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

Percentage Accurate: 98.1% → 98.1%

Time: 9.4s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+138}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{+72}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 10^{+43}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e+138)
   (+ x y)
   (if (<= t -3.1e+72)
     (- x (* y (/ z t)))
     (if (<= t 1e+43) (+ x (/ y (/ a z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+138) {
		tmp = x + y;
	} else if (t <= -3.1e+72) {
		tmp = x - (y * (z / t));
	} else if (t <= 1e+43) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7d+138)) then
        tmp = x + y
    else if (t <= (-3.1d+72)) then
        tmp = x - (y * (z / t))
    else if (t <= 1d+43) then
        tmp = x + (y / (a / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+138) {
		tmp = x + y;
	} else if (t <= -3.1e+72) {
		tmp = x - (y * (z / t));
	} else if (t <= 1e+43) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7e+138:
		tmp = x + y
	elif t <= -3.1e+72:
		tmp = x - (y * (z / t))
	elif t <= 1e+43:
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e+138)
		tmp = Float64(x + y);
	elseif (t <= -3.1e+72)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 1e+43)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7e+138)
		tmp = x + y;
	elseif (t <= -3.1e+72)
		tmp = x - (y * (z / t));
	elseif (t <= 1e+43)
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e+138], N[(x + y), $MachinePrecision], If[LessEqual[t, -3.1e+72], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+43], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.9999999999999996e138 or 1.00000000000000001e43 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.1%

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

   if -6.9999999999999996e138 < t < -3.09999999999999988e72

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf 93.3%

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

   4. Taylor expanded in x around 0 93.5%

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

      1. +-commutative 93.5%

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

      2. *-commutative 93.5%

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

      3. associate-/l* 87.2%

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

   6. Simplified 87.2%

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

   7. Taylor expanded in a around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. associate-*r/ 86.8%

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

      3. sub-neg 86.8%

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

   9. Simplified 86.8%

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

   if -3.09999999999999988e72 < t < 1.00000000000000001e43

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 71.4%

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

      1. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+138}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{+72}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 10^{+43}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.25 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.65e+136)
   (+ x y)
   (if (<= t -3.25e+72)
     (- x (/ y (/ t z)))
     (if (<= t 3.2e+42) (+ x (/ y (/ a z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.65e+136) {
		tmp = x + y;
	} else if (t <= -3.25e+72) {
		tmp = x - (y / (t / z));
	} else if (t <= 3.2e+42) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.65d+136)) then
        tmp = x + y
    else if (t <= (-3.25d+72)) then
        tmp = x - (y / (t / z))
    else if (t <= 3.2d+42) then
        tmp = x + (y / (a / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.65e+136) {
		tmp = x + y;
	} else if (t <= -3.25e+72) {
		tmp = x - (y / (t / z));
	} else if (t <= 3.2e+42) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.65e+136:
		tmp = x + y
	elif t <= -3.25e+72:
		tmp = x - (y / (t / z))
	elif t <= 3.2e+42:
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.65e+136)
		tmp = Float64(x + y);
	elseif (t <= -3.25e+72)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	elseif (t <= 3.2e+42)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.65e+136)
		tmp = x + y;
	elseif (t <= -3.25e+72)
		tmp = x - (y / (t / z));
	elseif (t <= 3.2e+42)
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.65e+136], N[(x + y), $MachinePrecision], If[LessEqual[t, -3.25e+72], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+42], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.64999999999999996e136 or 3.20000000000000002e42 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.1%

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

   if -1.64999999999999996e136 < t < -3.2500000000000001e72

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf 93.5%

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

      1. associate-/l* 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in a around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. unsub-neg 87.0%

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

      3. associate-/l* 87.1%

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

   8. Simplified 87.1%

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

   if -3.2500000000000001e72 < t < 3.20000000000000002e42

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 71.4%

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

      1. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.25 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+137} \lor \neg \left(t \leq 5.6 \cdot 10^{+63}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.5e+137) (not (<= t 5.6e+63)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.5e+137) || !(t <= 5.6e+63)) {
		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 <= (-6.5d+137)) .or. (.not. (t <= 5.6d+63))) 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 <= -6.5e+137) || !(t <= 5.6e+63)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.5e+137) or not (t <= 5.6e+63):
		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 <= -6.5e+137) || !(t <= 5.6e+63))
		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 <= -6.5e+137) || ~((t <= 5.6e+63)))
		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, -6.5e+137], N[Not[LessEqual[t, 5.6e+63]], $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 < -6.5000000000000002e137 or 5.59999999999999974e63 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 83.7%

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

   if -6.5000000000000002e137 < t < 5.59999999999999974e63

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 87.6%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+137} \lor \neg \left(t \leq 5.6 \cdot 10^{+63}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-49} \lor \neg \left(z \leq 1.05 \cdot 10^{+56}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e-49) (not (<= z 1.05e+56)))
   (+ x (* y (/ z (- a t))))
   (+ x (* y (/ t (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e-49) || !(z <= 1.05e+56)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (y * (t / (t - 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 ((z <= (-1.2d-49)) .or. (.not. (z <= 1.05d+56))) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x + (y * (t / (t - 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 ((z <= -1.2e-49) || !(z <= 1.05e+56)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e-49) or not (z <= 1.05e+56):
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + (y * (t / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e-49) || !(z <= 1.05e+56))
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.2e-49) || ~((z <= 1.05e+56)))
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + (y * (t / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e-49], N[Not[LessEqual[z, 1.05e+56]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999996e-49 or 1.05000000000000009e56 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 90.8%

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

   if -1.19999999999999996e-49 < z < 1.05000000000000009e56

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 93.7%

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

      1. neg-mul-1 93.7%

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

      2. distribute-neg-frac 93.7%

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

   5. Simplified 93.7%

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

      1. *-commutative 93.7%

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

      2. div-inv 93.7%

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

      3. associate-*l* 87.3%

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

      4. add-sqr-sqrt 37.3%

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

      5. sqrt-unprod 54.3%

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

      6. sqr-neg 54.3%

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

      7. sqrt-unprod 34.7%

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

      8. add-sqr-sqrt 61.5%

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

      9. associate-/r/ 61.5%

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

      10. div-inv 61.5%

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

      11. frac-2neg 61.5%

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

      12. add-sqr-sqrt 26.8%

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

      13. sqrt-unprod 58.1%

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

      14. sqr-neg 58.1%

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

      15. sqrt-unprod 49.8%

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

      16. add-sqr-sqrt 87.6%

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

      17. distribute-neg-frac 87.6%

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

      18. sub-neg 87.6%

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

      19. distribute-neg-in 87.6%

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

      20. remove-double-neg 87.6%

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

   7. Applied egg-rr 87.6%

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

      1. associate-/r/ 93.7%

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

      2. +-commutative 93.7%

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

      3. unsub-neg 93.7%

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

   9. Simplified 93.7%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-49} \lor \neg \left(z \leq 1.05 \cdot 10^{+56}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+86} \lor \neg \left(t \leq 2.7 \cdot 10^{+42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7e+86) (not (<= t 2.7e+42))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7e+86) || !(t <= 2.7e+42)) {
		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 <= (-7d+86)) .or. (.not. (t <= 2.7d+42))) 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 <= -7e+86) || !(t <= 2.7e+42)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7e+86) or not (t <= 2.7e+42):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7e+86) || !(t <= 2.7e+42))
		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 <= -7e+86) || ~((t <= 2.7e+42)))
		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, -7e+86], N[Not[LessEqual[t, 2.7e+42]], $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 < -7.00000000000000038e86 or 2.7000000000000001e42 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 79.2%

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

   if -7.00000000000000038e86 < t < 2.7000000000000001e42

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 77.1%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+86} \lor \neg \left(t \leq 2.7 \cdot 10^{+42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+86} \lor \neg \left(t \leq 3.4 \cdot 10^{+43}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.7e+86) (not (<= t 3.4e+43))) (+ x y) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.7e+86) || !(t <= 3.4e+43)) {
		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 <= (-1.7d+86)) .or. (.not. (t <= 3.4d+43))) 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 <= -1.7e+86) || !(t <= 3.4e+43)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.7e+86) or not (t <= 3.4e+43):
		tmp = x + y
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.7e+86) || !(t <= 3.4e+43))
		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 <= -1.7e+86) || ~((t <= 3.4e+43)))
		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, -1.7e+86], N[Not[LessEqual[t, 3.4e+43]], $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 < -1.6999999999999999e86 or 3.40000000000000012e43 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 79.2%

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

   if -1.6999999999999999e86 < t < 3.40000000000000012e43

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 71.0%

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

      1. associate-/l* 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+86} \lor \neg \left(t \leq 3.4 \cdot 10^{+43}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+96}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.45e+107) x (if (<= a 7.6e+96) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.45e+107) {
		tmp = x;
	} else if (a <= 7.6e+96) {
		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 <= (-1.45d+107)) then
        tmp = x
    else if (a <= 7.6d+96) 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 <= -1.45e+107) {
		tmp = x;
	} else if (a <= 7.6e+96) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.45e+107:
		tmp = x
	elif a <= 7.6e+96:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.45e+107)
		tmp = x;
	elseif (a <= 7.6e+96)
		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 <= -1.45e+107)
		tmp = x;
	elseif (a <= 7.6e+96)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.45e+107], x, If[LessEqual[a, 7.6e+96], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.44999999999999994e107 or 7.6000000000000003e96 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 79.4%

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

      1. associate-/l* 90.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in x around inf 71.4%

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

   if -1.44999999999999994e107 < a < 7.6000000000000003e96

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 66.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+96}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.8% 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 99.9%

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

3. Taylor expanded in z around inf 72.6%

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

   1. associate-/l* 79.1%

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

5. Simplified 79.1%

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

6. Taylor expanded in x around inf 53.1%

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

7. Final simplification 53.1%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024021 
(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)))))