Average Error: 28.2 → 28.4
Time: 1.4m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{(\left((y \cdot \left((\left(y + a\right) \cdot y + b)_*\right) + c)_*\right) \cdot y + i)_*}{(y \cdot \left((y \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + 230661.510616)_*\right) + t)_*}}\]
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r6431221 = x;
        double r6431222 = y;
        double r6431223 = r6431221 * r6431222;
        double r6431224 = z;
        double r6431225 = r6431223 + r6431224;
        double r6431226 = r6431225 * r6431222;
        double r6431227 = 27464.7644705;
        double r6431228 = r6431226 + r6431227;
        double r6431229 = r6431228 * r6431222;
        double r6431230 = 230661.510616;
        double r6431231 = r6431229 + r6431230;
        double r6431232 = r6431231 * r6431222;
        double r6431233 = t;
        double r6431234 = r6431232 + r6431233;
        double r6431235 = a;
        double r6431236 = r6431222 + r6431235;
        double r6431237 = r6431236 * r6431222;
        double r6431238 = b;
        double r6431239 = r6431237 + r6431238;
        double r6431240 = r6431239 * r6431222;
        double r6431241 = c;
        double r6431242 = r6431240 + r6431241;
        double r6431243 = r6431242 * r6431222;
        double r6431244 = i;
        double r6431245 = r6431243 + r6431244;
        double r6431246 = r6431234 / r6431245;
        return r6431246;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r6431247 = 1.0;
        double r6431248 = y;
        double r6431249 = a;
        double r6431250 = r6431248 + r6431249;
        double r6431251 = b;
        double r6431252 = fma(r6431250, r6431248, r6431251);
        double r6431253 = c;
        double r6431254 = fma(r6431248, r6431252, r6431253);
        double r6431255 = i;
        double r6431256 = fma(r6431254, r6431248, r6431255);
        double r6431257 = x;
        double r6431258 = z;
        double r6431259 = fma(r6431248, r6431257, r6431258);
        double r6431260 = 27464.7644705;
        double r6431261 = fma(r6431248, r6431259, r6431260);
        double r6431262 = 230661.510616;
        double r6431263 = fma(r6431248, r6431261, r6431262);
        double r6431264 = t;
        double r6431265 = fma(r6431248, r6431263, r6431264);
        double r6431266 = r6431256 / r6431265;
        double r6431267 = r6431247 / r6431266;
        return r6431267;
}


\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}{\frac{(\left((y \cdot \left((\left(y + a\right) \cdot y + b)_*\right) + c)_*\right) \cdot y + i)_*}{(y \cdot \left((y \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + 230661.510616)_*\right) + t)_*}}

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

Derivation

  1. Initial program 28.2

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

  2. Simplified28.2

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

  4. Applied clear-num28.4

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

  5. Final simplification28.4

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

Reproduce

herbie shell --seed 2019101 +o rules:numerics
(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)))