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

Percentage Accurate: 91.3% → 96.0%

Time: 8.2s

Alternatives: 6

Speedup: 0.6×

• 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: 91.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - (z * t)) / a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \frac{x}{z \cdot a} - \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 (- INFINITY))
     (* y (/ (- x (* t (/ z y))) a))
     (if (<= t_1 5e+297) (/ t_1 a) (* z (- (* y (/ x (* z a))) (/ t a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else if (t_1 <= 5e+297) {
		tmp = t_1 / a;
	} else {
		tmp = z * ((y * (x / (z * a))) - (t / a));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else if (t_1 <= 5e+297) {
		tmp = t_1 / a;
	} else {
		tmp = z * ((y * (x / (z * a))) - (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * ((x - (t * (z / y))) / a)
	elif t_1 <= 5e+297:
		tmp = t_1 / a
	else:
		tmp = z * ((y * (x / (z * a))) - (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(x - Float64(t * Float64(z / y))) / a));
	elseif (t_1 <= 5e+297)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(z * Float64(Float64(y * Float64(x / Float64(z * a))) - Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * ((x - (t * (z / y))) / a);
	elseif (t_1 <= 5e+297)
		tmp = t_1 / a;
	else
		tmp = z * ((y * (x / (z * a))) - (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(N[(x - N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+297], N[(t$95$1 / a), $MachinePrecision], N[(z * N[(N[(y * N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 72.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 72.7%

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

      1. associate-/l* 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in y around inf 83.9%

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

      1. +-commutative 83.9%

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

      2. mul-1-neg 83.9%

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

      3. sub-neg 83.9%

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

      4. *-commutative 83.9%

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

      5. associate-/r* 84.4%

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

      6. div-sub 90.8%

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

      7. associate-/l* 99.9%

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

   8. Simplified 99.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999998e297

   1. Initial program 98.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 4.9999999999999998e297 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 61.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.3%

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

      1. +-commutative 83.3%

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

      2. mul-1-neg 83.3%

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

      3. unsub-neg 83.3%

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

      4. *-commutative 83.3%

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

      5. associate-/l* 93.2%

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

      6. *-commutative 93.2%

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

   5. Simplified 93.2%

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

Alternative 2: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+267}\right):\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+267)))
     (* y (/ (- x (* t (/ z y))) a))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+267)) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+267)) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+267):
		tmp = y * ((x - (t * (z / y))) / a)
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+267))
		tmp = Float64(y * Float64(Float64(x - Float64(t * Float64(z / y))) / a));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+267)))
		tmp = y * ((x - (t * (z / y))) / a);
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+267]], $MachinePrecision]], N[(y * N[(N[(x - N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 3.9999999999999999e267 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 68.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 67.4%

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

      1. associate-/l* 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in y around inf 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. sub-neg 75.6%

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

      4. *-commutative 75.6%

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

      5. associate-/r* 76.1%

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

      6. div-sub 82.3%

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

      7. associate-/l* 88.2%

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

   8. Simplified 88.2%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 3.9999999999999999e267

   1. Initial program 98.2%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 4 \cdot 10^{+267}\right):\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+80}:\\ \;\;\;\;\frac{z \cdot t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+34)
   (* x (/ y a))
   (if (<= (* x y) 1e+80) (/ (* z t) (- a)) (/ y (/ a x)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+34) {
		tmp = x * (y / a);
	} else if ((x * y) <= 1e+80) {
		tmp = (z * t) / -a;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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+34)) then
        tmp = x * (y / a)
    else if ((x * y) <= 1d+80) then
        tmp = (z * t) / -a
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+34) {
		tmp = x * (y / a);
	} else if ((x * y) <= 1e+80) {
		tmp = (z * t) / -a;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+34:
		tmp = x * (y / a)
	elif (x * y) <= 1e+80:
		tmp = (z * t) / -a
	else:
		tmp = y / (a / x)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+34)
		tmp = Float64(x * Float64(y / a));
	elseif (Float64(x * y) <= 1e+80)
		tmp = Float64(Float64(z * t) / Float64(-a));
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+34)
		tmp = x * (y / a);
	elseif ((x * y) <= 1e+80)
		tmp = (z * t) / -a;
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+34], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+80], N[(N[(z * t), $MachinePrecision] / (-a)), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999998e34

   1. Initial program 84.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.0%

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

      1. associate-*r/ 71.9%

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

   5. Simplified 71.9%

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

   if -4.9999999999999998e34 < (*.f64 x y) < 1e80

   1. Initial program 94.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. *-commutative 78.9%

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

      3. distribute-rgt-neg-in 78.9%

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

   5. Simplified 78.9%

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

   if 1e80 < (*.f64 x y)

   1. Initial program 86.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 91.9%

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

      1. +-commutative 91.9%

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

      2. mul-1-neg 91.9%

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

      3. unsub-neg 91.9%

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

      4. associate-/l* 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in x around inf 81.9%

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

      1. clear-num 81.8%

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

      2. un-div-inv 81.9%

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

   8. Applied egg-rr 81.9%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+80}:\\ \;\;\;\;\frac{z \cdot t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+80}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+34)
   (* x (/ y a))
   (if (<= (* x y) 1e+80) (* t (/ z (- a))) (/ y (/ a x)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+34) {
		tmp = x * (y / a);
	} else if ((x * y) <= 1e+80) {
		tmp = t * (z / -a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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+34)) then
        tmp = x * (y / a)
    else if ((x * y) <= 1d+80) then
        tmp = t * (z / -a)
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+34) {
		tmp = x * (y / a);
	} else if ((x * y) <= 1e+80) {
		tmp = t * (z / -a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+34:
		tmp = x * (y / a)
	elif (x * y) <= 1e+80:
		tmp = t * (z / -a)
	else:
		tmp = y / (a / x)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+34)
		tmp = Float64(x * Float64(y / a));
	elseif (Float64(x * y) <= 1e+80)
		tmp = Float64(t * Float64(z / Float64(-a)));
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+34)
		tmp = x * (y / a);
	elseif ((x * y) <= 1e+80)
		tmp = t * (z / -a);
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+34], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+80], N[(t * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999998e34

   1. Initial program 84.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.0%

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

      1. associate-*r/ 71.9%

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

   5. Simplified 71.9%

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

   if -4.9999999999999998e34 < (*.f64 x y) < 1e80

   1. Initial program 94.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. associate-/l* 77.8%

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

      3. distribute-rgt-neg-in 77.8%

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

      4. distribute-neg-frac2 77.8%

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

   5. Simplified 77.8%

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

   if 1e80 < (*.f64 x y)

   1. Initial program 86.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 91.9%

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

      1. +-commutative 91.9%

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

      2. mul-1-neg 91.9%

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

      3. unsub-neg 91.9%

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

      4. associate-/l* 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in x around inf 81.9%

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

      1. clear-num 81.8%

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

      2. un-div-inv 81.9%

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

   8. Applied egg-rr 81.9%

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

Alternative 5: 92.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+197}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) -4e+197) (* z (/ t (- a))) (/ (- (* x y) (* z t)) a)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -4e+197) {
		tmp = z * (t / -a);
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z * t) <= (-4d+197)) then
        tmp = z * (t / -a)
    else
        tmp = ((x * y) - (z * t)) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -4e+197) {
		tmp = z * (t / -a);
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -4e+197:
		tmp = z * (t / -a)
	else:
		tmp = ((x * y) - (z * t)) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= -4e+197)
		tmp = Float64(z * Float64(t / Float64(-a)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= -4e+197)
		tmp = z * (t / -a);
	else
		tmp = ((x * y) - (z * t)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], -4e+197], N[(z * N[(t / (-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 z t) < -3.9999999999999998e197

   1. Initial program 78.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.1%

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

      1. *-commutative 81.1%

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

      2. associate-*r/ 99.8%

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

      3. neg-mul-1 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. distribute-frac-neg 99.8%

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

   5. Simplified 99.8%

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

   if -3.9999999999999998e197 < (*.f64 z t)

   1. Initial program 93.2%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+197}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x * (y / a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.9%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 43.6%

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

   1. associate-*r/ 45.4%

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

5. Simplified 45.4%

   \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
6. Add Preprocessing

Developer Target 1: 92.0% accurate, 0.4× 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 2024139 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -246868496869954800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6309831121978371/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z)))))

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