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

Percentage Accurate: 91.3% → 97.2%

Time: 8.0s

Alternatives: 9

Speedup: 0.5×

• 28.0% 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: 91.3% 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: 97.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{a} - t \cdot \frac{z}{a}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+285}:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y 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))
     (- (* y (/ x a)) (* t (/ z a)))
     (if (<= t_1 4e+285) (/ t_1 a) (- (/ x (/ a y)) (/ z (/ a t)))))))

C

assert(x < y);
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 = (y * (x / a)) - (t * (z / a));
	} else if (t_1 <= 4e+285) {
		tmp = t_1 / a;
	} else {
		tmp = (x / (a / y)) - (z / (a / t));
	}
	return tmp;
}

Java

assert x < y;
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 = (y * (x / a)) - (t * (z / a));
	} else if (t_1 <= 4e+285) {
		tmp = t_1 / a;
	} else {
		tmp = (x / (a / y)) - (z / (a / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y * (x / a)) - (t * (z / a))
	elif t_1 <= 4e+285:
		tmp = t_1 / a
	else:
		tmp = (x / (a / y)) - (z / (a / t))
	return tmp

Julia

x, y = sort([x, y])
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(Float64(y * Float64(x / a)) - Float64(t * Float64(z / a)));
	elseif (t_1 <= 4e+285)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y * (x / a)) - (t * (z / a));
	elseif (t_1 <= 4e+285)
		tmp = t_1 / a;
	else
		tmp = (x / (a / y)) - (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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[(N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+285], N[(t$95$1 / a), $MachinePrecision], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 66.6%

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

   2. Taylor expanded in x around 0 63.0%

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

      1. +-commutative 63.0%

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

      2. mul-1-neg 63.0%

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

      3. unsub-neg 63.0%

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

      4. associate-*l/ 72.6%

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

      5. *-commutative 72.6%

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

      6. div-inv 72.6%

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

      7. associate-*l* 92.6%

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

      8. div-inv 92.6%

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

   4. Applied egg-rr 92.6%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 3.9999999999999999e285

   1. Initial program 99.7%

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

   if 3.9999999999999999e285 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 65.2%

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

      1. div-sub 55.2%

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

      2. associate-/l* 64.3%

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

      3. associate-/l* 79.9%

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

   3. Applied egg-rr 79.9%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{a} - t \cdot \frac{z}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 4 \cdot 10^{+285}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 2: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+276}\right):\\ \;\;\;\;y \cdot \frac{x}{a} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y 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+276)))
     (- (* y (/ x a)) (* t (/ z a)))
     (/ t_1 a))))

C

assert(x < y);
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+276)) {
		tmp = (y * (x / a)) - (t * (z / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Java

assert x < y;
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+276)) {
		tmp = (y * (x / a)) - (t * (z / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
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+276):
		tmp = (y * (x / a)) - (t * (z / a))
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y = sort([x, y])
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+276))
		tmp = Float64(Float64(y * Float64(x / a)) - Float64(t * Float64(z / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
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+276)))
		tmp = (y * (x / a)) - (t * (z / a));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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+276]], $MachinePrecision]], N[(N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $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 2.0000000000000001e276 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 67.0%

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

   2. Taylor expanded in x around 0 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

      4. associate-*l/ 71.0%

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

      5. *-commutative 71.0%

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

      6. div-inv 71.0%

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

      7. associate-*l* 88.2%

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

      8. div-inv 88.1%

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

   4. Applied egg-rr 88.1%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2.0000000000000001e276

   1. Initial program 99.7%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 2 \cdot 10^{+276}\right):\\ \;\;\;\;y \cdot \frac{x}{a} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 3: 94.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \cdot t \leq 10^{+284}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) -2e+194)
   (* z (/ (- t) a))
   (if (<= (* z t) 1e+284) (/ (- (* x y) (* z t)) a) (/ (- t) (/ a z)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -2e+194) {
		tmp = z * (-t / a);
	} else if ((z * t) <= 1e+284) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = -t / (a / z);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 ((z * t) <= (-2d+194)) then
        tmp = z * (-t / a)
    else if ((z * t) <= 1d+284) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = -t / (a / z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -2e+194) {
		tmp = z * (-t / a);
	} else if ((z * t) <= 1e+284) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = -t / (a / z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -2e+194:
		tmp = z * (-t / a)
	elif (z * t) <= 1e+284:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = -t / (a / z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= -2e+194)
		tmp = Float64(z * Float64(Float64(-t) / a));
	elseif (Float64(z * t) <= 1e+284)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(-t) / Float64(a / z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= -2e+194)
		tmp = z * (-t / a);
	elseif ((z * t) <= 1e+284)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = -t / (a / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], -2e+194], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+284], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.99999999999999989e194

   1. Initial program 79.5%

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

   2. Taylor expanded in x around 0 72.3%

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

      1. clear-num 72.3%

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

      2. associate-/r/ 72.3%

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

   4. Applied egg-rr 72.3%

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

      1. +-commutative 72.3%

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

      2. associate-*r* 72.3%

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

      3. mul-1-neg 72.3%

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

      4. cancel-sign-sub-inv 72.3%

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

      5. div-inv 72.3%

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

      6. *-commutative 72.3%

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

      7. distribute-rgt-out-- 79.4%

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

   6. Applied egg-rr 79.4%

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

   7. Taylor expanded in x around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-*r/ 96.3%

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

      4. distribute-rgt-neg-in 96.3%

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

      5. distribute-neg-frac 96.3%

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

   9. Simplified 96.3%

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

   if -1.99999999999999989e194 < (*.f64 z t) < 1.00000000000000008e284

   1. Initial program 96.3%

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

   if 1.00000000000000008e284 < (*.f64 z t)

   1. Initial program 52.6%

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

   2. Taylor expanded in x around 0 52.6%

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

      1. mul-1-neg 52.6%

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

      2. associate-/l* 92.6%

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

   4. Simplified 92.6%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \cdot t \leq 10^{+284}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \end{array} \]

Alternative 4: 65.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+63} \lor \neg \left(z \leq 6.6 \cdot 10^{-137}\right):\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.9e+63) (not (<= z 6.6e-137)))
   (/ (- t) (/ a z))
   (/ (* x y) a)))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.9e+63) || !(z <= 6.6e-137)) {
		tmp = -t / (a / z);
	} else {
		tmp = (x * y) / a;
	}
	return tmp;
}

Fortran

NOTE: x and y 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 ((z <= (-2.9d+63)) .or. (.not. (z <= 6.6d-137))) then
        tmp = -t / (a / z)
    else
        tmp = (x * y) / a
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.9e+63) || !(z <= 6.6e-137)) {
		tmp = -t / (a / z);
	} else {
		tmp = (x * y) / a;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.9e+63) or not (z <= 6.6e-137):
		tmp = -t / (a / z)
	else:
		tmp = (x * y) / a
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.9e+63) || !(z <= 6.6e-137))
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = Float64(Float64(x * y) / a);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.9e+63) || ~((z <= 6.6e-137)))
		tmp = -t / (a / z);
	else
		tmp = (x * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.9e+63], N[Not[LessEqual[z, 6.6e-137]], $MachinePrecision]], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8999999999999999e63 or 6.6000000000000004e-137 < z

   1. Initial program 89.2%

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

   2. Taylor expanded in x around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. associate-/l* 66.4%

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

   4. Simplified 66.4%

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

   if -2.8999999999999999e63 < z < 6.6000000000000004e-137

   1. Initial program 95.6%

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

   2. Taylor expanded in x around inf 69.3%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+63} \lor \neg \left(z \leq 6.6 \cdot 10^{-137}\right):\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]

Alternative 5: 64.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+63}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.95e+63)
   (/ (- t) (/ a z))
   (if (<= z 4.6e-144) (/ (* x y) a) (* z (/ (- t) a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.95e+63) {
		tmp = -t / (a / z);
	} else if (z <= 4.6e-144) {
		tmp = (x * y) / a;
	} else {
		tmp = z * (-t / a);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 (z <= (-2.95d+63)) then
        tmp = -t / (a / z)
    else if (z <= 4.6d-144) then
        tmp = (x * y) / a
    else
        tmp = z * (-t / a)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.95e+63) {
		tmp = -t / (a / z);
	} else if (z <= 4.6e-144) {
		tmp = (x * y) / a;
	} else {
		tmp = z * (-t / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.95e+63:
		tmp = -t / (a / z)
	elif z <= 4.6e-144:
		tmp = (x * y) / a
	else:
		tmp = z * (-t / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.95e+63)
		tmp = Float64(Float64(-t) / Float64(a / z));
	elseif (z <= 4.6e-144)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(z * Float64(Float64(-t) / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.95e+63)
		tmp = -t / (a / z);
	elseif (z <= 4.6e-144)
		tmp = (x * y) / a;
	else
		tmp = z * (-t / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.95e+63], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-144], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.95000000000000014e63

   1. Initial program 89.6%

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

   2. Taylor expanded in x around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. associate-/l* 70.1%

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

   4. Simplified 70.1%

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

   if -2.95000000000000014e63 < z < 4.6e-144

   1. Initial program 95.5%

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

   2. Taylor expanded in x around inf 68.5%

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

   if 4.6e-144 < z

   1. Initial program 89.4%

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

   2. Taylor expanded in x around 0 86.0%

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

      1. clear-num 86.0%

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

      2. associate-/r/ 86.0%

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

   4. Applied egg-rr 86.0%

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

      1. +-commutative 86.0%

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

      2. associate-*r* 86.0%

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

      3. mul-1-neg 86.0%

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

      4. cancel-sign-sub-inv 86.0%

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

      5. div-inv 86.0%

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

      6. *-commutative 86.0%

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

      7. distribute-rgt-out-- 89.3%

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

   6. Applied egg-rr 89.3%

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

   7. Taylor expanded in x around 0 62.0%

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

      1. mul-1-neg 62.0%

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

      2. *-commutative 62.0%

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

      3. associate-*r/ 62.9%

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

      4. distribute-rgt-neg-in 62.9%

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

      5. distribute-neg-frac 62.9%

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

   9. Simplified 62.9%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+63}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \]

Alternative 6: 64.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.05e+63)
   (* t (/ (- z) a))
   (if (<= z 4.6e-144) (/ (* x y) a) (* z (/ (- t) a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.05e+63) {
		tmp = t * (-z / a);
	} else if (z <= 4.6e-144) {
		tmp = (x * y) / a;
	} else {
		tmp = z * (-t / a);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 (z <= (-2.05d+63)) then
        tmp = t * (-z / a)
    else if (z <= 4.6d-144) then
        tmp = (x * y) / a
    else
        tmp = z * (-t / a)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.05e+63) {
		tmp = t * (-z / a);
	} else if (z <= 4.6e-144) {
		tmp = (x * y) / a;
	} else {
		tmp = z * (-t / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.05e+63:
		tmp = t * (-z / a)
	elif z <= 4.6e-144:
		tmp = (x * y) / a
	else:
		tmp = z * (-t / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.05e+63)
		tmp = Float64(t * Float64(Float64(-z) / a));
	elseif (z <= 4.6e-144)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(z * Float64(Float64(-t) / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.05e+63)
		tmp = t * (-z / a);
	elseif (z <= 4.6e-144)
		tmp = (x * y) / a;
	else
		tmp = z * (-t / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.05e+63], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-144], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.04999999999999996e63

   1. Initial program 89.6%

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

   2. Taylor expanded in x around 0 65.1%

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

      1. *-commutative 65.1%

         \[\leadsto -1 \cdot \frac{\color{blue}{z \cdot t}}{a} \]

      2. associate-*l/ 71.7%

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

      3. associate-*r* 71.7%

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

      4. neg-mul-1 71.7%

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

      5. distribute-frac-neg 71.7%

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

   4. Simplified 71.7%

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

   if -2.04999999999999996e63 < z < 4.6e-144

   1. Initial program 95.5%

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

   2. Taylor expanded in x around inf 68.5%

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

   if 4.6e-144 < z

   1. Initial program 89.4%

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

   2. Taylor expanded in x around 0 86.0%

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

      1. clear-num 86.0%

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

      2. associate-/r/ 86.0%

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

   4. Applied egg-rr 86.0%

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

      1. +-commutative 86.0%

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

      2. associate-*r* 86.0%

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

      3. mul-1-neg 86.0%

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

      4. cancel-sign-sub-inv 86.0%

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

      5. div-inv 86.0%

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

      6. *-commutative 86.0%

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

      7. distribute-rgt-out-- 89.3%

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

   6. Applied egg-rr 89.3%

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

   7. Taylor expanded in x around 0 62.0%

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

      1. mul-1-neg 62.0%

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

      2. *-commutative 62.0%

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

      3. associate-*r/ 62.9%

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

      4. distribute-rgt-neg-in 62.9%

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

      5. distribute-neg-frac 62.9%

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

   9. Simplified 62.9%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \]

Alternative 7: 50.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= a 7.8e-83) (* y (/ x a)) (* x (/ y a))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 7.8e-83) {
		tmp = y * (x / a);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 (a <= 7.8d-83) then
        tmp = y * (x / a)
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 7.8e-83) {
		tmp = y * (x / a);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if a <= 7.8e-83:
		tmp = y * (x / a)
	else:
		tmp = x * (y / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 7.8e-83)
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 7.8e-83)
		tmp = y * (x / a);
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[a, 7.8e-83], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 7.800000000000001e-83

   1. Initial program 92.9%

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

   2. Taylor expanded in x around inf 50.0%

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

      1. associate-*l/ 49.7%

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

   4. Simplified 49.7%

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

   if 7.800000000000001e-83 < a

   1. Initial program 90.5%

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

   2. Taylor expanded in x around 0 90.5%

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

   3. Taylor expanded in t around 0 46.1%

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

      1. associate-*r/ 42.5%

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

   5. Simplified 42.5%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 51.2% accurate, 1.8× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x and y 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 92.1%

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

2. Taylor expanded in x around 0 88.9%

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

3. Taylor expanded in t around 0 48.6%

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

   1. associate-*r/ 45.5%

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

5. Simplified 45.5%

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

6. Final simplification 45.5%

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

Alternative 9: 50.1% accurate, 1.8× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.1%

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

2. Taylor expanded in x around inf 48.6%

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

3. Final simplification 48.6%

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

Developer target: 91.5% accurate, 0.6× 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 2023312 
(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))