Average Error: 7.6 → 1.0
Time: 13.4s
Precision: binary64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5.059425435089155 \cdot 10^{+174} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4.604298394816803 \cdot 10^{+286}\right):\\ \;\;\;\;\frac{x}{\frac{2}{y} \cdot a} - 4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{2 \cdot a} - \frac{z \cdot \left(9 \cdot t\right)}{2 \cdot a}\\ \end{array}\]
\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 -5.059425435089155 \cdot 10^{+174} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4.604298394816803 \cdot 10^{+286}\right):\\
\;\;\;\;\frac{x}{\frac{2}{y} \cdot a} - 4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\

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

\end{array}
(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- (* x y) (* (* z 9.0) t)) -5.059425435089155e+174)
         (not (<= (- (* x y) (* (* z 9.0) t)) 4.604298394816803e+286)))
   (- (/ x (* (/ 2.0 y) a)) (* 4.5 (* t (/ z a))))
   (- (/ (* x y) (* 2.0 a)) (/ (* z (* 9.0 t)) (* 2.0 a)))))
double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((((x * y) - ((z * 9.0) * t)) <= -5.059425435089155e+174) || !(((x * y) - ((z * 9.0) * t)) <= 4.604298394816803e+286)) {
		tmp = (x / ((2.0 / y) * a)) - (4.5 * (t * (z / a)));
	} else {
		tmp = ((x * y) / (2.0 * a)) - ((z * (9.0 * t)) / (2.0 * a));
	}
	return tmp;
}

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
Target5.4
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -5.05942543508915475e174 or 4.6042983948168027e286 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

    1. Initial program 33.5

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

    2. Simplified33.3

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

    4. Applied div-sub_binary64_1440533.3

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

    5. Simplified18.5

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

    6. Taylor expanded around 0 33.1

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - \color{blue}{4.5 \cdot \frac{t \cdot z}{a}}\]

    7. Simplified18.4

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - \color{blue}{4.5 \cdot \left(t \cdot \frac{z}{a}\right)}\]
    8. Using strategy rm

    9. Applied associate-/l*_binary64_143451.4

      \[\leadsto \color{blue}{\frac{x}{\frac{a \cdot 2}{y}}} - 4.5 \cdot \left(t \cdot \frac{z}{a}\right)\]

    10. Simplified1.4

      \[\leadsto \frac{x}{\color{blue}{\frac{2}{y} \cdot a}} - 4.5 \cdot \left(t \cdot \frac{z}{a}\right)\]

    if -5.05942543508915475e174 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 4.6042983948168027e286

    1. Initial program 0.8

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

    2. Simplified0.8

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

    4. Applied div-sub_binary64_144050.8

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5.059425435089155 \cdot 10^{+174} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4.604298394816803 \cdot 10^{+286}\right):\\ \;\;\;\;\frac{x}{\frac{2}{y} \cdot a} - 4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{2 \cdot a} - \frac{z \cdot \left(9 \cdot t\right)}{2 \cdot a}\\ \end{array}\]

Reproduce

herbie shell --seed 2021176 
(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)))