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

Percentage Accurate: 91.5% → 93.2%

Time: 7.4s

Alternatives: 6

Speedup: 0.7×

• 27.9% 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: 93.2% accurate, 0.1× speedup

Math

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

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

C

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

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = fma(x, Float64(y / a), Float64(-Float64(z / Float64(a / t))));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	end
	return 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], (-Infinity)], N[(x * N[(y / a), $MachinePrecision] + (-N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 64.7%

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

      1. div-sub 64.7%

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

      2. *-un-lft-identity 64.7%

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

      3. times-frac 96.6%

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

      4. fma-neg 96.6%

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

      5. associate-/l* 96.3%

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

   3. Applied egg-rr 96.3%

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

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

   1. Initial program 96.5%

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

4. Final simplification 96.5%

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

Alternative 2: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := y \cdot \frac{x}{a}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -100:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-100}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ x a))))
   (if (<= (* x y) -2e+195)
     t_1
     (if (<= (* x y) -100.0)
       (/ (* x y) a)
       (if (<= (* x y) 5e-100)
         (/ (* z (- t)) a)
         (if (<= (* x y) 5e+14)
           t_1
           (if (<= (* x y) 5e+127) (* t (/ (- z) a)) (* x (/ y a)))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (x / a);
	double tmp;
	if ((x * y) <= -2e+195) {
		tmp = t_1;
	} else if ((x * y) <= -100.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 5e-100) {
		tmp = (z * -t) / a;
	} else if ((x * y) <= 5e+14) {
		tmp = t_1;
	} else if ((x * y) <= 5e+127) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * (x / a)
    if ((x * y) <= (-2d+195)) then
        tmp = t_1
    else if ((x * y) <= (-100.0d0)) then
        tmp = (x * y) / a
    else if ((x * y) <= 5d-100) then
        tmp = (z * -t) / a
    else if ((x * y) <= 5d+14) then
        tmp = t_1
    else if ((x * y) <= 5d+127) 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 t_1 = y * (x / a);
	double tmp;
	if ((x * y) <= -2e+195) {
		tmp = t_1;
	} else if ((x * y) <= -100.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 5e-100) {
		tmp = (z * -t) / a;
	} else if ((x * y) <= 5e+14) {
		tmp = t_1;
	} else if ((x * y) <= 5e+127) {
		tmp = t * (-z / a);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = y * (x / a)
	tmp = 0
	if (x * y) <= -2e+195:
		tmp = t_1
	elif (x * y) <= -100.0:
		tmp = (x * y) / a
	elif (x * y) <= 5e-100:
		tmp = (z * -t) / a
	elif (x * y) <= 5e+14:
		tmp = t_1
	elif (x * y) <= 5e+127:
		tmp = t * (-z / a)
	else:
		tmp = x * (y / a)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(x / a))
	tmp = 0.0
	if (Float64(x * y) <= -2e+195)
		tmp = t_1;
	elseif (Float64(x * y) <= -100.0)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 5e-100)
		tmp = Float64(Float64(z * Float64(-t)) / a);
	elseif (Float64(x * y) <= 5e+14)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+127)
		tmp = Float64(t * Float64(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)
	t_1 = y * (x / a);
	tmp = 0.0;
	if ((x * y) <= -2e+195)
		tmp = t_1;
	elseif ((x * y) <= -100.0)
		tmp = (x * y) / a;
	elseif ((x * y) <= 5e-100)
		tmp = (z * -t) / a;
	elseif ((x * y) <= 5e+14)
		tmp = t_1;
	elseif ((x * y) <= 5e+127)
		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_] := Block[{t$95$1 = N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+195], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -100.0], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-100], N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+14], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+127], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.99999999999999995e195 or 5.0000000000000001e-100 < (*.f64 x y) < 5e14

   1. Initial program 83.1%

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

   2. Taylor expanded in x around inf 74.8%

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

      1. associate-*r/ 85.6%

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

   4. Simplified 85.6%

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

   if -1.99999999999999995e195 < (*.f64 x y) < -100

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 86.1%

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

   if -100 < (*.f64 x y) < 5.0000000000000001e-100

   1. Initial program 96.9%

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

   2. Taylor expanded in x around 0 84.8%

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

      1. associate-*r/ 84.8%

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

      2. associate-*r* 84.8%

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

      3. neg-mul-1 84.8%

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

   4. Simplified 84.8%

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

   if 5e14 < (*.f64 x y) < 5.0000000000000004e127

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 67.5%

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

      1. mul-1-neg 67.5%

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

      2. *-commutative 67.5%

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

      3. associate-*l/ 67.8%

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

      4. *-commutative 67.8%

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

      5. distribute-lft-neg-in 67.8%

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

   4. Simplified 67.8%

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

   if 5.0000000000000004e127 < (*.f64 x y)

   1. Initial program 88.3%

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

   2. Taylor expanded in x around inf 79.7%

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

      1. associate-/l* 91.3%

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

   4. Simplified 91.3%

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

      1. associate-/r/ 91.3%

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

   6. Applied egg-rr 91.3%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+195}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq -100:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-100}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3: 93.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+265}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \end{array} \]

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) -5e+265)
   (- (/ x (/ a y)) (* z (/ t a)))
   (/ (- (* x y) (* z t)) a)))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+265) {
		tmp = (x / (a / y)) - (z * (t / a));
	} else {
		tmp = ((x * y) - (z * t)) / 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) <= (-5d+265)) then
        tmp = (x / (a / y)) - (z * (t / a))
    else
        tmp = ((x * y) - (z * t)) / 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) <= -5e+265) {
		tmp = (x / (a / y)) - (z * (t / a));
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+265:
		tmp = (x / (a / y)) - (z * (t / a))
	else:
		tmp = ((x * y) - (z * t)) / a
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+265)
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z * Float64(t / a)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / 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) <= -5e+265)
		tmp = (x / (a / y)) - (z * (t / a));
	else
		tmp = ((x * y) - (z * t)) / 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], -5e+265], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.0000000000000002e265

   1. Initial program 69.2%

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

      1. div-sub 69.2%

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

      2. associate-/l* 96.9%

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

      3. associate-/l* 96.7%

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

   3. Applied egg-rr 96.7%

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

      1. clear-num 96.7%

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

      2. associate-/r/ 96.7%

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

      3. clear-num 96.7%

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

   5. Applied egg-rr 96.7%

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

   if -5.0000000000000002e265 < (*.f64 x y)

   1. Initial program 96.5%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+265}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 4: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{-z}{a}\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

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 (* t (/ (- z) a))))
   (if (<= y -8.2e-91)
     (/ y (/ a x))
     (if (<= y 3.4e-35)
       t_1
       (if (<= y 1.55e+82)
         (/ x (/ a y))
         (if (<= y 2.3e+96) t_1 (* y (/ x a))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-z / a);
	double tmp;
	if (y <= -8.2e-91) {
		tmp = y / (a / x);
	} else if (y <= 3.4e-35) {
		tmp = t_1;
	} else if (y <= 1.55e+82) {
		tmp = x / (a / y);
	} else if (y <= 2.3e+96) {
		tmp = t_1;
	} else {
		tmp = y * (x / 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 = t * (-z / a)
    if (y <= (-8.2d-91)) then
        tmp = y / (a / x)
    else if (y <= 3.4d-35) then
        tmp = t_1
    else if (y <= 1.55d+82) then
        tmp = x / (a / y)
    else if (y <= 2.3d+96) then
        tmp = t_1
    else
        tmp = y * (x / 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 = t * (-z / a);
	double tmp;
	if (y <= -8.2e-91) {
		tmp = y / (a / x);
	} else if (y <= 3.4e-35) {
		tmp = t_1;
	} else if (y <= 1.55e+82) {
		tmp = x / (a / y);
	} else if (y <= 2.3e+96) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = t * (-z / a)
	tmp = 0
	if y <= -8.2e-91:
		tmp = y / (a / x)
	elif y <= 3.4e-35:
		tmp = t_1
	elif y <= 1.55e+82:
		tmp = x / (a / y)
	elif y <= 2.3e+96:
		tmp = t_1
	else:
		tmp = y * (x / a)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-z) / a))
	tmp = 0.0
	if (y <= -8.2e-91)
		tmp = Float64(y / Float64(a / x));
	elseif (y <= 3.4e-35)
		tmp = t_1;
	elseif (y <= 1.55e+82)
		tmp = Float64(x / Float64(a / y));
	elseif (y <= 2.3e+96)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-z / a);
	tmp = 0.0;
	if (y <= -8.2e-91)
		tmp = y / (a / x);
	elseif (y <= 3.4e-35)
		tmp = t_1;
	elseif (y <= 1.55e+82)
		tmp = x / (a / y);
	elseif (y <= 2.3e+96)
		tmp = t_1;
	else
		tmp = y * (x / 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[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e-91], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-35], t$95$1, If[LessEqual[y, 1.55e+82], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+96], t$95$1, N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.20000000000000048e-91

   1. Initial program 91.1%

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

   2. Taylor expanded in x around inf 57.1%

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

      1. associate-/l* 58.9%

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

   4. Simplified 58.9%

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

   if -8.20000000000000048e-91 < y < 3.4000000000000003e-35 or 1.55000000000000016e82 < y < 2.30000000000000015e96

   1. Initial program 95.8%

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

   2. Taylor expanded in x around 0 74.2%

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

      1. mul-1-neg 74.2%

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

      2. *-commutative 74.2%

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

      3. associate-*l/ 71.1%

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

      4. *-commutative 71.1%

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

      5. distribute-lft-neg-in 71.1%

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

   4. Simplified 71.1%

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

   if 3.4000000000000003e-35 < y < 1.55000000000000016e82

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 81.9%

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

      1. associate-*r/ 82.0%

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

   4. Simplified 82.0%

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

      1. *-commutative 82.0%

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

      2. associate-/r/ 81.9%

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

   6. Applied egg-rr 81.9%

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

   if 2.30000000000000015e96 < y

   1. Initial program 85.9%

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

   2. Taylor expanded in x around inf 69.4%

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

      1. associate-*r/ 78.8%

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

   4. Simplified 78.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 5: 93.5% accurate, 0.7× speedup

Math

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

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

C

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

Java

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

Python

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

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / 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) <= -Inf)
		tmp = y * (x / a);
	else
		tmp = ((x * y) - (z * t)) / 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], (-Infinity)], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 64.7%

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

   2. Taylor expanded in x around inf 64.7%

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

      1. associate-*r/ 96.3%

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

   4. Simplified 96.3%

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

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

   1. Initial program 96.5%

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

4. Final simplification 96.5%

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

Alternative 6: 51.9% 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 93.2%

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

2. Taylor expanded in x around inf 52.9%

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

   1. associate-*r/ 54.1%

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

4. Simplified 54.1%

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

5. Final simplification 54.1%

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

Developer target: 91.6% 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 2023279 
(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))