Average Error: 7.9 → 0.8
Time: 5.7s
Precision: binary64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1.735744315352809 \cdot 10^{+297}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - 4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4.564173446679101 \cdot 10^{+256}:\\ \;\;\;\;\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - \left(9 \cdot t\right) \cdot \frac{z}{a \cdot 2}\\ \end{array}\]
\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 \leq -1.735744315352809 \cdot 10^{+297}:\\
\;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - 4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\

\mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4.564173446679101 \cdot 10^{+256}:\\
\;\;\;\;\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{1}{a \cdot 2}\\

\mathbf{else}:\\
\;\;\;\;y \cdot \frac{x}{a \cdot 2} - \left(9 \cdot t\right) \cdot \frac{z}{a \cdot 2}\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return (((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)))) <= -1.735744315352809e+297)) {
		VAR = ((double) (((double) (0.5 * ((double) (y * (x / a))))) - ((double) (4.5 * ((double) (z * (t / a)))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) <= 4.564173446679101e+256)) {
			VAR_1 = ((double) (((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) * (1.0 / ((double) (a * 2.0)))));
		} else {
			VAR_1 = ((double) (((double) (y * (x / ((double) (a * 2.0))))) - ((double) (((double) (9.0 * t)) * (z / ((double) (a * 2.0)))))));
		}
		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

Original7.9
Target5.9
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* (* z 9.0) t)) < -1.735744315352809e297

    1. Initial program Error: 59.2 bits

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

    2. Taylor expanded around 0 Error: 58.6 bits

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

    3. SimplifiedError: 0.4 bits

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

    if -1.735744315352809e297 < (- (* x y) (* (* z 9.0) t)) < 4.5641734466791008e256

    1. Initial program Error: 0.8 bits

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

    3. Applied div-invError: 0.9 bits

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

    if 4.5641734466791008e256 < (- (* x y) (* (* z 9.0) t))

    1. Initial program Error: 42.0 bits

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

    2. SimplifiedError: 41.5 bits

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

    4. Applied div-subError: 41.5 bits

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

    5. SimplifiedError: 21.9 bits

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

    6. SimplifiedError: 0.8 bits

      \[\leadsto y \cdot \frac{x}{a \cdot 2} - \color{blue}{\left(9 \cdot t\right) \cdot \frac{z}{a \cdot 2}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplificationError: 0.8 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1.735744315352809 \cdot 10^{+297}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - 4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4.564173446679101 \cdot 10^{+256}:\\ \;\;\;\;\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - \left(9 \cdot t\right) \cdot \frac{z}{a \cdot 2}\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(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)))