Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A

Percentage Accurate: 98.1% → 98.1%

Time: 7.7s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

   \[x + y \cdot \frac{z - t}{z - a} \]

2. Final simplification 98.7%

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

Alternative 2: 82.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.86 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-75} \lor \neg \left(z \leq 1.9 \cdot 10^{+37}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ z (- z t))))))
   (if (<= z -4.5e+40)
     t_1
     (if (<= z -1.86e-59)
       (+ x (* y (/ z (- z a))))
       (if (or (<= z -6e-75) (not (<= z 1.9e+37)))
         t_1
         (+ x (* (- t z) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -4.5e+40) {
		tmp = t_1;
	} else if (z <= -1.86e-59) {
		tmp = x + (y * (z / (z - a)));
	} else if ((z <= -6e-75) || !(z <= 1.9e+37)) {
		tmp = t_1;
	} else {
		tmp = x + ((t - z) * (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) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (z / (z - t)))
    if (z <= (-4.5d+40)) then
        tmp = t_1
    else if (z <= (-1.86d-59)) then
        tmp = x + (y * (z / (z - a)))
    else if ((z <= (-6d-75)) .or. (.not. (z <= 1.9d+37))) then
        tmp = t_1
    else
        tmp = x + ((t - z) * (y / 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 / (z - t)));
	double tmp;
	if (z <= -4.5e+40) {
		tmp = t_1;
	} else if (z <= -1.86e-59) {
		tmp = x + (y * (z / (z - a)));
	} else if ((z <= -6e-75) || !(z <= 1.9e+37)) {
		tmp = t_1;
	} else {
		tmp = x + ((t - z) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (z / (z - t)))
	tmp = 0
	if z <= -4.5e+40:
		tmp = t_1
	elif z <= -1.86e-59:
		tmp = x + (y * (z / (z - a)))
	elif (z <= -6e-75) or not (z <= 1.9e+37):
		tmp = t_1
	else:
		tmp = x + ((t - z) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(z / Float64(z - t))))
	tmp = 0.0
	if (z <= -4.5e+40)
		tmp = t_1;
	elseif (z <= -1.86e-59)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif ((z <= -6e-75) || !(z <= 1.9e+37))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(t - z) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (z / (z - t)));
	tmp = 0.0;
	if (z <= -4.5e+40)
		tmp = t_1;
	elseif (z <= -1.86e-59)
		tmp = x + (y * (z / (z - a)));
	elseif ((z <= -6e-75) || ~((z <= 1.9e+37)))
		tmp = t_1;
	else
		tmp = x + ((t - z) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+40], t$95$1, If[LessEqual[z, -1.86e-59], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -6e-75], N[Not[LessEqual[z, 1.9e+37]], $MachinePrecision]], t$95$1, N[(x + N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.50000000000000032e40 or -1.86000000000000004e-59 < z < -5.9999999999999997e-75 or 1.89999999999999995e37 < z

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-*r/ 77.9%

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

      3. associate-*l/ 91.4%

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

      4. *-commutative 91.4%

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

      5. fma-def 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in a around 0 68.7%

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

      1. associate-/l* 89.5%

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

   6. Simplified 89.5%

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

   if -4.50000000000000032e40 < z < -1.86000000000000004e-59

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around 0 90.4%

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

   if -5.9999999999999997e-75 < z < 1.89999999999999995e37

   1. Initial program 97.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in a around inf 83.1%

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

      1. associate-*r/ 83.1%

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

      2. neg-mul-1 83.1%

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

   4. Simplified 83.1%

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

   5. Taylor expanded in y around 0 79.9%

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

      1. associate-/l* 82.4%

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

      2. associate-/r/ 80.6%

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

   7. Simplified 80.6%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq -1.86 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-75} \lor \neg \left(z \leq 1.9 \cdot 10^{+37}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.86 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-75} \lor \neg \left(z \leq 5.3 \cdot 10^{+34}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ z (- z t))))))
   (if (<= z -4e+39)
     t_1
     (if (<= z -1.86e-59)
       (+ x (/ (* y z) (- z a)))
       (if (or (<= z -6.2e-75) (not (<= z 5.3e+34)))
         t_1
         (+ x (* (- t z) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -4e+39) {
		tmp = t_1;
	} else if (z <= -1.86e-59) {
		tmp = x + ((y * z) / (z - a));
	} else if ((z <= -6.2e-75) || !(z <= 5.3e+34)) {
		tmp = t_1;
	} else {
		tmp = x + ((t - z) * (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) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (z / (z - t)))
    if (z <= (-4d+39)) then
        tmp = t_1
    else if (z <= (-1.86d-59)) then
        tmp = x + ((y * z) / (z - a))
    else if ((z <= (-6.2d-75)) .or. (.not. (z <= 5.3d+34))) then
        tmp = t_1
    else
        tmp = x + ((t - z) * (y / 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 / (z - t)));
	double tmp;
	if (z <= -4e+39) {
		tmp = t_1;
	} else if (z <= -1.86e-59) {
		tmp = x + ((y * z) / (z - a));
	} else if ((z <= -6.2e-75) || !(z <= 5.3e+34)) {
		tmp = t_1;
	} else {
		tmp = x + ((t - z) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (z / (z - t)))
	tmp = 0
	if z <= -4e+39:
		tmp = t_1
	elif z <= -1.86e-59:
		tmp = x + ((y * z) / (z - a))
	elif (z <= -6.2e-75) or not (z <= 5.3e+34):
		tmp = t_1
	else:
		tmp = x + ((t - z) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(z / Float64(z - t))))
	tmp = 0.0
	if (z <= -4e+39)
		tmp = t_1;
	elseif (z <= -1.86e-59)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(z - a)));
	elseif ((z <= -6.2e-75) || !(z <= 5.3e+34))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(t - z) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (z / (z - t)));
	tmp = 0.0;
	if (z <= -4e+39)
		tmp = t_1;
	elseif (z <= -1.86e-59)
		tmp = x + ((y * z) / (z - a));
	elseif ((z <= -6.2e-75) || ~((z <= 5.3e+34)))
		tmp = t_1;
	else
		tmp = x + ((t - z) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+39], t$95$1, If[LessEqual[z, -1.86e-59], N[(x + N[(N[(y * z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -6.2e-75], N[Not[LessEqual[z, 5.3e+34]], $MachinePrecision]], t$95$1, N[(x + N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.99999999999999976e39 or -1.86000000000000004e-59 < z < -6.20000000000000013e-75 or 5.3000000000000005e34 < z

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-*r/ 77.9%

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

      3. associate-*l/ 91.4%

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

      4. *-commutative 91.4%

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

      5. fma-def 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in a around 0 68.7%

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

      1. associate-/l* 89.5%

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

   6. Simplified 89.5%

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

   if -3.99999999999999976e39 < z < -1.86000000000000004e-59

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 89.9%

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

      3. associate-*l/ 99.8%

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

      4. *-commutative 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 90.4%

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

   if -6.20000000000000013e-75 < z < 5.3000000000000005e34

   1. Initial program 97.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in a around inf 83.1%

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

      1. associate-*r/ 83.1%

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

      2. neg-mul-1 83.1%

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

   4. Simplified 83.1%

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

   5. Taylor expanded in y around 0 79.9%

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

      1. associate-/l* 82.4%

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

      2. associate-/r/ 80.6%

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

   7. Simplified 80.6%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq -1.86 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-75} \lor \neg \left(z \leq 5.3 \cdot 10^{+34}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-77}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 10^{+36}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ z (- z t))))))
   (if (<= z -2.1e+42)
     t_1
     (if (<= z -4e-59)
       (+ x (/ (* y z) (- z a)))
       (if (<= z -7.2e-77)
         (+ x (/ (* y (- z t)) z))
         (if (<= z 1e+36) (+ x (* (- t z) (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -2.1e+42) {
		tmp = t_1;
	} else if (z <= -4e-59) {
		tmp = x + ((y * z) / (z - a));
	} else if (z <= -7.2e-77) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 1e+36) {
		tmp = x + ((t - z) * (y / 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 = x + (y / (z / (z - t)))
    if (z <= (-2.1d+42)) then
        tmp = t_1
    else if (z <= (-4d-59)) then
        tmp = x + ((y * z) / (z - a))
    else if (z <= (-7.2d-77)) then
        tmp = x + ((y * (z - t)) / z)
    else if (z <= 1d+36) then
        tmp = x + ((t - z) * (y / 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 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -2.1e+42) {
		tmp = t_1;
	} else if (z <= -4e-59) {
		tmp = x + ((y * z) / (z - a));
	} else if (z <= -7.2e-77) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 1e+36) {
		tmp = x + ((t - z) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (z / (z - t)))
	tmp = 0
	if z <= -2.1e+42:
		tmp = t_1
	elif z <= -4e-59:
		tmp = x + ((y * z) / (z - a))
	elif z <= -7.2e-77:
		tmp = x + ((y * (z - t)) / z)
	elif z <= 1e+36:
		tmp = x + ((t - z) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(z / Float64(z - t))))
	tmp = 0.0
	if (z <= -2.1e+42)
		tmp = t_1;
	elseif (z <= -4e-59)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(z - a)));
	elseif (z <= -7.2e-77)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / z));
	elseif (z <= 1e+36)
		tmp = Float64(x + Float64(Float64(t - z) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (z / (z - t)));
	tmp = 0.0;
	if (z <= -2.1e+42)
		tmp = t_1;
	elseif (z <= -4e-59)
		tmp = x + ((y * z) / (z - a));
	elseif (z <= -7.2e-77)
		tmp = x + ((y * (z - t)) / z);
	elseif (z <= 1e+36)
		tmp = x + ((t - z) * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+42], t$95$1, If[LessEqual[z, -4e-59], N[(x + N[(N[(y * z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.2e-77], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+36], N[(x + N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.09999999999999995e42 or 1.00000000000000004e36 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 76.2%

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

      3. associate-*l/ 90.8%

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

      4. *-commutative 90.8%

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

      5. fma-def 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in a around 0 67.2%

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

      1. associate-/l* 90.2%

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

   6. Simplified 90.2%

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

   if -2.09999999999999995e42 < z < -4.0000000000000001e-59

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 89.9%

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

      3. associate-*l/ 99.8%

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

      4. *-commutative 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 90.4%

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

   if -4.0000000000000001e-59 < z < -7.2e-77

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. associate-*r/ 100.0%

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

      3. associate-*l/ 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 88.9%

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

   if -7.2e-77 < z < 1.00000000000000004e36

   1. Initial program 97.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in a around inf 83.1%

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

      1. associate-*r/ 83.1%

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

      2. neg-mul-1 83.1%

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

   4. Simplified 83.1%

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

   5. Taylor expanded in y around 0 79.9%

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

      1. associate-/l* 82.4%

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

      2. associate-/r/ 80.6%

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

   7. Simplified 80.6%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-77}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 10^{+36}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 5: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+39}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ z (- z t))))))
   (if (<= z -2.8e+40)
     t_1
     (if (<= z -3.7e-59)
       (+ x (/ (* y z) (- z a)))
       (if (<= z -1.65e-80)
         (+ x (/ (* y (- z t)) z))
         (if (<= z 1.7e+39) (- x (/ y (/ a (- z t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -2.8e+40) {
		tmp = t_1;
	} else if (z <= -3.7e-59) {
		tmp = x + ((y * z) / (z - a));
	} else if (z <= -1.65e-80) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 1.7e+39) {
		tmp = x - (y / (a / (z - t)));
	} 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 = x + (y / (z / (z - t)))
    if (z <= (-2.8d+40)) then
        tmp = t_1
    else if (z <= (-3.7d-59)) then
        tmp = x + ((y * z) / (z - a))
    else if (z <= (-1.65d-80)) then
        tmp = x + ((y * (z - t)) / z)
    else if (z <= 1.7d+39) then
        tmp = x - (y / (a / (z - t)))
    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 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -2.8e+40) {
		tmp = t_1;
	} else if (z <= -3.7e-59) {
		tmp = x + ((y * z) / (z - a));
	} else if (z <= -1.65e-80) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 1.7e+39) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (z / (z - t)))
	tmp = 0
	if z <= -2.8e+40:
		tmp = t_1
	elif z <= -3.7e-59:
		tmp = x + ((y * z) / (z - a))
	elif z <= -1.65e-80:
		tmp = x + ((y * (z - t)) / z)
	elif z <= 1.7e+39:
		tmp = x - (y / (a / (z - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(z / Float64(z - t))))
	tmp = 0.0
	if (z <= -2.8e+40)
		tmp = t_1;
	elseif (z <= -3.7e-59)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(z - a)));
	elseif (z <= -1.65e-80)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / z));
	elseif (z <= 1.7e+39)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (z / (z - t)));
	tmp = 0.0;
	if (z <= -2.8e+40)
		tmp = t_1;
	elseif (z <= -3.7e-59)
		tmp = x + ((y * z) / (z - a));
	elseif (z <= -1.65e-80)
		tmp = x + ((y * (z - t)) / z);
	elseif (z <= 1.7e+39)
		tmp = x - (y / (a / (z - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+40], t$95$1, If[LessEqual[z, -3.7e-59], N[(x + N[(N[(y * z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e-80], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+39], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8000000000000001e40 or 1.6999999999999999e39 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 76.2%

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

      3. associate-*l/ 90.8%

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

      4. *-commutative 90.8%

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

      5. fma-def 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in a around 0 67.2%

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

      1. associate-/l* 90.2%

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

   6. Simplified 90.2%

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

   if -2.8000000000000001e40 < z < -3.6999999999999999e-59

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 89.9%

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

      3. associate-*l/ 99.8%

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

      4. *-commutative 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 90.4%

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

   if -3.6999999999999999e-59 < z < -1.65e-80

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. associate-*r/ 100.0%

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

      3. associate-*l/ 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 88.9%

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

   if -1.65e-80 < z < 1.6999999999999999e39

   1. Initial program 97.9%

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

      1. +-commutative 97.9%

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

      2. associate-*r/ 92.8%

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

      3. associate-*l/ 93.7%

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

      4. *-commutative 93.7%

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

      5. fma-def 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in a around inf 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. unsub-neg 79.9%

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

      4. associate-/l* 82.4%

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

   6. Simplified 82.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+39}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 6: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+34}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ z (- z t))))))
   (if (<= z -4.6e+40)
     t_1
     (if (<= z -4.2e-59)
       (+ x (/ (* y z) (- z a)))
       (if (<= z -2.7e-80)
         (+ x (/ (* y (- z t)) z))
         (if (<= z 5e+34) (- x (* y (/ (- z t) a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -4.6e+40) {
		tmp = t_1;
	} else if (z <= -4.2e-59) {
		tmp = x + ((y * z) / (z - a));
	} else if (z <= -2.7e-80) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 5e+34) {
		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 = x + (y / (z / (z - t)))
    if (z <= (-4.6d+40)) then
        tmp = t_1
    else if (z <= (-4.2d-59)) then
        tmp = x + ((y * z) / (z - a))
    else if (z <= (-2.7d-80)) then
        tmp = x + ((y * (z - t)) / z)
    else if (z <= 5d+34) 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 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -4.6e+40) {
		tmp = t_1;
	} else if (z <= -4.2e-59) {
		tmp = x + ((y * z) / (z - a));
	} else if (z <= -2.7e-80) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 5e+34) {
		tmp = x - (y * ((z - t) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (z / (z - t)))
	tmp = 0
	if z <= -4.6e+40:
		tmp = t_1
	elif z <= -4.2e-59:
		tmp = x + ((y * z) / (z - a))
	elif z <= -2.7e-80:
		tmp = x + ((y * (z - t)) / z)
	elif z <= 5e+34:
		tmp = x - (y * ((z - t) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(z / Float64(z - t))))
	tmp = 0.0
	if (z <= -4.6e+40)
		tmp = t_1;
	elseif (z <= -4.2e-59)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(z - a)));
	elseif (z <= -2.7e-80)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / z));
	elseif (z <= 5e+34)
		tmp = Float64(x - Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (z / (z - t)));
	tmp = 0.0;
	if (z <= -4.6e+40)
		tmp = t_1;
	elseif (z <= -4.2e-59)
		tmp = x + ((y * z) / (z - a));
	elseif (z <= -2.7e-80)
		tmp = x + ((y * (z - t)) / z);
	elseif (z <= 5e+34)
		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[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+40], t$95$1, If[LessEqual[z, -4.2e-59], N[(x + N[(N[(y * z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-80], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+34], N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.59999999999999987e40 or 4.9999999999999998e34 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 76.2%

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

      3. associate-*l/ 90.8%

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

      4. *-commutative 90.8%

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

      5. fma-def 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in a around 0 67.2%

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

      1. associate-/l* 90.2%

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

   6. Simplified 90.2%

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

   if -4.59999999999999987e40 < z < -4.19999999999999993e-59

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 89.9%

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

      3. associate-*l/ 99.8%

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

      4. *-commutative 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 90.4%

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

   if -4.19999999999999993e-59 < z < -2.7000000000000002e-80

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. associate-*r/ 100.0%

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

      3. associate-*l/ 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 88.9%

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

   if -2.7000000000000002e-80 < z < 4.9999999999999998e34

   1. Initial program 97.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in a around inf 83.1%

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

      1. associate-*r/ 83.1%

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

      2. neg-mul-1 83.1%

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

   4. Simplified 83.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+34}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 7: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-20} \lor \neg \left(z \leq 8 \cdot 10^{-135}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e-20) (not (<= z 8e-135)))
   (+ x (* y (/ z (- z a))))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e-20) || !(z <= 8e-135)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.45d-20)) .or. (.not. (z <= 8d-135))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e-20) || !(z <= 8e-135)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e-20) or not (z <= 8e-135):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e-20) || !(z <= 8e-135))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.45e-20) || ~((z <= 8e-135)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e-20], N[Not[LessEqual[z, 8e-135]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e-20 or 8.0000000000000003e-135 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around 0 80.4%

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

   if -1.45e-20 < z < 8.0000000000000003e-135

   1. Initial program 96.8%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 78.6%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-20} \lor \neg \left(z \leq 8 \cdot 10^{-135}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 8: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-20} \lor \neg \left(z \leq 0.00088\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e-20) (not (<= z 0.00088)))
   (+ x (* y (/ z (- z a))))
   (+ x (* (- t z) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e-20) || !(z <= 0.00088)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + ((t - z) * (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 <= (-1.45d-20)) .or. (.not. (z <= 0.00088d0))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + ((t - z) * (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 <= -1.45e-20) || !(z <= 0.00088)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + ((t - z) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e-20) or not (z <= 0.00088):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + ((t - z) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e-20) || !(z <= 0.00088))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(t - z) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.45e-20) || ~((z <= 0.00088)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + ((t - z) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e-20], N[Not[LessEqual[z, 0.00088]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e-20 or 8.80000000000000031e-4 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around 0 81.4%

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

   if -1.45e-20 < z < 8.80000000000000031e-4

   1. Initial program 97.2%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in a around inf 82.1%

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

      1. associate-*r/ 82.1%

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

      2. neg-mul-1 82.1%

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

   4. Simplified 82.1%

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

   5. Taylor expanded in y around 0 78.3%

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

      1. associate-/l* 81.4%

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

      2. associate-/r/ 79.8%

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

   7. Simplified 79.8%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-20} \lor \neg \left(z \leq 0.00088\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+142} \lor \neg \left(t \leq 2.15 \cdot 10^{-40}\right):\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.12e+142) (not (<= t 2.15e-40)))
   (- x (/ (* y t) (- z a)))
   (+ x (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.12e+142) || !(t <= 2.15e-40)) {
		tmp = x - ((y * t) / (z - a));
	} else {
		tmp = x + (y * (z / (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 ((t <= (-1.12d+142)) .or. (.not. (t <= 2.15d-40))) then
        tmp = x - ((y * t) / (z - a))
    else
        tmp = x + (y * (z / (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 ((t <= -1.12e+142) || !(t <= 2.15e-40)) {
		tmp = x - ((y * t) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.12e+142) or not (t <= 2.15e-40):
		tmp = x - ((y * t) / (z - a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.12e+142) || !(t <= 2.15e-40))
		tmp = Float64(x - Float64(Float64(y * t) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.12e+142) || ~((t <= 2.15e-40)))
		tmp = x - ((y * t) / (z - a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.12e+142], N[Not[LessEqual[t, 2.15e-40]], $MachinePrecision]], N[(x - N[(N[(y * t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.11999999999999996e142 or 2.1500000000000001e-40 < t

   1. Initial program 97.0%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around inf 81.5%

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

      1. associate-*r/ 81.5%

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

      2. mul-1-neg 81.5%

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

      3. distribute-rgt-neg-out 81.5%

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

   4. Simplified 81.5%

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

   if -1.11999999999999996e142 < t < 2.1500000000000001e-40

   1. Initial program 99.7%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in t around 0 87.5%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+142} \lor \neg \left(t \leq 2.15 \cdot 10^{-40}\right):\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 10: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-20}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e-20) (+ x y) (if (<= z 3.05e+41) (+ x (* y (/ t a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e-20) {
		tmp = x + y;
	} else if (z <= 3.05e+41) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + 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) :: tmp
    if (z <= (-8.5d-20)) then
        tmp = x + y
    else if (z <= 3.05d+41) then
        tmp = x + (y * (t / a))
    else
        tmp = x + y
    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 <= -8.5e-20) {
		tmp = x + y;
	} else if (z <= 3.05e+41) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e-20:
		tmp = x + y
	elif z <= 3.05e+41:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e-20)
		tmp = Float64(x + y);
	elseif (z <= 3.05e+41)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e-20)
		tmp = x + y;
	elseif (z <= 3.05e+41)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e-20], N[(x + y), $MachinePrecision], If[LessEqual[z, 3.05e+41], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000005e-20 or 3.04999999999999999e41 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 77.1%

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

      3. associate-*l/ 91.4%

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

      4. *-commutative 91.4%

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

      5. fma-def 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in z around inf 74.5%

      \[\leadsto \color{blue}{y + x} \]

   if -8.5000000000000005e-20 < z < 3.04999999999999999e41

   1. Initial program 97.4%

      \[x + y \cdot \frac{z - t}{z - a} \]

   2. Taylor expanded in z around 0 74.4%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-20}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 61.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+189}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5e-84) x (if (<= a 1.65e+189) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e-84) {
		tmp = x;
	} else if (a <= 1.65e+189) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	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 <= (-5d-84)) then
        tmp = x
    else if (a <= 1.65d+189) then
        tmp = x + y
    else
        tmp = x
    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 <= -5e-84) {
		tmp = x;
	} else if (a <= 1.65e+189) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5e-84:
		tmp = x
	elif a <= 1.65e+189:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5e-84)
		tmp = x;
	elseif (a <= 1.65e+189)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5e-84)
		tmp = x;
	elseif (a <= 1.65e+189)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5e-84], x, If[LessEqual[a, 1.65e+189], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.0000000000000002e-84 or 1.6500000000000001e189 < a

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*r/ 84.5%

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

      3. associate-*l/ 94.3%

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

      4. *-commutative 94.3%

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

      5. fma-def 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around 0 63.5%

      \[\leadsto \color{blue}{x} \]

   if -5.0000000000000002e-84 < a < 1.6500000000000001e189

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. associate-*r/ 85.4%

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

      3. associate-*l/ 92.3%

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

      4. *-commutative 92.3%

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

      5. fma-def 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in z around inf 59.0%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+189}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 50.2% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 98.7%

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

   1. +-commutative 98.7%

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

   2. associate-*r/ 85.1%

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

   3. associate-*l/ 93.0%

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

   4. *-commutative 93.0%

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

   5. fma-def 93.0%

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

3. Simplified 93.0%

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

4. Taylor expanded in y around 0 48.1%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 48.1%

   \[\leadsto x \]

Developer target: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - a) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023181 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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