Average Error: 7.9 → 1.1
Time: 6.8s
Precision: binary64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -3.516223051018324 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - \left(9 \cdot t\right) \cdot \frac{z}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2.586343466927032 \cdot 10^{+183}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - \left(z \cdot 4.5\right) \cdot \frac{t}{a}\\ \end{array}\]
\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 \leq -3.516223051018324 \cdot 10^{+194}:\\
\;\;\;\;y \cdot \frac{x}{a \cdot 2} - \left(9 \cdot t\right) \cdot \frac{z}{a \cdot 2}\\

\mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2.586343466927032 \cdot 10^{+183}:\\
\;\;\;\;\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) - \left(z \cdot 4.5\right) \cdot \frac{t}{a}\\

\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)))) <= -3.516223051018324e+194)) {
		VAR = ((double) (((double) (y * (x / ((double) (a * 2.0))))) - ((double) (((double) (9.0 * t)) * (z / ((double) (a * 2.0)))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) <= 2.586343466927032e+183)) {
			VAR_1 = (((double) (((double) (x * y)) - ((double) (((double) (z * 9.0)) * t)))) / ((double) (a * 2.0)));
		} else {
			VAR_1 = ((double) (((double) (0.5 * ((double) (y * (x / a))))) - ((double) (((double) (z * 4.5)) * (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

Original7.9
Target5.7
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* (* z 9.0) t)) < -3.5162230510183241e194

    1. Initial program 26.7

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

    2. Simplified26.7

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

    4. Applied div-sub26.7

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

    5. Simplified15.2

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

    6. Simplified1.8

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

    if -3.5162230510183241e194 < (- (* x y) (* (* z 9.0) t)) < 2.5863434669270321e183

    1. Initial program 0.9

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

    if 2.5863434669270321e183 < (- (* x y) (* (* z 9.0) t))

    1. Initial program 28.1

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

    2. Simplified28.0

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

    3. Taylor expanded around 0 27.8

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

    4. Simplified1.8

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

    6. Applied associate-*r*1.9

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

    7. Simplified1.9

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -3.516223051018324 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - \left(9 \cdot t\right) \cdot \frac{z}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2.586343466927032 \cdot 10^{+183}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - \left(z \cdot 4.5\right) \cdot \frac{t}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020199 
(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)))