Average Error: 7.8 → 0.6
Time: 7.2s
Precision: binary64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -5.49262794841371819 \cdot 10^{305} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le -2.58112263377951956 \cdot 10^{-262} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 0.0 \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 2.3725596294869886 \cdot 10^{159}\right)\right)\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a} - \frac{4.5 \cdot \left(t \cdot z\right)}{a}\\ \end{array}\]
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -5.49262794841371819 \cdot 10^{305} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le -2.58112263377951956 \cdot 10^{-262} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 0.0 \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 2.3725596294869886 \cdot 10^{159}\right)\right)\right):\\
\;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\

\mathbf{else}:\\
\;\;\;\;0.5 \cdot \frac{x \cdot y}{a} - \frac{4.5 \cdot \left(t \cdot z\right)}{a}\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) / ((double) (a * 2.0))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) <= -5.492627948413718e+305) || !((((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) <= -2.5811226337795196e-262) || !((((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) <= 0.0) || !(((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) <= 2.3725596294869886e+159))))) {
		VAR = ((double) (((double) (0.5 * ((double) (x / ((double) (a / y)))))) - ((double) (4.5 * ((double) (t / ((double) (a / z))))))));
	} else {
		VAR = ((double) (((double) (0.5 * ((double) (((double) (x * y)) / a)))) - ((double) (((double) (4.5 * ((double) (t * z)))) / a))));
	}
	return VAR;
}

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
Target5.6
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.14403070783397609 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* (* z 9.0) t)) < -5.49262794841371819e305 or -2.58112263377951956e-262 < (- (* x y) (* (* z 9.0) t)) < 0.0 or 2.3725596294869886e159 < (- (* x y) (* (* z 9.0) t))

    1. Initial program 31.5

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

    2. Taylor expanded around 0 31.2

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \frac{t \cdot z}{a}}\]
    3. Using strategy rm

    4. Applied associate-/l*16.7

      \[\leadsto 0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}}\]
    5. Using strategy rm

    6. Applied associate-/l*1.3

      \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} - 4.5 \cdot \frac{t}{\frac{a}{z}}\]

    if -5.49262794841371819e305 < (- (* x y) (* (* z 9.0) t)) < -2.58112263377951956e-262 or 0.0 < (- (* x y) (* (* z 9.0) t)) < 2.3725596294869886e159

    1. Initial program 0.3

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

    2. Taylor expanded around 0 0.3

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \frac{t \cdot z}{a}}\]
    3. Using strategy rm

    4. Applied associate-*r/0.3

      \[\leadsto 0.5 \cdot \frac{x \cdot y}{a} - \color{blue}{\frac{4.5 \cdot \left(t \cdot z\right)}{a}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -5.49262794841371819 \cdot 10^{305} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le -2.58112263377951956 \cdot 10^{-262} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 0.0 \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 2.3725596294869886 \cdot 10^{159}\right)\right)\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a} - \frac{4.5 \cdot \left(t \cdot z\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020171 
(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 (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

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