Average Error: 7.9 → 4.6
Time: 5.5s
Precision: binary64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y = -inf.0:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t \cdot z}{a}\\ \mathbf{elif}\;x \cdot y \le 6.57685065068012406 \cdot 10^{170}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{t}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z}{\sqrt[3]{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{t \cdot z}{a}\\ \end{array}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y = -inf.0:\\
\;\;\;\;x \cdot \frac{y}{a} - \frac{t \cdot z}{a}\\

\mathbf{elif}\;x \cdot y \le 6.57685065068012406 \cdot 10^{170}:\\
\;\;\;\;\frac{x \cdot y}{a} - \frac{t}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z}{\sqrt[3]{a}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{a}{y}} - \frac{t \cdot z}{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) (x * y)) <= -inf.0)) {
		VAR = ((double) (((double) (x * ((double) (y / a)))) - ((double) (((double) (t * z)) / a))));
	} else {
		double VAR_1;
		if ((((double) (x * y)) <= 6.576850650680124e+170)) {
			VAR_1 = ((double) (((double) (((double) (x * y)) / a)) - ((double) (((double) (t / ((double) (((double) cbrt(a)) * ((double) cbrt(a)))))) * ((double) (z / ((double) cbrt(a))))))));
		} else {
			VAR_1 = ((double) (((double) (x / ((double) (a / y)))) - ((double) (((double) (t * z)) / a))));
		}
		VAR = VAR_1;
	}
	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

Original7.9
Target6.1
Herbie4.6
\[\begin{array}{l} \mathbf{if}\;z \lt -2.46868496869954822 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.30983112197837121 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -inf.0

    1. Initial program 64.0

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

    3. Applied div-sub64.0

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

    4. Simplified64.0

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

    6. Applied *-un-lft-identity64.0

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

    7. Applied times-frac6.8

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

    8. Simplified6.8

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

    if -inf.0 < (* x y) < 6.57685065068012406e170

    1. Initial program 4.3

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

    3. Applied div-sub4.3

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

    4. Simplified4.3

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

    6. Applied add-cube-cbrt4.8

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

    7. Applied times-frac4.3

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

    if 6.57685065068012406e170 < (* x y)

    1. Initial program 23.5

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

    3. Applied div-sub23.5

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

    4. Simplified23.5

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

    6. Applied associate-/l*6.6

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

  4. Final simplification4.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y = -inf.0:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t \cdot z}{a}\\ \mathbf{elif}\;x \cdot y \le 6.57685065068012406 \cdot 10^{170}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{t}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z}{\sqrt[3]{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{t \cdot z}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020177 
(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))