Average Error: 7.5 → 0.3
Time: 6.4s
Precision: binary64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t = -inf.0 \lor \neg \left(x \cdot y - z \cdot t \le -9.83050506131517413 \cdot 10^{-263} \lor \neg \left(x \cdot y - z \cdot t \le 9.585633402 \cdot 10^{-316}\right) \land x \cdot y - z \cdot t \le 2.5576774278082848 \cdot 10^{288}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \sqrt[3]{z \cdot \frac{t}{a}} \cdot \left(\sqrt[3]{z \cdot \frac{t}{a}} \cdot \sqrt[3]{z \cdot \frac{t}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot t = -inf.0 \lor \neg \left(x \cdot y - z \cdot t \le -9.83050506131517413 \cdot 10^{-263} \lor \neg \left(x \cdot y - z \cdot t \le 9.585633402 \cdot 10^{-316}\right) \land x \cdot y - z \cdot t \le 2.5576774278082848 \cdot 10^{288}\right):\\
\;\;\;\;x \cdot \frac{y}{a} - \sqrt[3]{z \cdot \frac{t}{a}} \cdot \left(\sqrt[3]{z \cdot \frac{t}{a}} \cdot \sqrt[3]{z \cdot \frac{t}{a}}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (((double) (((double) (x * y)) - ((double) (z * t)))) / a));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((((double) (((double) (x * y)) - ((double) (z * t)))) <= -inf.0) || !((((double) (((double) (x * y)) - ((double) (z * t)))) <= -9.830505061315174e-263) || (!(((double) (((double) (x * y)) - ((double) (z * t)))) <= 9.5856334022835e-316) && (((double) (((double) (x * y)) - ((double) (z * t)))) <= 2.557677427808285e+288))))) {
		VAR = ((double) (((double) (x * ((double) (y / a)))) - ((double) (((double) cbrt(((double) (z * ((double) (t / a)))))) * ((double) (((double) cbrt(((double) (z * ((double) (t / a)))))) * ((double) cbrt(((double) (z * ((double) (t / a))))))))))));
	} else {
		VAR = ((double) (((double) (((double) (x * y)) - ((double) (z * t)))) / a));
	}
	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

Original7.5
Target5.8
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z \lt -2.46868496869954822 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.30983112197837121 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* z t)) < -inf.0 or -9.83050506131517413e-263 < (- (* x y) (* z t)) < 9.585633402e-316 or 2.5576774278082848e288 < (- (* x y) (* z t))

    1. Initial program 49.7

      \[\frac{x \cdot y - z \cdot t}{a}\]
    2. Using strategy rm

    3. Applied div-sub49.7

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

    4. Simplified26.8

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

    5. Simplified0.2

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

    7. Applied add-cube-cbrt0.7

      \[\leadsto x \cdot \frac{y}{a} - \color{blue}{\left(\sqrt[3]{z \cdot \frac{t}{a}} \cdot \sqrt[3]{z \cdot \frac{t}{a}}\right) \cdot \sqrt[3]{z \cdot \frac{t}{a}}}\]

    if -inf.0 < (- (* x y) (* z t)) < -9.83050506131517413e-263 or 9.585633402e-316 < (- (* x y) (* z t)) < 2.5576774278082848e288

    1. Initial program 0.2

      \[\frac{x \cdot y - z \cdot t}{a}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t = -inf.0 \lor \neg \left(x \cdot y - z \cdot t \le -9.83050506131517413 \cdot 10^{-263} \lor \neg \left(x \cdot y - z \cdot t \le 9.585633402 \cdot 10^{-316}\right) \land x \cdot y - z \cdot t \le 2.5576774278082848 \cdot 10^{288}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \sqrt[3]{z \cdot \frac{t}{a}} \cdot \left(\sqrt[3]{z \cdot \frac{t}{a}} \cdot \sqrt[3]{z \cdot \frac{t}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.468684968699548e+170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

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