Data.Colour.Matrix:inverse from colour-2.3.3, B

Percentage Accurate: 91.5% → 95.7%

Time: 8.5s

Alternatives: 10

Speedup: 0.4×

• 28.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - (z * t)) / a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Python

def code(x, y, z, t, a):
	return ((x * y) - (z * t)) / a

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * t)) / a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Initial Program: 91.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - (z * t)) / a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Python

def code(x, y, z, t, a):
	return ((x * y) - (z * t)) / a

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * t)) / a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Alternative 1: 95.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot \frac{y}{z \cdot a} - \frac{t}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} - \frac{t}{a} \cdot \frac{z}{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 (- INFINITY))
     (* z (- (* x (/ y (* z a))) (/ t a)))
     (if (<= t_1 5e+268)
       (/ (fma x y (* t (- z))) a)
       (* y (- (/ x a) (* (/ t a) (/ z y))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z * ((x * (y / (z * a))) - (t / a));
	} else if (t_1 <= 5e+268) {
		tmp = fma(x, y, (t * -z)) / a;
	} else {
		tmp = y * ((x / a) - ((t / a) * (z / y)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x * Float64(y / Float64(z * a))) - Float64(t / a)));
	elseif (t_1 <= 5e+268)
		tmp = Float64(fma(x, y, Float64(t * Float64(-z))) / a);
	else
		tmp = Float64(y * Float64(Float64(x / a) - Float64(Float64(t / a) * Float64(z / y))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(N[(x * N[(y / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+268], N[(N[(x * y + N[(t * (-z)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(N[(x / a), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0

   1. Initial program 70.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 90.2%

      \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \frac{t}{a} + \frac{x \cdot y}{a \cdot z}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

      4. associate-/l* 93.8%

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

      5. *-commutative 93.8%

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

   5. Simplified 93.8%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.0000000000000002e268

   1. Initial program 98.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

      1. div-sub 97.2%

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

      2. *-commutative 97.2%

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

      3. div-sub 98.7%

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

      4. *-commutative 98.7%

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

      5. fmm-def 98.7%

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

      6. distribute-rgt-neg-out 98.7%

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

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}} \]
   4. Add Preprocessing

   if 5.0000000000000002e268 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 58.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot z}{a \cdot y} + \frac{x}{a}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 76.2%

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

      2. mul-1-neg 76.2%

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

      3. unsub-neg 76.2%

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

      4. times-frac 94.1%

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

   5. Simplified 94.1%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot \frac{y}{z \cdot a} - \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} - \frac{t}{a} \cdot \frac{z}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+256}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{a} - t \cdot \frac{\frac{z}{x}}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+256)))
     (* x (- (/ y a) (* t (/ (/ z x) a))))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+256)) {
		tmp = x * ((y / a) - (t * ((z / x) / a)));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+256)) {
		tmp = x * ((y / a) - (t * ((z / x) / a)));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+256):
		tmp = x * ((y / a) - (t * ((z / x) / a)))
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+256))
		tmp = Float64(x * Float64(Float64(y / a) - Float64(t * Float64(Float64(z / x) / a))));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+256)))
		tmp = x * ((y / a) - (t * ((z / x) / a)));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+256]], $MachinePrecision]], N[(x * N[(N[(y / a), $MachinePrecision] - N[(t * N[(N[(z / x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 2.0000000000000001e256 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 66.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 71.3%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \frac{t \cdot z}{a \cdot x} + \frac{y}{a}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

      4. associate-/l* 80.4%

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

      5. *-commutative 80.4%

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

      6. associate-/r* 89.9%

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

   5. Simplified 89.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2.0000000000000001e256

   1. Initial program 98.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 2 \cdot 10^{+256}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{a} - t \cdot \frac{\frac{z}{x}}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot \frac{y}{z \cdot a} - \frac{t}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} - \frac{t}{a} \cdot \frac{z}{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 (- INFINITY))
     (* z (- (* x (/ y (* z a))) (/ t a)))
     (if (<= t_1 5e+268) (/ t_1 a) (* y (- (/ x a) (* (/ t a) (/ z y))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z * ((x * (y / (z * a))) - (t / a));
	} else if (t_1 <= 5e+268) {
		tmp = t_1 / a;
	} else {
		tmp = y * ((x / a) - ((t / a) * (z / y)));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((x * (y / (z * a))) - (t / a));
	} else if (t_1 <= 5e+268) {
		tmp = t_1 / a;
	} else {
		tmp = y * ((x / a) - ((t / a) * (z / y)));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z * ((x * (y / (z * a))) - (t / a))
	elif t_1 <= 5e+268:
		tmp = t_1 / a
	else:
		tmp = y * ((x / a) - ((t / a) * (z / y)))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x * Float64(y / Float64(z * a))) - Float64(t / a)));
	elseif (t_1 <= 5e+268)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(y * Float64(Float64(x / a) - Float64(Float64(t / a) * Float64(z / y))));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z * ((x * (y / (z * a))) - (t / a));
	elseif (t_1 <= 5e+268)
		tmp = t_1 / a;
	else
		tmp = y * ((x / a) - ((t / a) * (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(N[(x * N[(y / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+268], N[(t$95$1 / a), $MachinePrecision], N[(y * N[(N[(x / a), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0

   1. Initial program 70.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 90.2%

      \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \frac{t}{a} + \frac{x \cdot y}{a \cdot z}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

      4. associate-/l* 93.8%

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

      5. *-commutative 93.8%

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

   5. Simplified 93.8%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.0000000000000002e268

   1. Initial program 98.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 5.0000000000000002e268 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 58.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot z}{a \cdot y} + \frac{x}{a}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 76.2%

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

      2. mul-1-neg 76.2%

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

      3. unsub-neg 76.2%

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

      4. times-frac 94.1%

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

   5. Simplified 94.1%

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

Alternative 4: 96.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{a} - t \cdot \frac{\frac{z}{x}}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} - \frac{t}{a} \cdot \frac{z}{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 (- INFINITY))
     (* x (- (/ y a) (* t (/ (/ z x) a))))
     (if (<= t_1 5e+268) (/ t_1 a) (* y (- (/ x a) (* (/ t a) (/ z y))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x * ((y / a) - (t * ((z / x) / a)));
	} else if (t_1 <= 5e+268) {
		tmp = t_1 / a;
	} else {
		tmp = y * ((x / a) - ((t / a) * (z / y)));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((y / a) - (t * ((z / x) / a)));
	} else if (t_1 <= 5e+268) {
		tmp = t_1 / a;
	} else {
		tmp = y * ((x / a) - ((t / a) * (z / y)));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x * ((y / a) - (t * ((z / x) / a)))
	elif t_1 <= 5e+268:
		tmp = t_1 / a
	else:
		tmp = y * ((x / a) - ((t / a) * (z / y)))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y / a) - Float64(t * Float64(Float64(z / x) / a))));
	elseif (t_1 <= 5e+268)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(y * Float64(Float64(x / a) - Float64(Float64(t / a) * Float64(z / y))));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x * ((y / a) - (t * ((z / x) / a)));
	elseif (t_1 <= 5e+268)
		tmp = t_1 / a;
	else
		tmp = y * ((x / a) - ((t / a) * (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x * N[(N[(y / a), $MachinePrecision] - N[(t * N[(N[(z / x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+268], N[(t$95$1 / a), $MachinePrecision], N[(y * N[(N[(x / a), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0

   1. Initial program 70.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 72.2%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \frac{t \cdot z}{a \cdot x} + \frac{y}{a}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

      4. associate-/l* 82.7%

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

      5. *-commutative 82.7%

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

      6. associate-/r* 90.7%

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

   5. Simplified 90.7%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.0000000000000002e268

   1. Initial program 98.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 5.0000000000000002e268 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 58.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot z}{a \cdot y} + \frac{x}{a}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 76.2%

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

      2. mul-1-neg 76.2%

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

      3. unsub-neg 76.2%

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

      4. times-frac 94.1%

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

   5. Simplified 94.1%

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

Alternative 5: 75.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-68}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+166}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+31)
   (/ y (/ a x))
   (if (<= (* x y) 2e-68)
     (/ (* t (- z)) a)
     (if (<= (* x y) 1e+166) (/ (* x y) a) (/ x (/ a y))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+31) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e-68) {
		tmp = (t * -z) / a;
	} else if ((x * y) <= 1e+166) {
		tmp = (x * y) / a;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-5d+31)) then
        tmp = y / (a / x)
    else if ((x * y) <= 2d-68) then
        tmp = (t * -z) / a
    else if ((x * y) <= 1d+166) then
        tmp = (x * y) / a
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+31) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e-68) {
		tmp = (t * -z) / a;
	} else if ((x * y) <= 1e+166) {
		tmp = (x * y) / a;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+31:
		tmp = y / (a / x)
	elif (x * y) <= 2e-68:
		tmp = (t * -z) / a
	elif (x * y) <= 1e+166:
		tmp = (x * y) / a
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+31)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 2e-68)
		tmp = Float64(Float64(t * Float64(-z)) / a);
	elseif (Float64(x * y) <= 1e+166)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+31)
		tmp = y / (a / x);
	elseif ((x * y) <= 2e-68)
		tmp = (t * -z) / a;
	elseif ((x * y) <= 1e+166)
		tmp = (x * y) / a;
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+31], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-68], N[(N[(t * (-z)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+166], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -5.00000000000000027e31

   1. Initial program 92.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.3%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 77.6%

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

   5. Simplified 77.6%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
   6. Step-by-step derivation

      1. *-commutative 77.6%

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

      2. associate-*l/ 76.3%

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

   7. Applied egg-rr 76.3%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 74.1%

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

      2. *-commutative 74.1%

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

   9. Applied egg-rr 74.1%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 74.1%

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

       2. clear-num 74.0%

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

       3. un-div-inv 74.7%

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

   11. Applied egg-rr 74.7%

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

   if -5.00000000000000027e31 < (*.f64 x y) < 2.00000000000000013e-68

   1. Initial program 94.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(t \cdot z\right)}}{a} \]
   4. Step-by-step derivation

      1. mul-1-neg 84.6%

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

      2. *-commutative 84.6%

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

      3. distribute-rgt-neg-in 84.6%

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

   5. Simplified 84.6%

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

   if 2.00000000000000013e-68 < (*.f64 x y) < 9.9999999999999994e165

   1. Initial program 86.5%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 59.9%

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

   if 9.9999999999999994e165 < (*.f64 x y)

   1. Initial program 79.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 93.9%

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

   5. Simplified 93.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
   6. Step-by-step derivation

      1. clear-num 93.9%

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

      2. un-div-inv 94.0%

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

   7. Applied egg-rr 94.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-68}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+166}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+232}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (* t (/ (- z) a))
   (if (<= (* z t) 2e+232) (/ (- (* x y) (* z t)) a) (* (/ t a) (- z)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = t * (-z / a);
	} else if ((z * t) <= 2e+232) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (t / a) * -z;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = t * (-z / a);
	} else if ((z * t) <= 2e+232) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (t / a) * -z;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = t * (-z / a)
	elif (z * t) <= 2e+232:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = (t / a) * -z
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(t * Float64(Float64(-z) / a));
	elseif (Float64(z * t) <= 2e+232)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(t / a) * Float64(-z));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = t * (-z / a);
	elseif ((z * t) <= 2e+232)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = (t / a) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+232], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -inf.0

   1. Initial program 53.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 53.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. mul-1-neg 53.1%

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

      2. associate-/l* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. distribute-neg-frac2 99.9%

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

   5. Simplified 99.9%

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

   if -inf.0 < (*.f64 z t) < 2.00000000000000011e232

   1. Initial program 95.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 2.00000000000000011e232 < (*.f64 z t)

   1. Initial program 73.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 73.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. mul-1-neg 73.7%

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

      2. *-commutative 73.7%

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

      3. associate-*r/ 96.5%

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

      4. distribute-rgt-neg-in 96.5%

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

      5. distribute-frac-neg 96.5%

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

   5. Simplified 96.5%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+232}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+31)
   (/ y (/ a x))
   (if (<= (* x y) 2e+70) (* (/ t a) (- z)) (/ x (/ a y)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+31) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e+70) {
		tmp = (t / a) * -z;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-5d+31)) then
        tmp = y / (a / x)
    else if ((x * y) <= 2d+70) then
        tmp = (t / a) * -z
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+31) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e+70) {
		tmp = (t / a) * -z;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+31:
		tmp = y / (a / x)
	elif (x * y) <= 2e+70:
		tmp = (t / a) * -z
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+31)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 2e+70)
		tmp = Float64(Float64(t / a) * Float64(-z));
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+31)
		tmp = y / (a / x);
	elseif ((x * y) <= 2e+70)
		tmp = (t / a) * -z;
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+31], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+70], N[(N[(t / a), $MachinePrecision] * (-z)), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.00000000000000027e31

   1. Initial program 92.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.3%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 77.6%

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

   5. Simplified 77.6%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
   6. Step-by-step derivation

      1. *-commutative 77.6%

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

      2. associate-*l/ 76.3%

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

   7. Applied egg-rr 76.3%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 74.1%

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

      2. *-commutative 74.1%

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

   9. Applied egg-rr 74.1%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 74.1%

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

       2. clear-num 74.0%

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

       3. un-div-inv 74.7%

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

   11. Applied egg-rr 74.7%

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

   if -5.00000000000000027e31 < (*.f64 x y) < 2.00000000000000015e70

   1. Initial program 92.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 75.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. mul-1-neg 75.0%

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

      2. *-commutative 75.0%

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

      3. associate-*r/ 73.9%

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

      4. distribute-rgt-neg-in 73.9%

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

      5. distribute-frac-neg 73.9%

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

   5. Simplified 73.9%

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

   if 2.00000000000000015e70 < (*.f64 x y)

   1. Initial program 81.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.6%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 76.4%

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

   5. Simplified 76.4%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
   6. Step-by-step derivation

      1. clear-num 76.4%

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

      2. un-div-inv 77.4%

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

   7. Applied egg-rr 77.4%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-49)
   (/ y (/ a x))
   (if (<= (* x y) 2e+70) (* t (/ (- z) a)) (/ x (/ a y)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-49) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e+70) {
		tmp = t * (-z / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-2d-49)) then
        tmp = y / (a / x)
    else if ((x * y) <= 2d+70) then
        tmp = t * (-z / a)
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-49) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e+70) {
		tmp = t * (-z / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-49:
		tmp = y / (a / x)
	elif (x * y) <= 2e+70:
		tmp = t * (-z / a)
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-49)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 2e+70)
		tmp = Float64(t * Float64(Float64(-z) / a));
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-49)
		tmp = y / (a / x);
	elseif ((x * y) <= 2e+70)
		tmp = t * (-z / a);
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-49], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+70], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999987e-49

   1. Initial program 92.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 70.5%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 71.5%

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

   5. Simplified 71.5%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
   6. Step-by-step derivation

      1. *-commutative 71.5%

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

      2. associate-*l/ 70.5%

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

   7. Applied egg-rr 70.5%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 68.6%

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

      2. *-commutative 68.6%

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

   9. Applied egg-rr 68.6%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 68.6%

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

       2. clear-num 68.5%

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

       3. un-div-inv 69.1%

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

   11. Applied egg-rr 69.1%

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

   if -1.99999999999999987e-49 < (*.f64 x y) < 2.00000000000000015e70

   1. Initial program 93.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. mul-1-neg 76.1%

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

      2. associate-/l* 76.0%

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

      3. distribute-rgt-neg-in 76.0%

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

      4. distribute-neg-frac2 76.0%

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

   5. Simplified 76.0%

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

   if 2.00000000000000015e70 < (*.f64 x y)

   1. Initial program 81.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.6%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 76.4%

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

   5. Simplified 76.4%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
   6. Step-by-step derivation

      1. clear-num 76.4%

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

      2. un-div-inv 77.4%

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

   7. Applied egg-rr 77.4%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 0:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) 0.0) (* y (/ x a)) (* x (/ y a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 0.0) {
		tmp = y * (x / a);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= 0.0d0) then
        tmp = y * (x / a)
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 0.0) {
		tmp = y * (x / a);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= 0.0:
		tmp = y * (x / a)
	else:
		tmp = x * (y / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= 0.0)
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= 0.0)
		tmp = y * (x / a);
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], 0.0], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 0.0

   1. Initial program 93.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 45.6%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 47.3%

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

   5. Simplified 47.3%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
   6. Step-by-step derivation

      1. *-commutative 47.3%

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

      2. associate-*l/ 45.6%

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

   7. Applied egg-rr 45.6%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 45.5%

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

      2. *-commutative 45.5%

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

   9. Applied egg-rr 45.5%

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

   if 0.0 < (*.f64 x y)

   1. Initial program 87.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 50.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 47.6%

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

   5. Simplified 47.6%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 0:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ x \cdot \frac{y}{a} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* x (/ y a)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return x * (y / a);
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x * (y / a)
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return x * (y / a);
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return x * (y / a)

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(x * Float64(y / a))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = x * (y / a);
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.6%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 48.0%

   \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
4. Step-by-step derivation

   1. associate-*r/ 47.4%

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

5. Simplified 47.4%

   \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
6. Add Preprocessing

Developer Target 1: 90.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* (/ y a) x) (* (/ t a) z))))
   (if (< z -2.468684968699548e+170)
     t_1
     (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y / a) * x) - ((t / a) * z)
    if (z < (-2.468684968699548d+170)) then
        tmp = t_1
    else if (z < 6.309831121978371d-71) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y / a) * x) - ((t / a) * z)
	tmp = 0
	if z < -2.468684968699548e+170:
		tmp = t_1
	elif z < 6.309831121978371e-71:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y / a) * x) - Float64(Float64(t / a) * z))
	tmp = 0.0
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y / a) * x) - ((t / a) * z);
	tmp = 0.0;
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.468684968699548e+170], t$95$1, If[Less[z, 6.309831121978371e-71], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024180 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -246868496869954800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6309831121978371/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z)))))

  (/ (- (* x y) (* z t)) a))