Average Error: 7.8 → 7.9
Time: 3.4s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\frac{1}{a} \cdot \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2}\]
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}
↓
\frac{1}{a} \cdot \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2}
double f(double x, double y, double z, double t, double a) {
        double r797840 = x;
        double r797841 = y;
        double r797842 = r797840 * r797841;
        double r797843 = z;
        double r797844 = 9.0;
        double r797845 = r797843 * r797844;
        double r797846 = t;
        double r797847 = r797845 * r797846;
        double r797848 = r797842 - r797847;
        double r797849 = a;
        double r797850 = 2.0;
        double r797851 = r797849 * r797850;
        double r797852 = r797848 / r797851;
        return r797852;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r797853 = 1.0;
        double r797854 = a;
        double r797855 = r797853 / r797854;
        double r797856 = x;
        double r797857 = y;
        double r797858 = r797856 * r797857;
        double r797859 = z;
        double r797860 = 9.0;
        double r797861 = r797859 * r797860;
        double r797862 = t;
        double r797863 = r797861 * r797862;
        double r797864 = r797858 - r797863;
        double r797865 = 2.0;
        double r797866 = r797864 / r797865;
        double r797867 = r797855 * r797866;
        return r797867;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.8
Target5.8
Herbie7.9
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709043451944897028999329376 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.144030707833976090627817222818061808815 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Initial program 7.8

    \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity7.8

    \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)}}{a \cdot 2}\]

  4. Applied times-frac7.9

    \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2}}\]

  5. Final simplification7.9

    \[\leadsto \frac{1}{a} \cdot \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2}\]

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9 t))) (* a 2)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9) t)) (* a 2)))