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

Percentage Accurate: 98.1% → 98.3%

Time: 9.6s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. clear-num 97.6%

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

   2. un-div-inv 97.7%

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

4. Applied egg-rr 97.7%

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

Alternative 2: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+97}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.05e-70)
   (+ x y)
   (if (<= t 3.25e-83)
     (+ x (/ y (/ a z)))
     (if (<= t 4.5e+97) (- x (/ y (/ t z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e-70) {
		tmp = x + y;
	} else if (t <= 3.25e-83) {
		tmp = x + (y / (a / z));
	} else if (t <= 4.5e+97) {
		tmp = x - (y / (t / z));
	} 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 (t <= (-1.05d-70)) then
        tmp = x + y
    else if (t <= 3.25d-83) then
        tmp = x + (y / (a / z))
    else if (t <= 4.5d+97) then
        tmp = x - (y / (t / z))
    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 (t <= -1.05e-70) {
		tmp = x + y;
	} else if (t <= 3.25e-83) {
		tmp = x + (y / (a / z));
	} else if (t <= 4.5e+97) {
		tmp = x - (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.05e-70:
		tmp = x + y
	elif t <= 3.25e-83:
		tmp = x + (y / (a / z))
	elif t <= 4.5e+97:
		tmp = x - (y / (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.05e-70)
		tmp = Float64(x + y);
	elseif (t <= 3.25e-83)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 4.5e+97)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.05e-70)
		tmp = x + y;
	elseif (t <= 3.25e-83)
		tmp = x + (y / (a / z));
	elseif (t <= 4.5e+97)
		tmp = x - (y / (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.05e-70], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.25e-83], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+97], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0500000000000001e-70 or 4.49999999999999976e97 < t

   1. Initial program 99.1%

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

   3. Taylor expanded in t around inf 72.1%

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

      1. +-commutative 72.1%

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

   5. Simplified 72.1%

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

   if -1.0500000000000001e-70 < t < 3.25e-83

   1. Initial program 95.0%

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

   3. Taylor expanded in t around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

      1. clear-num 85.3%

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

      2. un-div-inv 85.4%

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

   7. Applied egg-rr 85.4%

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

   if 3.25e-83 < t < 4.49999999999999976e97

   1. Initial program 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 86.7%

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

   6. Taylor expanded in a around 0 79.4%

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

      1. neg-mul-1 79.4%

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

      2. distribute-neg-frac2 79.4%

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

   8. Simplified 79.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+97}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-72}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+97}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.5e-72)
   (+ x y)
   (if (<= t 2.9e-81)
     (+ x (/ y (/ a z)))
     (if (<= t 6.2e+97) (- x (* y (/ z t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e-72) {
		tmp = x + y;
	} else if (t <= 2.9e-81) {
		tmp = x + (y / (a / z));
	} else if (t <= 6.2e+97) {
		tmp = x - (y * (z / t));
	} 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 (t <= (-9.5d-72)) then
        tmp = x + y
    else if (t <= 2.9d-81) then
        tmp = x + (y / (a / z))
    else if (t <= 6.2d+97) then
        tmp = x - (y * (z / t))
    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 (t <= -9.5e-72) {
		tmp = x + y;
	} else if (t <= 2.9e-81) {
		tmp = x + (y / (a / z));
	} else if (t <= 6.2e+97) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.5e-72:
		tmp = x + y
	elif t <= 2.9e-81:
		tmp = x + (y / (a / z))
	elif t <= 6.2e+97:
		tmp = x - (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.5e-72)
		tmp = Float64(x + y);
	elseif (t <= 2.9e-81)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 6.2e+97)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.5e-72)
		tmp = x + y;
	elseif (t <= 2.9e-81)
		tmp = x + (y / (a / z));
	elseif (t <= 6.2e+97)
		tmp = x - (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.5e-72], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.9e-81], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+97], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4999999999999998e-72 or 6.19999999999999962e97 < t

   1. Initial program 99.1%

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

   3. Taylor expanded in t around inf 72.1%

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

      1. +-commutative 72.1%

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

   5. Simplified 72.1%

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

   if -9.4999999999999998e-72 < t < 2.89999999999999989e-81

   1. Initial program 95.0%

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

   3. Taylor expanded in t around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

      1. clear-num 85.3%

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

      2. un-div-inv 85.4%

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

   7. Applied egg-rr 85.4%

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

   if 2.89999999999999989e-81 < t < 6.19999999999999962e97

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 82.1%

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

   4. Taylor expanded in a around 0 77.2%

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

      1. mul-1-neg 77.2%

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

      2. unsub-neg 77.2%

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

      3. associate-/l* 79.4%

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

   6. Simplified 79.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-72}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+97}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+74} \lor \neg \left(t \leq 1.45 \cdot 10^{+99}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+74) (not (<= t 1.45e+99)))
   (+ x (* y (/ (- t z) t)))
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+74) || !(t <= 1.45e+99)) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.05d+74)) .or. (.not. (t <= 1.45d+99))) then
        tmp = x + (y * ((t - z) / t))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+74) || !(t <= 1.45e+99)) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+74) or not (t <= 1.45e+99):
		tmp = x + (y * ((t - z) / t))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+74) || !(t <= 1.45e+99))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e+74) || ~((t <= 1.45e+99)))
		tmp = x + (y * ((t - z) / t));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+74], N[Not[LessEqual[t, 1.45e+99]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0499999999999999e74 or 1.4500000000000001e99 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 62.5%

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

      1. mul-1-neg 62.5%

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

      2. associate-/l* 85.4%

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

      3. distribute-rgt-neg-in 85.4%

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

      4. distribute-frac-neg 85.4%

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

      5. neg-sub0 85.4%

         \[\leadsto x + y \cdot \frac{\color{blue}{0 - \left(z - t\right)}}{t} \]

      6. sub-neg 85.4%

         \[\leadsto x + y \cdot \frac{0 - \color{blue}{\left(z + \left(-t\right)\right)}}{t} \]

      7. +-commutative 85.4%

         \[\leadsto x + y \cdot \frac{0 - \color{blue}{\left(\left(-t\right) + z\right)}}{t} \]

      8. associate--r+ 85.4%

         \[\leadsto x + y \cdot \frac{\color{blue}{\left(0 - \left(-t\right)\right) - z}}{t} \]

      9. neg-sub0 85.4%

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

      10. remove-double-neg 85.4%

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

   5. Simplified 85.4%

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

   if -1.0499999999999999e74 < t < 1.4500000000000001e99

   1. Initial program 96.3%

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

      1. clear-num 96.3%

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

      2. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in z around inf 88.5%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+74} \lor \neg \left(t \leq 1.45 \cdot 10^{+99}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+82} \lor \neg \left(t \leq 9.5 \cdot 10^{+96}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.9e+82) (not (<= t 9.5e+96)))
   (+ x (* y (/ (- t z) t)))
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.9e+82) || !(t <= 9.5e+96)) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.9d+82)) .or. (.not. (t <= 9.5d+96))) then
        tmp = x + (y * ((t - z) / t))
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.9e+82) || !(t <= 9.5e+96)) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.9e+82) or not (t <= 9.5e+96):
		tmp = x + (y * ((t - z) / t))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.9e+82) || !(t <= 9.5e+96))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.9e+82) || ~((t <= 9.5e+96)))
		tmp = x + (y * ((t - z) / t));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.9e+82], N[Not[LessEqual[t, 9.5e+96]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.90000000000000017e82 or 9.50000000000000089e96 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. associate-/l* 85.0%

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

      3. distribute-rgt-neg-in 85.0%

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

      4. distribute-frac-neg 85.0%

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

      5. neg-sub0 85.0%

         \[\leadsto x + y \cdot \frac{\color{blue}{0 - \left(z - t\right)}}{t} \]

      6. sub-neg 85.0%

         \[\leadsto x + y \cdot \frac{0 - \color{blue}{\left(z + \left(-t\right)\right)}}{t} \]

      7. +-commutative 85.0%

         \[\leadsto x + y \cdot \frac{0 - \color{blue}{\left(\left(-t\right) + z\right)}}{t} \]

      8. associate--r+ 85.0%

         \[\leadsto x + y \cdot \frac{\color{blue}{\left(0 - \left(-t\right)\right) - z}}{t} \]

      9. neg-sub0 85.0%

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

      10. remove-double-neg 85.0%

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

   5. Simplified 85.0%

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

   if -1.90000000000000017e82 < t < 9.50000000000000089e96

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 87.1%

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

      1. associate-/l* 88.5%

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

   5. Simplified 88.5%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+82} \lor \neg \left(t \leq 9.5 \cdot 10^{+96}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+82} \lor \neg \left(t \leq 2.8 \cdot 10^{+182}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.3e+82) (not (<= t 2.8e+182)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e+82) || !(t <= 2.8e+182)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.3d+82)) .or. (.not. (t <= 2.8d+182))) then
        tmp = x + y
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e+82) || !(t <= 2.8e+182)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.3e+82) or not (t <= 2.8e+182):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.3e+82) || !(t <= 2.8e+182))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.3e+82) || ~((t <= 2.8e+182)))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.3e+82], N[Not[LessEqual[t, 2.8e+182]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.29999999999999988e82 or 2.80000000000000006e182 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 83.9%

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

      1. +-commutative 83.9%

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

   5. Simplified 83.9%

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

   if -2.29999999999999988e82 < t < 2.80000000000000006e182

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 81.6%

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

      1. associate-/l* 84.8%

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

   5. Simplified 84.8%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+82} \lor \neg \left(t \leq 2.8 \cdot 10^{+182}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-48}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e-45)
   (+ x (/ y (/ (- a t) z)))
   (if (<= z 8.8e-48) (- x (/ y (+ (/ a t) -1.0))) (+ x (* y (/ z (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e-45) {
		tmp = x + (y / ((a - t) / z));
	} else if (z <= 8.8e-48) {
		tmp = x - (y / ((a / t) + -1.0));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	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-45)) then
        tmp = x + (y / ((a - t) / z))
    else if (z <= 8.8d-48) then
        tmp = x - (y / ((a / t) + (-1.0d0)))
    else
        tmp = x + (y * (z / (a - t)))
    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-45) {
		tmp = x + (y / ((a - t) / z));
	} else if (z <= 8.8e-48) {
		tmp = x - (y / ((a / t) + -1.0));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e-45:
		tmp = x + (y / ((a - t) / z))
	elif z <= 8.8e-48:
		tmp = x - (y / ((a / t) + -1.0))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e-45)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	elseif (z <= 8.8e-48)
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.4e-45)
		tmp = x + (y / ((a - t) / z));
	elseif (z <= 8.8e-48)
		tmp = x - (y / ((a / t) + -1.0));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e-45], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e-48], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.39999999999999987e-45

   1. Initial program 96.9%

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

      1. clear-num 96.8%

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

      2. un-div-inv 97.2%

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

   4. Applied egg-rr 97.2%

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

   5. Taylor expanded in z around inf 87.5%

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

   if -4.39999999999999987e-45 < z < 8.8000000000000005e-48

   1. Initial program 98.3%

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

      1. clear-num 98.3%

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

      2. un-div-inv 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in z around 0 92.6%

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

      1. mul-1-neg 92.6%

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

      2. div-sub 92.6%

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

      3. sub-neg 92.6%

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

      4. *-inverses 92.6%

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

      5. metadata-eval 92.6%

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

   7. Simplified 92.6%

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

   if 8.8000000000000005e-48 < z

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf 85.7%

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

      1. associate-/l* 93.5%

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

   5. Simplified 93.5%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-48}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e-46)
   (+ x (/ y (/ (- a t) z)))
   (if (<= z 2.45e-48) (+ x (* y (/ t (- t a)))) (+ x (* y (/ z (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e-46) {
		tmp = x + (y / ((a - t) / z));
	} else if (z <= 2.45e-48) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.5d-46)) then
        tmp = x + (y / ((a - t) / z))
    else if (z <= 2.45d-48) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e-46) {
		tmp = x + (y / ((a - t) / z));
	} else if (z <= 2.45e-48) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e-46:
		tmp = x + (y / ((a - t) / z))
	elif z <= 2.45e-48:
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e-46)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	elseif (z <= 2.45e-48)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e-46)
		tmp = x + (y / ((a - t) / z));
	elseif (z <= 2.45e-48)
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e-46], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e-48], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000027e-46

   1. Initial program 96.9%

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

      1. clear-num 96.8%

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

      2. un-div-inv 97.2%

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

   4. Applied egg-rr 97.2%

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

   5. Taylor expanded in z around inf 87.5%

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

   if -7.50000000000000027e-46 < z < 2.4500000000000001e-48

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 80.7%

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

      1. +-commutative 80.7%

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

      2. associate-*r/ 80.7%

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

      3. mul-1-neg 80.7%

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

      4. distribute-lft-neg-out 80.7%

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

      5. *-commutative 80.7%

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

      6. *-lft-identity 80.7%

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

      7. times-frac 92.5%

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

      8. /-rgt-identity 92.5%

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

      9. distribute-neg-frac 92.5%

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

      10. distribute-neg-frac2 92.5%

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

      11. neg-sub0 92.5%

          \[\leadsto y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} + x \]

      12. sub-neg 92.5%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(a + \left(-t\right)\right)}} + x \]

      13. +-commutative 92.5%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(\left(-t\right) + a\right)}} + x \]

      14. associate--r+ 92.5%

          \[\leadsto y \cdot \frac{t}{\color{blue}{\left(0 - \left(-t\right)\right) - a}} + x \]

      15. neg-sub0 92.5%

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

      16. remove-double-neg 92.5%

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

   5. Simplified 92.5%

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

   if 2.4500000000000001e-48 < z

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf 85.7%

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

      1. associate-/l* 93.5%

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

   5. Simplified 93.5%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-72} \lor \neg \left(t \leq 4.8 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.7e-72) (not (<= t 4.8e-66))) (+ x y) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.7e-72) || !(t <= 4.8e-66)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.7d-72)) .or. (.not. (t <= 4.8d-66))) then
        tmp = x + y
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.7e-72) || !(t <= 4.8e-66)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.7e-72) or not (t <= 4.8e-66):
		tmp = x + y
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.7e-72) || !(t <= 4.8e-66))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.7e-72) || ~((t <= 4.8e-66)))
		tmp = x + y;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.7e-72], N[Not[LessEqual[t, 4.8e-66]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7e-72 or 4.80000000000000052e-66 < t

   1. Initial program 99.3%

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

   3. Taylor expanded in t around inf 67.8%

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

      1. +-commutative 67.8%

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

   5. Simplified 67.8%

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

   if -2.7e-72 < t < 4.80000000000000052e-66

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

      1. clear-num 84.6%

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

      2. un-div-inv 84.6%

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

   7. Applied egg-rr 84.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-72} \lor \neg \left(t \leq 4.8 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-70} \lor \neg \left(t \leq 4.2 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1e-70) (not (<= t 4.2e-66))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1e-70) || !(t <= 4.2e-66)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1d-70)) .or. (.not. (t <= 4.2d-66))) then
        tmp = x + y
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1e-70) || !(t <= 4.2e-66)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1e-70) or not (t <= 4.2e-66):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1e-70) || !(t <= 4.2e-66))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1e-70) || ~((t <= 4.2e-66)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1e-70], N[Not[LessEqual[t, 4.2e-66]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.99999999999999996e-71 or 4.2000000000000001e-66 < t

   1. Initial program 99.3%

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

   3. Taylor expanded in t around inf 67.8%

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

      1. +-commutative 67.8%

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

   5. Simplified 67.8%

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

   if -9.99999999999999996e-71 < t < 4.2000000000000001e-66

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-70} \lor \neg \left(t \leq 4.2 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-70} \lor \neg \left(t \leq 3.8 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e-70) (not (<= t 3.8e-66))) (+ x y) (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e-70) || !(t <= 3.8e-66)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.15d-70)) .or. (.not. (t <= 3.8d-66))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e-70) || !(t <= 3.8e-66)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.15e-70) or not (t <= 3.8e-66):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.15e-70) || !(t <= 3.8e-66))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.15e-70) || ~((t <= 3.8e-66)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.15e-70], N[Not[LessEqual[t, 3.8e-66]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15e-70 or 3.7999999999999998e-66 < t

   1. Initial program 99.3%

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

   3. Taylor expanded in t around inf 67.8%

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

      1. +-commutative 67.8%

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

   5. Simplified 67.8%

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

   if -1.15e-70 < t < 3.7999999999999998e-66

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0 83.6%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-70} \lor \neg \left(t \leq 3.8 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-71} \lor \neg \left(t \leq 5 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6e-71) (not (<= t 5e-66))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6e-71) || !(t <= 5e-66)) {
		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 ((t <= (-6d-71)) .or. (.not. (t <= 5d-66))) 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 ((t <= -6e-71) || !(t <= 5e-66)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6e-71) or not (t <= 5e-66):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6e-71) || !(t <= 5e-66))
		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 ((t <= -6e-71) || ~((t <= 5e-66)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6e-71], N[Not[LessEqual[t, 5e-66]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -6.0000000000000003e-71 or 4.99999999999999962e-66 < t

   1. Initial program 99.3%

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

   3. Taylor expanded in t around inf 67.8%

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

      1. +-commutative 67.8%

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

   5. Simplified 67.8%

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

   if -6.0000000000000003e-71 < t < 4.99999999999999962e-66

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 54.2%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-71} \lor \neg \left(t \leq 5 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

Alternative 14: 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 97.7%

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

3. Taylor expanded in x around inf 52.5%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024180 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -8508084860551241/100000000000000000000000000000000) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t)))))))

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