Average Error: 7.9 → 1.2
Time: 5.5s
Precision: binary64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -4.2557295129471394 \cdot 10^{+138} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 1.0490715896809505 \cdot 10^{+236}\right):\\ \;\;\;\;\frac{y}{a} \cdot \frac{x}{2} - t \cdot \left(\frac{z}{a} \cdot \frac{9}{2}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array}\]
\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 -4.2557295129471394 \cdot 10^{+138} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 1.0490715896809505 \cdot 10^{+236}\right):\\
\;\;\;\;\frac{y}{a} \cdot \frac{x}{2} - t \cdot \left(\frac{z}{a} \cdot \frac{9}{2}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{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)))) <= -4.2557295129471394e+138) || !(((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) <= 1.0490715896809505e+236))) {
		VAR = ((double) (((double) ((y / a) * (x / 2.0))) - ((double) (t * ((double) ((z / a) * (9.0 / 2.0)))))));
	} else {
		VAR = (((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) / ((double) (a * 2.0)));
	}
	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
Target5.5
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* (* z 9.0) t)) < -4.2557295129471394e138 or 1.04907158968095051e236 < (- (* x y) (* (* z 9.0) t))

    1. Initial program 26.1

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

    3. Applied div-sub26.1

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

    4. Simplified14.6

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

    5. Simplified2.1

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

    7. Applied *-un-lft-identity2.1

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

    8. Applied times-frac2.2

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

    9. Applied associate-*r*1.9

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

    10. Simplified1.9

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

    if -4.2557295129471394e138 < (- (* x y) (* (* z 9.0) t)) < 1.04907158968095051e236

    1. Initial program 0.9

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -4.2557295129471394 \cdot 10^{+138} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 1.0490715896809505 \cdot 10^{+236}\right):\\ \;\;\;\;\frac{y}{a} \cdot \frac{x}{2} - t \cdot \left(\frac{z}{a} \cdot \frac{9}{2}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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)))