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

Percentage Accurate: 98.2% → 98.2%

Time: 9.9s

Alternatives: 16

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: 98.2% 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: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. +-commutative 97.7%

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

   2. fma-def 97.7%

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

3. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 2: 82.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-58}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-81}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))))
   (if (<= z -3.5e+99)
     t_1
     (if (<= z -1.3e-58)
       (+ x (* y (- 1.0 (/ t z))))
       (if (<= z 1.85e-81) (+ x (* y (/ t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -3.5e+99) {
		tmp = t_1;
	} else if (z <= -1.3e-58) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 1.85e-81) {
		tmp = x + (y * (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 - a)))
    if (z <= (-3.5d+99)) then
        tmp = t_1
    else if (z <= (-1.3d-58)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= 1.85d-81) then
        tmp = x + (y * (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 - a)));
	double tmp;
	if (z <= -3.5e+99) {
		tmp = t_1;
	} else if (z <= -1.3e-58) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 1.85e-81) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	tmp = 0
	if z <= -3.5e+99:
		tmp = t_1
	elif z <= -1.3e-58:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= 1.85e-81:
		tmp = x + (y * (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 - a))))
	tmp = 0.0
	if (z <= -3.5e+99)
		tmp = t_1;
	elseif (z <= -1.3e-58)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= 1.85e-81)
		tmp = Float64(x + Float64(y * Float64(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 - a)));
	tmp = 0.0;
	if (z <= -3.5e+99)
		tmp = t_1;
	elseif (z <= -1.3e-58)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= 1.85e-81)
		tmp = x + (y * (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 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+99], t$95$1, If[LessEqual[z, -1.3e-58], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-81], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999998e99 or 1.84999999999999993e-81 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 73.7%

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

      1. expm1-log1p-u 62.9%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot z}{z - a}\right)\right)} \]

      2. expm1-udef 53.0%

         \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot z}{z - a}\right)} - 1\right)} \]

      3. associate-/l* 56.8%

         \[\leadsto x + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{z - a}{z}}}\right)} - 1\right) \]

      4. associate-/r/ 56.8%

         \[\leadsto x + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{z - a} \cdot z}\right)} - 1\right) \]

   4. Applied egg-rr 56.8%

      \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{z - a} \cdot z\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-def 59.7%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{z - a} \cdot z\right)\right)} \]

      2. expm1-log1p 80.4%

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

      3. associate-*l/ 73.7%

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

      4. associate-*r/ 87.5%

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

   6. Simplified 87.5%

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

   if -3.4999999999999998e99 < z < -1.30000000000000003e-58

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 90.1%

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

      1. div-sub 90.1%

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

      2. *-inverses 90.1%

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

   4. Simplified 90.1%

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

   if -1.30000000000000003e-58 < z < 1.84999999999999993e-81

   1. Initial program 93.6%

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

   2. Taylor expanded in z around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-/l* 77.6%

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

      3. associate-/r/ 78.8%

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

   4. Simplified 78.8%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+99}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-58}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-81}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 3: 81.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-81}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))))
   (if (<= z -1.5e+98)
     t_1
     (if (<= z -1.8e-133)
       (+ x (/ (* y (- z t)) z))
       (if (<= z 2.7e-81) (+ x (* y (/ t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -1.5e+98) {
		tmp = t_1;
	} else if (z <= -1.8e-133) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 2.7e-81) {
		tmp = x + (y * (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 - a)))
    if (z <= (-1.5d+98)) then
        tmp = t_1
    else if (z <= (-1.8d-133)) then
        tmp = x + ((y * (z - t)) / z)
    else if (z <= 2.7d-81) then
        tmp = x + (y * (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 - a)));
	double tmp;
	if (z <= -1.5e+98) {
		tmp = t_1;
	} else if (z <= -1.8e-133) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 2.7e-81) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	tmp = 0
	if z <= -1.5e+98:
		tmp = t_1
	elif z <= -1.8e-133:
		tmp = x + ((y * (z - t)) / z)
	elif z <= 2.7e-81:
		tmp = x + (y * (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 - a))))
	tmp = 0.0
	if (z <= -1.5e+98)
		tmp = t_1;
	elseif (z <= -1.8e-133)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / z));
	elseif (z <= 2.7e-81)
		tmp = Float64(x + Float64(y * Float64(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 - a)));
	tmp = 0.0;
	if (z <= -1.5e+98)
		tmp = t_1;
	elseif (z <= -1.8e-133)
		tmp = x + ((y * (z - t)) / z);
	elseif (z <= 2.7e-81)
		tmp = x + (y * (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 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+98], t$95$1, If[LessEqual[z, -1.8e-133], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-81], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5000000000000001e98 or 2.6999999999999999e-81 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 73.7%

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

      1. expm1-log1p-u 62.9%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot z}{z - a}\right)\right)} \]

      2. expm1-udef 53.0%

         \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot z}{z - a}\right)} - 1\right)} \]

      3. associate-/l* 56.8%

         \[\leadsto x + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{z - a}{z}}}\right)} - 1\right) \]

      4. associate-/r/ 56.8%

         \[\leadsto x + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{z - a} \cdot z}\right)} - 1\right) \]

   4. Applied egg-rr 56.8%

      \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{z - a} \cdot z\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-def 59.7%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{z - a} \cdot z\right)\right)} \]

      2. expm1-log1p 80.4%

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

      3. associate-*l/ 73.7%

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

      4. associate-*r/ 87.5%

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

   6. Simplified 87.5%

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

   if -1.5000000000000001e98 < z < -1.8000000000000002e-133

   1. Initial program 97.7%

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

   2. Taylor expanded in a around 0 87.4%

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

   if -1.8000000000000002e-133 < z < 2.6999999999999999e-81

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. associate-/l* 78.5%

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

      3. associate-/r/ 79.8%

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

   4. Simplified 79.8%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+98}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-81}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 4: 81.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-81}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (- 1.0 (/ a z))))))
   (if (<= z -1.8e+100)
     t_1
     (if (<= z -1.8e-133)
       (+ x (/ (* y (- z t)) z))
       (if (<= z 2e-81) (+ x (* y (/ t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (1.0 - (a / z)));
	double tmp;
	if (z <= -1.8e+100) {
		tmp = t_1;
	} else if (z <= -1.8e-133) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 2e-81) {
		tmp = x + (y * (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 / (1.0d0 - (a / z)))
    if (z <= (-1.8d+100)) then
        tmp = t_1
    else if (z <= (-1.8d-133)) then
        tmp = x + ((y * (z - t)) / z)
    else if (z <= 2d-81) then
        tmp = x + (y * (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 / (1.0 - (a / z)));
	double tmp;
	if (z <= -1.8e+100) {
		tmp = t_1;
	} else if (z <= -1.8e-133) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 2e-81) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (1.0 - (a / z)))
	tmp = 0
	if z <= -1.8e+100:
		tmp = t_1
	elif z <= -1.8e-133:
		tmp = x + ((y * (z - t)) / z)
	elif z <= 2e-81:
		tmp = x + (y * (t / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))))
	tmp = 0.0
	if (z <= -1.8e+100)
		tmp = t_1;
	elseif (z <= -1.8e-133)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / z));
	elseif (z <= 2e-81)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (1.0 - (a / z)));
	tmp = 0.0;
	if (z <= -1.8e+100)
		tmp = t_1;
	elseif (z <= -1.8e-133)
		tmp = x + ((y * (z - t)) / z);
	elseif (z <= 2e-81)
		tmp = x + (y * (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[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+100], t$95$1, If[LessEqual[z, -1.8e-133], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-81], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e100 or 1.9999999999999999e-81 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. associate-/l* 87.5%

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

      3. div-sub 87.5%

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

      4. *-inverses 87.5%

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

   4. Simplified 87.5%

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

   if -1.8e100 < z < -1.8000000000000002e-133

   1. Initial program 97.7%

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

   2. Taylor expanded in a around 0 87.4%

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

   if -1.8000000000000002e-133 < z < 1.9999999999999999e-81

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. associate-/l* 78.5%

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

      3. associate-/r/ 79.8%

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

   4. Simplified 79.8%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-81}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]

Alternative 5: 82.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 0.25:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (- 1.0 (/ a z))))))
   (if (<= z -5.4e+100)
     t_1
     (if (<= z -1.8e-133)
       (+ x (/ (* y (- z t)) z))
       (if (<= z 0.25) (+ x (* (/ y a) (- t z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (1.0 - (a / z)));
	double tmp;
	if (z <= -5.4e+100) {
		tmp = t_1;
	} else if (z <= -1.8e-133) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 0.25) {
		tmp = x + ((y / a) * (t - z));
	} 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 / (1.0d0 - (a / z)))
    if (z <= (-5.4d+100)) then
        tmp = t_1
    else if (z <= (-1.8d-133)) then
        tmp = x + ((y * (z - t)) / z)
    else if (z <= 0.25d0) then
        tmp = x + ((y / a) * (t - z))
    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 / (1.0 - (a / z)));
	double tmp;
	if (z <= -5.4e+100) {
		tmp = t_1;
	} else if (z <= -1.8e-133) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 0.25) {
		tmp = x + ((y / a) * (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (1.0 - (a / z)))
	tmp = 0
	if z <= -5.4e+100:
		tmp = t_1
	elif z <= -1.8e-133:
		tmp = x + ((y * (z - t)) / z)
	elif z <= 0.25:
		tmp = x + ((y / a) * (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))))
	tmp = 0.0
	if (z <= -5.4e+100)
		tmp = t_1;
	elseif (z <= -1.8e-133)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / z));
	elseif (z <= 0.25)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (1.0 - (a / z)));
	tmp = 0.0;
	if (z <= -5.4e+100)
		tmp = t_1;
	elseif (z <= -1.8e-133)
		tmp = x + ((y * (z - t)) / z);
	elseif (z <= 0.25)
		tmp = x + ((y / a) * (t - z));
	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[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e+100], t$95$1, If[LessEqual[z, -1.8e-133], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.25], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.39999999999999997e100 or 0.25 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 73.1%

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

      1. +-commutative 73.1%

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

      2. associate-/l* 88.9%

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

      3. div-sub 88.9%

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

      4. *-inverses 88.9%

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

   4. Simplified 88.9%

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

   if -5.39999999999999997e100 < z < -1.8000000000000002e-133

   1. Initial program 97.7%

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

   2. Taylor expanded in a around 0 87.4%

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

   if -1.8000000000000002e-133 < z < 0.25

   1. Initial program 95.1%

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

   2. Taylor expanded in a around inf 84.1%

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

      1. mul-1-neg 84.1%

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

      2. unsub-neg 84.1%

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

      3. associate-/l* 84.2%

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

      4. associate-/r/ 83.1%

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

   4. Simplified 83.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 0.25:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]

Alternative 6: 76.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+101}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-59}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.75e+101)
   (+ y x)
   (if (<= z -3.5e-59)
     (- x (* y (/ t z)))
     (if (<= z 3.15e+41) (+ x (* y (/ t a))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e+101) {
		tmp = y + x;
	} else if (z <= -3.5e-59) {
		tmp = x - (y * (t / z));
	} else if (z <= 3.15e+41) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + 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 (z <= (-1.75d+101)) then
        tmp = y + x
    else if (z <= (-3.5d-59)) then
        tmp = x - (y * (t / z))
    else if (z <= 3.15d+41) then
        tmp = x + (y * (t / a))
    else
        tmp = y + 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 (z <= -1.75e+101) {
		tmp = y + x;
	} else if (z <= -3.5e-59) {
		tmp = x - (y * (t / z));
	} else if (z <= 3.15e+41) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.75e+101:
		tmp = y + x
	elif z <= -3.5e-59:
		tmp = x - (y * (t / z))
	elif z <= 3.15e+41:
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.75e+101)
		tmp = Float64(y + x);
	elseif (z <= -3.5e-59)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= 3.15e+41)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.75e+101)
		tmp = y + x;
	elseif (z <= -3.5e-59)
		tmp = x - (y * (t / z));
	elseif (z <= 3.15e+41)
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.75e+101], N[(y + x), $MachinePrecision], If[LessEqual[z, -3.5e-59], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.15e+41], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75000000000000012e101 or 3.1499999999999999e41 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 77.2%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 77.2%

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

   4. Simplified 77.2%

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

   if -1.75000000000000012e101 < z < -3.5000000000000001e-59

   1. Initial program 100.0%

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

      1. associate-*r/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in z around 0 82.9%

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

      1. mul-1-neg 82.9%

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

      2. distribute-lft-neg-out 82.9%

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

      3. *-commutative 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in z around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

      3. associate-/l* 76.9%

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

      4. associate-/r/ 76.9%

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

   9. Simplified 76.9%

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

   if -3.5000000000000001e-59 < z < 3.1499999999999999e41

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-/l* 77.1%

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

      3. associate-/r/ 78.0%

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

   4. Simplified 78.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+101}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-59}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+101}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-133}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+37}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.7e+101)
   (+ y x)
   (if (<= z -1.75e-133)
     (- x (/ y (/ z t)))
     (if (<= z 5e+37) (+ x (* y (/ t a))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e+101) {
		tmp = y + x;
	} else if (z <= -1.75e-133) {
		tmp = x - (y / (z / t));
	} else if (z <= 5e+37) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + 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 (z <= (-4.7d+101)) then
        tmp = y + x
    else if (z <= (-1.75d-133)) then
        tmp = x - (y / (z / t))
    else if (z <= 5d+37) then
        tmp = x + (y * (t / a))
    else
        tmp = y + 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 (z <= -4.7e+101) {
		tmp = y + x;
	} else if (z <= -1.75e-133) {
		tmp = x - (y / (z / t));
	} else if (z <= 5e+37) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.7e+101:
		tmp = y + x
	elif z <= -1.75e-133:
		tmp = x - (y / (z / t))
	elif z <= 5e+37:
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.7e+101)
		tmp = Float64(y + x);
	elseif (z <= -1.75e-133)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	elseif (z <= 5e+37)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.7e+101)
		tmp = y + x;
	elseif (z <= -1.75e-133)
		tmp = x - (y / (z / t));
	elseif (z <= 5e+37)
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.7e+101], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.75e-133], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+37], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.69999999999999971e101 or 4.99999999999999989e37 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 77.2%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 77.2%

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

   4. Simplified 77.2%

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

   if -4.69999999999999971e101 < z < -1.75000000000000001e-133

   1. Initial program 97.7%

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

      1. associate-*r/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-lft-neg-out 84.6%

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

      3. *-commutative 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in z around inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. unsub-neg 77.3%

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

      3. associate-/l* 77.3%

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

      4. associate-/r/ 75.1%

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

   9. Simplified 75.1%

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

       1. *-commutative 75.1%

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

       2. clear-num 75.1%

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

       3. un-div-inv 77.3%

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

   11. Applied egg-rr 77.3%

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

   if -1.75000000000000001e-133 < z < 4.99999999999999989e37

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. associate-/l* 77.7%

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

      3. associate-/r/ 78.6%

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

   4. Simplified 78.6%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+101}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-133}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+37}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+101}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+35}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.35e+101)
   (+ y x)
   (if (<= z -1.8e-133)
     (- x (/ (* y t) z))
     (if (<= z 1.45e+35) (+ x (* y (/ t a))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.35e+101) {
		tmp = y + x;
	} else if (z <= -1.8e-133) {
		tmp = x - ((y * t) / z);
	} else if (z <= 1.45e+35) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + 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 (z <= (-2.35d+101)) then
        tmp = y + x
    else if (z <= (-1.8d-133)) then
        tmp = x - ((y * t) / z)
    else if (z <= 1.45d+35) then
        tmp = x + (y * (t / a))
    else
        tmp = y + 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 (z <= -2.35e+101) {
		tmp = y + x;
	} else if (z <= -1.8e-133) {
		tmp = x - ((y * t) / z);
	} else if (z <= 1.45e+35) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.35e+101:
		tmp = y + x
	elif z <= -1.8e-133:
		tmp = x - ((y * t) / z)
	elif z <= 1.45e+35:
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.35e+101)
		tmp = Float64(y + x);
	elseif (z <= -1.8e-133)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	elseif (z <= 1.45e+35)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.35e+101)
		tmp = y + x;
	elseif (z <= -1.8e-133)
		tmp = x - ((y * t) / z);
	elseif (z <= 1.45e+35)
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.35e+101], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.8e-133], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+35], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.34999999999999985e101 or 1.44999999999999997e35 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 77.2%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 77.2%

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

   4. Simplified 77.2%

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

   if -2.34999999999999985e101 < z < -1.8000000000000002e-133

   1. Initial program 97.7%

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

      1. associate-*r/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-lft-neg-out 84.6%

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

      3. *-commutative 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in x around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. associate-*r/ 89.0%

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

      3. distribute-lft-neg-in 89.0%

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

      4. cancel-sign-sub-inv 89.0%

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

      5. associate-*r/ 84.6%

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

   9. Simplified 84.6%

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

   10. Taylor expanded in z around inf 77.3%

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

   if -1.8000000000000002e-133 < z < 1.44999999999999997e35

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. associate-/l* 77.7%

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

      3. associate-/r/ 78.6%

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

   4. Simplified 78.6%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+101}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+35}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+101}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-134}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+101)
   (+ y x)
   (if (<= z -4.4e-134)
     (- x (/ t (/ z y)))
     (if (<= z 1.5e+41) (+ x (* y (/ t a))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+101) {
		tmp = y + x;
	} else if (z <= -4.4e-134) {
		tmp = x - (t / (z / y));
	} else if (z <= 1.5e+41) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + 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 (z <= (-3.3d+101)) then
        tmp = y + x
    else if (z <= (-4.4d-134)) then
        tmp = x - (t / (z / y))
    else if (z <= 1.5d+41) then
        tmp = x + (y * (t / a))
    else
        tmp = y + 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 (z <= -3.3e+101) {
		tmp = y + x;
	} else if (z <= -4.4e-134) {
		tmp = x - (t / (z / y));
	} else if (z <= 1.5e+41) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+101:
		tmp = y + x
	elif z <= -4.4e-134:
		tmp = x - (t / (z / y))
	elif z <= 1.5e+41:
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+101)
		tmp = Float64(y + x);
	elseif (z <= -4.4e-134)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	elseif (z <= 1.5e+41)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+101)
		tmp = y + x;
	elseif (z <= -4.4e-134)
		tmp = x - (t / (z / y));
	elseif (z <= 1.5e+41)
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+101], N[(y + x), $MachinePrecision], If[LessEqual[z, -4.4e-134], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+41], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000011e101 or 1.4999999999999999e41 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 77.2%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 77.2%

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

   4. Simplified 77.2%

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

   if -3.30000000000000011e101 < z < -4.3999999999999999e-134

   1. Initial program 97.7%

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

      1. associate-*r/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-lft-neg-out 84.6%

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

      3. *-commutative 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in z around inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. associate-/l* 77.3%

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

      3. distribute-neg-frac 77.3%

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

   9. Simplified 77.3%

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

   if -4.3999999999999999e-134 < z < 1.4999999999999999e41

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. associate-/l* 77.7%

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

      3. associate-/r/ 78.6%

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

   4. Simplified 78.6%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+101}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-134}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-59} \lor \neg \left(z \leq 7 \cdot 10^{+34}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e-59) (not (<= z 7e+34)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e-59) || !(z <= 7e+34)) {
		tmp = x + (y * (1.0 - (t / z)));
	} 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 <= (-5.5d-59)) .or. (.not. (z <= 7d+34))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    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 <= -5.5e-59) || !(z <= 7e+34)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.5e-59) or not (z <= 7e+34):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e-59) || !(z <= 7e+34))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	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 <= -5.5e-59) || ~((z <= 7e+34)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e-59], N[Not[LessEqual[z, 7e+34]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000014e-59 or 6.99999999999999996e34 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 86.2%

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

      1. div-sub 86.2%

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

      2. *-inverses 86.2%

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

   4. Simplified 86.2%

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

   if -5.50000000000000014e-59 < z < 6.99999999999999996e34

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-/l* 77.1%

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

      3. associate-/r/ 78.0%

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

   4. Simplified 78.0%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-59} \lor \neg \left(z \leq 7 \cdot 10^{+34}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 11: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+97} \lor \neg \left(z \leq 1.35 \cdot 10^{+25}\right):\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.4e+97) (not (<= z 1.35e+25)))
   (+ x (/ y (- 1.0 (/ a z))))
   (- x (/ (* y t) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e+97) || !(z <= 1.35e+25)) {
		tmp = x + (y / (1.0 - (a / z)));
	} else {
		tmp = x - ((y * t) / (z - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.4d+97)) .or. (.not. (z <= 1.35d+25))) then
        tmp = x + (y / (1.0d0 - (a / z)))
    else
        tmp = x - ((y * t) / (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e+97) || !(z <= 1.35e+25)) {
		tmp = x + (y / (1.0 - (a / z)));
	} else {
		tmp = x - ((y * t) / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.4e+97) or not (z <= 1.35e+25):
		tmp = x + (y / (1.0 - (a / z)))
	else:
		tmp = x - ((y * t) / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.4e+97) || !(z <= 1.35e+25))
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	else
		tmp = Float64(x - Float64(Float64(y * t) / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.4e+97) || ~((z <= 1.35e+25)))
		tmp = x + (y / (1.0 - (a / z)));
	else
		tmp = x - ((y * t) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.4e+97], N[Not[LessEqual[z, 1.35e+25]], $MachinePrecision]], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4000000000000002e97 or 1.35e25 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 73.2%

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

      1. +-commutative 73.2%

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

      2. associate-/l* 89.4%

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

      3. div-sub 89.4%

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

      4. *-inverses 89.4%

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

   4. Simplified 89.4%

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

   if -4.4000000000000002e97 < z < 1.35e25

   1. Initial program 95.9%

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

      1. associate-*r/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around 0 89.2%

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

      1. mul-1-neg 89.2%

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

      2. distribute-lft-neg-out 89.2%

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

      3. *-commutative 89.2%

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

   6. Simplified 89.2%

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

   7. Taylor expanded in x around 0 89.2%

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

      1. mul-1-neg 89.2%

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

      2. associate-*r/ 90.5%

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

      3. distribute-lft-neg-in 90.5%

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

      4. cancel-sign-sub-inv 90.5%

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

      5. associate-*r/ 89.2%

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

   9. Simplified 89.2%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+97} \lor \neg \left(z \leq 1.35 \cdot 10^{+25}\right):\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \end{array} \]

Alternative 12: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-32} \lor \neg \left(z \leq 1.85 \cdot 10^{+33}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e-32) (not (<= z 1.85e+33))) (+ y x) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e-32) || !(z <= 1.85e+33)) {
		tmp = y + x;
	} else {
		tmp = x + (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 <= (-1.6d-32)) .or. (.not. (z <= 1.85d+33))) then
        tmp = y + x
    else
        tmp = x + (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 <= -1.6e-32) || !(z <= 1.85e+33)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.6e-32) or not (z <= 1.85e+33):
		tmp = y + x
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e-32) || !(z <= 1.85e+33))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.6e-32) || ~((z <= 1.85e+33)))
		tmp = y + x;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e-32], N[Not[LessEqual[z, 1.85e+33]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6000000000000001e-32 or 1.8499999999999999e33 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 72.0%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 72.0%

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

   4. Simplified 72.0%

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

   if -1.6000000000000001e-32 < z < 1.8499999999999999e33

   1. Initial program 95.2%

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

   2. Taylor expanded in t around 0 62.4%

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

   3. Taylor expanded in z around 0 60.8%

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

      1. mul-1-neg 60.8%

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

      2. associate-/l* 60.8%

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

      3. distribute-neg-frac 60.8%

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

   5. Simplified 60.8%

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

      1. associate-/r/ 61.6%

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

      2. add-sqr-sqrt 28.8%

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

      3. sqrt-unprod 55.9%

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

      4. sqr-neg 55.9%

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

      5. sqrt-unprod 30.1%

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

      6. add-sqr-sqrt 57.3%

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

   7. Applied egg-rr 57.3%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-32} \lor \neg \left(z \leq 1.85 \cdot 10^{+33}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 13: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+101} \lor \neg \left(z \leq 4.1 \cdot 10^{+40}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.75e+101) (not (<= z 4.1e+40))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.75e+101) || !(z <= 4.1e+40)) {
		tmp = y + x;
	} 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 <= (-1.75d+101)) .or. (.not. (z <= 4.1d+40))) then
        tmp = y + x
    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 <= -1.75e+101) || !(z <= 4.1e+40)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.75e+101) or not (z <= 4.1e+40):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.75e+101) || !(z <= 4.1e+40))
		tmp = Float64(y + x);
	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 <= -1.75e+101) || ~((z <= 4.1e+40)))
		tmp = y + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.75e+101], N[Not[LessEqual[z, 4.1e+40]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75000000000000012e101 or 4.1000000000000002e40 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 77.2%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 77.2%

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

   4. Simplified 77.2%

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

   if -1.75000000000000012e101 < z < 4.1000000000000002e40

   1. Initial program 96.1%

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

   2. Taylor expanded in z around 0 72.7%

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

      1. +-commutative 72.7%

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

      2. associate-/l* 73.3%

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

      3. associate-/r/ 74.0%

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

   4. Simplified 74.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+101} \lor \neg \left(z \leq 4.1 \cdot 10^{+40}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 14: 98.2% 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 97.7%

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

2. Final simplification 97.7%

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

Alternative 15: 64.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-59} \lor \neg \left(z \leq 1.8 \cdot 10^{+33}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e-59) (not (<= z 1.8e+33))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e-59) || !(z <= 1.8e+33)) {
		tmp = y + x;
	} 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 ((z <= (-9.5d-59)) .or. (.not. (z <= 1.8d+33))) then
        tmp = y + x
    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 ((z <= -9.5e-59) || !(z <= 1.8e+33)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e-59) or not (z <= 1.8e+33):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e-59) || !(z <= 1.8e+33))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.5e-59) || ~((z <= 1.8e+33)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e-59], N[Not[LessEqual[z, 1.8e+33]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999994e-59 or 1.8000000000000001e33 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 71.9%

      \[\leadsto \color{blue}{x + y} \]
   3. Step-by-step derivation

      1. +-commutative 71.9%

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

   4. Simplified 71.9%

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

   if -9.4999999999999994e-59 < z < 1.8000000000000001e33

   1. Initial program 95.0%

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

   2. Taylor expanded in x around inf 56.0%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-59} \lor \neg \left(z \leq 1.8 \cdot 10^{+33}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 51.1% 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 97.7%

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

2. Taylor expanded in x around inf 53.4%

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

3. Final simplification 53.4%

   \[\leadsto x \]

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 2023318 
(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)))))