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

Percentage Accurate: 91.4% → 93.2%

Time: 9.9s

Alternatives: 11

Speedup: 0.6×

• 28.6% 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: 93.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 63.8%

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

   3. Taylor expanded in x around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. *-commutative 70.0%

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

      3. associate-*l/ 93.8%

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

      4. distribute-rgt-neg-in 93.8%

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

   5. Simplified 93.8%

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

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

   1. Initial program 96.1%

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

4. Final simplification 96.0%

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

Alternative 2: 91.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a} \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

   1. div-sub 91.7%

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

   2. *-commutative 91.7%

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

   3. div-sub 94.1%

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

   4. fma-neg 94.5%

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

   5. *-commutative 94.5%

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

   6. distribute-rgt-neg-out 94.5%

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

3. Simplified 94.5%

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

5. Final simplification 94.5%

   \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a} \]
6. Add Preprocessing

Alternative 3: 71.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;-\frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) a)))
   (if (<= (* x y) -2e+87)
     t_1
     (if (<= (* x y) -4e+55)
       (/ (- z) (/ a t))
       (if (<= (* x y) -2e+35)
         t_1
         (if (<= (* x y) 5e-27)
           (- (/ (* z t) a))
           (if (<= (* x y) 1e+59)
             t_1
             (if (<= (* x y) 2e+70) (/ (- t) (/ a z)) (/ x (/ a y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = t_1;
	} else if ((x * y) <= -4e+55) {
		tmp = -z / (a / t);
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = -((z * t) / a);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -t / (a / z);
	} else {
		tmp = x / (a / y);
	}
	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) <= (-2d+87)) then
        tmp = t_1
    else if ((x * y) <= (-4d+55)) then
        tmp = -z / (a / t)
    else if ((x * y) <= (-2d+35)) then
        tmp = t_1
    else if ((x * y) <= 5d-27) then
        tmp = -((z * t) / a)
    else if ((x * y) <= 1d+59) then
        tmp = t_1
    else if ((x * y) <= 2d+70) then
        tmp = -t / (a / z)
    else
        tmp = x / (a / y)
    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) <= -2e+87) {
		tmp = t_1;
	} else if ((x * y) <= -4e+55) {
		tmp = -z / (a / t);
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = -((z * t) / a);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -t / (a / z);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) / a
	tmp = 0
	if (x * y) <= -2e+87:
		tmp = t_1
	elif (x * y) <= -4e+55:
		tmp = -z / (a / t)
	elif (x * y) <= -2e+35:
		tmp = t_1
	elif (x * y) <= 5e-27:
		tmp = -((z * t) / a)
	elif (x * y) <= 1e+59:
		tmp = t_1
	elif (x * y) <= 2e+70:
		tmp = -t / (a / z)
	else:
		tmp = x / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+87)
		tmp = t_1;
	elseif (Float64(x * y) <= -4e+55)
		tmp = Float64(Float64(-z) / Float64(a / t));
	elseif (Float64(x * y) <= -2e+35)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(-Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 1e+59)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+70)
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = Float64(x / Float64(a / y));
	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) <= -2e+87)
		tmp = t_1;
	elseif ((x * y) <= -4e+55)
		tmp = -z / (a / t);
	elseif ((x * y) <= -2e+35)
		tmp = t_1;
	elseif ((x * y) <= 5e-27)
		tmp = -((z * t) / a);
	elseif ((x * y) <= 1e+59)
		tmp = t_1;
	elseif ((x * y) <= 2e+70)
		tmp = -t / (a / z);
	else
		tmp = x / (a / y);
	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], -2e+87], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -4e+55], N[((-z) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e+35], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], (-N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), If[LessEqual[N[(x * y), $MachinePrecision], 1e+59], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+70], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.9999999999999999e87 or -4.00000000000000004e55 < (*.f64 x y) < -1.9999999999999999e35 or 5.0000000000000002e-27 < (*.f64 x y) < 9.99999999999999972e58

   1. Initial program 92.3%

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

   3. Taylor expanded in x around inf 80.4%

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

   if -1.9999999999999999e87 < (*.f64 x y) < -4.00000000000000004e55

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0 74.7%

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

      1. mul-1-neg 74.7%

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

      2. *-commutative 74.7%

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

      3. associate-*l/ 72.7%

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

      4. distribute-rgt-neg-in 72.7%

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

   5. Simplified 72.7%

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

      1. distribute-rgt-neg-out 72.7%

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

      2. associate-/r/ 74.7%

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

      3. distribute-neg-frac 74.7%

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

   7. Applied egg-rr 74.7%

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

   if -1.9999999999999999e35 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. distribute-rgt-neg-in 79.2%

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

   5. Simplified 79.2%

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

   if 9.99999999999999972e58 < (*.f64 x y) < 2.00000000000000015e70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   if 2.00000000000000015e70 < (*.f64 x y)

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 78.4%

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

      1. associate-*l/ 80.7%

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

   5. Simplified 80.7%

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

      1. associate-/r/ 76.5%

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

   7. Applied egg-rr 76.5%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;-\frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{a}{x \cdot y}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;-\frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ a (* x y)))))
   (if (<= (* x y) -2e+87)
     (/ (* x y) a)
     (if (<= (* x y) -4e+55)
       (/ (- z) (/ a t))
       (if (<= (* x y) -2e+35)
         t_1
         (if (<= (* x y) 5e-27)
           (- (/ (* z t) a))
           (if (<= (* x y) 1e+59)
             t_1
             (if (<= (* x y) 2e+70) (/ (- t) (/ a z)) (/ x (/ a y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 1.0 / (a / (x * y));
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = (x * y) / a;
	} else if ((x * y) <= -4e+55) {
		tmp = -z / (a / t);
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = -((z * t) / a);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -t / (a / z);
	} else {
		tmp = x / (a / y);
	}
	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 = 1.0d0 / (a / (x * y))
    if ((x * y) <= (-2d+87)) then
        tmp = (x * y) / a
    else if ((x * y) <= (-4d+55)) then
        tmp = -z / (a / t)
    else if ((x * y) <= (-2d+35)) then
        tmp = t_1
    else if ((x * y) <= 5d-27) then
        tmp = -((z * t) / a)
    else if ((x * y) <= 1d+59) then
        tmp = t_1
    else if ((x * y) <= 2d+70) then
        tmp = -t / (a / z)
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 1.0 / (a / (x * y));
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = (x * y) / a;
	} else if ((x * y) <= -4e+55) {
		tmp = -z / (a / t);
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = -((z * t) / a);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -t / (a / z);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 1.0 / (a / (x * y))
	tmp = 0
	if (x * y) <= -2e+87:
		tmp = (x * y) / a
	elif (x * y) <= -4e+55:
		tmp = -z / (a / t)
	elif (x * y) <= -2e+35:
		tmp = t_1
	elif (x * y) <= 5e-27:
		tmp = -((z * t) / a)
	elif (x * y) <= 1e+59:
		tmp = t_1
	elif (x * y) <= 2e+70:
		tmp = -t / (a / z)
	else:
		tmp = x / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(1.0 / Float64(a / Float64(x * y)))
	tmp = 0.0
	if (Float64(x * y) <= -2e+87)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= -4e+55)
		tmp = Float64(Float64(-z) / Float64(a / t));
	elseif (Float64(x * y) <= -2e+35)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(-Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 1e+59)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+70)
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 1.0 / (a / (x * y));
	tmp = 0.0;
	if ((x * y) <= -2e+87)
		tmp = (x * y) / a;
	elseif ((x * y) <= -4e+55)
		tmp = -z / (a / t);
	elseif ((x * y) <= -2e+35)
		tmp = t_1;
	elseif ((x * y) <= 5e-27)
		tmp = -((z * t) / a);
	elseif ((x * y) <= 1e+59)
		tmp = t_1;
	elseif ((x * y) <= 2e+70)
		tmp = -t / (a / z);
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(1.0 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+87], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e+55], N[((-z) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e+35], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], (-N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), If[LessEqual[N[(x * y), $MachinePrecision], 1e+59], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+70], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 x y) < -1.9999999999999999e87

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 84.0%

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

   if -1.9999999999999999e87 < (*.f64 x y) < -4.00000000000000004e55

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0 74.7%

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

      1. mul-1-neg 74.7%

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

      2. *-commutative 74.7%

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

      3. associate-*l/ 72.7%

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

      4. distribute-rgt-neg-in 72.7%

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

   5. Simplified 72.7%

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

      1. distribute-rgt-neg-out 72.7%

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

      2. associate-/r/ 74.7%

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

      3. distribute-neg-frac 74.7%

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

   7. Applied egg-rr 74.7%

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

   if -4.00000000000000004e55 < (*.f64 x y) < -1.9999999999999999e35 or 5.0000000000000002e-27 < (*.f64 x y) < 9.99999999999999972e58

   1. Initial program 95.3%

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

   3. Taylor expanded in x around inf 71.1%

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

      1. associate-*l/ 62.4%

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

   5. Simplified 62.4%

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

      1. associate-*l/ 71.1%

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

      2. clear-num 71.3%

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

   7. Applied egg-rr 71.3%

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

   if -1.9999999999999999e35 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. distribute-rgt-neg-in 79.2%

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

   5. Simplified 79.2%

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

   if 9.99999999999999972e58 < (*.f64 x y) < 2.00000000000000015e70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   if 2.00000000000000015e70 < (*.f64 x y)

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 78.4%

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

      1. associate-*l/ 80.7%

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

   5. Simplified 80.7%

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

      1. associate-/r/ 76.5%

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

   7. Applied egg-rr 76.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;-\frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{a}{x \cdot y}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{\frac{1}{y}}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;-\frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ a (* x y)))))
   (if (<= (* x y) -2e+87)
     (* (/ 1.0 a) (/ x (/ 1.0 y)))
     (if (<= (* x y) -4e+55)
       (/ (- z) (/ a t))
       (if (<= (* x y) -2e+35)
         t_1
         (if (<= (* x y) 5e-27)
           (- (/ (* z t) a))
           (if (<= (* x y) 1e+59)
             t_1
             (if (<= (* x y) 2e+70) (/ (- t) (/ a z)) (/ x (/ a y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 1.0 / (a / (x * y));
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = (1.0 / a) * (x / (1.0 / y));
	} else if ((x * y) <= -4e+55) {
		tmp = -z / (a / t);
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = -((z * t) / a);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -t / (a / z);
	} else {
		tmp = x / (a / y);
	}
	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 = 1.0d0 / (a / (x * y))
    if ((x * y) <= (-2d+87)) then
        tmp = (1.0d0 / a) * (x / (1.0d0 / y))
    else if ((x * y) <= (-4d+55)) then
        tmp = -z / (a / t)
    else if ((x * y) <= (-2d+35)) then
        tmp = t_1
    else if ((x * y) <= 5d-27) then
        tmp = -((z * t) / a)
    else if ((x * y) <= 1d+59) then
        tmp = t_1
    else if ((x * y) <= 2d+70) then
        tmp = -t / (a / z)
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 1.0 / (a / (x * y));
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = (1.0 / a) * (x / (1.0 / y));
	} else if ((x * y) <= -4e+55) {
		tmp = -z / (a / t);
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = -((z * t) / a);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -t / (a / z);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 1.0 / (a / (x * y))
	tmp = 0
	if (x * y) <= -2e+87:
		tmp = (1.0 / a) * (x / (1.0 / y))
	elif (x * y) <= -4e+55:
		tmp = -z / (a / t)
	elif (x * y) <= -2e+35:
		tmp = t_1
	elif (x * y) <= 5e-27:
		tmp = -((z * t) / a)
	elif (x * y) <= 1e+59:
		tmp = t_1
	elif (x * y) <= 2e+70:
		tmp = -t / (a / z)
	else:
		tmp = x / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(1.0 / Float64(a / Float64(x * y)))
	tmp = 0.0
	if (Float64(x * y) <= -2e+87)
		tmp = Float64(Float64(1.0 / a) * Float64(x / Float64(1.0 / y)));
	elseif (Float64(x * y) <= -4e+55)
		tmp = Float64(Float64(-z) / Float64(a / t));
	elseif (Float64(x * y) <= -2e+35)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(-Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 1e+59)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+70)
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 1.0 / (a / (x * y));
	tmp = 0.0;
	if ((x * y) <= -2e+87)
		tmp = (1.0 / a) * (x / (1.0 / y));
	elseif ((x * y) <= -4e+55)
		tmp = -z / (a / t);
	elseif ((x * y) <= -2e+35)
		tmp = t_1;
	elseif ((x * y) <= 5e-27)
		tmp = -((z * t) / a);
	elseif ((x * y) <= 1e+59)
		tmp = t_1;
	elseif ((x * y) <= 2e+70)
		tmp = -t / (a / z);
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(1.0 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+87], N[(N[(1.0 / a), $MachinePrecision] * N[(x / N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e+55], N[((-z) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e+35], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], (-N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), If[LessEqual[N[(x * y), $MachinePrecision], 1e+59], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+70], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 x y) < -1.9999999999999999e87

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 84.0%

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

      1. associate-*l/ 84.0%

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

   5. Simplified 84.0%

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

      1. associate-/r/ 79.1%

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

   7. Applied egg-rr 79.1%

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

      1. *-un-lft-identity 79.1%

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

      2. div-inv 79.1%

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

      3. times-frac 84.0%

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

   9. Applied egg-rr 84.0%

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

   if -1.9999999999999999e87 < (*.f64 x y) < -4.00000000000000004e55

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0 74.7%

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

      1. mul-1-neg 74.7%

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

      2. *-commutative 74.7%

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

      3. associate-*l/ 72.7%

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

      4. distribute-rgt-neg-in 72.7%

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

   5. Simplified 72.7%

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

      1. distribute-rgt-neg-out 72.7%

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

      2. associate-/r/ 74.7%

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

      3. distribute-neg-frac 74.7%

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

   7. Applied egg-rr 74.7%

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

   if -4.00000000000000004e55 < (*.f64 x y) < -1.9999999999999999e35 or 5.0000000000000002e-27 < (*.f64 x y) < 9.99999999999999972e58

   1. Initial program 95.3%

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

   3. Taylor expanded in x around inf 71.1%

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

      1. associate-*l/ 62.4%

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

   5. Simplified 62.4%

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

      1. associate-*l/ 71.1%

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

      2. clear-num 71.3%

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

   7. Applied egg-rr 71.3%

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

   if -1.9999999999999999e35 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. distribute-rgt-neg-in 79.2%

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

   5. Simplified 79.2%

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

   if 9.99999999999999972e58 < (*.f64 x y) < 2.00000000000000015e70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   if 2.00000000000000015e70 < (*.f64 x y)

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 78.4%

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

      1. associate-*l/ 80.7%

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

   5. Simplified 80.7%

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

      1. associate-/r/ 76.5%

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

   7. Applied egg-rr 76.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{\frac{1}{y}}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;-\frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) a)))
   (if (<= (* x y) -2e+87)
     t_1
     (if (<= (* x y) 5e-27)
       (* (- z) (/ t a))
       (if (<= (* x y) 1e+59)
         t_1
         (if (<= (* x y) 2e+70) (/ (- t) (/ a z)) (/ x (/ a y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = -z * (t / a);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -t / (a / z);
	} else {
		tmp = x / (a / y);
	}
	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) <= (-2d+87)) then
        tmp = t_1
    else if ((x * y) <= 5d-27) then
        tmp = -z * (t / a)
    else if ((x * y) <= 1d+59) then
        tmp = t_1
    else if ((x * y) <= 2d+70) then
        tmp = -t / (a / z)
    else
        tmp = x / (a / y)
    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) <= -2e+87) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = -z * (t / a);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -t / (a / z);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) / a
	tmp = 0
	if (x * y) <= -2e+87:
		tmp = t_1
	elif (x * y) <= 5e-27:
		tmp = -z * (t / a)
	elif (x * y) <= 1e+59:
		tmp = t_1
	elif (x * y) <= 2e+70:
		tmp = -t / (a / z)
	else:
		tmp = x / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+87)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(Float64(-z) * Float64(t / a));
	elseif (Float64(x * y) <= 1e+59)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+70)
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = Float64(x / Float64(a / y));
	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) <= -2e+87)
		tmp = t_1;
	elseif ((x * y) <= 5e-27)
		tmp = -z * (t / a);
	elseif ((x * y) <= 1e+59)
		tmp = t_1;
	elseif ((x * y) <= 2e+70)
		tmp = -t / (a / z);
	else
		tmp = x / (a / y);
	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], -2e+87], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+59], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+70], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.9999999999999999e87 or 5.0000000000000002e-27 < (*.f64 x y) < 9.99999999999999972e58

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf 81.0%

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

   if -1.9999999999999999e87 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.6%

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

      1. div-sub 95.6%

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

      2. associate-/l* 89.7%

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

      3. associate-/l* 83.9%

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

   4. Applied egg-rr 83.9%

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

   5. Taylor expanded in x around 0 75.3%

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

      1. associate-*l/ 67.3%

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

      2. associate-*l* 67.3%

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

      3. neg-mul-1 67.3%

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

      4. *-commutative 67.3%

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

   7. Simplified 67.3%

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

   if 9.99999999999999972e58 < (*.f64 x y) < 2.00000000000000015e70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   if 2.00000000000000015e70 < (*.f64 x y)

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 78.4%

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

      1. associate-*l/ 80.7%

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

   5. Simplified 80.7%

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

      1. associate-/r/ 76.5%

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

   7. Applied egg-rr 76.5%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+30} \lor \neg \left(z \leq 1.9 \cdot 10^{-119}\right):\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e+30) (not (<= z 1.9e-119)))
   (/ (- t) (/ a z))
   (/ (* x y) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e+30) || !(z <= 1.9e-119)) {
		tmp = -t / (a / z);
	} 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 ((z <= (-7.2d+30)) .or. (.not. (z <= 1.9d-119))) then
        tmp = -t / (a / z)
    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 ((z <= -7.2e+30) || !(z <= 1.9e-119)) {
		tmp = -t / (a / z);
	} else {
		tmp = (x * y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e+30) or not (z <= 1.9e-119):
		tmp = -t / (a / z)
	else:
		tmp = (x * y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e+30) || !(z <= 1.9e-119))
		tmp = Float64(Float64(-t) / Float64(a / z));
	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 ((z <= -7.2e+30) || ~((z <= 1.9e-119)))
		tmp = -t / (a / z);
	else
		tmp = (x * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e+30], N[Not[LessEqual[z, 1.9e-119]], $MachinePrecision]], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2000000000000004e30 or 1.89999999999999987e-119 < z

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

   if -7.2000000000000004e30 < z < 1.89999999999999987e-119

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 70.8%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+30} \lor \neg \left(z \leq 1.9 \cdot 10^{-119}\right):\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.95 \cdot 10^{-188}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a 1.95e-188) (* x (/ y a)) (/ (* x y) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 1.95e-188) {
		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 <= 1.95d-188) 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 <= 1.95e-188) {
		tmp = x * (y / a);
	} else {
		tmp = (x * y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 1.95e-188:
		tmp = x * (y / a)
	else:
		tmp = (x * y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 1.95e-188)
		tmp = Float64(x * Float64(y / 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 (a <= 1.95e-188)
		tmp = x * (y / a);
	else
		tmp = (x * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 1.95e-188], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.94999999999999988e-188

   1. Initial program 93.1%

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

   3. Taylor expanded in x around inf 49.6%

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

      1. *-commutative 49.6%

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

      2. associate-*l/ 44.3%

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

   5. Applied egg-rr 44.3%

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

   if 1.94999999999999988e-188 < a

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf 54.5%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.95 \cdot 10^{-188}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.8% 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 94.1%

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

3. Taylor expanded in x around inf 51.4%

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

   1. associate-*l/ 50.3%

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

5. Simplified 50.3%

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

6. Final simplification 50.3%

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

Alternative 10: 51.0% 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 94.1%

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

3. Taylor expanded in x around inf 51.4%

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

   1. *-commutative 51.4%

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

   2. associate-*l/ 47.2%

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

5. Applied egg-rr 47.2%

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

6. Final simplification 47.2%

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

Alternative 11: 51.0% 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 94.1%

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

3. Taylor expanded in x around inf 51.4%

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

   1. associate-*l/ 50.3%

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

5. Simplified 50.3%

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

   1. associate-/r/ 47.5%

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

7. Applied egg-rr 47.5%

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

8. Final simplification 47.5%

   \[\leadsto \frac{x}{\frac{a}{y}} \]
9. Add Preprocessing

Developer target: 91.2% 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 2024040 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.468684968699548e+170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

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