Average Error: 7.1 → 1.5
Time: 4.1s
Precision: 64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \le -3.64204206634211584 \cdot 10^{177} \lor \neg \left(x \cdot y - z \cdot t \le 1.17082506323268331 \cdot 10^{137}\right):\\ \;\;\;\;\frac{y}{\frac{a}{x}} - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}\\ \end{array}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot t \le -3.64204206634211584 \cdot 10^{177} \lor \neg \left(x \cdot y - z \cdot t \le 1.17082506323268331 \cdot 10^{137}\right):\\
\;\;\;\;\frac{y}{\frac{a}{x}} - \frac{t}{\frac{a}{z}}\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{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)))) <= -3.642042066342116e+177) || !(((double) (((double) (x * y)) - ((double) (z * t)))) <= 1.1708250632326833e+137))) {
		VAR = ((double) (((double) (y / ((double) (a / x)))) - ((double) (t / ((double) (a / z))))));
	} else {
		VAR = ((double) (((double) (((double) (x * y)) - ((double) (z * t)))) * ((double) (1.0 / 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

Original7.1
Target6.0
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt -2.46868496869954822 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.30983112197837121 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* z t)) < -3.642042066342116e+177 or 1.1708250632326833e+137 < (- (* x y) (* z t))

    1. Initial program 20.7

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

    3. Applied add-cube-cbrt21.4

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

    4. Applied associate-/r*21.4

      \[\leadsto \color{blue}{\frac{\frac{x \cdot y - z \cdot t}{\sqrt[3]{a} \cdot \sqrt[3]{a}}}{\sqrt[3]{a}}}\]
    5. Using strategy rm

    6. Applied div-sub21.4

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

    7. Applied div-sub21.4

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

    8. Simplified12.8

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

    9. Simplified2.7

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

    if -3.642042066342116e+177 < (- (* x y) (* z t)) < 1.1708250632326833e+137

    1. Initial program 0.9

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

    3. Applied div-inv1.0

      \[\leadsto \color{blue}{\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \le -3.64204206634211584 \cdot 10^{177} \lor \neg \left(x \cdot y - z \cdot t \le 1.17082506323268331 \cdot 10^{137}\right):\\ \;\;\;\;\frac{y}{\frac{a}{x}} - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020128 
(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))