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

Percentage Accurate: 91.5% → 94.4%

Time: 6.8s

Alternatives: 8

Speedup: 0.7×

• 27.7% 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: 94.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq 10^{+272}:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t 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 1e+272) (/ t_1 a) (- (/ x (/ a y)) (/ z (/ a t))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= 1e+272) {
		tmp = t_1 / a;
	} else {
		tmp = (x / (a / y)) - (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: z and t 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if (t_1 <= 1d+272) then
        tmp = t_1 / a
    else
        tmp = (x / (a / y)) - (z / (a / t))
    end if
    code = tmp
end function

Java

assert z < t;
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 <= 1e+272) {
		tmp = t_1 / a;
	} else {
		tmp = (x / (a / y)) - (z / (a / t));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= 1e+272:
		tmp = t_1 / a
	else:
		tmp = (x / (a / y)) - (z / (a / t))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= 1e+272)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= 1e+272)
		tmp = t_1 / a;
	else
		tmp = (x / (a / y)) - (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t 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, 1e+272], 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 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < 1.0000000000000001e272

   1. Initial program 97.6%

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

   if 1.0000000000000001e272 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 72.5%

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

      1. div-sub 72.5%

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

      2. associate-/l* 84.8%

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

      3. associate-/l* 94.6%

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

   3. Applied egg-rr 94.6%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq 10^{+272}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 2: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \left(-\frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-\frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) a)))
   (if (<= (* x y) -2000000000.0)
     t_1
     (if (<= (* x y) 5e-19)
       (* z (- (/ t a)))
       (if (<= (* x y) 5e+79)
         t_1
         (if (<= (* x y) 2e+90) (- (/ t (/ a z))) (* x (/ y a))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e-19) {
		tmp = z * -(t / a);
	} else if ((x * y) <= 5e+79) {
		tmp = t_1;
	} else if ((x * y) <= 2e+90) {
		tmp = -(t / (a / z));
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

NOTE: z and t 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) / a
    if ((x * y) <= (-2000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 5d-19) then
        tmp = z * -(t / a)
    else if ((x * y) <= 5d+79) then
        tmp = t_1
    else if ((x * y) <= 2d+90) then
        tmp = -(t / (a / z))
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e-19) {
		tmp = z * -(t / a);
	} else if ((x * y) <= 5e+79) {
		tmp = t_1;
	} else if ((x * y) <= 2e+90) {
		tmp = -(t / (a / z));
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) / a
	tmp = 0
	if (x * y) <= -2000000000.0:
		tmp = t_1
	elif (x * y) <= 5e-19:
		tmp = z * -(t / a)
	elif (x * y) <= 5e+79:
		tmp = t_1
	elif (x * y) <= 2e+90:
		tmp = -(t / (a / z))
	else:
		tmp = x * (y / a)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / a)
	tmp = 0.0
	if (Float64(x * y) <= -2000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-19)
		tmp = Float64(z * Float64(-Float64(t / a)));
	elseif (Float64(x * y) <= 5e+79)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+90)
		tmp = Float64(-Float64(t / Float64(a / z)));
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / a;
	tmp = 0.0;
	if ((x * y) <= -2000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 5e-19)
		tmp = z * -(t / a);
	elseif ((x * y) <= 5e+79)
		tmp = t_1;
	elseif ((x * y) <= 2e+90)
		tmp = -(t / (a / z));
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t 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] / a), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-19], N[(z * (-N[(t / a), $MachinePrecision])), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+79], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+90], (-N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2e9 or 5.0000000000000004e-19 < (*.f64 x y) < 5e79

   1. Initial program 94.7%

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

   2. Taylor expanded in x around inf 77.0%

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

   if -2e9 < (*.f64 x y) < 5.0000000000000004e-19

   1. Initial program 96.9%

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

      1. div-sub 96.9%

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

      2. associate-/l* 94.6%

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

      3. associate-/l* 94.0%

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

   3. Applied egg-rr 94.0%

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

   4. Taylor expanded in x around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. associate-*l/ 77.5%

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

      3. distribute-lft-neg-in 77.5%

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

      4. *-commutative 77.5%

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

   6. Simplified 77.5%

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

   if 5e79 < (*.f64 x y) < 1.99999999999999993e90

   1. Initial program 76.5%

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

   2. Taylor expanded in x around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   if 1.99999999999999993e90 < (*.f64 x y)

   1. Initial program 84.9%

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

   2. Taylor expanded in x around inf 80.3%

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

      1. associate-*l/ 86.8%

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

   4. Simplified 86.8%

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

      1. associate-/r/ 90.8%

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

   6. Applied egg-rr 90.8%

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

      1. clear-num 90.9%

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

      2. associate-/r/ 90.7%

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

      3. clear-num 90.8%

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

   8. Applied egg-rr 90.8%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \left(-\frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-\frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-19}:\\ \;\;\;\;\frac{z}{\frac{-a}{t}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-\frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) a)))
   (if (<= (* x y) -2000000000.0)
     t_1
     (if (<= (* x y) 5e-19)
       (/ z (/ (- a) t))
       (if (<= (* x y) 5e+79)
         t_1
         (if (<= (* x y) 2e+90) (- (/ t (/ a z))) (* x (/ y a))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e-19) {
		tmp = z / (-a / t);
	} else if ((x * y) <= 5e+79) {
		tmp = t_1;
	} else if ((x * y) <= 2e+90) {
		tmp = -(t / (a / z));
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

NOTE: z and t 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) / a
    if ((x * y) <= (-2000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 5d-19) then
        tmp = z / (-a / t)
    else if ((x * y) <= 5d+79) then
        tmp = t_1
    else if ((x * y) <= 2d+90) then
        tmp = -(t / (a / z))
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e-19) {
		tmp = z / (-a / t);
	} else if ((x * y) <= 5e+79) {
		tmp = t_1;
	} else if ((x * y) <= 2e+90) {
		tmp = -(t / (a / z));
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) / a
	tmp = 0
	if (x * y) <= -2000000000.0:
		tmp = t_1
	elif (x * y) <= 5e-19:
		tmp = z / (-a / t)
	elif (x * y) <= 5e+79:
		tmp = t_1
	elif (x * y) <= 2e+90:
		tmp = -(t / (a / z))
	else:
		tmp = x * (y / a)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / a)
	tmp = 0.0
	if (Float64(x * y) <= -2000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-19)
		tmp = Float64(z / Float64(Float64(-a) / t));
	elseif (Float64(x * y) <= 5e+79)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+90)
		tmp = Float64(-Float64(t / Float64(a / z)));
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / a;
	tmp = 0.0;
	if ((x * y) <= -2000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 5e-19)
		tmp = z / (-a / t);
	elseif ((x * y) <= 5e+79)
		tmp = t_1;
	elseif ((x * y) <= 2e+90)
		tmp = -(t / (a / z));
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t 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] / a), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-19], N[(z / N[((-a) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+79], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+90], (-N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2e9 or 5.0000000000000004e-19 < (*.f64 x y) < 5e79

   1. Initial program 94.7%

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

   2. Taylor expanded in x around inf 77.0%

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

   if -2e9 < (*.f64 x y) < 5.0000000000000004e-19

   1. Initial program 96.9%

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

   2. Taylor expanded in x around 0 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*l/ 72.6%

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

      3. associate-*r* 72.6%

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

      4. neg-mul-1 72.6%

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

      5. distribute-frac-neg 72.6%

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

   4. Simplified 72.6%

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

      1. frac-2neg 72.6%

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

      2. remove-double-neg 72.6%

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

      3. associate-*l/ 78.9%

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

   6. Applied egg-rr 78.9%

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

      1. associate-/l* 78.2%

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

   8. Simplified 78.2%

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

   if 5e79 < (*.f64 x y) < 1.99999999999999993e90

   1. Initial program 76.5%

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

   2. Taylor expanded in x around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   if 1.99999999999999993e90 < (*.f64 x y)

   1. Initial program 84.9%

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

   2. Taylor expanded in x around inf 80.3%

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

      1. associate-*l/ 86.8%

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

   4. Simplified 86.8%

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

      1. associate-/r/ 90.8%

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

   6. Applied egg-rr 90.8%

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

      1. clear-num 90.9%

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

      2. associate-/r/ 90.7%

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

      3. clear-num 90.8%

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

   8. Applied egg-rr 90.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-19}:\\ \;\;\;\;\frac{z}{\frac{-a}{t}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-\frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-\frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2000000000.0)
   (/ (* x y) a)
   (if (<= (* x y) 2e+90) (- (/ t (/ a z))) (* x (/ y a)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 2e+90) {
		tmp = -(t / (a / z));
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

NOTE: z and t 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) <= (-2000000000.0d0)) then
        tmp = (x * y) / a
    else if ((x * y) <= 2d+90) then
        tmp = -(t / (a / z))
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 2e+90) {
		tmp = -(t / (a / z));
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2000000000.0:
		tmp = (x * y) / a
	elif (x * y) <= 2e+90:
		tmp = -(t / (a / z))
	else:
		tmp = x * (y / a)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2000000000.0)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 2e+90)
		tmp = Float64(-Float64(t / Float64(a / z)));
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2000000000.0)
		tmp = (x * y) / a;
	elseif ((x * y) <= 2e+90)
		tmp = -(t / (a / z));
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2000000000.0], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+90], (-N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e9

   1. Initial program 93.9%

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

   2. Taylor expanded in x around inf 78.9%

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

   if -2e9 < (*.f64 x y) < 1.99999999999999993e90

   1. Initial program 96.5%

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

   2. Taylor expanded in x around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. associate-/l* 70.2%

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

   4. Simplified 70.2%

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

   if 1.99999999999999993e90 < (*.f64 x y)

   1. Initial program 84.9%

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

   2. Taylor expanded in x around inf 80.3%

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

      1. associate-*l/ 86.8%

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

   4. Simplified 86.8%

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

      1. associate-/r/ 90.8%

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

   6. Applied egg-rr 90.8%

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

      1. clear-num 90.9%

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

      2. associate-/r/ 90.7%

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

      3. clear-num 90.8%

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

   8. Applied egg-rr 90.8%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-\frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 5: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-19}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2000000000.0)
   (/ (* x y) a)
   (if (<= (* x y) 5e-19) (/ (* t (- z)) a) (* x (/ y a)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 5e-19) {
		tmp = (t * -z) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

NOTE: z and t 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) <= (-2000000000.0d0)) then
        tmp = (x * y) / a
    else if ((x * y) <= 5d-19) then
        tmp = (t * -z) / a
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 5e-19) {
		tmp = (t * -z) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2000000000.0:
		tmp = (x * y) / a
	elif (x * y) <= 5e-19:
		tmp = (t * -z) / a
	else:
		tmp = x * (y / a)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2000000000.0)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 5e-19)
		tmp = Float64(Float64(t * Float64(-z)) / a);
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2000000000.0)
		tmp = (x * y) / a;
	elseif ((x * y) <= 5e-19)
		tmp = (t * -z) / a;
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2000000000.0], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-19], N[(N[(t * (-z)), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e9

   1. Initial program 93.9%

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

   2. Taylor expanded in x around inf 78.9%

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

   if -2e9 < (*.f64 x y) < 5.0000000000000004e-19

   1. Initial program 96.9%

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

   2. Taylor expanded in x around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. distribute-rgt-neg-in 78.9%

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

   4. Simplified 78.9%

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

   if 5.0000000000000004e-19 < (*.f64 x y)

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 72.3%

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

      1. associate-*l/ 74.1%

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

   4. Simplified 74.1%

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

      1. associate-/r/ 80.2%

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

   6. Applied egg-rr 80.2%

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

      1. clear-num 80.2%

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

      2. associate-/r/ 80.1%

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

      3. clear-num 80.1%

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

   8. Applied egg-rr 80.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-19}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 10^{+262}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) 1e+262) (/ (- (* x y) (* z t)) a) (* x (/ y a))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 1e+262) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

NOTE: z and t 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) <= 1d+262) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 1e+262) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= 1e+262:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = x * (y / a)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= 1e+262)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= 1e+262)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], 1e+262], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 1e262

   1. Initial program 95.7%

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

   if 1e262 < (*.f64 x y)

   1. Initial program 74.3%

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

   2. Taylor expanded in x around inf 74.3%

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

      1. associate-*l/ 100.0%

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

   4. Simplified 100.0%

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

      1. associate-/r/ 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.8%

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

   8. Applied egg-rr 99.8%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 10^{+262}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 51.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: z and t 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 = y * (x / a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

2. Taylor expanded in x around inf 50.9%

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

   1. associate-*l/ 50.7%

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

4. Simplified 50.7%

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

5. Final simplification 50.7%

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

Alternative 8: 51.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: z and t 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 93.9%

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

2. Taylor expanded in x around inf 50.9%

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

   1. associate-*l/ 50.7%

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

4. Simplified 50.7%

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

   1. associate-/r/ 51.9%

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

6. Applied egg-rr 51.9%

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

   1. clear-num 51.9%

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

   2. associate-/r/ 51.8%

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

   3. clear-num 51.9%

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

8. Applied egg-rr 51.9%

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

9. Final simplification 51.9%

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

Developer target: 91.4% 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 2023320 
(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))