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

Percentage Accurate: 91.6% → 96.6%

Time: 7.8s

Alternatives: 8

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: 91.6% 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: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+294}:\\ \;\;\;\;\left(x \cdot \frac{y}{z} - t\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t\_1 \leq 2.5 \cdot 10^{+305}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x \cdot \frac{y}{t} - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 -5e+294)
     (* (- (* x (/ y z)) t) (/ z a))
     (if (<= t_1 2.5e+305) (/ t_1 a) (* t (/ (- (* x (/ y t)) z) 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 <= -5e+294) {
		tmp = ((x * (y / z)) - t) * (z / a);
	} else if (t_1 <= 2.5e+305) {
		tmp = t_1 / a;
	} else {
		tmp = t * (((x * (y / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if (t_1 <= (-5d+294)) then
        tmp = ((x * (y / z)) - t) * (z / a)
    else if (t_1 <= 2.5d+305) then
        tmp = t_1 / a
    else
        tmp = t * (((x * (y / 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 t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -5e+294) {
		tmp = ((x * (y / z)) - t) * (z / a);
	} else if (t_1 <= 2.5e+305) {
		tmp = t_1 / a;
	} else {
		tmp = t * (((x * (y / t)) - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -5e+294:
		tmp = ((x * (y / z)) - t) * (z / a)
	elif t_1 <= 2.5e+305:
		tmp = t_1 / a
	else:
		tmp = t * (((x * (y / t)) - z) / 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 <= -5e+294)
		tmp = Float64(Float64(Float64(x * Float64(y / z)) - t) * Float64(z / a));
	elseif (t_1 <= 2.5e+305)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(t * Float64(Float64(Float64(x * Float64(y / t)) - z) / 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 <= -5e+294)
		tmp = ((x * (y / z)) - t) * (z / a);
	elseif (t_1 <= 2.5e+305)
		tmp = t_1 / a;
	else
		tmp = t * (((x * (y / t)) - z) / 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[LessEqual[t$95$1, -5e+294], N[(N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.5e+305], N[(t$95$1 / a), $MachinePrecision], N[(t * N[(N[(N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -4.9999999999999999e294

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf 92.8%

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

      1. +-commutative 92.8%

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

      2. mul-1-neg 92.8%

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

      3. unsub-neg 92.8%

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

      4. *-commutative 92.8%

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

      5. associate-/l* 92.8%

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

      6. *-commutative 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in z around inf 92.8%

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

      1. +-commutative 92.8%

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

      2. mul-1-neg 92.8%

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

      3. sub-neg 92.8%

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

      4. times-frac 92.7%

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

      5. associate-*l/ 95.2%

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

      6. associate-/l* 92.9%

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

      7. div-sub 95.3%

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

      8. associate-/l* 76.9%

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

      9. *-commutative 76.9%

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

      10. associate-/l* 95.2%

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

      11. associate-/l* 97.5%

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

   8. Simplified 97.5%

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

   if -4.9999999999999999e294 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2.50000000000000004e305

   1. Initial program 97.8%

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

   if 2.50000000000000004e305 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 64.2%

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

   3. Taylor expanded in t around inf 75.5%

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

      1. +-commutative 75.5%

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

      2. mul-1-neg 75.5%

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

      3. unsub-neg 75.5%

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

      4. times-frac 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in t around inf 75.5%

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

      1. associate-/l* 83.3%

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

      2. associate-/l/ 87.3%

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

      3. +-commutative 87.3%

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

      4. mul-1-neg 87.3%

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

      5. sub-neg 87.3%

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

      6. associate-*r/ 87.3%

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

      7. div-sub 99.8%

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

   8. Simplified 99.8%

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

Alternative 2: 69.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-48} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) a)))
   (if (<= (* x y) -4e-132)
     t_1
     (if (<= (* x y) 4e-95)
       (* t (/ (- z) a))
       (if (or (<= (* x y) 2e-48) (not (<= (* x y) 5e-11)))
         t_1
         (/ (* t (- z)) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -4e-132) {
		tmp = t_1;
	} else if ((x * y) <= 4e-95) {
		tmp = t * (-z / a);
	} else if (((x * y) <= 2e-48) || !((x * y) <= 5e-11)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) / a
    if ((x * y) <= (-4d-132)) then
        tmp = t_1
    else if ((x * y) <= 4d-95) then
        tmp = t * (-z / a)
    else if (((x * y) <= 2d-48) .or. (.not. ((x * y) <= 5d-11))) then
        tmp = t_1
    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 t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -4e-132) {
		tmp = t_1;
	} else if ((x * y) <= 4e-95) {
		tmp = t * (-z / a);
	} else if (((x * y) <= 2e-48) || !((x * y) <= 5e-11)) {
		tmp = t_1;
	} else {
		tmp = (t * -z) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) / a
	tmp = 0
	if (x * y) <= -4e-132:
		tmp = t_1
	elif (x * y) <= 4e-95:
		tmp = t * (-z / a)
	elif ((x * y) <= 2e-48) or not ((x * y) <= 5e-11):
		tmp = t_1
	else:
		tmp = (t * -z) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / a)
	tmp = 0.0
	if (Float64(x * y) <= -4e-132)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e-95)
		tmp = Float64(t * Float64(Float64(-z) / a));
	elseif ((Float64(x * y) <= 2e-48) || !(Float64(x * y) <= 5e-11))
		tmp = t_1;
	else
		tmp = Float64(Float64(t * Float64(-z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / a;
	tmp = 0.0;
	if ((x * y) <= -4e-132)
		tmp = t_1;
	elseif ((x * y) <= 4e-95)
		tmp = t * (-z / a);
	elseif (((x * y) <= 2e-48) || ~(((x * y) <= 5e-11)))
		tmp = t_1;
	else
		tmp = (t * -z) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e-132], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e-95], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 2e-48], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e-11]], $MachinePrecision]], t$95$1, N[(N[(t * (-z)), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.9999999999999999e-132 or 3.99999999999999996e-95 < (*.f64 x y) < 1.9999999999999999e-48 or 5.00000000000000018e-11 < (*.f64 x y)

   1. Initial program 92.4%

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

   3. Taylor expanded in x around inf 73.6%

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

   if -3.9999999999999999e-132 < (*.f64 x y) < 3.99999999999999996e-95

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0 77.4%

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

      1. mul-1-neg 77.4%

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

      2. associate-/l* 80.1%

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

      3. distribute-rgt-neg-in 80.1%

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

      4. distribute-neg-frac2 80.1%

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

   5. Simplified 80.1%

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

   if 1.9999999999999999e-48 < (*.f64 x y) < 5.00000000000000018e-11

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 82.4%

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

      1. associate-*r* 82.4%

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

      2. mul-1-neg 82.4%

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

   5. Simplified 82.4%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-132}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-48} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+294} \lor \neg \left(t\_1 \leq 2.5 \cdot 10^{+305}\right):\\ \;\;\;\;t \cdot \frac{x \cdot \frac{y}{t} - z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 -5e+294) (not (<= t_1 2.5e+305)))
     (* t (/ (- (* x (/ y t)) z) 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 <= -5e+294) || !(t_1 <= 2.5e+305)) {
		tmp = t * (((x * (y / t)) - z) / a);
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if ((t_1 <= (-5d+294)) .or. (.not. (t_1 <= 2.5d+305))) then
        tmp = t * (((x * (y / t)) - z) / a)
    else
        tmp = t_1 / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -5e+294) || !(t_1 <= 2.5e+305)) {
		tmp = t * (((x * (y / t)) - z) / 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 <= -5e+294) or not (t_1 <= 2.5e+305):
		tmp = t * (((x * (y / t)) - z) / 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 <= -5e+294) || !(t_1 <= 2.5e+305))
		tmp = Float64(t * Float64(Float64(Float64(x * Float64(y / t)) - z) / 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 <= -5e+294) || ~((t_1 <= 2.5e+305)))
		tmp = t * (((x * (y / t)) - z) / 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, -5e+294], N[Not[LessEqual[t$95$1, 2.5e+305]], $MachinePrecision]], N[(t * N[(N[(N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision] - z), $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)) < -4.9999999999999999e294 or 2.50000000000000004e305 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 72.2%

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

   3. Taylor expanded in t around inf 84.9%

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

      1. +-commutative 84.9%

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

      2. mul-1-neg 84.9%

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

      3. unsub-neg 84.9%

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

      4. times-frac 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in t around inf 84.9%

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

      1. associate-/l* 89.2%

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

      2. associate-/l/ 92.2%

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

      3. +-commutative 92.2%

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

      4. mul-1-neg 92.2%

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

      5. sub-neg 92.2%

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

      6. associate-*r/ 89.3%

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

      7. div-sub 97.0%

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

   8. Simplified 97.0%

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

   if -4.9999999999999999e294 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2.50000000000000004e305

   1. Initial program 97.8%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+294} \lor \neg \left(x \cdot y - z \cdot t \leq 2.5 \cdot 10^{+305}\right):\\ \;\;\;\;t \cdot \frac{x \cdot \frac{y}{t} - z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-28} \lor \neg \left(t \leq 2.35 \cdot 10^{-7}\right) \land \left(t \leq 3.3 \cdot 10^{+25} \lor \neg \left(t \leq 9 \cdot 10^{+142}\right)\right):\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.6e-28)
         (and (not (<= t 2.35e-7)) (or (<= t 3.3e+25) (not (<= t 9e+142)))))
   (* t (/ (- z) a))
   (/ (* x y) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.6e-28) || (!(t <= 2.35e-7) && ((t <= 3.3e+25) || !(t <= 9e+142)))) {
		tmp = t * (-z / 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 ((t <= (-5.6d-28)) .or. (.not. (t <= 2.35d-7)) .and. (t <= 3.3d+25) .or. (.not. (t <= 9d+142))) then
        tmp = t * (-z / 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 ((t <= -5.6e-28) || (!(t <= 2.35e-7) && ((t <= 3.3e+25) || !(t <= 9e+142)))) {
		tmp = t * (-z / a);
	} else {
		tmp = (x * y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.6e-28) or (not (t <= 2.35e-7) and ((t <= 3.3e+25) or not (t <= 9e+142))):
		tmp = t * (-z / a)
	else:
		tmp = (x * y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.6e-28) || (!(t <= 2.35e-7) && ((t <= 3.3e+25) || !(t <= 9e+142))))
		tmp = Float64(t * Float64(Float64(-z) / 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 ((t <= -5.6e-28) || (~((t <= 2.35e-7)) && ((t <= 3.3e+25) || ~((t <= 9e+142)))))
		tmp = t * (-z / a);
	else
		tmp = (x * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.6e-28], And[N[Not[LessEqual[t, 2.35e-7]], $MachinePrecision], Or[LessEqual[t, 3.3e+25], N[Not[LessEqual[t, 9e+142]], $MachinePrecision]]]], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5999999999999996e-28 or 2.35e-7 < t < 3.3000000000000001e25 or 8.9999999999999998e142 < t

   1. Initial program 84.9%

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

   3. Taylor expanded in x around 0 59.0%

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

      1. mul-1-neg 59.0%

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

      2. associate-/l* 67.8%

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

      3. distribute-rgt-neg-in 67.8%

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

      4. distribute-neg-frac2 67.8%

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

   5. Simplified 67.8%

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

   if -5.5999999999999996e-28 < t < 2.35e-7 or 3.3000000000000001e25 < t < 8.9999999999999998e142

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 70.9%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-28} \lor \neg \left(t \leq 2.35 \cdot 10^{-7}\right) \land \left(t \leq 3.3 \cdot 10^{+25} \lor \neg \left(t \leq 9 \cdot 10^{+142}\right)\right):\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ t_2 := t \cdot \frac{-z}{a}\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+25}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) a)) (t_2 (* t (/ (- z) a))))
   (if (<= t -3.9e-25)
     t_2
     (if (<= t 1e-6)
       t_1
       (if (<= t 7e+25) (* z (/ t (- a))) (if (<= t 9e+143) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double t_2 = t * (-z / a);
	double tmp;
	if (t <= -3.9e-25) {
		tmp = t_2;
	} else if (t <= 1e-6) {
		tmp = t_1;
	} else if (t <= 7e+25) {
		tmp = z * (t / -a);
	} else if (t <= 9e+143) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x * y) / a
    t_2 = t * (-z / a)
    if (t <= (-3.9d-25)) then
        tmp = t_2
    else if (t <= 1d-6) then
        tmp = t_1
    else if (t <= 7d+25) then
        tmp = z * (t / -a)
    else if (t <= 9d+143) then
        tmp = t_1
    else
        tmp = t_2
    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) / a;
	double t_2 = t * (-z / a);
	double tmp;
	if (t <= -3.9e-25) {
		tmp = t_2;
	} else if (t <= 1e-6) {
		tmp = t_1;
	} else if (t <= 7e+25) {
		tmp = z * (t / -a);
	} else if (t <= 9e+143) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) / a
	t_2 = t * (-z / a)
	tmp = 0
	if t <= -3.9e-25:
		tmp = t_2
	elif t <= 1e-6:
		tmp = t_1
	elif t <= 7e+25:
		tmp = z * (t / -a)
	elif t <= 9e+143:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / a)
	t_2 = Float64(t * Float64(Float64(-z) / a))
	tmp = 0.0
	if (t <= -3.9e-25)
		tmp = t_2;
	elseif (t <= 1e-6)
		tmp = t_1;
	elseif (t <= 7e+25)
		tmp = Float64(z * Float64(t / Float64(-a)));
	elseif (t <= 9e+143)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / a;
	t_2 = t * (-z / a);
	tmp = 0.0;
	if (t <= -3.9e-25)
		tmp = t_2;
	elseif (t <= 1e-6)
		tmp = t_1;
	elseif (t <= 7e+25)
		tmp = z * (t / -a);
	elseif (t <= 9e+143)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e-25], t$95$2, If[LessEqual[t, 1e-6], t$95$1, If[LessEqual[t, 7e+25], N[(z * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+143], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.9e-25 or 8.9999999999999993e143 < t

   1. Initial program 83.9%

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

   3. Taylor expanded in x around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. associate-/l* 68.4%

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

      3. distribute-rgt-neg-in 68.4%

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

      4. distribute-neg-frac2 68.4%

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

   5. Simplified 68.4%

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

   if -3.9e-25 < t < 9.99999999999999955e-7 or 6.99999999999999999e25 < t < 8.9999999999999993e143

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf 71.1%

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

   if 9.99999999999999955e-7 < t < 6.99999999999999999e25

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 67.8%

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

      1. *-commutative 67.8%

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

      2. associate-*r/ 67.9%

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

      3. neg-mul-1 67.9%

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

      4. distribute-rgt-neg-in 67.9%

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

      5. distribute-frac-neg 67.9%

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

   5. Simplified 67.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;t \leq 10^{-6}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+25}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+143}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) 5e+276) (/ (- (* x y) (* z t)) a) (* t (/ (- z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= 5e+276) {
		tmp = ((x * y) - (z * t)) / 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 ((z * t) <= 5d+276) then
        tmp = ((x * y) - (z * t)) / 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 ((z * t) <= 5e+276) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t * (-z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= 5e+276:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t * (-z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= 5e+276)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(t * Float64(Float64(-z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= 5e+276)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t * (-z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], 5e+276], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 5.00000000000000001e276

   1. Initial program 94.5%

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

   if 5.00000000000000001e276 < (*.f64 z t)

   1. Initial program 61.8%

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

   3. Taylor expanded in x around 0 65.8%

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

      1. mul-1-neg 65.8%

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

      2. associate-/l* 95.9%

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

      3. distribute-rgt-neg-in 95.9%

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

      4. distribute-neg-frac2 95.9%

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

   5. Simplified 95.9%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.05 \cdot 10^{-58}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.05e-58) (/ (* x y) a) (* x (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.05e-58) {
		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 (t <= 1.05d-58) 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 (t <= 1.05e-58) {
		tmp = (x * y) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.05e-58:
		tmp = (x * y) / a
	else:
		tmp = x * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.05e-58)
		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 (t <= 1.05e-58)
		tmp = (x * y) / a;
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.05e-58], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.04999999999999994e-58

   1. Initial program 93.5%

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

   3. Taylor expanded in x around inf 64.3%

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

   if 1.04999999999999994e-58 < t

   1. Initial program 85.7%

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

   3. Taylor expanded in x around inf 37.7%

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

      1. associate-*r/ 42.3%

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

   5. Simplified 42.3%

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

Alternative 8: 50.5% 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 91.3%

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

3. Taylor expanded in x around inf 56.6%

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

   1. associate-*r/ 55.8%

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

5. Simplified 55.8%

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

Developer target: 91.3% 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 2024111 
(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))