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

Percentage Accurate: 86.2% → 98.2%

Time: 9.7s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

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(Float64(y * 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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 86.2% accurate, 1.0× speedup

Math

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

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(Float64(y * 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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

   1. *-commutative 84.4%

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

   2. associate-/l* 96.8%

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

   3. associate-/r/ 99.2%

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

3. Applied egg-rr 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+57} \lor \neg \left(z \leq 8.4 \cdot 10^{-27}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.52e+57) (not (<= z 8.4e-27)))
   (+ x (* z (/ y (- a t))))
   (+ x (/ y (/ (- t a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.52e+57) || !(z <= 8.4e-27)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y / ((t - 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 <= (-1.52d+57)) .or. (.not. (z <= 8.4d-27))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (y / ((t - 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 <= -1.52e+57) || !(z <= 8.4e-27)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y / ((t - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.52e+57) or not (z <= 8.4e-27):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (y / ((t - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.52e+57) || !(z <= 8.4e-27))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(t - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.52e+57) || ~((z <= 8.4e-27)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (y / ((t - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.52e+57], N[Not[LessEqual[z, 8.4e-27]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(t - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.51999999999999998e57 or 8.40000000000000061e-27 < z

   1. Initial program 83.1%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around inf 79.5%

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

      1. associate-*l/ 87.4%

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

      2. *-commutative 87.4%

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

   6. Simplified 87.4%

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

   if -1.51999999999999998e57 < z < 8.40000000000000061e-27

   1. Initial program 85.8%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around 0 79.6%

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

      1. associate-*r/ 79.6%

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

      2. mul-1-neg 79.6%

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

      3. *-commutative 79.6%

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

      4. distribute-rgt-neg-out 79.6%

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

      5. associate-*l/ 90.4%

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

   6. Simplified 90.4%

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

      1. associate-*l/ 79.6%

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

      2. associate-/l* 92.9%

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

      3. frac-2neg 92.9%

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

      4. neg-sub0 92.9%

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

      5. associate-+l- 92.9%

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

      6. neg-sub0 92.9%

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

      7. +-commutative 92.9%

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

      8. sub-neg 92.9%

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

      9. remove-double-neg 92.9%

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

   8. Applied egg-rr 92.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+57} \lor \neg \left(z \leq 8.4 \cdot 10^{-27}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \end{array} \]

Alternative 3: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+79}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+88}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e+79)
   (+ x y)
   (if (<= t 2.8e+88) (+ x (* z (/ y (- a t)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+79) {
		tmp = x + y;
	} else if (t <= 2.8e+88) {
		tmp = x + (z * (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 (t <= (-4.5d+79)) then
        tmp = x + y
    else if (t <= 2.8d+88) then
        tmp = x + (z * (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 (t <= -4.5e+79) {
		tmp = x + y;
	} else if (t <= 2.8e+88) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.5e+79:
		tmp = x + y
	elif t <= 2.8e+88:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e+79)
		tmp = Float64(x + y);
	elseif (t <= 2.8e+88)
		tmp = Float64(x + Float64(z * 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 (t <= -4.5e+79)
		tmp = x + y;
	elseif (t <= 2.8e+88)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e+79], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.8e+88], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.49999999999999994e79 or 2.79999999999999989e88 < t

   1. Initial program 63.5%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around inf 90.2%

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

      1. +-commutative 90.2%

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

   6. Simplified 90.2%

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

   if -4.49999999999999994e79 < t < 2.79999999999999989e88

   1. Initial program 96.5%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around inf 84.6%

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

      1. associate-*l/ 85.8%

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

      2. *-commutative 85.8%

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

   6. Simplified 85.8%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+79}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+88}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+57}:\\ \;\;\;\;x - \frac{y}{\frac{t - a}{z}}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e+57)
   (- x (/ y (/ (- t a) z)))
   (if (<= z 2.55e-27) (+ x (/ y (/ (- t a) t))) (+ x (* z (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e+57) {
		tmp = x - (y / ((t - a) / z));
	} else if (z <= 2.55e-27) {
		tmp = x + (y / ((t - a) / t));
	} else {
		tmp = x + (z * (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 <= (-1.65d+57)) then
        tmp = x - (y / ((t - a) / z))
    else if (z <= 2.55d-27) then
        tmp = x + (y / ((t - a) / t))
    else
        tmp = x + (z * (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 <= -1.65e+57) {
		tmp = x - (y / ((t - a) / z));
	} else if (z <= 2.55e-27) {
		tmp = x + (y / ((t - a) / t));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.65e+57:
		tmp = x - (y / ((t - a) / z))
	elif z <= 2.55e-27:
		tmp = x + (y / ((t - a) / t))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.65e+57)
		tmp = Float64(x - Float64(y / Float64(Float64(t - a) / z)));
	elseif (z <= 2.55e-27)
		tmp = Float64(x + Float64(y / Float64(Float64(t - a) / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.65e+57)
		tmp = x - (y / ((t - a) / z));
	elseif (z <= 2.55e-27)
		tmp = x + (y / ((t - a) / t));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.65e+57], N[(x - N[(y / N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.55e-27], N[(x + N[(y / N[(N[(t - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6500000000000001e57

   1. Initial program 91.8%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

      1. associate-*l/ 91.8%

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

      2. frac-2neg 91.8%

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

      3. distribute-frac-neg 91.8%

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

      4. remove-double-neg 91.8%

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

      5. distribute-frac-neg 91.8%

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

      6. frac-2neg 91.8%

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

      7. associate-*l/ 93.9%

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

      8. unsub-neg 93.9%

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

      9. associate-*l/ 91.8%

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

      10. frac-2neg 91.8%

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

      11. distribute-frac-neg 91.8%

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

      12. remove-double-neg 91.8%

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

      13. associate-/l* 99.9%

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

      14. neg-sub0 99.9%

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

      15. sub-neg 99.9%

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

      16. +-commutative 99.9%

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

      17. associate--r+ 99.9%

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

      18. neg-sub0 99.9%

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

      19. remove-double-neg 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 93.9%

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

   if -1.6500000000000001e57 < z < 2.55e-27

   1. Initial program 85.8%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around 0 79.6%

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

      1. associate-*r/ 79.6%

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

      2. mul-1-neg 79.6%

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

      3. *-commutative 79.6%

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

      4. distribute-rgt-neg-out 79.6%

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

      5. associate-*l/ 90.4%

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

   6. Simplified 90.4%

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

      1. associate-*l/ 79.6%

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

      2. associate-/l* 92.9%

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

      3. frac-2neg 92.9%

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

      4. neg-sub0 92.9%

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

      5. associate-+l- 92.9%

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

      6. neg-sub0 92.9%

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

      7. +-commutative 92.9%

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

      8. sub-neg 92.9%

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

      9. remove-double-neg 92.9%

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

   8. Applied egg-rr 92.9%

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

   if 2.55e-27 < z

   1. Initial program 78.4%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around inf 74.0%

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

      1. associate-*l/ 86.0%

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

      2. *-commutative 86.0%

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

   6. Simplified 86.0%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+57}:\\ \;\;\;\;x - \frac{y}{\frac{t - a}{z}}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 5: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.95:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.32e+70) (+ x y) (if (<= t 1.95) (+ x (* z (/ y a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.32e+70) {
		tmp = x + y;
	} else if (t <= 1.95) {
		tmp = x + (z * (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 (t <= (-1.32d+70)) then
        tmp = x + y
    else if (t <= 1.95d0) then
        tmp = x + (z * (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 (t <= -1.32e+70) {
		tmp = x + y;
	} else if (t <= 1.95) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.32e+70:
		tmp = x + y
	elif t <= 1.95:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.32e+70)
		tmp = Float64(x + y);
	elseif (t <= 1.95)
		tmp = Float64(x + Float64(z * 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 (t <= -1.32e+70)
		tmp = x + y;
	elseif (t <= 1.95)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.32e+70], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.95], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3199999999999999e70 or 1.94999999999999996 < t

   1. Initial program 69.6%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around inf 87.1%

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

      1. +-commutative 87.1%

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

   6. Simplified 87.1%

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

   if -1.3199999999999999e70 < t < 1.94999999999999996

   1. Initial program 96.6%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 85.0%

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

      1. associate-*l/ 86.4%

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

      2. *-commutative 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in a around inf 76.3%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.95:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+68}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.35:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e+68) (+ x y) (if (<= t 1.35) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+68) {
		tmp = x + y;
	} else if (t <= 1.35) {
		tmp = x + (y * (z / 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 (t <= (-4.5d+68)) then
        tmp = x + y
    else if (t <= 1.35d0) then
        tmp = x + (y * (z / 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 (t <= -4.5e+68) {
		tmp = x + y;
	} else if (t <= 1.35) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.5e+68:
		tmp = x + y
	elif t <= 1.35:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e+68)
		tmp = Float64(x + y);
	elseif (t <= 1.35)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.5e+68)
		tmp = x + y;
	elseif (t <= 1.35)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e+68], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.35], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5000000000000003e68 or 1.3500000000000001 < t

   1. Initial program 69.6%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around inf 87.1%

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

      1. +-commutative 87.1%

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

   6. Simplified 87.1%

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

   if -4.5000000000000003e68 < t < 1.3500000000000001

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

      2. associate-/l* 97.2%

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

      3. associate-/r/ 98.6%

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

   3. Applied egg-rr 98.6%

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

   4. Taylor expanded in t around 0 77.0%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+68}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.35:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

   1. associate-*l/ 96.8%

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

3. Simplified 96.8%

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

4. Final simplification 96.8%

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

Alternative 8: 61.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+186}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+250}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e+186)
   (* y (/ z a))
   (if (<= z 4.2e+250) (+ x y) (* z (/ (- y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+186) {
		tmp = y * (z / a);
	} else if (z <= 4.2e+250) {
		tmp = x + y;
	} else {
		tmp = z * (-y / 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 <= (-3d+186)) then
        tmp = y * (z / a)
    else if (z <= 4.2d+250) then
        tmp = x + y
    else
        tmp = z * (-y / 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 <= -3e+186) {
		tmp = y * (z / a);
	} else if (z <= 4.2e+250) {
		tmp = x + y;
	} else {
		tmp = z * (-y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e+186:
		tmp = y * (z / a)
	elif z <= 4.2e+250:
		tmp = x + y
	else:
		tmp = z * (-y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e+186)
		tmp = Float64(y * Float64(z / a));
	elseif (z <= 4.2e+250)
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(Float64(-y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e+186)
		tmp = y * (z / a);
	elseif (z <= 4.2e+250)
		tmp = x + y;
	else
		tmp = z * (-y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e+186], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+250], N[(x + y), $MachinePrecision], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999982e186

   1. Initial program 87.6%

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

      1. associate-*l/ 87.7%

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

   3. Simplified 87.7%

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

      1. associate-*l/ 87.6%

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

      2. frac-2neg 87.6%

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

      3. distribute-frac-neg 87.6%

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

      4. remove-double-neg 87.6%

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

      5. distribute-frac-neg 87.6%

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

      6. frac-2neg 87.6%

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

      7. associate-*l/ 87.7%

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

      8. unsub-neg 87.7%

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

      9. associate-*l/ 87.6%

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

      10. frac-2neg 87.6%

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

      11. distribute-frac-neg 87.6%

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

      12. remove-double-neg 87.6%

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

      13. associate-/l* 99.9%

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

      14. neg-sub0 99.9%

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

      15. sub-neg 99.9%

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

      16. +-commutative 99.9%

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

      17. associate--r+ 99.9%

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

      18. neg-sub0 99.9%

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

      19. remove-double-neg 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-*r/ 62.3%

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

      4. sub0-neg 62.3%

         \[\leadsto \color{blue}{0 - z \cdot \frac{y}{t - a}} \]

      5. cancel-sign-sub-inv 62.3%

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

      6. +-lft-identity 62.3%

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

   8. Simplified 62.3%

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

   9. Taylor expanded in z around 0 62.2%

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

       1. mul-1-neg 62.2%

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

       2. distribute-frac-neg 62.2%

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

       3. distribute-rgt-neg-out 62.2%

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

       4. associate-*r/ 70.5%

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

   11. Simplified 70.5%

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

   12. Taylor expanded in t around 0 66.5%

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

   if -2.99999999999999982e186 < z < 4.2000000000000003e250

   1. Initial program 84.7%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in t around inf 70.2%

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

      1. +-commutative 70.2%

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

   6. Simplified 70.2%

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

   if 4.2000000000000003e250 < z

   1. Initial program 68.4%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*l/ 68.4%

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

      2. frac-2neg 68.4%

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

      3. distribute-frac-neg 68.4%

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

      4. remove-double-neg 68.4%

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

      5. distribute-frac-neg 68.4%

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

      6. frac-2neg 68.4%

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

      7. associate-*l/ 99.7%

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

      8. unsub-neg 99.7%

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

      9. associate-*l/ 68.4%

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

      10. frac-2neg 68.4%

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

      11. distribute-frac-neg 68.4%

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

      12. remove-double-neg 68.4%

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

      13. associate-/l* 78.8%

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

      14. neg-sub0 78.8%

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

      15. sub-neg 78.8%

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

      16. +-commutative 78.8%

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

      17. associate--r+ 78.8%

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

      18. neg-sub0 78.8%

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

      19. remove-double-neg 78.8%

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

   5. Applied egg-rr 78.8%

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

   6. Taylor expanded in z around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. *-commutative 57.5%

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

      3. associate-*r/ 84.7%

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

      4. sub0-neg 84.7%

         \[\leadsto \color{blue}{0 - z \cdot \frac{y}{t - a}} \]

      5. cancel-sign-sub-inv 84.7%

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

      6. +-lft-identity 84.7%

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

   8. Simplified 84.7%

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

   9. Taylor expanded in t around inf 74.9%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+186}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+250}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \end{array} \]

Alternative 9: 60.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+186}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+186) (* y (/ z a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+186) {
		tmp = y * (z / 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 <= (-2.7d+186)) then
        tmp = y * (z / 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 <= -2.7e+186) {
		tmp = y * (z / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+186:
		tmp = y * (z / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+186)
		tmp = Float64(y * Float64(z / 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 <= -2.7e+186)
		tmp = y * (z / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+186], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e186

   1. Initial program 87.6%

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

      1. associate-*l/ 87.7%

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

   3. Simplified 87.7%

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

      1. associate-*l/ 87.6%

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

      2. frac-2neg 87.6%

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

      3. distribute-frac-neg 87.6%

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

      4. remove-double-neg 87.6%

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

      5. distribute-frac-neg 87.6%

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

      6. frac-2neg 87.6%

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

      7. associate-*l/ 87.7%

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

      8. unsub-neg 87.7%

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

      9. associate-*l/ 87.6%

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

      10. frac-2neg 87.6%

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

      11. distribute-frac-neg 87.6%

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

      12. remove-double-neg 87.6%

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

      13. associate-/l* 99.9%

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

      14. neg-sub0 99.9%

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

      15. sub-neg 99.9%

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

      16. +-commutative 99.9%

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

      17. associate--r+ 99.9%

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

      18. neg-sub0 99.9%

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

      19. remove-double-neg 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-*r/ 62.3%

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

      4. sub0-neg 62.3%

         \[\leadsto \color{blue}{0 - z \cdot \frac{y}{t - a}} \]

      5. cancel-sign-sub-inv 62.3%

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

      6. +-lft-identity 62.3%

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

   8. Simplified 62.3%

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

   9. Taylor expanded in z around 0 62.2%

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

       1. mul-1-neg 62.2%

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

       2. distribute-frac-neg 62.2%

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

       3. distribute-rgt-neg-out 62.2%

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

       4. associate-*r/ 70.5%

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

   11. Simplified 70.5%

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

   12. Taylor expanded in t around 0 66.5%

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

   if -2.6999999999999999e186 < z

   1. Initial program 84.1%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in t around inf 68.1%

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

      1. +-commutative 68.1%

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

   6. Simplified 68.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+186}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 62.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.02 \cdot 10^{+192}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 1.02e+192) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 1.02e+192) {
		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+192) 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+192) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 1.02e+192:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 1.02e+192)
		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+192)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 1.02e+192], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 1.01999999999999996e192

   1. Initial program 83.8%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around inf 65.3%

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

      1. +-commutative 65.3%

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

   6. Simplified 65.3%

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

   if 1.01999999999999996e192 < a

   1. Initial program 91.0%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around inf 87.0%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.02 \cdot 10^{+192}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 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 84.4%

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

   1. associate-*l/ 96.8%

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

3. Simplified 96.8%

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

4. Taylor expanded in x around inf 51.0%

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

5. Final simplification 51.0%

   \[\leadsto x \]

Developer target: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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