Average Error: 7.9 → 0.9
Time: 5.1s
Precision: binary64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot y - z \cdot t}{a} = -inf.0:\\ \;\;\;\;x \cdot \frac{y}{a} - \sqrt[3]{\frac{t}{a}} \cdot \left(z \cdot \left(\sqrt[3]{\frac{t}{a}} \cdot \sqrt[3]{\frac{t}{a}}\right)\right)\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot t}{a} \le 8.0761594453370666 \cdot 10^{307}:\\ \;\;\;\;\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot \frac{y}{a} - z \cdot \frac{t}{a}} \cdot \sqrt{x \cdot \frac{y}{a} - z \cdot \frac{t}{a}}\\ \end{array}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot y - z \cdot t}{a} = -inf.0:\\
\;\;\;\;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}\;\frac{x \cdot y - z \cdot t}{a} \le 8.0761594453370666 \cdot 10^{307}:\\
\;\;\;\;\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}\\

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

\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)))) / a) <= -inf.0)) {
		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)))) / a) <= 8.076159445337067e+307)) {
			VAR_1 = ((double) (((double) (((double) (x * y)) - ((double) (z * t)))) * (1.0 / a)));
		} else {
			VAR_1 = ((double) (((double) sqrt(((double) (((double) (x * (y / a))) - ((double) (z * (t / a))))))) * ((double) sqrt(((double) (((double) (x * (y / a))) - ((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

Original7.9
Target6.0
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;z \lt -2.46868496869954822 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.30983112197837121 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (- (* x y) (* z t)) a) < -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. Simplified35.9

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

    5. Simplified0.3

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

    7. Applied add-cube-cbrt0.9

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

    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 -inf.0 < (/ (- (* x y) (* z t)) a) < 8.0761594453370666e307

    1. Initial program 0.7

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

    3. Applied div-inv0.8

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

    if 8.0761594453370666e307 < (/ (- (* x y) (* z t)) a)

    1. Initial program 63.9

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

    3. Applied div-sub63.9

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

    4. Simplified35.1

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

    5. Simplified0.3

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

    7. Applied add-sqr-sqrt2.3

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y - z \cdot t}{a} = -inf.0:\\ \;\;\;\;x \cdot \frac{y}{a} - \sqrt[3]{\frac{t}{a}} \cdot \left(z \cdot \left(\sqrt[3]{\frac{t}{a}} \cdot \sqrt[3]{\frac{t}{a}}\right)\right)\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot t}{a} \le 8.0761594453370666 \cdot 10^{307}:\\ \;\;\;\;\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot \frac{y}{a} - z \cdot \frac{t}{a}} \cdot \sqrt{x \cdot \frac{y}{a} - z \cdot \frac{t}{a}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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))