Average Error: 7.8 → 0.8
Time: 5.6s
Precision: binary64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{y}{a}\right) - z \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 9.781667072520984 \cdot 10^{+296}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - \sqrt[3]{z \cdot \frac{t}{a}} \cdot \left(\sqrt[3]{z \cdot \frac{t}{a}} \cdot \sqrt[3]{z \cdot \frac{t}{a}}\right)\\ \end{array}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\
\;\;\;\;\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{y}{a}\right) - z \cdot \frac{t}{a}\\

\mathbf{elif}\;x \cdot y - z \cdot t \leq 9.781667072520984 \cdot 10^{+296}:\\
\;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\

\mathbf{else}:\\
\;\;\;\;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)\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return (((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)))) <= ((double) -(((double) INFINITY))))) {
		VAR = ((double) (((double) (((double) (((double) cbrt(x)) * ((double) cbrt(x)))) * ((double) (((double) cbrt(x)) * (y / a))))) - ((double) (z * (t / a)))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * y)) - ((double) (z * t)))) <= 9.781667072520984e+296)) {
			VAR_1 = (((double) (((double) (x * y)) - ((double) (z * t)))) / a);
		} else {
			VAR_1 = ((double) (((double) (x * (y / a))) - ((double) (((double) cbrt(((double) (z * (t / a))))) * ((double) (((double) cbrt(((double) (z * (t / a))))) * ((double) cbrt(((double) (z * (t / 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

Original7.8
Target5.7
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* z t)) < -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. Simplified31.5

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

    5. Simplified0.2

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

    7. Applied add-cube-cbrt0.8

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

    8. Applied associate-*l*0.8

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

    9. Simplified0.8

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

    if -inf.0 < (- (* x y) (* z t)) < 9.78166707252098428e296

    1. Initial program 0.8

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

    if 9.78166707252098428e296 < (- (* x y) (* z t))

    1. Initial program 59.4

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

    3. Applied div-sub59.4

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

    4. Simplified31.2

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

    5. Simplified0.3

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

    7. Applied add-cube-cbrt0.8

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{y}{a}\right) - z \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 9.781667072520984 \cdot 10^{+296}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - \sqrt[3]{z \cdot \frac{t}{a}} \cdot \left(\sqrt[3]{z \cdot \frac{t}{a}} \cdot \sqrt[3]{z \cdot \frac{t}{a}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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))