Average Error: 28.1 → 28.4
Time: 37.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}\]
\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}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2273767 = x;
        double r2273768 = y;
        double r2273769 = r2273767 * r2273768;
        double r2273770 = z;
        double r2273771 = r2273769 + r2273770;
        double r2273772 = r2273771 * r2273768;
        double r2273773 = 27464.7644705;
        double r2273774 = r2273772 + r2273773;
        double r2273775 = r2273774 * r2273768;
        double r2273776 = 230661.510616;
        double r2273777 = r2273775 + r2273776;
        double r2273778 = r2273777 * r2273768;
        double r2273779 = t;
        double r2273780 = r2273778 + r2273779;
        double r2273781 = a;
        double r2273782 = r2273768 + r2273781;
        double r2273783 = r2273782 * r2273768;
        double r2273784 = b;
        double r2273785 = r2273783 + r2273784;
        double r2273786 = r2273785 * r2273768;
        double r2273787 = c;
        double r2273788 = r2273786 + r2273787;
        double r2273789 = r2273788 * r2273768;
        double r2273790 = i;
        double r2273791 = r2273789 + r2273790;
        double r2273792 = r2273780 / r2273791;
        return r2273792;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2273793 = 1.0;
        double r2273794 = y;
        double r2273795 = x;
        double r2273796 = z;
        double r2273797 = fma(r2273794, r2273795, r2273796);
        double r2273798 = 27464.7644705;
        double r2273799 = fma(r2273794, r2273797, r2273798);
        double r2273800 = 230661.510616;
        double r2273801 = fma(r2273794, r2273799, r2273800);
        double r2273802 = t;
        double r2273803 = fma(r2273794, r2273801, r2273802);
        double r2273804 = r2273793 / r2273803;
        double r2273805 = a;
        double r2273806 = r2273794 + r2273805;
        double r2273807 = b;
        double r2273808 = fma(r2273806, r2273794, r2273807);
        double r2273809 = c;
        double r2273810 = fma(r2273794, r2273808, r2273809);
        double r2273811 = i;
        double r2273812 = fma(r2273810, r2273794, r2273811);
        double r2273813 = r2273804 * r2273812;
        double r2273814 = r2273793 / r2273813;
        return r2273814;
}

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 28.1

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

  2. Simplified28.1

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

  4. Applied *-un-lft-identity28.1

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

  5. Applied associate-/l*28.4

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

  7. Applied div-inv28.4

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

  8. Final simplification28.4

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

Reproduce

herbie shell --seed 2019141 +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)))