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

Percentage Accurate: 98.0% → 98.0%

Time: 8.7s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

2. Final simplification 98.1%

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

Alternative 2: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+95}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-114}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.5e+95)
   (+ x y)
   (if (<= t -1.4e-114)
     (- x (* y (/ z t)))
     (if (<= t 3.5e+66) (+ x (/ (* y z) a)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.5e+95) {
		tmp = x + y;
	} else if (t <= -1.4e-114) {
		tmp = x - (y * (z / t));
	} else if (t <= 3.5e+66) {
		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 <= (-8.5d+95)) then
        tmp = x + y
    else if (t <= (-1.4d-114)) then
        tmp = x - (y * (z / t))
    else if (t <= 3.5d+66) 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 <= -8.5e+95) {
		tmp = x + y;
	} else if (t <= -1.4e-114) {
		tmp = x - (y * (z / t));
	} else if (t <= 3.5e+66) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.5e+95:
		tmp = x + y
	elif t <= -1.4e-114:
		tmp = x - (y * (z / t))
	elif t <= 3.5e+66:
		tmp = x + ((y * z) / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.5e+95)
		tmp = Float64(x + y);
	elseif (t <= -1.4e-114)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 3.5e+66)
		tmp = Float64(x + Float64(Float64(y * 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 <= -8.5e+95)
		tmp = x + y;
	elseif (t <= -1.4e-114)
		tmp = x - (y * (z / t));
	elseif (t <= 3.5e+66)
		tmp = x + ((y * z) / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.5e+95], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.4e-114], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+66], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.5000000000000002e95 or 3.4999999999999997e66 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 82.9%

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

   if -8.5000000000000002e95 < t < -1.4000000000000001e-114

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 91.1%

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

   3. Taylor expanded in a around 0 72.1%

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

      1. mul-1-neg 72.1%

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

      2. associate-/l* 70.1%

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

      3. unsub-neg 70.1%

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

      4. associate-/l* 72.1%

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

      5. associate-*r/ 70.1%

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

   5. Simplified 70.1%

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

   if -1.4000000000000001e-114 < t < 3.4999999999999997e66

   1. Initial program 96.4%

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

   2. Taylor expanded in t around 0 79.2%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+95}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-114}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+96}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-115}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.02e+96)
   (+ x y)
   (if (<= t -6.2e-115)
     (- x (/ (* y z) t))
     (if (<= t 3.5e+66) (+ x (/ (* y z) a)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e+96) {
		tmp = x + y;
	} else if (t <= -6.2e-115) {
		tmp = x - ((y * z) / t);
	} else if (t <= 3.5e+66) {
		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 <= (-1.02d+96)) then
        tmp = x + y
    else if (t <= (-6.2d-115)) then
        tmp = x - ((y * z) / t)
    else if (t <= 3.5d+66) 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 <= -1.02e+96) {
		tmp = x + y;
	} else if (t <= -6.2e-115) {
		tmp = x - ((y * z) / t);
	} else if (t <= 3.5e+66) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.02e+96:
		tmp = x + y
	elif t <= -6.2e-115:
		tmp = x - ((y * z) / t)
	elif t <= 3.5e+66:
		tmp = x + ((y * z) / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.02e+96)
		tmp = Float64(x + y);
	elseif (t <= -6.2e-115)
		tmp = Float64(x - Float64(Float64(y * z) / t));
	elseif (t <= 3.5e+66)
		tmp = Float64(x + Float64(Float64(y * 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 <= -1.02e+96)
		tmp = x + y;
	elseif (t <= -6.2e-115)
		tmp = x - ((y * z) / t);
	elseif (t <= 3.5e+66)
		tmp = x + ((y * z) / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.02e+96], N[(x + y), $MachinePrecision], If[LessEqual[t, -6.2e-115], N[(x - N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+66], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02000000000000001e96 or 3.4999999999999997e66 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 82.9%

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

   if -1.02000000000000001e96 < t < -6.20000000000000013e-115

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 87.1%

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

      1. associate-/l* 91.2%

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

   4. Simplified 91.2%

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

   5. Taylor expanded in a around 0 72.1%

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

      1. +-commutative 72.1%

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

      2. associate-*r/ 72.1%

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

      3. neg-mul-1 72.1%

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

      4. distribute-rgt-neg-in 72.1%

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

   7. Simplified 72.1%

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

   if -6.20000000000000013e-115 < t < 3.4999999999999997e66

   1. Initial program 96.4%

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

   2. Taylor expanded in t around 0 79.2%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+96}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-115}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+96} \lor \neg \left(t \leq 2.8 \cdot 10^{+201}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5e+96) (not (<= t 2.8e+201)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e+96) || !(t <= 2.8e+201)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5d+96)) .or. (.not. (t <= 2.8d+201))) then
        tmp = x + y
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e+96) || !(t <= 2.8e+201)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5e+96) or not (t <= 2.8e+201):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5e+96) || !(t <= 2.8e+201))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5e+96) || ~((t <= 2.8e+201)))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5e+96], N[Not[LessEqual[t, 2.8e+201]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.0000000000000004e96 or 2.80000000000000005e201 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 86.3%

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

   if -5.0000000000000004e96 < t < 2.80000000000000005e201

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf 88.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+96} \lor \neg \left(t \leq 2.8 \cdot 10^{+201}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 5: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+95} \lor \neg \left(t \leq 4.8 \cdot 10^{+82}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+95) (not (<= t 4.8e+82)))
   (+ x (* y (/ t (- t a))))
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+95) || !(t <= 4.8e+82)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.4d+95)) .or. (.not. (t <= 4.8d+82))) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+95) || !(t <= 4.8e+82)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e+95) or not (t <= 4.8e+82):
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+95) || !(t <= 4.8e+82))
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.4e+95) || ~((t <= 4.8e+82)))
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+95], N[Not[LessEqual[t, 4.8e+82]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4e95 or 4.79999999999999996e82 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 89.4%

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

      1. neg-mul-1 89.4%

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

      2. distribute-neg-frac 89.4%

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

   4. Simplified 89.4%

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

      1. *-commutative 89.4%

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

      2. div-inv 89.4%

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

      3. associate-*l* 84.4%

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

      4. add-sqr-sqrt 44.8%

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

      5. sqrt-unprod 26.3%

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

      6. sqr-neg 26.3%

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

      7. sqrt-unprod 27.3%

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

      8. add-sqr-sqrt 54.9%

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

      9. associate-/r/ 54.9%

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

      10. div-inv 54.9%

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

      11. frac-2neg 54.9%

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

      12. add-sqr-sqrt 27.6%

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

      13. sqrt-unprod 25.5%

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

      14. sqr-neg 25.5%

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

      15. sqrt-unprod 39.3%

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

      16. add-sqr-sqrt 84.4%

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

      17. distribute-neg-frac 84.4%

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

      18. sub-neg 84.4%

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

      19. distribute-neg-in 84.4%

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

      20. remove-double-neg 84.4%

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

   6. Applied egg-rr 84.4%

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

      1. associate-/r/ 89.4%

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

      2. +-commutative 89.4%

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

      3. unsub-neg 89.4%

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

   8. Simplified 89.4%

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

   if -2.4e95 < t < 4.79999999999999996e82

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf 90.4%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+95} \lor \neg \left(t \leq 4.8 \cdot 10^{+82}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 6: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+95} \lor \neg \left(t \leq 5.4 \cdot 10^{+81}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.7e+95) (not (<= t 5.4e+81)))
   (+ x (* y (/ t (- t a))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.7e+95) || !(t <= 5.4e+81)) {
		tmp = x + (y * (t / (t - a)));
	} 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 ((t <= (-2.7d+95)) .or. (.not. (t <= 5.4d+81))) then
        tmp = x + (y * (t / (t - a)))
    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 ((t <= -2.7e+95) || !(t <= 5.4e+81)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.7e+95) or not (t <= 5.4e+81):
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.7e+95) || !(t <= 5.4e+81))
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	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 ((t <= -2.7e+95) || ~((t <= 5.4e+81)))
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.7e+95], N[Not[LessEqual[t, 5.4e+81]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7e95 or 5.3999999999999999e81 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 89.4%

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

      1. neg-mul-1 89.4%

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

      2. distribute-neg-frac 89.4%

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

   4. Simplified 89.4%

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

      1. *-commutative 89.4%

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

      2. div-inv 89.4%

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

      3. associate-*l* 84.4%

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

      4. add-sqr-sqrt 44.8%

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

      5. sqrt-unprod 26.3%

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

      6. sqr-neg 26.3%

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

      7. sqrt-unprod 27.3%

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

      8. add-sqr-sqrt 54.9%

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

      9. associate-/r/ 54.9%

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

      10. div-inv 54.9%

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

      11. frac-2neg 54.9%

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

      12. add-sqr-sqrt 27.6%

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

      13. sqrt-unprod 25.5%

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

      14. sqr-neg 25.5%

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

      15. sqrt-unprod 39.3%

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

      16. add-sqr-sqrt 84.4%

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

      17. distribute-neg-frac 84.4%

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

      18. sub-neg 84.4%

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

      19. distribute-neg-in 84.4%

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

      20. remove-double-neg 84.4%

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

   6. Applied egg-rr 84.4%

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

      1. associate-/r/ 89.4%

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

      2. +-commutative 89.4%

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

      3. unsub-neg 89.4%

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

   8. Simplified 89.4%

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

   if -2.7e95 < t < 5.3999999999999999e81

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf 89.5%

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

      1. associate-/l* 91.0%

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

   4. Simplified 91.0%

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

      1. associate-/r/ 90.8%

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

   6. Applied egg-rr 90.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+95} \lor \neg \left(t \leq 5.4 \cdot 10^{+81}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 7: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+95} \lor \neg \left(t \leq 3.3 \cdot 10^{+81}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+95) (not (<= t 3.3e+81)))
   (+ x (* y (/ t (- t a))))
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+95) || !(t <= 3.3e+81)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.05d+95)) .or. (.not. (t <= 3.3d+81))) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+95) || !(t <= 3.3e+81)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+95) or not (t <= 3.3e+81):
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+95) || !(t <= 3.3e+81))
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e+95) || ~((t <= 3.3e+81)))
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+95], N[Not[LessEqual[t, 3.3e+81]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e95 or 3.3e81 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 89.4%

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

      1. neg-mul-1 89.4%

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

      2. distribute-neg-frac 89.4%

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

   4. Simplified 89.4%

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

      1. *-commutative 89.4%

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

      2. div-inv 89.4%

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

      3. associate-*l* 84.4%

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

      4. add-sqr-sqrt 44.8%

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

      5. sqrt-unprod 26.3%

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

      6. sqr-neg 26.3%

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

      7. sqrt-unprod 27.3%

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

      8. add-sqr-sqrt 54.9%

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

      9. associate-/r/ 54.9%

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

      10. div-inv 54.9%

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

      11. frac-2neg 54.9%

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

      12. add-sqr-sqrt 27.6%

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

      13. sqrt-unprod 25.5%

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

      14. sqr-neg 25.5%

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

      15. sqrt-unprod 39.3%

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

      16. add-sqr-sqrt 84.4%

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

      17. distribute-neg-frac 84.4%

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

      18. sub-neg 84.4%

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

      19. distribute-neg-in 84.4%

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

      20. remove-double-neg 84.4%

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

   6. Applied egg-rr 84.4%

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

      1. associate-/r/ 89.4%

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

      2. +-commutative 89.4%

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

      3. unsub-neg 89.4%

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

   8. Simplified 89.4%

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

   if -1.05e95 < t < 3.3e81

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf 89.5%

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

      1. associate-/l* 91.0%

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

   4. Simplified 91.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+95} \lor \neg \left(t \leq 3.3 \cdot 10^{+81}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 8: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+95} \lor \neg \left(t \leq 3.5 \cdot 10^{+101}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.15e+95) (not (<= t 3.5e+101)))
   (+ x (* y (/ (- t z) t)))
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.15e+95) || !(t <= 3.5e+101)) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.15d+95)) .or. (.not. (t <= 3.5d+101))) then
        tmp = x + (y * ((t - z) / t))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.15e+95) || !(t <= 3.5e+101)) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.15e+95) or not (t <= 3.5e+101):
		tmp = x + (y * ((t - z) / t))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.15e+95) || !(t <= 3.5e+101))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.15e+95) || ~((t <= 3.5e+101)))
		tmp = x + (y * ((t - z) / t));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.15e+95], N[Not[LessEqual[t, 3.5e+101]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.15e95 or 3.50000000000000023e101 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 95.1%

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

      1. associate-*r/ 95.1%

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

      2. neg-mul-1 95.1%

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

   4. Simplified 95.1%

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

   if -2.15e95 < t < 3.50000000000000023e101

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 88.6%

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

      1. associate-/l* 90.1%

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

   4. Simplified 90.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+95} \lor \neg \left(t \leq 3.5 \cdot 10^{+101}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 9: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+56} \lor \neg \left(t \leq 1.42 \cdot 10^{+67}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+56) (not (<= t 1.42e+67))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+56) || !(t <= 1.42e+67)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.05d+56)) .or. (.not. (t <= 1.42d+67))) then
        tmp = x + y
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+56) || !(t <= 1.42e+67)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+56) or not (t <= 1.42e+67):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+56) || !(t <= 1.42e+67))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e+56) || ~((t <= 1.42e+67)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+56], N[Not[LessEqual[t, 1.42e+67]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05000000000000009e56 or 1.41999999999999992e67 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 81.6%

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

   if -1.05000000000000009e56 < t < 1.41999999999999992e67

   1. Initial program 96.6%

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

   2. Taylor expanded in t around 0 73.1%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+56} \lor \neg \left(t \leq 1.42 \cdot 10^{+67}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 10: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+56} \lor \neg \left(t \leq 3.5 \cdot 10^{+66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.65e+56) (not (<= t 3.5e+66))) (+ x y) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.65e+56) || !(t <= 3.5e+66)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.65d+56)) .or. (.not. (t <= 3.5d+66))) then
        tmp = x + y
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.65e+56) || !(t <= 3.5e+66)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.65e+56) or not (t <= 3.5e+66):
		tmp = x + y
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.65e+56) || !(t <= 3.5e+66))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.65e+56) || ~((t <= 3.5e+66)))
		tmp = x + y;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.65e+56], N[Not[LessEqual[t, 3.5e+66]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65000000000000001e56 or 3.4999999999999997e66 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 81.6%

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

   if -1.65000000000000001e56 < t < 3.4999999999999997e66

   1. Initial program 96.6%

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

   2. Taylor expanded in t around 0 73.6%

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

      1. associate-/l* 73.4%

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

   4. Simplified 73.4%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+56} \lor \neg \left(t \leq 3.5 \cdot 10^{+66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 11: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+55} \lor \neg \left(t \leq 3.5 \cdot 10^{+66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.8e+55) (not (<= t 3.5e+66))) (+ x y) (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.8e+55) || !(t <= 3.5e+66)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8.8d+55)) .or. (.not. (t <= 3.5d+66))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.8e+55) || !(t <= 3.5e+66)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.8e+55) or not (t <= 3.5e+66):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.8e+55) || !(t <= 3.5e+66))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.8e+55) || ~((t <= 3.5e+66)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.8e+55], N[Not[LessEqual[t, 3.5e+66]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.80000000000000042e55 or 3.4999999999999997e66 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 81.6%

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

   if -8.80000000000000042e55 < t < 3.4999999999999997e66

   1. Initial program 96.6%

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

   2. Taylor expanded in t around 0 73.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+55} \lor \neg \left(t \leq 3.5 \cdot 10^{+66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]

Alternative 12: 61.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -4.7e+119) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.7e+119) {
		tmp = x;
	} 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 (a <= (-4.7d+119)) then
        tmp = x
    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 (a <= -4.7e+119) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.7e+119:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.7e+119)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.7e+119)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.7e+119], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.70000000000000008e119

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 81.7%

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

   3. Taylor expanded in x around inf 74.3%

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

   if -4.70000000000000008e119 < a

   1. Initial program 97.8%

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

   2. Taylor expanded in t around inf 61.2%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

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 98.1%

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

2. Taylor expanded in t around 0 61.0%

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

3. Taylor expanded in x around inf 53.1%

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

4. Final simplification 53.1%

   \[\leadsto x \]

Developer target: 99.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023318 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

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

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