Average Error: 7.6 → 0.5
Time: 7.1s
Precision: binary64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -1.4045951477552184 \cdot 10^{259}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \left(\frac{z}{a} \cdot \frac{9}{2}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -2.37434969989275507 \cdot 10^{-155} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 7.62129135130543908 \cdot 10^{-201}\right) \land x \cdot y - \left(z \cdot 9\right) \cdot t \le 8.7252802097409812 \cdot 10^{239}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - 4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array}\]
\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 -1.4045951477552184 \cdot 10^{259}:\\
\;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \left(\frac{z}{a} \cdot \frac{9}{2}\right)\\

\mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -2.37434969989275507 \cdot 10^{-155} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 7.62129135130543908 \cdot 10^{-201}\right) \land x \cdot y - \left(z \cdot 9\right) \cdot t \le 8.7252802097409812 \cdot 10^{239}:\\
\;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\

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

\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)))) <= -1.4045951477552184e+259)) {
		VAR = ((double) (((double) (y * ((double) (x / ((double) (a * 2.0)))))) - ((double) (t * ((double) (((double) (z / a)) * ((double) (9.0 / 2.0))))))));
	} else {
		double VAR_1;
		if (((((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) <= -2.374349699892755e-155) || (!(((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) <= 7.621291351305439e-201) && (((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) <= 8.725280209740981e+239)))) {
			VAR_1 = ((double) (((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) / ((double) (a * 2.0))));
		} else {
			VAR_1 = ((double) (((double) (0.5 * ((double) (y * ((double) (x / a)))))) - ((double) (4.5 * ((double) (z * ((double) (t / a))))))));
		}
		VAR = VAR_1;
	}
	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

Original7.6
Target5.3
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.14403070783397609 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* (* z 9.0) t)) < -1.4045951477552184e259

    1. Initial program 42.9

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

    3. Applied div-sub42.9

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

    4. Simplified22.1

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

    5. Simplified0.4

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

    if -1.4045951477552184e259 < (- (* x y) (* (* z 9.0) t)) < -2.37434969989275507e-155 or 7.62129135130543908e-201 < (- (* x y) (* (* z 9.0) t)) < 8.7252802097409812e239

    1. Initial program 0.3

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

    if -2.37434969989275507e-155 < (- (* x y) (* (* z 9.0) t)) < 7.62129135130543908e-201 or 8.7252802097409812e239 < (- (* x y) (* (* z 9.0) t))

    1. Initial program 21.9

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

    2. Taylor expanded around 0 21.8

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

    3. Simplified1.4

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -1.4045951477552184 \cdot 10^{259}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \left(\frac{z}{a} \cdot \frac{9}{2}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -2.37434969989275507 \cdot 10^{-155} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 7.62129135130543908 \cdot 10^{-201}\right) \land x \cdot y - \left(z \cdot 9\right) \cdot t \le 8.7252802097409812 \cdot 10^{239}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - 4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(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)))