Average Error: 7.7 → 0.7
Time: 4.4s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -7.16631312148373275 \cdot 10^{279} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 2.6286390614941382 \cdot 10^{302}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, \frac{y}{2}, -\frac{t}{2} \cdot \frac{z \cdot 9}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array}\]
\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 \le -7.16631312148373275 \cdot 10^{279} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 2.6286390614941382 \cdot 10^{302}\right):\\
\;\;\;\;\mathsf{fma}\left(\frac{x}{a}, \frac{y}{2}, -\frac{t}{2} \cdot \frac{z \cdot 9}{a}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot y}{a \cdot 2} - \frac{\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 (((x * y) - ((z * 9.0) * t)) / (a * 2.0));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((((x * y) - ((z * 9.0) * t)) <= -7.166313121483733e+279) || !(((x * y) - ((z * 9.0) * t)) <= 2.628639061494138e+302))) {
		VAR = fma((x / a), (y / 2.0), -((t / 2.0) * ((z * 9.0) / a)));
	} else {
		VAR = (((x * y) / (a * 2.0)) - (((z * 9.0) * t) / (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

Original7.7
Target5.5
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.14403070783397609 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* (* z 9.0) t)) < -7.166313121483733e+279 or 2.628639061494138e+302 < (- (* x y) (* (* z 9.0) t))

    1. Initial program 54.0

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

    3. Applied div-sub54.0

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

    5. Applied times-frac29.0

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

    6. Applied fma-neg29.0

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

    7. Simplified0.6

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

    if -7.166313121483733e+279 < (- (* x y) (* (* z 9.0) t)) < 2.628639061494138e+302

    1. Initial program 0.7

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

    3. Applied div-sub0.7

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \le -7.16631312148373275 \cdot 10^{279} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 2.6286390614941382 \cdot 10^{302}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, \frac{y}{2}, -\frac{t}{2} \cdot \frac{z \cdot 9}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array}\]

Reproduce

herbie shell --seed 2020103 +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)))