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

Percentage Accurate: 91.2% → 97.4%

Time: 10.4s

Alternatives: 11

Speedup: 0.5×

• 28.3% 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: 91.2% 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: 97.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{a}, \frac{-z}{\frac{a}{t}}\right)\\ \mathbf{elif}\;t_1 \leq 10^{+289}:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 (- INFINITY))
     (fma x (/ y a) (/ (- z) (/ a t)))
     (if (<= t_1 1e+289) (/ t_1 a) (- (/ x (/ a y)) (/ z (/ a t)))))))

C

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 = fma(x, (y / a), (-z / (a / t)));
	} else if (t_1 <= 1e+289) {
		tmp = t_1 / a;
	} else {
		tmp = (x / (a / y)) - (z / (a / t));
	}
	return tmp;
}

Julia

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 = fma(x, Float64(y / a), Float64(Float64(-z) / Float64(a / t)));
	elseif (t_1 <= 1e+289)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	end
	return tmp
end

Wolfram

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[(y / a), $MachinePrecision] + N[((-z) / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+289], 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 58.9%

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

      1. div-sub 56.0%

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

      2. *-un-lft-identity 56.0%

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

      3. times-frac 83.3%

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

      4. fma-neg 86.2%

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

      5. associate-/l* 99.9%

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

   3. Applied egg-rr 99.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.0000000000000001e289

   1. Initial program 99.2%

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

   if 1.0000000000000001e289 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 65.1%

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

      1. div-sub 62.1%

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

      2. associate-/l* 82.2%

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

      3. associate-/l* 93.8%

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

   3. Applied egg-rr 93.8%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{a}, \frac{-z}{\frac{a}{t}}\right)\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 10^{+289}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 2: 97.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+275} \lor \neg \left(t_1 \leq 10^{+289}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 -2e+275) (not (<= t_1 1e+289)))
     (- (/ x (/ a y)) (/ z (/ a t)))
     (/ t_1 a))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -2e+275) || !(t_1 <= 1e+289)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1 / a;
	}
	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 = (x * y) - (z * t)
    if ((t_1 <= (-2d+275)) .or. (.not. (t_1 <= 1d+289))) then
        tmp = (x / (a / y)) - (z / (a / t))
    else
        tmp = t_1 / a
    end if
    code = tmp
end function

Java

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 <= -2e+275) || !(t_1 <= 1e+289)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -2e+275) or not (t_1 <= 1e+289):
		tmp = (x / (a / y)) - (z / (a / t))
	else:
		tmp = t_1 / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= -2e+275) || !(t_1 <= 1e+289))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -2e+275) || ~((t_1 <= 1e+289)))
		tmp = (x / (a / y)) - (z / (a / t));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

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, -2e+275], N[Not[LessEqual[t$95$1, 1e+289]], $MachinePrecision]], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $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)) < -1.99999999999999992e275 or 1.0000000000000001e289 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 66.9%

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

      1. div-sub 64.3%

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

      2. associate-/l* 85.0%

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

      3. associate-/l* 96.0%

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

   3. Applied egg-rr 96.0%

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

   if -1.99999999999999992e275 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.0000000000000001e289

   1. Initial program 99.1%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -2 \cdot 10^{+275} \lor \neg \left(x \cdot y - z \cdot t \leq 10^{+289}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 3: 94.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+275}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+211}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-1}{\frac{-a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+275)
   (/ x (/ a y))
   (if (<= (* x y) 1e+211)
     (/ (- (* x y) (* z t)) a)
     (* x (/ -1.0 (/ (- a) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+275) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e+211) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x * (-1.0 / (-a / y));
	}
	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) :: tmp
    if ((x * y) <= (-2d+275)) then
        tmp = x / (a / y)
    else if ((x * y) <= 1d+211) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = x * ((-1.0d0) / (-a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+275) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e+211) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x * (-1.0 / (-a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+275:
		tmp = x / (a / y)
	elif (x * y) <= 1e+211:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = x * (-1.0 / (-a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+275)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 1e+211)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(x * Float64(-1.0 / Float64(Float64(-a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+275)
		tmp = x / (a / y);
	elseif ((x * y) <= 1e+211)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = x * (-1.0 / (-a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+275], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+211], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(-1.0 / N[((-a) / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999992e275

   1. Initial program 54.9%

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

   2. Taylor expanded in x around inf 54.9%

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

      1. associate-*r/ 92.0%

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

   4. Simplified 92.0%

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

      1. *-commutative 92.0%

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

      2. associate-/r/ 92.1%

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

   6. Applied egg-rr 92.1%

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

   if -1.99999999999999992e275 < (*.f64 x y) < 9.9999999999999996e210

   1. Initial program 96.0%

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

   if 9.9999999999999996e210 < (*.f64 x y)

   1. Initial program 70.4%

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

   2. Taylor expanded in x around inf 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-/l* 99.6%

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

      3. frac-2neg 99.6%

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

      4. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+275}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+211}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-1}{\frac{-a}{y}}\\ \end{array} \]

Alternative 4: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 1.5 \cdot 10^{+33}:\\ \;\;\;\;-\frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-1}{\frac{-a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e-7)
   (/ y (/ a x))
   (if (<= (* x y) 1.5e+33) (- (/ (* z t) a)) (* x (/ -1.0 (/ (- a) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-7) {
		tmp = y / (a / x);
	} else if ((x * y) <= 1.5e+33) {
		tmp = -((z * t) / a);
	} else {
		tmp = x * (-1.0 / (-a / y));
	}
	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) :: tmp
    if ((x * y) <= (-4d-7)) then
        tmp = y / (a / x)
    else if ((x * y) <= 1.5d+33) then
        tmp = -((z * t) / a)
    else
        tmp = x * ((-1.0d0) / (-a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-7) {
		tmp = y / (a / x);
	} else if ((x * y) <= 1.5e+33) {
		tmp = -((z * t) / a);
	} else {
		tmp = x * (-1.0 / (-a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e-7:
		tmp = y / (a / x)
	elif (x * y) <= 1.5e+33:
		tmp = -((z * t) / a)
	else:
		tmp = x * (-1.0 / (-a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e-7)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 1.5e+33)
		tmp = Float64(-Float64(Float64(z * t) / a));
	else
		tmp = Float64(x * Float64(-1.0 / Float64(Float64(-a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e-7)
		tmp = y / (a / x);
	elseif ((x * y) <= 1.5e+33)
		tmp = -((z * t) / a);
	else
		tmp = x * (-1.0 / (-a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e-7], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.5e+33], (-N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), N[(x * N[(-1.0 / N[((-a) / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.9999999999999998e-7

   1. Initial program 79.6%

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

   2. Taylor expanded in x around inf 64.1%

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

      1. associate-/l* 75.4%

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

   4. Simplified 75.4%

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

   if -3.9999999999999998e-7 < (*.f64 x y) < 1.49999999999999992e33

   1. Initial program 96.8%

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

   2. Taylor expanded in x around 0 77.4%

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

      1. associate-*r/ 77.4%

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

      2. associate-*r* 77.4%

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

      3. neg-mul-1 77.4%

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

   4. Simplified 77.4%

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

   if 1.49999999999999992e33 < (*.f64 x y)

   1. Initial program 83.5%

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

   2. Taylor expanded in x around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-/l* 72.1%

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

      3. frac-2neg 72.1%

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

      4. div-inv 71.7%

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

   4. Applied egg-rr 71.7%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 1.5 \cdot 10^{+33}:\\ \;\;\;\;-\frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-1}{\frac{-a}{y}}\\ \end{array} \]

Alternative 5: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+176}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-13} \lor \neg \left(z \leq 1.25 \cdot 10^{-38}\right):\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.4e+176)
   (* z (/ (- t) a))
   (if (<= z -8.2e+80)
     (/ y (/ a x))
     (if (or (<= z -4.4e-13) (not (<= z 1.25e-38)))
       (* t (- (/ z a)))
       (* x (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.4e+176) {
		tmp = z * (-t / a);
	} else if (z <= -8.2e+80) {
		tmp = y / (a / x);
	} else if ((z <= -4.4e-13) || !(z <= 1.25e-38)) {
		tmp = t * -(z / a);
	} else {
		tmp = x * (y / a);
	}
	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) :: tmp
    if (z <= (-6.4d+176)) then
        tmp = z * (-t / a)
    else if (z <= (-8.2d+80)) then
        tmp = y / (a / x)
    else if ((z <= (-4.4d-13)) .or. (.not. (z <= 1.25d-38))) then
        tmp = t * -(z / a)
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.4e+176) {
		tmp = z * (-t / a);
	} else if (z <= -8.2e+80) {
		tmp = y / (a / x);
	} else if ((z <= -4.4e-13) || !(z <= 1.25e-38)) {
		tmp = t * -(z / a);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.4e+176:
		tmp = z * (-t / a)
	elif z <= -8.2e+80:
		tmp = y / (a / x)
	elif (z <= -4.4e-13) or not (z <= 1.25e-38):
		tmp = t * -(z / a)
	else:
		tmp = x * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.4e+176)
		tmp = Float64(z * Float64(Float64(-t) / a));
	elseif (z <= -8.2e+80)
		tmp = Float64(y / Float64(a / x));
	elseif ((z <= -4.4e-13) || !(z <= 1.25e-38))
		tmp = Float64(t * Float64(-Float64(z / a)));
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.4e+176)
		tmp = z * (-t / a);
	elseif (z <= -8.2e+80)
		tmp = y / (a / x);
	elseif ((z <= -4.4e-13) || ~((z <= 1.25e-38)))
		tmp = t * -(z / a);
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.4e+176], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.2e+80], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.4e-13], N[Not[LessEqual[z, 1.25e-38]], $MachinePrecision]], N[(t * (-N[(z / a), $MachinePrecision])), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.3999999999999996e176

   1. Initial program 85.5%

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

      1. div-sub 81.8%

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

      2. *-un-lft-identity 81.8%

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

      3. times-frac 78.5%

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

      4. fma-neg 82.2%

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

      5. associate-/l* 92.6%

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

   3. Applied egg-rr 92.6%

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

      1. fma-udef 88.9%

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

      2. frac-times 91.1%

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

      3. *-commutative 91.1%

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

      4. *-un-lft-identity 91.1%

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

      5. associate-*r/ 91.2%

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

      6. associate-*r/ 91.1%

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

      7. distribute-neg-frac 91.1%

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

      8. frac-add 59.8%

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

   5. Applied egg-rr 59.8%

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

      1. distribute-rgt-neg-out 59.8%

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

      2. sub-neg 59.8%

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

      3. div-sub 45.0%

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

      4. times-frac 48.9%

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

      5. *-inverses 56.3%

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

      6. associate-*l/ 56.3%

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

      7. *-rgt-identity 56.3%

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

      8. associate-*l/ 56.3%

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

      9. *-commutative 56.3%

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

      10. *-commutative 56.3%

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

      11. *-commutative 56.3%

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

      12. times-frac 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. associate-*l/ 89.2%

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

      3. distribute-rgt-neg-in 89.2%

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

   10. Simplified 89.2%

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

   if -6.3999999999999996e176 < z < -8.20000000000000003e80

   1. Initial program 94.2%

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

   2. Taylor expanded in x around inf 58.4%

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

      1. associate-/l* 58.2%

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

   4. Simplified 58.2%

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

   if -8.20000000000000003e80 < z < -4.39999999999999993e-13 or 1.25000000000000008e-38 < z

   1. Initial program 88.5%

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

   2. Taylor expanded in x around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. *-commutative 56.9%

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

      3. associate-*l/ 59.9%

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

      4. *-commutative 59.9%

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

      5. distribute-lft-neg-in 59.9%

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

   4. Simplified 59.9%

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

   if -4.39999999999999993e-13 < z < 1.25000000000000008e-38

   1. Initial program 90.4%

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

   2. Taylor expanded in x around inf 59.4%

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

      1. associate-/l* 65.8%

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

      2. associate-/r/ 61.1%

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

   4. Applied egg-rr 61.1%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+176}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-13} \lor \neg \left(z \leq 1.25 \cdot 10^{-38}\right):\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-\frac{z}{a}\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- (/ z a)))))
   (if (<= y -4.4e-120)
     (* x (/ y a))
     (if (<= y 2.65e-11)
       t_1
       (if (<= y 6.2e+56)
         (/ (* x y) a)
         (if (<= y 7e+96) t_1 (* y (/ x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * -(z / a);
	double tmp;
	if (y <= -4.4e-120) {
		tmp = x * (y / a);
	} else if (y <= 2.65e-11) {
		tmp = t_1;
	} else if (y <= 6.2e+56) {
		tmp = (x * y) / a;
	} else if (y <= 7e+96) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	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 = t * -(z / a)
    if (y <= (-4.4d-120)) then
        tmp = x * (y / a)
    else if (y <= 2.65d-11) then
        tmp = t_1
    else if (y <= 6.2d+56) then
        tmp = (x * y) / a
    else if (y <= 7d+96) then
        tmp = t_1
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * -(z / a);
	double tmp;
	if (y <= -4.4e-120) {
		tmp = x * (y / a);
	} else if (y <= 2.65e-11) {
		tmp = t_1;
	} else if (y <= 6.2e+56) {
		tmp = (x * y) / a;
	} else if (y <= 7e+96) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * -(z / a)
	tmp = 0
	if y <= -4.4e-120:
		tmp = x * (y / a)
	elif y <= 2.65e-11:
		tmp = t_1
	elif y <= 6.2e+56:
		tmp = (x * y) / a
	elif y <= 7e+96:
		tmp = t_1
	else:
		tmp = y * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(-Float64(z / a)))
	tmp = 0.0
	if (y <= -4.4e-120)
		tmp = Float64(x * Float64(y / a));
	elseif (y <= 2.65e-11)
		tmp = t_1;
	elseif (y <= 6.2e+56)
		tmp = Float64(Float64(x * y) / a);
	elseif (y <= 7e+96)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * -(z / a);
	tmp = 0.0;
	if (y <= -4.4e-120)
		tmp = x * (y / a);
	elseif (y <= 2.65e-11)
		tmp = t_1;
	elseif (y <= 6.2e+56)
		tmp = (x * y) / a;
	elseif (y <= 7e+96)
		tmp = t_1;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * (-N[(z / a), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[y, -4.4e-120], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e-11], t$95$1, If[LessEqual[y, 6.2e+56], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 7e+96], t$95$1, N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.40000000000000025e-120

   1. Initial program 86.9%

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

   2. Taylor expanded in x around inf 50.5%

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

      1. associate-/l* 56.9%

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

      2. associate-/r/ 55.4%

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

   4. Applied egg-rr 55.4%

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

   if -4.40000000000000025e-120 < y < 2.6499999999999999e-11 or 6.20000000000000009e56 < y < 6.9999999999999998e96

   1. Initial program 95.9%

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

   2. Taylor expanded in x around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. *-commutative 74.6%

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

      3. associate-*l/ 70.7%

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

      4. *-commutative 70.7%

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

      5. distribute-lft-neg-in 70.7%

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

   4. Simplified 70.7%

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

   if 2.6499999999999999e-11 < y < 6.20000000000000009e56

   1. Initial program 92.9%

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

   2. Taylor expanded in x around inf 64.4%

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

   if 6.9999999999999998e96 < y

   1. Initial program 78.6%

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

   2. Taylor expanded in x around inf 64.0%

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

      1. associate-*r/ 78.0%

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

   4. Simplified 78.0%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 7: 65.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+176}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-12}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+176)
   (* z (/ (- t) a))
   (if (<= z -2.5e+80)
     (/ y (/ a x))
     (if (<= z -1.95e-12)
       (/ (- t) (/ a z))
       (if (<= z 1.8e-44) (* x (/ y a)) (* t (- (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+176) {
		tmp = z * (-t / a);
	} else if (z <= -2.5e+80) {
		tmp = y / (a / x);
	} else if (z <= -1.95e-12) {
		tmp = -t / (a / z);
	} else if (z <= 1.8e-44) {
		tmp = x * (y / a);
	} else {
		tmp = t * -(z / a);
	}
	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) :: tmp
    if (z <= (-2d+176)) then
        tmp = z * (-t / a)
    else if (z <= (-2.5d+80)) then
        tmp = y / (a / x)
    else if (z <= (-1.95d-12)) then
        tmp = -t / (a / z)
    else if (z <= 1.8d-44) then
        tmp = x * (y / a)
    else
        tmp = t * -(z / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+176) {
		tmp = z * (-t / a);
	} else if (z <= -2.5e+80) {
		tmp = y / (a / x);
	} else if (z <= -1.95e-12) {
		tmp = -t / (a / z);
	} else if (z <= 1.8e-44) {
		tmp = x * (y / a);
	} else {
		tmp = t * -(z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+176:
		tmp = z * (-t / a)
	elif z <= -2.5e+80:
		tmp = y / (a / x)
	elif z <= -1.95e-12:
		tmp = -t / (a / z)
	elif z <= 1.8e-44:
		tmp = x * (y / a)
	else:
		tmp = t * -(z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+176)
		tmp = Float64(z * Float64(Float64(-t) / a));
	elseif (z <= -2.5e+80)
		tmp = Float64(y / Float64(a / x));
	elseif (z <= -1.95e-12)
		tmp = Float64(Float64(-t) / Float64(a / z));
	elseif (z <= 1.8e-44)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(t * Float64(-Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+176)
		tmp = z * (-t / a);
	elseif (z <= -2.5e+80)
		tmp = y / (a / x);
	elseif (z <= -1.95e-12)
		tmp = -t / (a / z);
	elseif (z <= 1.8e-44)
		tmp = x * (y / a);
	else
		tmp = t * -(z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+176], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e+80], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-12], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-44], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(t * (-N[(z / a), $MachinePrecision])), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2e176

   1. Initial program 85.5%

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

      1. div-sub 81.8%

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

      2. *-un-lft-identity 81.8%

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

      3. times-frac 78.5%

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

      4. fma-neg 82.2%

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

      5. associate-/l* 92.6%

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

   3. Applied egg-rr 92.6%

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

      1. fma-udef 88.9%

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

      2. frac-times 91.1%

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

      3. *-commutative 91.1%

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

      4. *-un-lft-identity 91.1%

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

      5. associate-*r/ 91.2%

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

      6. associate-*r/ 91.1%

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

      7. distribute-neg-frac 91.1%

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

      8. frac-add 59.8%

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

   5. Applied egg-rr 59.8%

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

      1. distribute-rgt-neg-out 59.8%

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

      2. sub-neg 59.8%

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

      3. div-sub 45.0%

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

      4. times-frac 48.9%

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

      5. *-inverses 56.3%

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

      6. associate-*l/ 56.3%

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

      7. *-rgt-identity 56.3%

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

      8. associate-*l/ 56.3%

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

      9. *-commutative 56.3%

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

      10. *-commutative 56.3%

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

      11. *-commutative 56.3%

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

      12. times-frac 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. associate-*l/ 89.2%

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

      3. distribute-rgt-neg-in 89.2%

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

   10. Simplified 89.2%

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

   if -2e176 < z < -2.4999999999999998e80

   1. Initial program 94.2%

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

   2. Taylor expanded in x around inf 58.4%

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

      1. associate-/l* 58.2%

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

   4. Simplified 58.2%

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

   if -2.4999999999999998e80 < z < -1.94999999999999997e-12

   1. Initial program 95.0%

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

   2. Taylor expanded in x around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. associate-/l* 76.5%

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

      3. distribute-neg-frac 76.5%

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

   4. Simplified 76.5%

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

   if -1.94999999999999997e-12 < z < 1.7999999999999999e-44

   1. Initial program 90.2%

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

   2. Taylor expanded in x around inf 59.5%

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

      1. associate-/l* 66.0%

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

      2. associate-/r/ 61.3%

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

   4. Applied egg-rr 61.3%

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

   if 1.7999999999999999e-44 < z

   1. Initial program 86.9%

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

   2. Taylor expanded in x around 0 51.1%

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

      1. mul-1-neg 51.1%

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

      2. *-commutative 51.1%

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

      3. associate-*l/ 54.9%

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

      4. *-commutative 54.9%

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

      5. distribute-lft-neg-in 54.9%

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

   4. Simplified 54.9%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \frac{z}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+176}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-12}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right)\\ \end{array} \]

Alternative 8: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 1.5 \cdot 10^{+33}:\\ \;\;\;\;-\frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e-7)
   (/ y (/ a x))
   (if (<= (* x y) 1.5e+33) (- (/ (* z t) a)) (/ x (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-7) {
		tmp = y / (a / x);
	} else if ((x * y) <= 1.5e+33) {
		tmp = -((z * t) / a);
	} else {
		tmp = x / (a / y);
	}
	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) :: tmp
    if ((x * y) <= (-4d-7)) then
        tmp = y / (a / x)
    else if ((x * y) <= 1.5d+33) then
        tmp = -((z * t) / a)
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-7) {
		tmp = y / (a / x);
	} else if ((x * y) <= 1.5e+33) {
		tmp = -((z * t) / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e-7:
		tmp = y / (a / x)
	elif (x * y) <= 1.5e+33:
		tmp = -((z * t) / a)
	else:
		tmp = x / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e-7)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 1.5e+33)
		tmp = Float64(-Float64(Float64(z * t) / a));
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e-7)
		tmp = y / (a / x);
	elseif ((x * y) <= 1.5e+33)
		tmp = -((z * t) / a);
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e-7], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.5e+33], (-N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.9999999999999998e-7

   1. Initial program 79.6%

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

   2. Taylor expanded in x around inf 64.1%

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

      1. associate-/l* 75.4%

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

   4. Simplified 75.4%

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

   if -3.9999999999999998e-7 < (*.f64 x y) < 1.49999999999999992e33

   1. Initial program 96.8%

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

   2. Taylor expanded in x around 0 77.4%

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

      1. associate-*r/ 77.4%

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

      2. associate-*r* 77.4%

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

      3. neg-mul-1 77.4%

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

   4. Simplified 77.4%

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

   if 1.49999999999999992e33 < (*.f64 x y)

   1. Initial program 83.5%

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

   2. Taylor expanded in x around inf 68.4%

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

      1. associate-*r/ 78.1%

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

   4. Simplified 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-/r/ 72.1%

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

   6. Applied egg-rr 72.1%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 1.5 \cdot 10^{+33}:\\ \;\;\;\;-\frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 51.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -7e-306) (* x (/ y a)) (* y (/ x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7e-306) {
		tmp = x * (y / a);
	} else {
		tmp = y * (x / a);
	}
	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) :: tmp
    if (y <= (-7d-306)) then
        tmp = x * (y / a)
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7e-306) {
		tmp = x * (y / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -7e-306:
		tmp = x * (y / a)
	else:
		tmp = y * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -7e-306)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -7e-306)
		tmp = x * (y / a);
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -7e-306], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.00000000000000035e-306

   1. Initial program 89.4%

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

   2. Taylor expanded in x around inf 47.6%

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

      1. associate-/l* 50.2%

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

      2. associate-/r/ 49.9%

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

   4. Applied egg-rr 49.9%

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

   if -7.00000000000000035e-306 < y

   1. Initial program 89.4%

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

   2. Taylor expanded in x around inf 43.7%

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

      1. associate-*r/ 50.2%

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

   4. Simplified 50.2%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 10: 50.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.06 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.06e-291) (* x (/ y a)) (/ y (/ a x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.06e-291) {
		tmp = x * (y / a);
	} else {
		tmp = y / (a / x);
	}
	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) :: tmp
    if (y <= 1.06d-291) then
        tmp = x * (y / a)
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.06e-291) {
		tmp = x * (y / a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.06e-291:
		tmp = x * (y / a)
	else:
		tmp = y / (a / x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.06e-291)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.06e-291)
		tmp = x * (y / a);
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.06e-291], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.05999999999999992e-291

   1. Initial program 89.5%

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

   2. Taylor expanded in x around inf 47.3%

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

      1. associate-/l* 49.8%

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

      2. associate-/r/ 49.6%

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

   4. Applied egg-rr 49.6%

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

   if 1.05999999999999992e-291 < y

   1. Initial program 89.3%

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

   2. Taylor expanded in x around inf 44.0%

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

      1. associate-/l* 50.7%

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

   4. Simplified 50.7%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.06 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 11: 51.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return y * (x / 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 = y * (x / a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.4%

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

2. Taylor expanded in x around inf 45.8%

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

   1. associate-*r/ 50.2%

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

4. Simplified 50.2%

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

5. Final simplification 50.2%

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

Developer target: 91.2% 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 2023274 
(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))