Average Error: 7.6 → 7.5
Time: 17.3s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9.0\right) \cdot t}{a \cdot 2.0}\]
↓
\[\frac{x \cdot y - 9.0 \cdot \left(t \cdot z\right)}{a \cdot 2.0}\]
\frac{x \cdot y - \left(z \cdot 9.0\right) \cdot t}{a \cdot 2.0}
↓
\frac{x \cdot y - 9.0 \cdot \left(t \cdot z\right)}{a \cdot 2.0}
double f(double x, double y, double z, double t, double a) {
        double r38202850 = x;
        double r38202851 = y;
        double r38202852 = r38202850 * r38202851;
        double r38202853 = z;
        double r38202854 = 9.0;
        double r38202855 = r38202853 * r38202854;
        double r38202856 = t;
        double r38202857 = r38202855 * r38202856;
        double r38202858 = r38202852 - r38202857;
        double r38202859 = a;
        double r38202860 = 2.0;
        double r38202861 = r38202859 * r38202860;
        double r38202862 = r38202858 / r38202861;
        return r38202862;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r38202863 = x;
        double r38202864 = y;
        double r38202865 = r38202863 * r38202864;
        double r38202866 = 9.0;
        double r38202867 = t;
        double r38202868 = z;
        double r38202869 = r38202867 * r38202868;
        double r38202870 = r38202866 * r38202869;
        double r38202871 = r38202865 - r38202870;
        double r38202872 = a;
        double r38202873 = 2.0;
        double r38202874 = r38202872 * r38202873;
        double r38202875 = r38202871 / r38202874;
        return r38202875;
}

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

Original7.6
Target5.6
Herbie7.5
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9.0 \cdot t\right)}{a \cdot 2.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Initial program 7.6

    \[\frac{x \cdot y - \left(z \cdot 9.0\right) \cdot t}{a \cdot 2.0}\]

  2. Taylor expanded around 0 7.5

    \[\leadsto \frac{x \cdot y - \color{blue}{9.0 \cdot \left(t \cdot z\right)}}{a \cdot 2.0}\]

  3. Final simplification7.5

    \[\leadsto \frac{x \cdot y - 9.0 \cdot \left(t \cdot z\right)}{a \cdot 2.0}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"

  :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 (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))