Average Error: 7.7 → 1.4
Time: 4.1s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -4.68826952969413041 \cdot 10^{141} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 4.4252767597399196 \cdot 10^{204}\right):\\ \;\;\;\;\frac{x}{\frac{a \cdot 2}{y}} - \frac{z \cdot 9}{2} \cdot \frac{t - \left(\left(-t\right) + t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot y - 9 \cdot \left(t \cdot z\right)\right) + \left(z \cdot 9\right) \cdot \left(\left(-t\right) + t\right)}{a \cdot 2}\\ \end{array}\]
\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 \le -4.68826952969413041 \cdot 10^{141} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 4.4252767597399196 \cdot 10^{204}\right):\\
\;\;\;\;\frac{x}{\frac{a \cdot 2}{y}} - \frac{z \cdot 9}{2} \cdot \frac{t - \left(\left(-t\right) + t\right)}{a}\\

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

\end{array}
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 temp;
	if (((((x * y) - ((z * 9.0) * t)) <= -4.6882695296941304e+141) || !(((x * y) - ((z * 9.0) * t)) <= 4.4252767597399196e+204))) {
		temp = ((x / ((a * 2.0) / y)) - (((z * 9.0) / 2.0) * ((t - (-t + t)) / a)));
	} else {
		temp = ((((x * y) - (9.0 * (t * z))) + ((z * 9.0) * (-t + t))) / (a * 2.0));
	}
	return temp;
}

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
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.14403070783397609 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* (* z 9.0) t)) < -4.6882695296941304e+141 or 4.4252767597399196e+204 < (- (* x y) (* (* z 9.0) t))

    1. Initial program 23.5

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

    3. Applied prod-diff23.5

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

    4. Simplified23.5

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

    5. Simplified23.5

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

    7. Applied associate-+l-23.5

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

    8. Applied div-sub23.5

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

    9. Simplified13.1

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

    11. Applied associate-/l*2.3

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

    if -4.6882695296941304e+141 < (- (* x y) (* (* z 9.0) t)) < 4.4252767597399196e+204

    1. Initial program 1.0

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

    3. Applied prod-diff1.0

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

    4. Simplified1.0

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

    5. Simplified1.0

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -4.68826952969413041 \cdot 10^{141} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 4.4252767597399196 \cdot 10^{204}\right):\\ \;\;\;\;\frac{x}{\frac{a \cdot 2}{y}} - \frac{z \cdot 9}{2} \cdot \frac{t - \left(\left(-t\right) + t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot y - 9 \cdot \left(t \cdot z\right)\right) + \left(z \cdot 9\right) \cdot \left(\left(-t\right) + t\right)}{a \cdot 2}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(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 t))) (* a 2)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9) t)) (* a 2)))