4117267 / r4117278;
        double r4117280 = r4117266 * r4117279;
        return r4117280;
}

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 29.1

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

  3. Applied div-inv29.2

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

  4. Final simplification29.2

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

Reproduce

herbie shell --seed 2019165 
(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)))