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

Percentage Accurate: 91.4% → 97.1%

Time: 6.6s

Alternatives: 6

Speedup: 0.7×

• 27.2% 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: 91.4% 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: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot x - t \cdot z\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+272} \lor \neg \left(t_1 \leq 10^{+280}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* y x) (* t z))))
   (if (or (<= t_1 -1e+272) (not (<= t_1 1e+280)))
     (- (/ 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 = (y * x) - (t * z);
	double tmp;
	if ((t_1 <= -1e+272) || !(t_1 <= 1e+280)) {
		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 = (y * x) - (t * z)
    if ((t_1 <= (-1d+272)) .or. (.not. (t_1 <= 1d+280))) 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 = (y * x) - (t * z);
	double tmp;
	if ((t_1 <= -1e+272) || !(t_1 <= 1e+280)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * x) - (t * z)
	tmp = 0
	if (t_1 <= -1e+272) or not (t_1 <= 1e+280):
		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(y * x) - Float64(t * z))
	tmp = 0.0
	if ((t_1 <= -1e+272) || !(t_1 <= 1e+280))
		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 = (y * x) - (t * z);
	tmp = 0.0;
	if ((t_1 <= -1e+272) || ~((t_1 <= 1e+280)))
		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[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+272], N[Not[LessEqual[t$95$1, 1e+280]], $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)) < -1.0000000000000001e272 or 1e280 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 73.0%

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

      1. div-sub 68.1%

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

      2. associate-/l* 78.5%

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

      3. associate-/l* 92.6%

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

   3. Applied egg-rr 92.6%

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

   if -1.0000000000000001e272 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1e280

   1. Initial program 97.5%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x - t \cdot z \leq -1 \cdot 10^{+272} \lor \neg \left(y \cdot x - t \cdot z \leq 10^{+280}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - t \cdot z}{a}\\ \end{array} \]

Alternative 2: 93.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{y \cdot x - t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y x) 2e+307) (/ (- (* y x) (* t z)) a) (* y (/ x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= 2e+307) {
		tmp = ((y * x) - (t * z)) / 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 * x) <= 2d+307) then
        tmp = ((y * x) - (t * z)) / 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 * x) <= 2e+307) {
		tmp = ((y * x) - (t * z)) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= 2e+307:
		tmp = ((y * x) - (t * z)) / a
	else:
		tmp = y * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * x) <= 2e+307)
		tmp = Float64(Float64(Float64(y * x) - Float64(t * z)) / 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 * x) <= 2e+307)
		tmp = ((y * x) - (t * z)) / a;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], 2e+307], N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 1.99999999999999997e307

   1. Initial program 93.0%

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

   if 1.99999999999999997e307 < (*.f64 x y)

   1. Initial program 52.1%

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

   2. Taylor expanded in x around inf 57.5%

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

      1. associate-*r/ 91.2%

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

   4. Simplified 91.2%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{y \cdot x - t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 3: 87.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.24 \cdot 10^{-85}:\\ \;\;\;\;\frac{y}{\frac{a}{x}} - \frac{t}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - t \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.24e-85)
   (- (/ y (/ a x)) (* (/ t a) z))
   (/ (- (* y x) (* t z)) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.24e-85) {
		tmp = (y / (a / x)) - ((t / a) * z);
	} else {
		tmp = ((y * x) - (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 (y <= 1.24d-85) then
        tmp = (y / (a / x)) - ((t / a) * z)
    else
        tmp = ((y * x) - (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 (y <= 1.24e-85) {
		tmp = (y / (a / x)) - ((t / a) * z);
	} else {
		tmp = ((y * x) - (t * z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.24e-85:
		tmp = (y / (a / x)) - ((t / a) * z)
	else:
		tmp = ((y * x) - (t * z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.24e-85)
		tmp = Float64(Float64(y / Float64(a / x)) - Float64(Float64(t / a) * z));
	else
		tmp = Float64(Float64(Float64(y * x) - Float64(t * z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.24e-85)
		tmp = (y / (a / x)) - ((t / a) * z);
	else
		tmp = ((y * x) - (t * z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.24e-85], N[(N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.23999999999999995e-85

   1. Initial program 87.7%

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

      1. div-sub 85.4%

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

      2. *-commutative 85.4%

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

      3. add-cube-cbrt 85.0%

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

      4. times-frac 89.4%

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

      5. fma-neg 90.0%

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

      6. pow2 90.0%

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}}, \frac{x}{\sqrt[3]{a}}, -\frac{z \cdot t}{a}\right) \]

      7. associate-/l* 91.1%

         \[\leadsto \mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\color{blue}{\frac{z}{\frac{a}{t}}}\right) \]

   3. Applied egg-rr 91.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\frac{z}{\frac{a}{t}}\right)} \]
   4. Step-by-step derivation

      1. fma-neg 90.5%

         \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{z}{\frac{a}{t}}} \]

      2. associate-/l* 89.4%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{z \cdot t}{a}} \]

      3. *-commutative 89.4%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{\color{blue}{t \cdot z}}{a} \]

      4. associate-/l* 91.4%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{\frac{a}{z}}} \]

      5. associate-/r/ 91.0%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{a} \cdot z} \]

   5. Simplified 91.0%

      \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{t}{a} \cdot z} \]
   6. Step-by-step derivation

      1. frac-times 86.1%

         \[\leadsto \color{blue}{\frac{y \cdot x}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \sqrt[3]{a}}} - \frac{t}{a} \cdot z \]

      2. unpow2 86.1%

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

      3. add-cube-cbrt 86.5%

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

      4. associate-/l* 89.3%

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

   7. Applied egg-rr 89.3%

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

   if 1.23999999999999995e-85 < y

   1. Initial program 94.1%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.24 \cdot 10^{-85}:\\ \;\;\;\;\frac{y}{\frac{a}{x}} - \frac{t}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - t \cdot z}{a}\\ \end{array} \]

Alternative 4: 65.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-101} \lor \neg \left(t \leq 3.8 \cdot 10^{+67}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.7e-101) (not (<= t 3.8e+67)))
   (* (- t) (/ z a))
   (* y (/ x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.7e-101) || !(t <= 3.8e+67)) {
		tmp = -t * (z / 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 ((t <= (-2.7d-101)) .or. (.not. (t <= 3.8d+67))) then
        tmp = -t * (z / 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 ((t <= -2.7e-101) || !(t <= 3.8e+67)) {
		tmp = -t * (z / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.7e-101) or not (t <= 3.8e+67):
		tmp = -t * (z / a)
	else:
		tmp = y * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.7e-101) || !(t <= 3.8e+67))
		tmp = Float64(Float64(-t) * Float64(z / 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 ((t <= -2.7e-101) || ~((t <= 3.8e+67)))
		tmp = -t * (z / a);
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.7e-101], N[Not[LessEqual[t, 3.8e+67]], $MachinePrecision]], N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7000000000000002e-101 or 3.8000000000000002e67 < t

   1. Initial program 87.0%

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

   2. Taylor expanded in x around 0 64.7%

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

      1. mul-1-neg 64.7%

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

      2. *-commutative 64.7%

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

      3. associate-*l/ 69.0%

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

      4. *-commutative 69.0%

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

      5. distribute-lft-neg-in 69.0%

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

   4. Simplified 69.0%

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

   if -2.7000000000000002e-101 < t < 3.8000000000000002e67

   1. Initial program 93.6%

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

   2. Taylor expanded in x around inf 72.4%

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

      1. associate-*r/ 71.8%

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

   4. Simplified 71.8%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-101} \lor \neg \left(t \leq 3.8 \cdot 10^{+67}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 5: 65.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-97}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e-97)
   (* (- t) (/ z a))
   (if (<= t 2.75e+23) (* y (/ x a)) (* (/ t a) (- z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e-97) {
		tmp = -t * (z / a);
	} else if (t <= 2.75e+23) {
		tmp = y * (x / a);
	} else {
		tmp = (t / a) * -z;
	}
	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 (t <= (-2.6d-97)) then
        tmp = -t * (z / a)
    else if (t <= 2.75d+23) then
        tmp = y * (x / a)
    else
        tmp = (t / a) * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e-97) {
		tmp = -t * (z / a);
	} else if (t <= 2.75e+23) {
		tmp = y * (x / a);
	} else {
		tmp = (t / a) * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.6e-97:
		tmp = -t * (z / a)
	elif t <= 2.75e+23:
		tmp = y * (x / a)
	else:
		tmp = (t / a) * -z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e-97)
		tmp = Float64(Float64(-t) * Float64(z / a));
	elseif (t <= 2.75e+23)
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(Float64(t / a) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.6e-97)
		tmp = -t * (z / a);
	elseif (t <= 2.75e+23)
		tmp = y * (x / a);
	else
		tmp = (t / a) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e-97], N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.75e+23], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.60000000000000007e-97

   1. Initial program 92.2%

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

   2. Taylor expanded in x around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. *-commutative 63.8%

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

      3. associate-*l/ 66.7%

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

      4. *-commutative 66.7%

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

      5. distribute-lft-neg-in 66.7%

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

   4. Simplified 66.7%

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

   if -2.60000000000000007e-97 < t < 2.75000000000000002e23

   1. Initial program 93.3%

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

   2. Taylor expanded in x around inf 73.2%

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

      1. associate-*r/ 71.6%

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

   4. Simplified 71.6%

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

   if 2.75000000000000002e23 < t

   1. Initial program 81.0%

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

   2. Taylor expanded in x around 0 65.1%

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

      1. associate-*r/ 65.1%

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

      2. associate-*r* 65.1%

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

      3. neg-mul-1 65.1%

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

   4. Simplified 65.1%

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

      1. distribute-lft-neg-out 65.1%

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

      2. distribute-frac-neg 65.1%

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

      3. associate-*l/ 69.4%

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

      4. distribute-rgt-neg-in 69.4%

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

   6. Applied egg-rr 69.4%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-97}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \end{array} \]

Alternative 6: 51.7% 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 89.8%

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

2. Taylor expanded in x around inf 51.0%

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

   1. associate-*r/ 53.7%

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

4. Simplified 53.7%

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

5. Final simplification 53.7%

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

Developer target: 91.1% 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 2023268 
(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))