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

Percentage Accurate: 91.7% → 95.1%

Time: 8.3s

Alternatives: 10

Speedup: 0.6×

• 29.1% 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: 91.7% 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: 95.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - t \cdot z\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{a} \cdot z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - t \cdot \frac{z}{x}\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* t z))))
   (if (<= t_1 -1e+301)
     (- (* x (/ y a)) (* (/ t a) z))
     (if (<= t_1 5e+305) (/ t_1 a) (/ (* x (- y (* t (/ z x)))) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (t * z);
	double tmp;
	if (t_1 <= -1e+301) {
		tmp = (x * (y / a)) - ((t / a) * z);
	} else if (t_1 <= 5e+305) {
		tmp = t_1 / a;
	} else {
		tmp = (x * (y - (t * (z / x)))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (t * z)
    if (t_1 <= (-1d+301)) then
        tmp = (x * (y / a)) - ((t / a) * z)
    else if (t_1 <= 5d+305) then
        tmp = t_1 / a
    else
        tmp = (x * (y - (t * (z / x)))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (t * z);
	double tmp;
	if (t_1 <= -1e+301) {
		tmp = (x * (y / a)) - ((t / a) * z);
	} else if (t_1 <= 5e+305) {
		tmp = t_1 / a;
	} else {
		tmp = (x * (y - (t * (z / x)))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) - (t * z)
	tmp = 0
	if t_1 <= -1e+301:
		tmp = (x * (y / a)) - ((t / a) * z)
	elif t_1 <= 5e+305:
		tmp = t_1 / a
	else:
		tmp = (x * (y - (t * (z / x)))) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(t * z))
	tmp = 0.0
	if (t_1 <= -1e+301)
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(Float64(t / a) * z));
	elseif (t_1 <= 5e+305)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(x * Float64(y - Float64(t * Float64(z / x)))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (t * z);
	tmp = 0.0;
	if (t_1 <= -1e+301)
		tmp = (x * (y / a)) - ((t / a) * z);
	elseif (t_1 <= 5e+305)
		tmp = t_1 / a;
	else
		tmp = (x * (y - (t * (z / x)))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+301], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(t$95$1 / a), $MachinePrecision], N[(N[(x * N[(y - N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1.00000000000000005e301

   1. Initial program 61.5%

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

      1. div-sub 52.7%

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

      2. associate-/l* 79.9%

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

      3. associate-/l* 91.1%

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

   4. Applied egg-rr 91.1%

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

   if -1.00000000000000005e301 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000009e305

   1. Initial program 99.4%

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

   if 5.00000000000000009e305 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 66.2%

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

   3. Taylor expanded in x around inf 74.4%

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

      1. mul-1-neg 74.4%

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

      2. unsub-neg 74.4%

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

      3. associate-/l* 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot z \leq -1 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{a} \cdot z\\ \mathbf{elif}\;x \cdot y - t \cdot z \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x \cdot y - t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - t \cdot \frac{z}{x}\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.6% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* y (- (/ x a) (* (/ t a) (/ z y))))
   (/ (fma x y (* t (- z))) a)))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 35.2%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. +-commutative 77.1%

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

      2. mul-1-neg 77.1%

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

      3. unsub-neg 77.1%

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

      4. times-frac 95.3%

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

   5. Simplified 95.3%

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

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

   1. Initial program 94.7%

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

      1. div-sub 91.3%

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

      2. *-commutative 91.3%

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

      3. div-sub 94.7%

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

      4. *-commutative 94.7%

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

      5. fmm-def 95.1%

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

      6. distribute-rgt-neg-out 95.1%

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

   3. Simplified 95.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 95.1%

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

Alternative 3: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-40} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot z}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -5e-40) (not (<= (* x y) 2e-20)))
   (* y (/ x a))
   (/ (* t z) (- a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e-40) || !((x * y) <= 2e-20)) {
		tmp = y * (x / 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-40)) .or. (.not. ((x * y) <= 2d-20))) then
        tmp = y * (x / 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-40) || !((x * y) <= 2e-20)) {
		tmp = y * (x / a);
	} else {
		tmp = (t * z) / -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -5e-40) or not ((x * y) <= 2e-20):
		tmp = y * (x / a)
	else:
		tmp = (t * z) / -a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -5e-40) || !(Float64(x * y) <= 2e-20))
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(Float64(t * z) / Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -5e-40) || ~(((x * y) <= 2e-20)))
		tmp = y * (x / 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-40], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e-20]], $MachinePrecision]], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(N[(t * z), $MachinePrecision] / (-a)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.99999999999999965e-40 or 1.99999999999999989e-20 < (*.f64 x y)

   1. Initial program 85.1%

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

   3. Taylor expanded in y around inf 78.7%

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

      1. +-commutative 78.7%

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

      2. mul-1-neg 78.7%

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

      3. unsub-neg 78.7%

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

      4. times-frac 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in x around inf 65.1%

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

   if -4.99999999999999965e-40 < (*.f64 x y) < 1.99999999999999989e-20

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. *-commutative 80.7%

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

      3. distribute-rgt-neg-in 80.7%

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

   5. Simplified 80.7%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-40} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot z}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -2e+90) (not (<= (* x y) 2e-20)))
   (* y (/ x a))
   (* (/ t a) (- z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+90) || !((x * y) <= 2e-20)) {
		tmp = y * (x / a);
	} else {
		tmp = (t / a) * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((x * y) <= (-2d+90)) .or. (.not. ((x * y) <= 2d-20))) then
        tmp = y * (x / a)
    else
        tmp = (t / a) * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+90) || !((x * y) <= 2e-20)) {
		tmp = y * (x / a);
	} else {
		tmp = (t / a) * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -2e+90) or not ((x * y) <= 2e-20):
		tmp = y * (x / a)
	else:
		tmp = (t / a) * -z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+90) || !(Float64(x * y) <= 2e-20))
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(Float64(t / a) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -2e+90) || ~(((x * y) <= 2e-20)))
		tmp = y * (x / a);
	else
		tmp = (t / a) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+90], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e-20]], $MachinePrecision]], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.99999999999999993e90 or 1.99999999999999989e-20 < (*.f64 x y)

   1. Initial program 82.0%

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

   3. Taylor expanded in y around inf 82.4%

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

      1. +-commutative 82.4%

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

      2. mul-1-neg 82.4%

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

      3. unsub-neg 82.4%

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

      4. times-frac 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in x around inf 75.2%

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

   if -1.99999999999999993e90 < (*.f64 x y) < 1.99999999999999989e-20

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. *-commutative 72.6%

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

      3. associate-*r/ 73.6%

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

      4. distribute-rgt-neg-in 73.6%

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

      5. distribute-frac-neg 73.6%

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

   5. Simplified 73.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-40} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -5e-40) (not (<= (* x y) 2e-20)))
   (* y (/ x a))
   (* t (/ z (- a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e-40) || !((x * y) <= 2e-20)) {
		tmp = y * (x / 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-40)) .or. (.not. ((x * y) <= 2d-20))) then
        tmp = y * (x / 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-40) || !((x * y) <= 2e-20)) {
		tmp = y * (x / a);
	} else {
		tmp = t * (z / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -5e-40) or not ((x * y) <= 2e-20):
		tmp = y * (x / a)
	else:
		tmp = t * (z / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -5e-40) || !(Float64(x * y) <= 2e-20))
		tmp = Float64(y * Float64(x / 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-40) || ~(((x * y) <= 2e-20)))
		tmp = y * (x / 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-40], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e-20]], $MachinePrecision]], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.99999999999999965e-40 or 1.99999999999999989e-20 < (*.f64 x y)

   1. Initial program 85.1%

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

   3. Taylor expanded in y around inf 78.7%

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

      1. +-commutative 78.7%

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

      2. mul-1-neg 78.7%

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

      3. unsub-neg 78.7%

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

      4. times-frac 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in x around inf 65.1%

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

   if -4.99999999999999965e-40 < (*.f64 x y) < 1.99999999999999989e-20

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. associate-/l* 76.9%

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

      3. distribute-rgt-neg-in 76.9%

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

      4. distribute-neg-frac2 76.9%

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

   5. Simplified 76.9%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-40} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 35.2%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. +-commutative 77.1%

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

      2. mul-1-neg 77.1%

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

      3. unsub-neg 77.1%

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

      4. times-frac 95.3%

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

   5. Simplified 95.3%

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

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

   1. Initial program 94.7%

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

4. Final simplification 94.7%

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

Alternative 7: 93.6% accurate, 0.6× speedup

Math

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

FPCore

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

C

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) - (t * z)) / 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 * (x / a);
	} else {
		tmp = ((x * y) - (t * z)) / a;
	}
	return tmp;
}

Python

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

Julia

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(t * z)) / a);
	end
	return tmp
end

MATLAB

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

Wolfram

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[(t * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 35.2%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. +-commutative 77.1%

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

      2. mul-1-neg 77.1%

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

      3. unsub-neg 77.1%

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

      4. times-frac 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in x around inf 84.7%

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

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

   1. Initial program 94.7%

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

4. Final simplification 93.8%

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

Alternative 8: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8.2e+106) (* y (/ x a)) (/ (* x y) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.2e+106) {
		tmp = y * (x / 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 (x <= (-8.2d+106)) then
        tmp = y * (x / 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 (x <= -8.2e+106) {
		tmp = y * (x / a);
	} else {
		tmp = (x * y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -8.2e+106:
		tmp = y * (x / a)
	else:
		tmp = (x * y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8.2e+106)
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(Float64(x * y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -8.2e+106)
		tmp = y * (x / a);
	else
		tmp = (x * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8.2e+106], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.2000000000000005e106

   1. Initial program 80.6%

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

   3. Taylor expanded in y around inf 80.0%

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

      1. +-commutative 80.0%

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

      2. mul-1-neg 80.0%

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

      3. unsub-neg 80.0%

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

      4. times-frac 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in x around inf 77.0%

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

   if -8.2000000000000005e106 < x

   1. Initial program 91.2%

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

   3. Taylor expanded in x around inf 46.5%

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

Alternative 9: 51.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.6%

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

3. Taylor expanded in y around inf 78.2%

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

   1. +-commutative 78.2%

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

   2. mul-1-neg 78.2%

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

   3. unsub-neg 78.2%

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

   4. times-frac 77.0%

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

5. Simplified 77.0%

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

6. Taylor expanded in x around inf 49.0%

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

Alternative 10: 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 89.6%

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

3. Taylor expanded in x around inf 48.7%

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

   1. associate-*r/ 51.7%

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

5. Simplified 51.7%

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

Developer Target 1: 91.4% 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 2024163 
(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))