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

Percentage Accurate: 98.0% → 98.0%

Time: 10.8s

Alternatives: 9

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: 98.0% 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: 98.0% 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 98.7%

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

3. Final simplification 98.7%

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

Alternative 2: 77.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+68}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-27}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-58}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2e+68)
   (+ x y)
   (if (<= t -5.1e-27)
     (- x (* z (/ y t)))
     (if (<= t -4.2e-58)
       (- x (* y (/ t a)))
       (if (<= t 5e-33) (+ x (/ y (/ a z))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2e+68) {
		tmp = x + y;
	} else if (t <= -5.1e-27) {
		tmp = x - (z * (y / t));
	} else if (t <= -4.2e-58) {
		tmp = x - (y * (t / a));
	} else if (t <= 5e-33) {
		tmp = x + (y / (a / 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 <= (-2d+68)) then
        tmp = x + y
    else if (t <= (-5.1d-27)) then
        tmp = x - (z * (y / t))
    else if (t <= (-4.2d-58)) then
        tmp = x - (y * (t / a))
    else if (t <= 5d-33) then
        tmp = x + (y / (a / 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 <= -2e+68) {
		tmp = x + y;
	} else if (t <= -5.1e-27) {
		tmp = x - (z * (y / t));
	} else if (t <= -4.2e-58) {
		tmp = x - (y * (t / a));
	} else if (t <= 5e-33) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2e+68:
		tmp = x + y
	elif t <= -5.1e-27:
		tmp = x - (z * (y / t))
	elif t <= -4.2e-58:
		tmp = x - (y * (t / a))
	elif t <= 5e-33:
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2e+68)
		tmp = Float64(x + y);
	elseif (t <= -5.1e-27)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	elseif (t <= -4.2e-58)
		tmp = Float64(x - Float64(y * Float64(t / a)));
	elseif (t <= 5e-33)
		tmp = Float64(x + Float64(y / Float64(a / 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 <= -2e+68)
		tmp = x + y;
	elseif (t <= -5.1e-27)
		tmp = x - (z * (y / t));
	elseif (t <= -4.2e-58)
		tmp = x - (y * (t / a));
	elseif (t <= 5e-33)
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2e+68], N[(x + y), $MachinePrecision], If[LessEqual[t, -5.1e-27], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.2e-58], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-33], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.99999999999999991e68 or 5.00000000000000028e-33 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 80.9%

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

   if -1.99999999999999991e68 < t < -5.0999999999999999e-27

   1. Initial program 94.9%

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

      1. associate-*r/ 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-/l* 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in z around inf 69.8%

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

      1. *-commutative 69.8%

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

      2. associate-*r/ 80.0%

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

   7. Simplified 80.0%

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

   8. Taylor expanded in a around 0 74.8%

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

      1. associate-*r/ 74.8%

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

      2. neg-mul-1 74.8%

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

   10. Simplified 74.8%

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

       1. distribute-frac-neg 74.8%

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

       2. distribute-rgt-neg-out 74.8%

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

       3. add-sqr-sqrt 43.1%

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

       4. sqrt-unprod 49.5%

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

       5. sqr-neg 49.5%

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

       6. sqrt-unprod 15.6%

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

       7. add-sqr-sqrt 37.6%

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

       8. sub-neg 37.6%

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

       9. add-sqr-sqrt 15.6%

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

       10. sqrt-unprod 49.5%

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

       11. sqr-neg 49.5%

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

       12. sqrt-unprod 43.1%

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

       13. add-sqr-sqrt 74.8%

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

   12. Applied egg-rr 74.8%

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

   if -5.0999999999999999e-27 < t < -4.19999999999999975e-58

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 81.2%

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

      1. associate-/l* 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in z around 0 81.2%

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

      1. associate-*r/ 81.2%

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

      2. neg-mul-1 81.2%

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

   8. Simplified 81.2%

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

   9. Taylor expanded in x around 0 81.2%

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

       1. mul-1-neg 81.2%

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

       2. associate-*l/ 81.2%

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

       3. distribute-rgt-neg-in 81.2%

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

       4. *-commutative 81.2%

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

       5. cancel-sign-sub-inv 81.2%

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

   11. Simplified 81.2%

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

   if -4.19999999999999975e-58 < t < 5.00000000000000028e-33

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0 77.8%

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

      1. associate-/l* 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+68}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-27}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-58}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+69} \lor \neg \left(t \leq 1.3 \cdot 10^{+107}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e+69) (not (<= t 1.3e+107)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e+69) || !(t <= 1.3e+107)) {
		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 <= (-1.3d+69)) .or. (.not. (t <= 1.3d+107))) 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 <= -1.3e+69) || !(t <= 1.3e+107)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.3e+69) or not (t <= 1.3e+107):
		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 <= -1.3e+69) || !(t <= 1.3e+107))
		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 <= -1.3e+69) || ~((t <= 1.3e+107)))
		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, -1.3e+69], N[Not[LessEqual[t, 1.3e+107]], $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 < -1.3000000000000001e69 or 1.3000000000000001e107 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 84.8%

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

   if -1.3000000000000001e69 < t < 1.3000000000000001e107

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf 85.5%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+69} \lor \neg \left(t \leq 1.3 \cdot 10^{+107}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+37} \lor \neg \left(z \leq 1.1 \cdot 10^{-143}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+37) (not (<= z 1.1e-143)))
   (+ x (* z (/ y (- a t))))
   (- x (/ y (/ (- a t) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+37) || !(z <= 1.1e-143)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a - t) / 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 <= (-1.5d+37)) .or. (.not. (z <= 1.1d-143))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (y / ((a - t) / 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 <= -1.5e+37) || !(z <= 1.1e-143)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a - t) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+37) or not (z <= 1.1e-143):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (y / ((a - t) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+37) || !(z <= 1.1e-143))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a - t) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.5e+37) || ~((z <= 1.1e-143)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (y / ((a - t) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+37], N[Not[LessEqual[z, 1.1e-143]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000011e37 or 1.09999999999999995e-143 < z

   1. Initial program 98.5%

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

      1. associate-*r/ 87.5%

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

      2. *-commutative 87.5%

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

      3. associate-/l* 98.9%

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

   4. Applied egg-rr 98.9%

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

   5. Taylor expanded in z around inf 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-*r/ 90.8%

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

   7. Simplified 90.8%

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

   if -1.50000000000000011e37 < z < 1.09999999999999995e-143

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. associate-/l* 84.0%

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

      3. distribute-neg-frac 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in x around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. unsub-neg 77.3%

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

      3. *-commutative 77.3%

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

      4. associate-/l* 88.7%

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

   8. Simplified 88.7%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+37} \lor \neg \left(z \leq 1.1 \cdot 10^{-143}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-55} \lor \neg \left(t \leq 4.8 \cdot 10^{+86}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45e-55) (not (<= t 4.8e+86)))
   (- 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 <= -1.45e-55) || !(t <= 4.8e+86)) {
		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 <= (-1.45d-55)) .or. (.not. (t <= 4.8d+86))) 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 <= -1.45e-55) || !(t <= 4.8e+86)) {
		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 <= -1.45e-55) or not (t <= 4.8e+86):
		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 <= -1.45e-55) || !(t <= 4.8e+86))
		tmp = Float64(x - Float64(y / Float64(t / Float64(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 <= -1.45e-55) || ~((t <= 4.8e+86)))
		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, -1.45e-55], N[Not[LessEqual[t, 4.8e+86]], $MachinePrecision]], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $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 < -1.45e-55 or 4.8000000000000001e86 < t

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. associate-/l* 88.3%

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

      3. distribute-neg-frac 88.3%

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

   5. Simplified 88.3%

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

   if -1.45e-55 < t < 4.8000000000000001e86

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf 89.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-55} \lor \neg \left(t \leq 4.8 \cdot 10^{+86}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-58} \lor \neg \left(t \leq 7.5 \cdot 10^{-29}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.2e-58) (not (<= t 7.5e-29))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.2e-58) || !(t <= 7.5e-29)) {
		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 <= (-4.2d-58)) .or. (.not. (t <= 7.5d-29))) 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 <= -4.2e-58) || !(t <= 7.5e-29)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.2e-58) or not (t <= 7.5e-29):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.2e-58) || !(t <= 7.5e-29))
		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 <= -4.2e-58) || ~((t <= 7.5e-29)))
		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, -4.2e-58], N[Not[LessEqual[t, 7.5e-29]], $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 < -4.19999999999999975e-58 or 7.50000000000000006e-29 < t

   1. Initial program 99.2%

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

   3. Taylor expanded in t around inf 76.9%

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

   if -4.19999999999999975e-58 < t < 7.50000000000000006e-29

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0 78.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-58} \lor \neg \left(t \leq 7.5 \cdot 10^{-29}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{-54} \lor \neg \left(t \leq 5 \cdot 10^{-29}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.16e-54) (not (<= t 5e-29))) (+ x y) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.16e-54) || !(t <= 5e-29)) {
		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 <= (-1.16d-54)) .or. (.not. (t <= 5d-29))) 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 <= -1.16e-54) || !(t <= 5e-29)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.16e-54) or not (t <= 5e-29):
		tmp = x + y
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.16e-54) || !(t <= 5e-29))
		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 <= -1.16e-54) || ~((t <= 5e-29)))
		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, -1.16e-54], N[Not[LessEqual[t, 5e-29]], $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 < -1.16e-54 or 4.99999999999999986e-29 < t

   1. Initial program 99.2%

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

   3. Taylor expanded in t around inf 76.9%

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

   if -1.16e-54 < t < 4.99999999999999986e-29

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0 77.8%

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

      1. associate-/l* 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{-54} \lor \neg \left(t \leq 5 \cdot 10^{-29}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.02 \cdot 10^{+158}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 1.02e+158) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 1.02e+158) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 1.02d+158) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 1.02e+158) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 1.02e+158:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 1.02e+158)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 1.02e+158)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 1.02e+158], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 1.02e158

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf 58.2%

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

   if 1.02e158 < a

   1. Initial program 96.5%

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

   3. Taylor expanded in a around inf 82.7%

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

      1. associate-/l* 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in z around 0 79.6%

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

      1. associate-*r/ 79.6%

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

      2. neg-mul-1 79.6%

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

   8. Simplified 79.6%

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

   9. Taylor expanded in x around inf 72.4%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.02 \cdot 10^{+158}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 98.7%

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

3. Taylor expanded in a around inf 59.2%

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

   1. associate-/l* 60.2%

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

5. Simplified 60.2%

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

6. Taylor expanded in z around 0 43.3%

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

   1. associate-*r/ 43.3%

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

   2. neg-mul-1 43.3%

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

8. Simplified 43.3%

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

9. Taylor expanded in x around inf 48.2%

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

10. Final simplification 48.2%

    \[\leadsto x \]
11. Add Preprocessing

Developer target: 99.4% 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 2024020 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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