Average Error: 7.5 → 0.4
Time: 6.0s
Precision: binary64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5.597703280546908 \cdot 10^{+294}:\\ \;\;\;\;x \cdot \frac{y}{a} - \sqrt[3]{\frac{t}{a}} \cdot \left(z \cdot \left(\sqrt[3]{\frac{t}{a}} \cdot \sqrt[3]{\frac{t}{a}}\right)\right)\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq -3.5672081764824935 \cdot 10^{-218}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 0:\\ \;\;\;\;\sqrt[3]{\frac{y}{a}} \cdot \left(x \cdot \left(\sqrt[3]{\frac{y}{a}} \cdot \sqrt[3]{\frac{y}{a}}\right)\right) - z \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 7.300349531652721 \cdot 10^{+305}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - \sqrt[3]{\frac{t}{a}} \cdot \left(z \cdot \left(\sqrt[3]{\frac{t}{a}} \cdot \sqrt[3]{\frac{t}{a}}\right)\right)\\ \end{array}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot t \leq -5.597703280546908 \cdot 10^{+294}:\\
\;\;\;\;x \cdot \frac{y}{a} - \sqrt[3]{\frac{t}{a}} \cdot \left(z \cdot \left(\sqrt[3]{\frac{t}{a}} \cdot \sqrt[3]{\frac{t}{a}}\right)\right)\\

\mathbf{elif}\;x \cdot y - z \cdot t \leq -3.5672081764824935 \cdot 10^{-218}:\\
\;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\

\mathbf{elif}\;x \cdot y - z \cdot t \leq 0:\\
\;\;\;\;\sqrt[3]{\frac{y}{a}} \cdot \left(x \cdot \left(\sqrt[3]{\frac{y}{a}} \cdot \sqrt[3]{\frac{y}{a}}\right)\right) - z \cdot \frac{t}{a}\\

\mathbf{elif}\;x \cdot y - z \cdot t \leq 7.300349531652721 \cdot 10^{+305}:\\
\;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{y}{a} - \sqrt[3]{\frac{t}{a}} \cdot \left(z \cdot \left(\sqrt[3]{\frac{t}{a}} \cdot \sqrt[3]{\frac{t}{a}}\right)\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)))) <= -5.597703280546908e+294)) {
		VAR = ((double) (((double) (x * (y / a))) - ((double) (((double) cbrt((t / a))) * ((double) (z * ((double) (((double) cbrt((t / a))) * ((double) cbrt((t / a)))))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * y)) - ((double) (z * t)))) <= -3.5672081764824935e-218)) {
			VAR_1 = (((double) (((double) (x * y)) - ((double) (z * t)))) / a);
		} else {
			double VAR_2;
			if ((((double) (((double) (x * y)) - ((double) (z * t)))) <= 0.0)) {
				VAR_2 = ((double) (((double) (((double) cbrt((y / a))) * ((double) (x * ((double) (((double) cbrt((y / a))) * ((double) cbrt((y / a))))))))) - ((double) (z * (t / a)))));
			} else {
				double VAR_3;
				if ((((double) (((double) (x * y)) - ((double) (z * t)))) <= 7.300349531652721e+305)) {
					VAR_3 = (((double) (((double) (x * y)) - ((double) (z * t)))) / a);
				} else {
					VAR_3 = ((double) (((double) (x * (y / a))) - ((double) (((double) cbrt((t / a))) * ((double) (z * ((double) (((double) cbrt((t / a))) * ((double) cbrt((t / a)))))))))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		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

Original7.5
Target5.9
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* z t)) < -5.5977032805469076e294 or 7.3003495316527209e305 < (- (* x y) (* z t))

    1. Initial program 60.1

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

    3. Applied div-sub60.1

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

    4. Simplified32.2

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

    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

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

    8. Applied associate-*r*0.8

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

    if -5.5977032805469076e294 < (- (* x y) (* z t)) < -3.56720817648249347e-218 or 0.0 < (- (* x y) (* z t)) < 7.3003495316527209e305

    1. Initial program 0.3

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

    if -3.56720817648249347e-218 < (- (* x y) (* z t)) < 0.0

    1. Initial program 11.0

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

    3. Applied div-sub11.0

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

    4. Simplified7.6

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

    5. Simplified0.5

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

    7. Applied add-cube-cbrt0.7

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

    8. Applied associate-*r*0.7

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5.597703280546908 \cdot 10^{+294}:\\ \;\;\;\;x \cdot \frac{y}{a} - \sqrt[3]{\frac{t}{a}} \cdot \left(z \cdot \left(\sqrt[3]{\frac{t}{a}} \cdot \sqrt[3]{\frac{t}{a}}\right)\right)\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq -3.5672081764824935 \cdot 10^{-218}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 0:\\ \;\;\;\;\sqrt[3]{\frac{y}{a}} \cdot \left(x \cdot \left(\sqrt[3]{\frac{y}{a}} \cdot \sqrt[3]{\frac{y}{a}}\right)\right) - z \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 7.300349531652721 \cdot 10^{+305}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - \sqrt[3]{\frac{t}{a}} \cdot \left(z \cdot \left(\sqrt[3]{\frac{t}{a}} \cdot \sqrt[3]{\frac{t}{a}}\right)\right)\\ \end{array}\]

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))