Average Error: 7.7 → 1.3
Time: 5.6s
Precision: binary64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5.645308367208462 \cdot 10^{+181} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 8.297223431019089 \cdot 10^{+152}\right):\\ \;\;\;\;\frac{x}{\frac{a}{\frac{y}{2}}} - \left(z \cdot 4.5\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array}\]
\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 -5.645308367208462 \cdot 10^{+181} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 8.297223431019089 \cdot 10^{+152}\right):\\
\;\;\;\;\frac{x}{\frac{a}{\frac{y}{2}}} - \left(z \cdot 4.5\right) \cdot \frac{t}{a}\\

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

\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)) -5.645308367208462e+181)
         (not (<= (- (* x y) (* (* z 9.0) t)) 8.297223431019089e+152)))
   (- (/ x (/ a (/ y 2.0))) (* (* z 4.5) (/ t a)))
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))))
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)) <= -5.645308367208462e+181) || !(((x * y) - ((z * 9.0) * t)) <= 8.297223431019089e+152)) {
		tmp = (x / (a / (y / 2.0))) - ((z * 4.5) * (t / a));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	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

Original7.7
Target5.6
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -5.64530836720846197e181 or 8.297223431019089e152 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

    1. Initial program 23.0

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

    3. Applied associate-*l*_binary6422.9

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

    5. Applied div-sub_binary6422.9

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

    6. Simplified22.7

      \[\leadsto \frac{x \cdot y}{a \cdot 2} - \color{blue}{4.5 \cdot \frac{z \cdot t}{a}}\]
    7. Using strategy rm

    8. Applied associate-/l*_binary6413.2

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

    9. Simplified13.2

      \[\leadsto \frac{x}{\color{blue}{\frac{a}{\frac{y}{2}}}} - 4.5 \cdot \frac{z \cdot t}{a}\]
    10. Using strategy rm

    11. Applied *-un-lft-identity_binary6413.2

      \[\leadsto \frac{x}{\frac{a}{\frac{y}{2}}} - 4.5 \cdot \frac{z \cdot t}{\color{blue}{1 \cdot a}}\]

    12. Applied times-frac_binary642.2

      \[\leadsto \frac{x}{\frac{a}{\frac{y}{2}}} - 4.5 \cdot \color{blue}{\left(\frac{z}{1} \cdot \frac{t}{a}\right)}\]

    13. Applied associate-*r*_binary642.2

      \[\leadsto \frac{x}{\frac{a}{\frac{y}{2}}} - \color{blue}{\left(4.5 \cdot \frac{z}{1}\right) \cdot \frac{t}{a}}\]

    14. Simplified2.2

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

    if -5.64530836720846197e181 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 8.297223431019089e152

    1. Initial program 0.9

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

    3. Applied associate-*l*_binary640.9

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5.645308367208462 \cdot 10^{+181} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 8.297223431019089 \cdot 10^{+152}\right):\\ \;\;\;\;\frac{x}{\frac{a}{\frac{y}{2}}} - \left(z \cdot 4.5\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array}\]

Reproduce

herbie shell --seed 2020224 
(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)))