Average Error: 28.5 → 28.6
Time: 38.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(\left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(\left(a + y\right), y, b\right)\right), c\right)\right), y, i\right)} \cdot \left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y\right)\]
\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}
↓
\frac{1}{\mathsf{fma}\left(\left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(\left(a + y\right), y, b\right)\right), c\right)\right), y, i\right)} \cdot \left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2288956 = x;
        double r2288957 = y;
        double r2288958 = r2288956 * r2288957;
        double r2288959 = z;
        double r2288960 = r2288958 + r2288959;
        double r2288961 = r2288960 * r2288957;
        double r2288962 = 27464.7644705;
        double r2288963 = r2288961 + r2288962;
        double r2288964 = r2288963 * r2288957;
        double r2288965 = 230661.510616;
        double r2288966 = r2288964 + r2288965;
        double r2288967 = r2288966 * r2288957;
        double r2288968 = t;
        double r2288969 = r2288967 + r2288968;
        double r2288970 = a;
        double r2288971 = r2288957 + r2288970;
        double r2288972 = r2288971 * r2288957;
        double r2288973 = b;
        double r2288974 = r2288972 + r2288973;
        double r2288975 = r2288974 * r2288957;
        double r2288976 = c;
        double r2288977 = r2288975 + r2288976;
        double r2288978 = r2288977 * r2288957;
        double r2288979 = i;
        double r2288980 = r2288978 + r2288979;
        double r2288981 = r2288969 / r2288980;
        return r2288981;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2288982 = 1.0;
        double r2288983 = y;
        double r2288984 = a;
        double r2288985 = r2288984 + r2288983;
        double r2288986 = b;
        double r2288987 = fma(r2288985, r2288983, r2288986);
        double r2288988 = c;
        double r2288989 = fma(r2288983, r2288987, r2288988);
        double r2288990 = i;
        double r2288991 = fma(r2288989, r2288983, r2288990);
        double r2288992 = r2288982 / r2288991;
        double r2288993 = t;
        double r2288994 = z;
        double r2288995 = x;
        double r2288996 = r2288995 * r2288983;
        double r2288997 = r2288994 + r2288996;
        double r2288998 = r2288983 * r2288997;
        double r2288999 = 27464.7644705;
        double r2289000 = r2288998 + r2288999;
        double r2289001 = r2288983 * r2289000;
        double r2289002 = 230661.510616;
        double r2289003 = r2289001 + r2289002;
        double r2289004 = r2289003 * r2288983;
        double r2289005 = r2288993 + r2289004;
        double r2289006 = r2288992 * r2289005;
        return r2289006;
}

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 28.5

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

  3. Applied div-inv28.6

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

  4. Simplified28.6

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

  5. Final simplification28.6

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

Reproduce

herbie shell --seed 2019132 +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)))