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

Percentage Accurate: 91.4% → 96.5%

Time: 7.9s

Alternatives: 8

Speedup: 0.4×

• 28.1% 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: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+303}\right):\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+303)))
     (* y (/ (- x (* t (/ z y))) a))
     (/ t_1 a))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+303)) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+303)) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+303):
		tmp = y * ((x - (t * (z / y))) / a)
	else:
		tmp = t_1 / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+303))
		tmp = Float64(y * Float64(Float64(x - Float64(t * Float64(z / y))) / a));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+303)))
		tmp = y * ((x - (t * (z / y))) / a);
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+303]], $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 4.9999999999999997e303 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 79.0%

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

      1. clear-num 79.0%

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

      2. inv-pow 79.0%

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

      3. fma-neg 79.0%

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

      4. *-commutative 79.0%

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

      5. distribute-rgt-neg-in 79.0%

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

   4. Applied egg-rr 79.0%

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

   5. Taylor expanded in y around inf 88.4%

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

      1. +-commutative 88.4%

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

      2. mul-1-neg 88.4%

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

      3. sub-neg 88.4%

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

      4. *-commutative 88.4%

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

      5. associate-/r* 90.1%

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

      6. div-sub 91.6%

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

      7. associate-*r/ 95.8%

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

   7. Simplified 95.8%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999997e303

   1. Initial program 99.1%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+303}\right):\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+282}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (/ y (/ a x))
   (if (<= (* x y) 1e+282) (/ (- (* x y) (* z t)) a) (* y (/ x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = y / (a / x);
	} else if ((x * y) <= 1e+282) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = y / (a / x);
	} else if ((x * y) <= 1e+282) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = y / (a / x)
	elif (x * y) <= 1e+282:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = y * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 1e+282)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / 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 ((x * y) <= -Inf)
		tmp = y / (a / x);
	elseif ((x * y) <= 1e+282)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+282], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf 95.2%

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

      1. +-commutative 95.2%

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

      2. mul-1-neg 95.2%

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

      3. unsub-neg 95.2%

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

      4. times-frac 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around inf 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 x y) < 1.00000000000000003e282

   1. Initial program 97.1%

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

   if 1.00000000000000003e282 < (*.f64 x y)

   1. Initial program 66.3%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. times-frac 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in x around inf 100.0%

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

Alternative 3: 72.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+19} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+134}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -5e+19) (not (<= (* x y) 5e+134)))
   (* x (/ y a))
   (* (* z t) (/ -1.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e+19) || !((x * y) <= 5e+134)) {
		tmp = x * (y / a);
	} else {
		tmp = (z * t) * (-1.0 / 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 (((x * y) <= (-5d+19)) .or. (.not. ((x * y) <= 5d+134))) then
        tmp = x * (y / a)
    else
        tmp = (z * t) * ((-1.0d0) / 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 (((x * y) <= -5e+19) || !((x * y) <= 5e+134)) {
		tmp = x * (y / a);
	} else {
		tmp = (z * t) * (-1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -5e+19) or not ((x * y) <= 5e+134):
		tmp = x * (y / a)
	else:
		tmp = (z * t) * (-1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -5e+19) || !(Float64(x * y) <= 5e+134))
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(Float64(z * t) * Float64(-1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -5e+19) || ~(((x * y) <= 5e+134)))
		tmp = x * (y / a);
	else
		tmp = (z * t) * (-1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+19], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+134]], $MachinePrecision]], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5e19 or 4.99999999999999981e134 < (*.f64 x y)

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf 77.7%

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

      1. associate-*r/ 80.5%

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

   5. Simplified 80.5%

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

   if -5e19 < (*.f64 x y) < 4.99999999999999981e134

   1. Initial program 97.7%

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

   3. Taylor expanded in x around 0 78.2%

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

      1. associate-*r* 78.2%

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

      2. neg-mul-1 78.2%

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

   5. Simplified 78.2%

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

      1. frac-2neg 78.2%

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

      2. div-inv 78.2%

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

      3. distribute-lft-neg-out 78.2%

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

      4. remove-double-neg 78.2%

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

   7. Applied egg-rr 78.2%

      \[\leadsto \color{blue}{\left(t \cdot z\right) \cdot \frac{1}{-a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+19} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+134}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+19} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+134}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot t}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -5e+19) (not (<= (* x y) 5e+134)))
   (* x (/ y a))
   (/ (* z t) (- a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e+19) || !((x * y) <= 5e+134)) {
		tmp = x * (y / a);
	} else {
		tmp = (z * t) / -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 (((x * y) <= (-5d+19)) .or. (.not. ((x * y) <= 5d+134))) then
        tmp = x * (y / a)
    else
        tmp = (z * t) / -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 (((x * y) <= -5e+19) || !((x * y) <= 5e+134)) {
		tmp = x * (y / a);
	} else {
		tmp = (z * t) / -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -5e+19) or not ((x * y) <= 5e+134):
		tmp = x * (y / a)
	else:
		tmp = (z * t) / -a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -5e+19) || !(Float64(x * y) <= 5e+134))
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(Float64(z * t) / Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -5e+19) || ~(((x * y) <= 5e+134)))
		tmp = x * (y / a);
	else
		tmp = (z * t) / -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+19], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+134]], $MachinePrecision]], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] / (-a)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5e19 or 4.99999999999999981e134 < (*.f64 x y)

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf 77.7%

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

      1. associate-*r/ 80.5%

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

   5. Simplified 80.5%

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

   if -5e19 < (*.f64 x y) < 4.99999999999999981e134

   1. Initial program 97.7%

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

   3. Taylor expanded in x around 0 78.2%

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

      1. associate-*r* 78.2%

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

      2. neg-mul-1 78.2%

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

   5. Simplified 78.2%

      \[\leadsto \frac{\color{blue}{\left(-t\right) \cdot z}}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+19} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+134}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot t}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+19} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+134}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -5e+19) (not (<= (* x y) 5e+134)))
   (* x (/ y a))
   (* t (/ z (- a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e+19) || !((x * y) <= 5e+134)) {
		tmp = x * (y / a);
	} else {
		tmp = t * (z / -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((x * y) <= (-5d+19)) .or. (.not. ((x * y) <= 5d+134))) then
        tmp = x * (y / a)
    else
        tmp = t * (z / -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e+19) || !((x * y) <= 5e+134)) {
		tmp = x * (y / a);
	} else {
		tmp = t * (z / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -5e+19) or not ((x * y) <= 5e+134):
		tmp = x * (y / a)
	else:
		tmp = t * (z / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -5e+19) || !(Float64(x * y) <= 5e+134))
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(t * Float64(z / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -5e+19) || ~(((x * y) <= 5e+134)))
		tmp = x * (y / a);
	else
		tmp = t * (z / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+19], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+134]], $MachinePrecision]], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5e19 or 4.99999999999999981e134 < (*.f64 x y)

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf 77.7%

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

      1. associate-*r/ 80.5%

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

   5. Simplified 80.5%

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

   if -5e19 < (*.f64 x y) < 4.99999999999999981e134

   1. Initial program 97.7%

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

      1. clear-num 97.5%

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

      2. inv-pow 97.5%

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

      3. fma-neg 97.5%

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

      4. *-commutative 97.5%

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

      5. distribute-rgt-neg-in 97.5%

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

   4. Applied egg-rr 97.5%

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

   5. Taylor expanded in x around 0 78.2%

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

      1. mul-1-neg 78.2%

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

      2. associate-*r/ 75.9%

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

      3. distribute-rgt-neg-in 75.9%

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

      4. mul-1-neg 75.9%

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

      5. associate-*r/ 75.9%

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

      6. mul-1-neg 75.9%

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

   7. Simplified 75.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+19} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+134}\right):\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 5.1 \cdot 10^{+168}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a 5.1e+168) (/ (* x y) a) (* x (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 5.1e+168) {
		tmp = (x * y) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 5.1d+168) then
        tmp = (x * y) / a
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 5.1e+168) {
		tmp = (x * y) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 5.1e+168:
		tmp = (x * y) / a
	else:
		tmp = x * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 5.1e+168)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 5.1e+168)
		tmp = (x * y) / a;
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 5.1e+168], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5.10000000000000025e168

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf 48.6%

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

   if 5.10000000000000025e168 < a

   1. Initial program 87.1%

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

   3. Taylor expanded in x around inf 57.8%

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

      1. associate-*r/ 54.9%

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

   5. Simplified 54.9%

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

Alternative 7: 51.6% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 / (a / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

3. Taylor expanded in x around inf 49.7%

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

   1. associate-*r/ 49.8%

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

5. Simplified 49.8%

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

   1. clear-num 49.8%

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

   2. un-div-inv 49.8%

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

7. Applied egg-rr 49.8%

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

Alternative 8: 51.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

3. Taylor expanded in x around inf 49.7%

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

   1. associate-*r/ 49.8%

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

5. Simplified 49.8%

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

Developer target: 91.5% 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 2024086 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (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))