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

Percentage Accurate: 85.5% → 98.2%

Time: 10.9s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y * (z - t)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y * (z - t)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y * ((z - t) / (z - a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.7%

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

   1. associate-*l/ 95.1%

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

3. Simplified 95.1%

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

4. Taylor expanded in y around 0 84.7%

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

   1. associate-*r/ 99.5%

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

6. Simplified 99.5%

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

7. Final simplification 99.5%

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

Alternative 2: 80.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-56} \lor \neg \left(z \leq 2.1 \cdot 10^{-11}\right):\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.02e-56) (not (<= z 2.1e-11)))
   (+ x (* z (/ y (- z a))))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.02e-56) || !(z <= 2.1e-11)) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = x + (y / (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 <= (-1.02d-56)) .or. (.not. (z <= 2.1d-11))) then
        tmp = x + (z * (y / (z - a)))
    else
        tmp = x + (y / (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 <= -1.02e-56) || !(z <= 2.1e-11)) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.02e-56) or not (z <= 2.1e-11):
		tmp = x + (z * (y / (z - a)))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.02e-56) || !(z <= 2.1e-11))
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.02e-56) || ~((z <= 2.1e-11)))
		tmp = x + (z * (y / (z - a)));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.02e-56], N[Not[LessEqual[z, 2.1e-11]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e-56 or 2.0999999999999999e-11 < z

   1. Initial program 77.0%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around 0 64.9%

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

      1. associate-*l/ 78.7%

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

      2. *-commutative 78.7%

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

   6. Simplified 78.7%

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

   if -1.02e-56 < z < 2.0999999999999999e-11

   1. Initial program 94.0%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in y around 0 94.0%

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

      1. associate-*r/ 99.0%

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

   6. Simplified 99.0%

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

   7. Taylor expanded in z around 0 85.4%

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

      1. clear-num 85.4%

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

      2. un-div-inv 87.1%

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

   9. Applied egg-rr 87.1%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-56} \lor \neg \left(z \leq 2.1 \cdot 10^{-11}\right):\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 3: 80.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -52000000000 \lor \neg \left(z \leq 18500\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -52000000000.0) (not (<= z 18500.0)))
   (+ x (* (- z t) (/ y z)))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -52000000000.0) || !(z <= 18500.0)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y / (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 <= (-52000000000.0d0)) .or. (.not. (z <= 18500.0d0))) then
        tmp = x + ((z - t) * (y / z))
    else
        tmp = x + (y / (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 <= -52000000000.0) || !(z <= 18500.0)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -52000000000.0) or not (z <= 18500.0):
		tmp = x + ((z - t) * (y / z))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -52000000000.0) || !(z <= 18500.0))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -52000000000.0) || ~((z <= 18500.0)))
		tmp = x + ((z - t) * (y / z));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -52000000000.0], N[Not[LessEqual[z, 18500.0]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e10 or 18500 < z

   1. Initial program 73.9%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around inf 83.7%

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

   if -5.2e10 < z < 18500

   1. Initial program 94.8%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around 0 94.8%

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

      1. associate-*r/ 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in z around 0 82.9%

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

      1. clear-num 82.9%

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

      2. un-div-inv 84.3%

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

   9. Applied egg-rr 84.3%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -52000000000 \lor \neg \left(z \leq 18500\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 4: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -220000000000 \lor \neg \left(z \leq 1.48 \cdot 10^{-5}\right):\\ \;\;\;\;x + \left(y - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -220000000000.0) (not (<= z 1.48e-5)))
   (+ x (- y (* t (/ y z))))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -220000000000.0) || !(z <= 1.48e-5)) {
		tmp = x + (y - (t * (y / z)));
	} else {
		tmp = x + (y / (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 <= (-220000000000.0d0)) .or. (.not. (z <= 1.48d-5))) then
        tmp = x + (y - (t * (y / z)))
    else
        tmp = x + (y / (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 <= -220000000000.0) || !(z <= 1.48e-5)) {
		tmp = x + (y - (t * (y / z)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -220000000000.0) or not (z <= 1.48e-5):
		tmp = x + (y - (t * (y / z)))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -220000000000.0) || !(z <= 1.48e-5))
		tmp = Float64(x + Float64(y - Float64(t * Float64(y / z))));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -220000000000.0) || ~((z <= 1.48e-5)))
		tmp = x + (y - (t * (y / z)));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -220000000000.0], N[Not[LessEqual[z, 1.48e-5]], $MachinePrecision]], N[(x + N[(y - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e11 or 1.4800000000000001e-5 < z

   1. Initial program 73.9%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in a around 0 66.0%

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

      1. +-commutative 66.0%

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

      2. associate-/l* 88.9%

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

   6. Simplified 88.9%

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

   7. Taylor expanded in z around 0 80.4%

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

      1. associate-*r/ 80.4%

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

      2. associate-*r* 80.4%

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

      3. neg-mul-1 80.4%

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

      4. associate-*r/ 86.8%

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

      5. *-commutative 86.8%

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

      6. distribute-rgt-neg-out 86.8%

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

      7. unsub-neg 86.8%

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

   9. Simplified 86.8%

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

   if -2.2e11 < z < 1.4800000000000001e-5

   1. Initial program 94.8%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around 0 94.8%

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

      1. associate-*r/ 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in z around 0 82.9%

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

      1. clear-num 82.9%

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

      2. un-div-inv 84.3%

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

   9. Applied egg-rr 84.3%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -220000000000 \lor \neg \left(z \leq 1.48 \cdot 10^{-5}\right):\\ \;\;\;\;x + \left(y - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 5: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -57000000000 \lor \neg \left(z \leq 1.5 \cdot 10^{-5}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -57000000000.0) (not (<= z 1.5e-5)))
   (+ x (/ y (/ z (- z t))))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -57000000000.0) || !(z <= 1.5e-5)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (y / (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 <= (-57000000000.0d0)) .or. (.not. (z <= 1.5d-5))) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = x + (y / (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 <= -57000000000.0) || !(z <= 1.5e-5)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -57000000000.0) or not (z <= 1.5e-5):
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -57000000000.0) || !(z <= 1.5e-5))
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -57000000000.0) || ~((z <= 1.5e-5)))
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -57000000000.0], N[Not[LessEqual[z, 1.5e-5]], $MachinePrecision]], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7e10 or 1.50000000000000004e-5 < z

   1. Initial program 73.9%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in a around 0 66.0%

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

      1. +-commutative 66.0%

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

      2. associate-/l* 88.9%

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

   6. Simplified 88.9%

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

   if -5.7e10 < z < 1.50000000000000004e-5

   1. Initial program 94.8%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around 0 94.8%

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

      1. associate-*r/ 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in z around 0 82.9%

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

      1. clear-num 82.9%

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

      2. un-div-inv 84.3%

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

   9. Applied egg-rr 84.3%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -57000000000 \lor \neg \left(z \leq 1.5 \cdot 10^{-5}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 6: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1950000000000 \lor \neg \left(z \leq 3 \cdot 10^{+39}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1950000000000.0) (not (<= z 3e+39)))
   (+ x (/ y (/ z (- z t))))
   (- x (/ y (/ a (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1950000000000.0) || !(z <= 3e+39)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x - (y / (a / (z - 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 <= (-1950000000000.0d0)) .or. (.not. (z <= 3d+39))) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = x - (y / (a / (z - 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 <= -1950000000000.0) || !(z <= 3e+39)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1950000000000.0) or not (z <= 3e+39):
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x - (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1950000000000.0) || !(z <= 3e+39))
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1950000000000.0) || ~((z <= 3e+39)))
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x - (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1950000000000.0], N[Not[LessEqual[z, 3e+39]], $MachinePrecision]], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e12 or 3e39 < z

   1. Initial program 72.3%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in a around 0 67.3%

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

      1. +-commutative 67.3%

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

      2. associate-/l* 91.6%

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

   6. Simplified 91.6%

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

   if -1.95e12 < z < 3e39

   1. Initial program 95.0%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in a around inf 83.9%

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

      1. mul-1-neg 83.9%

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

      2. unsub-neg 83.9%

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

      3. associate-/l* 86.6%

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

   6. Simplified 86.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1950000000000 \lor \neg \left(z \leq 3 \cdot 10^{+39}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 7: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-56}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e-56)
   (+ x (* y (/ z (- z a))))
   (if (<= z 9.2e-5) (+ x (/ y (/ a t))) (+ x (* (- z t) (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e-56) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 9.2e-5) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + ((z - t) * (y / 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 (z <= (-1.8d-56)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 9.2d-5) then
        tmp = x + (y / (a / t))
    else
        tmp = x + ((z - t) * (y / 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 (z <= -1.8e-56) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 9.2e-5) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + ((z - t) * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e-56:
		tmp = x + (y * (z / (z - a)))
	elif z <= 9.2e-5:
		tmp = x + (y / (a / t))
	else:
		tmp = x + ((z - t) * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e-56)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 9.2e-5)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e-56)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 9.2e-5)
		tmp = x + (y / (a / t));
	else
		tmp = x + ((z - t) * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e-56], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-5], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999989e-56

   1. Initial program 75.9%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around 0 75.9%

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

      1. associate-*r/ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in t around 0 62.4%

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

      1. *-rgt-identity 62.4%

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

      2. *-commutative 62.4%

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

      3. times-frac 78.6%

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

      4. /-rgt-identity 78.6%

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

   9. Simplified 78.6%

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

   if -1.79999999999999989e-56 < z < 9.20000000000000001e-5

   1. Initial program 94.1%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in y around 0 94.1%

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

      1. associate-*r/ 99.0%

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

   6. Simplified 99.0%

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

   7. Taylor expanded in z around 0 85.5%

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

      1. clear-num 85.5%

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

      2. un-div-inv 87.2%

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

   9. Applied egg-rr 87.2%

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

   if 9.20000000000000001e-5 < z

   1. Initial program 78.1%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 85.1%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-56}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \]

Alternative 8: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-56}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e-56)
   (+ x (* y (/ z (- z a))))
   (if (<= z 5.2e-5) (+ x (/ y (/ a t))) (+ x (/ (- z t) (/ z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e-56) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 5.2e-5) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + ((z - t) / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.6d-56)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 5.2d-5) then
        tmp = x + (y / (a / t))
    else
        tmp = x + ((z - t) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e-56) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 5.2e-5) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + ((z - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e-56:
		tmp = x + (y * (z / (z - a)))
	elif z <= 5.2e-5:
		tmp = x + (y / (a / t))
	else:
		tmp = x + ((z - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e-56)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 5.2e-5)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e-56)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 5.2e-5)
		tmp = x + (y / (a / t));
	else
		tmp = x + ((z - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e-56], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-5], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.59999999999999997e-56

   1. Initial program 75.9%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around 0 75.9%

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

      1. associate-*r/ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in t around 0 62.4%

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

      1. *-rgt-identity 62.4%

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

      2. *-commutative 62.4%

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

      3. times-frac 78.6%

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

      4. /-rgt-identity 78.6%

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

   9. Simplified 78.6%

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

   if -2.59999999999999997e-56 < z < 5.19999999999999968e-5

   1. Initial program 94.1%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in y around 0 94.1%

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

      1. associate-*r/ 99.0%

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

   6. Simplified 99.0%

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

   7. Taylor expanded in z around 0 85.5%

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

      1. clear-num 85.5%

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

      2. un-div-inv 87.2%

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

   9. Applied egg-rr 87.2%

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

   if 5.19999999999999968e-5 < z

   1. Initial program 78.1%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

      1. *-commutative 97.2%

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

      2. clear-num 97.1%

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

      3. un-div-inv 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in z around inf 85.1%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-56}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 9: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -340000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-6}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -340000000000.0)
   (+ x y)
   (if (<= z 7.4e-6) (+ x (* t (/ y a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -340000000000.0) {
		tmp = x + y;
	} else if (z <= 7.4e-6) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-340000000000.0d0)) then
        tmp = x + y
    else if (z <= 7.4d-6) then
        tmp = x + (t * (y / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -340000000000.0) {
		tmp = x + y;
	} else if (z <= 7.4e-6) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -340000000000.0:
		tmp = x + y
	elif z <= 7.4e-6:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -340000000000.0)
		tmp = Float64(x + y);
	elseif (z <= 7.4e-6)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -340000000000.0)
		tmp = x + y;
	elseif (z <= 7.4e-6)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -340000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 7.4e-6], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4e11 or 7.4000000000000003e-6 < z

   1. Initial program 74.1%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   6. Simplified 75.9%

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

   if -3.4e11 < z < 7.4000000000000003e-6

   1. Initial program 94.7%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

      1. associate-*l/ 94.7%

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

      2. clear-num 94.7%

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

   5. Applied egg-rr 94.7%

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

   6. Taylor expanded in z around 0 81.5%

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

      1. associate-*r/ 81.3%

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

   8. Simplified 81.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -340000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-6}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -82000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -82000000000.0)
   (+ x y)
   (if (<= z 4.2e-6) (+ x (* y (/ t a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -82000000000.0) {
		tmp = x + y;
	} else if (z <= 4.2e-6) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-82000000000.0d0)) then
        tmp = x + y
    else if (z <= 4.2d-6) then
        tmp = x + (y * (t / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -82000000000.0) {
		tmp = x + y;
	} else if (z <= 4.2e-6) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -82000000000.0:
		tmp = x + y
	elif z <= 4.2e-6:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -82000000000.0)
		tmp = Float64(x + y);
	elseif (z <= 4.2e-6)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -82000000000.0)
		tmp = x + y;
	elseif (z <= 4.2e-6)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -82000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.2e-6], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2e10 or 4.1999999999999996e-6 < z

   1. Initial program 74.1%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   6. Simplified 75.9%

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

   if -8.2e10 < z < 4.1999999999999996e-6

   1. Initial program 94.7%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around 0 94.7%

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

      1. associate-*r/ 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in z around 0 82.7%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -82000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -110000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -110000000000.0)
   (+ x y)
   (if (<= z 8.8e-12) (+ x (/ y (/ a t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -110000000000.0) {
		tmp = x + y;
	} else if (z <= 8.8e-12) {
		tmp = x + (y / (a / 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 (z <= (-110000000000.0d0)) then
        tmp = x + y
    else if (z <= 8.8d-12) then
        tmp = x + (y / (a / 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 (z <= -110000000000.0) {
		tmp = x + y;
	} else if (z <= 8.8e-12) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -110000000000.0:
		tmp = x + y
	elif z <= 8.8e-12:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -110000000000.0)
		tmp = Float64(x + y);
	elseif (z <= 8.8e-12)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -110000000000.0)
		tmp = x + y;
	elseif (z <= 8.8e-12)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -110000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 8.8e-12], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e11 or 8.79999999999999966e-12 < z

   1. Initial program 74.1%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   6. Simplified 75.9%

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

   if -1.1e11 < z < 8.79999999999999966e-12

   1. Initial program 94.7%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around 0 94.7%

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

      1. associate-*r/ 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in z around 0 82.7%

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

      1. clear-num 82.7%

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

      2. un-div-inv 84.2%

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

   9. Applied egg-rr 84.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -110000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 60.3% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 84.7%

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

   1. associate-*l/ 95.1%

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

3. Simplified 95.1%

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

4. Taylor expanded in z around inf 59.7%

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

   1. +-commutative 59.7%

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

6. Simplified 59.7%

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

7. Final simplification 59.7%

   \[\leadsto x + y \]

Alternative 13: 50.7% 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 84.7%

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

   1. associate-*l/ 95.1%

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

3. Simplified 95.1%

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

4. Taylor expanded in x around inf 47.2%

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

5. Final simplification 47.2%

   \[\leadsto x \]

Developer target: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y / ((z - a) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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