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

Percentage Accurate: 98.3% → 98.3%

Time: 10.0s

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: 98.3% 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: 98.3% 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 99.0%

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

2. Final simplification 99.0%

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

Alternative 2: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+170}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -11800000:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-79}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+74}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e+170)
   (+ x y)
   (if (<= z -11800000.0)
     (- x (* y (/ t z)))
     (if (<= z -6.2e-79)
       (- x (* z (/ y a)))
       (if (<= z -1.46e-94)
         (* y (- 1.0 (/ t z)))
         (if (<= z 8.8e+74) (+ x (* y (/ t a))) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+170) {
		tmp = x + y;
	} else if (z <= -11800000.0) {
		tmp = x - (y * (t / z));
	} else if (z <= -6.2e-79) {
		tmp = x - (z * (y / a));
	} else if (z <= -1.46e-94) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 8.8e+74) {
		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 <= (-1.7d+170)) then
        tmp = x + y
    else if (z <= (-11800000.0d0)) then
        tmp = x - (y * (t / z))
    else if (z <= (-6.2d-79)) then
        tmp = x - (z * (y / a))
    else if (z <= (-1.46d-94)) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 8.8d+74) 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 <= -1.7e+170) {
		tmp = x + y;
	} else if (z <= -11800000.0) {
		tmp = x - (y * (t / z));
	} else if (z <= -6.2e-79) {
		tmp = x - (z * (y / a));
	} else if (z <= -1.46e-94) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 8.8e+74) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e+170:
		tmp = x + y
	elif z <= -11800000.0:
		tmp = x - (y * (t / z))
	elif z <= -6.2e-79:
		tmp = x - (z * (y / a))
	elif z <= -1.46e-94:
		tmp = y * (1.0 - (t / z))
	elif z <= 8.8e+74:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e+170)
		tmp = Float64(x + y);
	elseif (z <= -11800000.0)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= -6.2e-79)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	elseif (z <= -1.46e-94)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 8.8e+74)
		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 <= -1.7e+170)
		tmp = x + y;
	elseif (z <= -11800000.0)
		tmp = x - (y * (t / z));
	elseif (z <= -6.2e-79)
		tmp = x - (z * (y / a));
	elseif (z <= -1.46e-94)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 8.8e+74)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e+170], N[(x + y), $MachinePrecision], If[LessEqual[z, -11800000.0], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-79], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.46e-94], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+74], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.7000000000000001e170 or 8.8000000000000005e74 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 90.1%

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

   if -1.7000000000000001e170 < z < -1.18e7

   1. Initial program 99.9%

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

      1. associate-*r/ 88.9%

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

      2. add-cube-cbrt 88.3%

         \[\leadsto x + \frac{y \cdot \left(z - t\right)}{\color{blue}{\left(\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}\right) \cdot \sqrt[3]{z - a}}} \]

      3. associate-/r* 88.2%

         \[\leadsto x + \color{blue}{\frac{\frac{y \cdot \left(z - t\right)}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}}{\sqrt[3]{z - a}}} \]

      4. associate-/l* 99.1%

         \[\leadsto x + \frac{\color{blue}{\frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{z - t}}}}{\sqrt[3]{z - a}} \]

      5. pow2 99.1%

         \[\leadsto x + \frac{\frac{y}{\frac{\color{blue}{{\left(\sqrt[3]{z - a}\right)}^{2}}}{z - t}}}{\sqrt[3]{z - a}} \]

   3. Applied egg-rr 99.1%

      \[\leadsto x + \color{blue}{\frac{\frac{y}{\frac{{\left(\sqrt[3]{z - a}\right)}^{2}}{z - t}}}{\sqrt[3]{z - a}}} \]
   4. Step-by-step derivation

      1. associate-/l/ 99.1%

         \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{z - a} \cdot \frac{{\left(\sqrt[3]{z - a}\right)}^{2}}{z - t}}} \]

   5. Simplified 99.1%

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{z - a} \cdot \frac{{\left(\sqrt[3]{z - a}\right)}^{2}}{z - t}}} \]

   6. Taylor expanded in t around inf 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*r/ 75.3%

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

      3. mul-1-neg 75.3%

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

      4. distribute-rgt-neg-out 75.3%

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

      5. associate-/l* 80.6%

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

   8. Simplified 80.6%

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

   9. Taylor expanded in x around 0 75.3%

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

       1. *-commutative 75.3%

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

       2. associate-*r/ 80.6%

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

       3. neg-mul-1 80.6%

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

       4. sub-neg 80.6%

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

   11. Simplified 80.6%

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

   12. Taylor expanded in z around inf 69.5%

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

   if -1.18e7 < z < -6.1999999999999999e-79

   1. Initial program 96.5%

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

   2. Taylor expanded in a around inf 81.7%

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

      1. mul-1-neg 81.7%

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

      2. associate-/l* 75.9%

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

   4. Simplified 75.9%

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

   5. Taylor expanded in z around inf 75.8%

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

   6. Taylor expanded in x around 0 75.8%

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

      1. associate-/l* 70.0%

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

      2. mul-1-neg 70.0%

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

      3. sub-neg 70.0%

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

      4. associate-/r/ 81.4%

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

      5. *-commutative 81.4%

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

   8. Simplified 81.4%

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

   if -6.1999999999999999e-79 < z < -1.4599999999999999e-94

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 79.8%

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

      1. div-sub 79.8%

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

      2. *-inverses 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in x around 0 79.8%

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

   if -1.4599999999999999e-94 < z < 8.8000000000000005e74

   1. Initial program 98.3%

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

   2. Taylor expanded in z around 0 85.6%

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

      1. associate-/l* 87.1%

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

      2. associate-/r/ 89.4%

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

   4. Simplified 89.4%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+170}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -11800000:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-79}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+74}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{t}{z}\right)\\ t_2 := x + t_1\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-79}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-63}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ t z)))) (t_2 (+ x t_1)))
   (if (<= z -2.25e+36)
     t_2
     (if (<= z -6.2e-79)
       (- x (* z (/ y a)))
       (if (<= z -1.46e-94)
         t_1
         (if (<= z 3.2e-63) (+ x (* y (/ t a))) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (t / z));
	double t_2 = x + t_1;
	double tmp;
	if (z <= -2.25e+36) {
		tmp = t_2;
	} else if (z <= -6.2e-79) {
		tmp = x - (z * (y / a));
	} else if (z <= -1.46e-94) {
		tmp = t_1;
	} else if (z <= 3.2e-63) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (1.0d0 - (t / z))
    t_2 = x + t_1
    if (z <= (-2.25d+36)) then
        tmp = t_2
    else if (z <= (-6.2d-79)) then
        tmp = x - (z * (y / a))
    else if (z <= (-1.46d-94)) then
        tmp = t_1
    else if (z <= 3.2d-63) then
        tmp = x + (y * (t / a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (t / z));
	double t_2 = x + t_1;
	double tmp;
	if (z <= -2.25e+36) {
		tmp = t_2;
	} else if (z <= -6.2e-79) {
		tmp = x - (z * (y / a));
	} else if (z <= -1.46e-94) {
		tmp = t_1;
	} else if (z <= 3.2e-63) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (t / z))
	t_2 = x + t_1
	tmp = 0
	if z <= -2.25e+36:
		tmp = t_2
	elif z <= -6.2e-79:
		tmp = x - (z * (y / a))
	elif z <= -1.46e-94:
		tmp = t_1
	elif z <= 3.2e-63:
		tmp = x + (y * (t / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(t / z)))
	t_2 = Float64(x + t_1)
	tmp = 0.0
	if (z <= -2.25e+36)
		tmp = t_2;
	elseif (z <= -6.2e-79)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	elseif (z <= -1.46e-94)
		tmp = t_1;
	elseif (z <= 3.2e-63)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (t / z));
	t_2 = x + t_1;
	tmp = 0.0;
	if (z <= -2.25e+36)
		tmp = t_2;
	elseif (z <= -6.2e-79)
		tmp = x - (z * (y / a));
	elseif (z <= -1.46e-94)
		tmp = t_1;
	elseif (z <= 3.2e-63)
		tmp = x + (y * (t / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + t$95$1), $MachinePrecision]}, If[LessEqual[z, -2.25e+36], t$95$2, If[LessEqual[z, -6.2e-79], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.46e-94], t$95$1, If[LessEqual[z, 3.2e-63], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.24999999999999998e36 or 3.19999999999999989e-63 < z

   1. Initial program 99.2%

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

   2. Taylor expanded in a around 0 88.2%

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

      1. div-sub 88.2%

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

      2. *-inverses 88.2%

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

   4. Simplified 88.2%

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

   if -2.24999999999999998e36 < z < -6.1999999999999999e-79

   1. Initial program 97.9%

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

   2. Taylor expanded in a around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. associate-/l* 77.5%

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

   4. Simplified 77.5%

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

   5. Taylor expanded in z around inf 66.4%

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

   6. Taylor expanded in x around 0 66.4%

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

      1. associate-/l* 66.5%

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

      2. mul-1-neg 66.5%

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

      3. sub-neg 66.5%

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

      4. associate-/r/ 73.6%

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

      5. *-commutative 73.6%

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

   8. Simplified 73.6%

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

   if -6.1999999999999999e-79 < z < -1.4599999999999999e-94

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 79.8%

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

      1. div-sub 79.8%

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

      2. *-inverses 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in x around 0 79.8%

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

   if -1.4599999999999999e-94 < z < 3.19999999999999989e-63

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 88.0%

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

      1. associate-/l* 89.9%

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

      2. associate-/r/ 93.9%

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

   4. Simplified 93.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-79}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-63}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]

Alternative 4: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+36}:\\ \;\;\;\;x + t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-79}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-64}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ t z)))))
   (if (<= z -1.1e+36)
     (+ x t_1)
     (if (<= z -6.2e-79)
       (- x (* z (/ y a)))
       (if (<= z -1.18e-94)
         t_1
         (if (<= z 4.6e-64) (+ x (* y (/ t a))) (+ x (* y (/ z (- z a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (t / z));
	double tmp;
	if (z <= -1.1e+36) {
		tmp = x + t_1;
	} else if (z <= -6.2e-79) {
		tmp = x - (z * (y / a));
	} else if (z <= -1.18e-94) {
		tmp = t_1;
	} else if (z <= 4.6e-64) {
		tmp = x + (y * (t / 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) :: t_1
    real(8) :: tmp
    t_1 = y * (1.0d0 - (t / z))
    if (z <= (-1.1d+36)) then
        tmp = x + t_1
    else if (z <= (-6.2d-79)) then
        tmp = x - (z * (y / a))
    else if (z <= (-1.18d-94)) then
        tmp = t_1
    else if (z <= 4.6d-64) then
        tmp = x + (y * (t / 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 t_1 = y * (1.0 - (t / z));
	double tmp;
	if (z <= -1.1e+36) {
		tmp = x + t_1;
	} else if (z <= -6.2e-79) {
		tmp = x - (z * (y / a));
	} else if (z <= -1.18e-94) {
		tmp = t_1;
	} else if (z <= 4.6e-64) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (t / z))
	tmp = 0
	if z <= -1.1e+36:
		tmp = x + t_1
	elif z <= -6.2e-79:
		tmp = x - (z * (y / a))
	elif z <= -1.18e-94:
		tmp = t_1
	elif z <= 4.6e-64:
		tmp = x + (y * (t / a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(t / z)))
	tmp = 0.0
	if (z <= -1.1e+36)
		tmp = Float64(x + t_1);
	elseif (z <= -6.2e-79)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	elseif (z <= -1.18e-94)
		tmp = t_1;
	elseif (z <= 4.6e-64)
		tmp = Float64(x + Float64(y * Float64(t / 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)
	t_1 = y * (1.0 - (t / z));
	tmp = 0.0;
	if (z <= -1.1e+36)
		tmp = x + t_1;
	elseif (z <= -6.2e-79)
		tmp = x - (z * (y / a));
	elseif (z <= -1.18e-94)
		tmp = t_1;
	elseif (z <= 4.6e-64)
		tmp = x + (y * (t / a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+36], N[(x + t$95$1), $MachinePrecision], If[LessEqual[z, -6.2e-79], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.18e-94], t$95$1, If[LessEqual[z, 4.6e-64], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.1e36

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 88.0%

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

      1. div-sub 88.0%

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

      2. *-inverses 88.0%

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

   4. Simplified 88.0%

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

   if -1.1e36 < z < -6.1999999999999999e-79

   1. Initial program 97.9%

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

   2. Taylor expanded in a around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. associate-/l* 77.5%

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

   4. Simplified 77.5%

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

   5. Taylor expanded in z around inf 66.4%

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

   6. Taylor expanded in x around 0 66.4%

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

      1. associate-/l* 66.5%

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

      2. mul-1-neg 66.5%

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

      3. sub-neg 66.5%

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

      4. associate-/r/ 73.6%

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

      5. *-commutative 73.6%

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

   8. Simplified 73.6%

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

   if -6.1999999999999999e-79 < z < -1.18e-94

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 79.8%

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

      1. div-sub 79.8%

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

      2. *-inverses 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in x around 0 79.8%

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

   if -1.18e-94 < z < 4.6000000000000003e-64

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 88.8%

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

      1. associate-/l* 90.8%

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

      2. associate-/r/ 94.8%

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

   4. Simplified 94.8%

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

   if 4.6000000000000003e-64 < z

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0 68.4%

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

      1. associate-*r/ 90.1%

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

   4. Simplified 90.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-79}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-64}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 5: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -3.8:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-65}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -3.8)
     t_1
     (if (<= z -9.2e-67)
       (+ x (/ (* y z) (- z a)))
       (if (<= z -7e-95)
         t_1
         (if (<= z 6.5e-65) (+ x (* y (/ t a))) (+ x (* y (/ z (- z a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -3.8) {
		tmp = t_1;
	} else if (z <= -9.2e-67) {
		tmp = x + ((y * z) / (z - a));
	} else if (z <= -7e-95) {
		tmp = t_1;
	} else if (z <= 6.5e-65) {
		tmp = x + (y * (t / 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    if (z <= (-3.8d0)) then
        tmp = t_1
    else if (z <= (-9.2d-67)) then
        tmp = x + ((y * z) / (z - a))
    else if (z <= (-7d-95)) then
        tmp = t_1
    else if (z <= 6.5d-65) then
        tmp = x + (y * (t / 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 t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -3.8) {
		tmp = t_1;
	} else if (z <= -9.2e-67) {
		tmp = x + ((y * z) / (z - a));
	} else if (z <= -7e-95) {
		tmp = t_1;
	} else if (z <= 6.5e-65) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if z <= -3.8:
		tmp = t_1
	elif z <= -9.2e-67:
		tmp = x + ((y * z) / (z - a))
	elif z <= -7e-95:
		tmp = t_1
	elif z <= 6.5e-65:
		tmp = x + (y * (t / a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (z <= -3.8)
		tmp = t_1;
	elseif (z <= -9.2e-67)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(z - a)));
	elseif (z <= -7e-95)
		tmp = t_1;
	elseif (z <= 6.5e-65)
		tmp = Float64(x + Float64(y * Float64(t / 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)
	t_1 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (z <= -3.8)
		tmp = t_1;
	elseif (z <= -9.2e-67)
		tmp = x + ((y * z) / (z - a));
	elseif (z <= -7e-95)
		tmp = t_1;
	elseif (z <= 6.5e-65)
		tmp = x + (y * (t / a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8], t$95$1, If[LessEqual[z, -9.2e-67], N[(x + N[(N[(y * z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e-95], t$95$1, If[LessEqual[z, 6.5e-65], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7999999999999998 or -9.2000000000000002e-67 < z < -6.9999999999999994e-95

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 82.5%

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

      1. div-sub 82.6%

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

      2. *-inverses 82.6%

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

   4. Simplified 82.6%

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

   if -3.7999999999999998 < z < -9.2000000000000002e-67

   1. Initial program 95.7%

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

   2. Taylor expanded in t around 0 84.5%

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

   if -6.9999999999999994e-95 < z < 6.5e-65

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 88.8%

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

      1. associate-/l* 90.8%

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

      2. associate-/r/ 94.8%

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

   4. Simplified 94.8%

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

   if 6.5e-65 < z

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0 68.4%

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

      1. associate-*r/ 90.1%

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

   4. Simplified 90.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-95}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-65}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 6: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -1.9e+77)
     (+ x y)
     (if (<= z -2.55e-39)
       t_1
       (if (<= z -1.46e-94)
         (* y (- 1.0 (/ t z)))
         (if (<= z 3e+74) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -1.9e+77) {
		tmp = x + y;
	} else if (z <= -2.55e-39) {
		tmp = t_1;
	} else if (z <= -1.46e-94) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 3e+74) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (z <= (-1.9d+77)) then
        tmp = x + y
    else if (z <= (-2.55d-39)) then
        tmp = t_1
    else if (z <= (-1.46d-94)) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 3d+74) then
        tmp = t_1
    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 t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -1.9e+77) {
		tmp = x + y;
	} else if (z <= -2.55e-39) {
		tmp = t_1;
	} else if (z <= -1.46e-94) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 3e+74) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -1.9e+77:
		tmp = x + y
	elif z <= -2.55e-39:
		tmp = t_1
	elif z <= -1.46e-94:
		tmp = y * (1.0 - (t / z))
	elif z <= 3e+74:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -1.9e+77)
		tmp = Float64(x + y);
	elseif (z <= -2.55e-39)
		tmp = t_1;
	elseif (z <= -1.46e-94)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 3e+74)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -1.9e+77)
		tmp = x + y;
	elseif (z <= -2.55e-39)
		tmp = t_1;
	elseif (z <= -1.46e-94)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 3e+74)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+77], N[(x + y), $MachinePrecision], If[LessEqual[z, -2.55e-39], t$95$1, If[LessEqual[z, -1.46e-94], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+74], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9000000000000001e77 or 3e74 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 84.7%

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

   if -1.9000000000000001e77 < z < -2.54999999999999994e-39 or -1.4599999999999999e-94 < z < 3e74

   1. Initial program 98.2%

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

   2. Taylor expanded in z around 0 82.6%

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

      1. div-inv 82.5%

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

      2. associate-*l* 83.7%

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

      3. div-inv 83.7%

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

   4. Applied egg-rr 83.7%

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

   if -2.54999999999999994e-39 < z < -1.4599999999999999e-94

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 66.2%

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

      1. div-sub 66.2%

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

      2. *-inverses 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in x around 0 52.4%

      \[\leadsto \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-39}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+74}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))))
   (if (<= z -2.1e+77)
     (+ x y)
     (if (<= z -2.6e-39)
       t_1
       (if (<= z -1.46e-94)
         (* y (- 1.0 (/ t z)))
         (if (<= z 4.7e+73) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double tmp;
	if (z <= -2.1e+77) {
		tmp = x + y;
	} else if (z <= -2.6e-39) {
		tmp = t_1;
	} else if (z <= -1.46e-94) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 4.7e+73) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (t / a))
    if (z <= (-2.1d+77)) then
        tmp = x + y
    else if (z <= (-2.6d-39)) then
        tmp = t_1
    else if (z <= (-1.46d-94)) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 4.7d+73) then
        tmp = t_1
    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 t_1 = x + (y * (t / a));
	double tmp;
	if (z <= -2.1e+77) {
		tmp = x + y;
	} else if (z <= -2.6e-39) {
		tmp = t_1;
	} else if (z <= -1.46e-94) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 4.7e+73) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	tmp = 0
	if z <= -2.1e+77:
		tmp = x + y
	elif z <= -2.6e-39:
		tmp = t_1
	elif z <= -1.46e-94:
		tmp = y * (1.0 - (t / z))
	elif z <= 4.7e+73:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (z <= -2.1e+77)
		tmp = Float64(x + y);
	elseif (z <= -2.6e-39)
		tmp = t_1;
	elseif (z <= -1.46e-94)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 4.7e+73)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	tmp = 0.0;
	if (z <= -2.1e+77)
		tmp = x + y;
	elseif (z <= -2.6e-39)
		tmp = t_1;
	elseif (z <= -1.46e-94)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 4.7e+73)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+77], N[(x + y), $MachinePrecision], If[LessEqual[z, -2.6e-39], t$95$1, If[LessEqual[z, -1.46e-94], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e+73], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0999999999999999e77 or 4.7000000000000002e73 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 84.7%

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

   if -2.0999999999999999e77 < z < -2.6e-39 or -1.4599999999999999e-94 < z < 4.7000000000000002e73

   1. Initial program 98.2%

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

   2. Taylor expanded in z around 0 82.6%

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

      1. associate-/l* 83.8%

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

      2. associate-/r/ 85.8%

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

   4. Simplified 85.8%

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

   if -2.6e-39 < z < -1.4599999999999999e-94

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 66.2%

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

      1. div-sub 66.2%

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

      2. *-inverses 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in x around 0 52.4%

      \[\leadsto \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-39}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+73}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+82}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{-t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+82)
   (+ x (* y (- 1.0 (/ t z))))
   (if (<= z 2.6e+73)
     (+ x (/ y (/ (- z a) (- t))))
     (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+82) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 2.6e+73) {
		tmp = x + (y / ((z - a) / -t));
	} 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 (z <= (-2.7d+82)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= 2.6d+73) then
        tmp = x + (y / ((z - a) / -t))
    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 (z <= -2.7e+82) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 2.6e+73) {
		tmp = x + (y / ((z - a) / -t));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+82:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= 2.6e+73:
		tmp = x + (y / ((z - a) / -t))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+82)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= 2.6e+73)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / Float64(-t))));
	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 (z <= -2.7e+82)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= 2.6e+73)
		tmp = x + (y / ((z - a) / -t));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+82], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+73], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6999999999999999e82

   1. Initial program 99.9%

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

   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 90.2%

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

      2. *-inverses 90.2%

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

   4. Simplified 90.2%

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

   if -2.6999999999999999e82 < z < 2.6000000000000001e73

   1. Initial program 98.4%

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

      1. associate-*r/ 94.0%

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

      2. add-cube-cbrt 93.5%

         \[\leadsto x + \frac{y \cdot \left(z - t\right)}{\color{blue}{\left(\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}\right) \cdot \sqrt[3]{z - a}}} \]

      3. associate-/r* 93.6%

         \[\leadsto x + \color{blue}{\frac{\frac{y \cdot \left(z - t\right)}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}}{\sqrt[3]{z - a}}} \]

      4. associate-/l* 98.2%

         \[\leadsto x + \frac{\color{blue}{\frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{z - t}}}}{\sqrt[3]{z - a}} \]

      5. pow2 98.2%

         \[\leadsto x + \frac{\frac{y}{\frac{\color{blue}{{\left(\sqrt[3]{z - a}\right)}^{2}}}{z - t}}}{\sqrt[3]{z - a}} \]

   3. Applied egg-rr 98.2%

      \[\leadsto x + \color{blue}{\frac{\frac{y}{\frac{{\left(\sqrt[3]{z - a}\right)}^{2}}{z - t}}}{\sqrt[3]{z - a}}} \]
   4. Step-by-step derivation

      1. associate-/l/ 98.0%

         \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{z - a} \cdot \frac{{\left(\sqrt[3]{z - a}\right)}^{2}}{z - t}}} \]

   5. Simplified 98.0%

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{z - a} \cdot \frac{{\left(\sqrt[3]{z - a}\right)}^{2}}{z - t}}} \]

   6. Taylor expanded in t around inf 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-*r/ 87.4%

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

      3. mul-1-neg 87.4%

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

      4. distribute-rgt-neg-out 87.4%

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

      5. associate-/l* 91.3%

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

   8. Simplified 91.3%

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

   if 2.6000000000000001e73 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 63.5%

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

      1. associate-*r/ 94.0%

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

   4. Simplified 94.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+82}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{-t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 9: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+170}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-97}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+76}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.75e+170)
   (+ x y)
   (if (<= z -1.65e-97)
     (- x (* y (/ t z)))
     (if (<= z 1.22e+76) (+ x (* y (/ t a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e+170) {
		tmp = x + y;
	} else if (z <= -1.65e-97) {
		tmp = x - (y * (t / z));
	} else if (z <= 1.22e+76) {
		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 <= (-1.75d+170)) then
        tmp = x + y
    else if (z <= (-1.65d-97)) then
        tmp = x - (y * (t / z))
    else if (z <= 1.22d+76) 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 <= -1.75e+170) {
		tmp = x + y;
	} else if (z <= -1.65e-97) {
		tmp = x - (y * (t / z));
	} else if (z <= 1.22e+76) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.75e+170:
		tmp = x + y
	elif z <= -1.65e-97:
		tmp = x - (y * (t / z))
	elif z <= 1.22e+76:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.75e+170)
		tmp = Float64(x + y);
	elseif (z <= -1.65e-97)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= 1.22e+76)
		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 <= -1.75e+170)
		tmp = x + y;
	elseif (z <= -1.65e-97)
		tmp = x - (y * (t / z));
	elseif (z <= 1.22e+76)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.75e+170], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.65e-97], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e+76], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75000000000000003e170 or 1.22000000000000002e76 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 90.1%

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

   if -1.75000000000000003e170 < z < -1.6500000000000001e-97

   1. Initial program 98.9%

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

      1. associate-*r/ 93.1%

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

      2. add-cube-cbrt 92.3%

         \[\leadsto x + \frac{y \cdot \left(z - t\right)}{\color{blue}{\left(\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}\right) \cdot \sqrt[3]{z - a}}} \]

      3. associate-/r* 92.3%

         \[\leadsto x + \color{blue}{\frac{\frac{y \cdot \left(z - t\right)}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}}{\sqrt[3]{z - a}}} \]

      4. associate-/l* 99.0%

         \[\leadsto x + \frac{\color{blue}{\frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{z - t}}}}{\sqrt[3]{z - a}} \]

      5. pow2 99.0%

         \[\leadsto x + \frac{\frac{y}{\frac{\color{blue}{{\left(\sqrt[3]{z - a}\right)}^{2}}}{z - t}}}{\sqrt[3]{z - a}} \]

   3. Applied egg-rr 99.0%

      \[\leadsto x + \color{blue}{\frac{\frac{y}{\frac{{\left(\sqrt[3]{z - a}\right)}^{2}}{z - t}}}{\sqrt[3]{z - a}}} \]
   4. Step-by-step derivation

      1. associate-/l/ 97.3%

         \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{z - a} \cdot \frac{{\left(\sqrt[3]{z - a}\right)}^{2}}{z - t}}} \]

   5. Simplified 97.3%

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{z - a} \cdot \frac{{\left(\sqrt[3]{z - a}\right)}^{2}}{z - t}}} \]

   6. Taylor expanded in t around inf 72.5%

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

      1. *-commutative 72.5%

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

      2. associate-*r/ 72.5%

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

      3. mul-1-neg 72.5%

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

      4. distribute-rgt-neg-out 72.5%

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

      5. associate-/l* 75.8%

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

   8. Simplified 75.8%

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

   9. Taylor expanded in x around 0 72.5%

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

       1. *-commutative 72.5%

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

       2. associate-*r/ 75.8%

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

       3. neg-mul-1 75.8%

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

       4. sub-neg 75.8%

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

   11. Simplified 75.8%

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

   12. Taylor expanded in z around inf 63.5%

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

   if -1.6500000000000001e-97 < z < 1.22000000000000002e76

   1. Initial program 98.3%

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

   2. Taylor expanded in z around 0 85.6%

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

      1. associate-/l* 87.1%

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

      2. associate-/r/ 89.4%

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

   4. Simplified 89.4%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+170}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-97}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+76}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{+75}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e+83)
   (+ x (* y (- 1.0 (/ t z))))
   (if (<= z 6.7e+75) (- 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 (z <= -1.4e+83) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 6.7e+75) {
		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 (z <= (-1.4d+83)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= 6.7d+75) 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 (z <= -1.4e+83) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 6.7e+75) {
		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 z <= -1.4e+83:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= 6.7e+75:
		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 (z <= -1.4e+83)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= 6.7e+75)
		tmp = Float64(x - Float64(y * Float64(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 (z <= -1.4e+83)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= 6.7e+75)
		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[LessEqual[z, -1.4e+83], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.7e+75], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e83

   1. Initial program 99.9%

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

   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 90.2%

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

      2. *-inverses 90.2%

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

   4. Simplified 90.2%

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

   if -1.4e83 < z < 6.7000000000000001e75

   1. Initial program 98.4%

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

      1. associate-*r/ 94.0%

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

      2. add-cube-cbrt 93.5%

         \[\leadsto x + \frac{y \cdot \left(z - t\right)}{\color{blue}{\left(\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}\right) \cdot \sqrt[3]{z - a}}} \]

      3. associate-/r* 93.6%

         \[\leadsto x + \color{blue}{\frac{\frac{y \cdot \left(z - t\right)}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}}{\sqrt[3]{z - a}}} \]

      4. associate-/l* 98.2%

         \[\leadsto x + \frac{\color{blue}{\frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{z - t}}}}{\sqrt[3]{z - a}} \]

      5. pow2 98.2%

         \[\leadsto x + \frac{\frac{y}{\frac{\color{blue}{{\left(\sqrt[3]{z - a}\right)}^{2}}}{z - t}}}{\sqrt[3]{z - a}} \]

   3. Applied egg-rr 98.2%

      \[\leadsto x + \color{blue}{\frac{\frac{y}{\frac{{\left(\sqrt[3]{z - a}\right)}^{2}}{z - t}}}{\sqrt[3]{z - a}}} \]
   4. Step-by-step derivation

      1. associate-/l/ 98.0%

         \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{z - a} \cdot \frac{{\left(\sqrt[3]{z - a}\right)}^{2}}{z - t}}} \]

   5. Simplified 98.0%

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{z - a} \cdot \frac{{\left(\sqrt[3]{z - a}\right)}^{2}}{z - t}}} \]

   6. Taylor expanded in t around inf 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-*r/ 87.4%

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

      3. mul-1-neg 87.4%

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

      4. distribute-rgt-neg-out 87.4%

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

      5. associate-/l* 91.3%

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

   8. Simplified 91.3%

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

   9. Taylor expanded in x around 0 87.4%

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

       1. *-commutative 87.4%

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

       2. associate-*r/ 90.9%

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

       3. neg-mul-1 90.9%

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

       4. sub-neg 90.9%

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

   11. Simplified 90.9%

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

   if 6.7000000000000001e75 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 63.5%

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

      1. associate-*r/ 94.0%

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

   4. Simplified 94.0%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{+75}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 11: 62.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+81} \lor \neg \left(z \leq 2.3 \cdot 10^{+71}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e+81) (not (<= z 2.3e+71))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e+81) || !(z <= 2.3e+71)) {
		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 ((z <= (-1.65d+81)) .or. (.not. (z <= 2.3d+71))) 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 ((z <= -1.65e+81) || !(z <= 2.3e+71)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e+81) or not (z <= 2.3e+71):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e+81) || !(z <= 2.3e+71))
		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 ((z <= -1.65e+81) || ~((z <= 2.3e+71)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e+81], N[Not[LessEqual[z, 2.3e+71]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e81 or 2.3000000000000002e71 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 85.4%

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

   if -1.65e81 < z < 2.3000000000000002e71

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 76.9%

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

   3. Taylor expanded in x around inf 55.9%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+81} \lor \neg \left(z \leq 2.3 \cdot 10^{+71}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 51.5% 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 99.0%

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

2. Taylor expanded in z around 0 62.6%

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

3. Taylor expanded in x around inf 52.4%

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

4. Final simplification 52.4%

   \[\leadsto x \]

Developer target: 98.4% 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 2023301 
(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)))))