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

Percentage Accurate: 98.3% → 98.3%

Time: 8.4s

Alternatives: 12

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: 98.3% 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: 98.3% 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 99.0%

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

2. Final simplification 99.0%

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

Alternative 2: 78.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+79}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-10}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 14.2:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.5e+79)
   (+ x y)
   (if (<= t -4.3e-10)
     (- x (* z (/ y t)))
     (if (<= t 14.2) (+ x (* y (/ (- z t) a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e+79) {
		tmp = x + y;
	} else if (t <= -4.3e-10) {
		tmp = x - (z * (y / t));
	} else if (t <= 14.2) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.5d+79)) then
        tmp = x + y
    else if (t <= (-4.3d-10)) then
        tmp = x - (z * (y / t))
    else if (t <= 14.2d0) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e+79) {
		tmp = x + y;
	} else if (t <= -4.3e-10) {
		tmp = x - (z * (y / t));
	} else if (t <= 14.2) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.5e+79:
		tmp = x + y
	elif t <= -4.3e-10:
		tmp = x - (z * (y / t))
	elif t <= 14.2:
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.5e+79)
		tmp = Float64(x + y);
	elseif (t <= -4.3e-10)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	elseif (t <= 14.2)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.5e+79)
		tmp = x + y;
	elseif (t <= -4.3e-10)
		tmp = x - (z * (y / t));
	elseif (t <= 14.2)
		tmp = x + (y * ((z - t) / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.5e+79], N[(x + y), $MachinePrecision], If[LessEqual[t, -4.3e-10], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 14.2], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.50000000000000007e79 or 14.199999999999999 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 78.0%

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

   if -5.50000000000000007e79 < t < -4.30000000000000014e-10

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 73.3%

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

      1. associate-/l* 78.4%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in a around 0 67.3%

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

      1. +-commutative 67.3%

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

      2. mul-1-neg 67.3%

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

      3. unsub-neg 67.3%

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

      4. associate-/l* 72.3%

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

   7. Simplified 72.3%

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

      1. associate-/r/ 72.5%

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

   9. Applied egg-rr 72.5%

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

   if -4.30000000000000014e-10 < t < 14.199999999999999

   1. Initial program 98.0%

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

   2. Taylor expanded in a around inf 79.8%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+79}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-10}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 14.2:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+80}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-61}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 0.041:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e+80)
   (+ x y)
   (if (<= t -9.6e-61)
     (- x (* y (/ z t)))
     (if (<= t 0.041) (+ x (* y (/ z a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e+80) {
		tmp = x + y;
	} else if (t <= -9.6e-61) {
		tmp = x - (y * (z / t));
	} else if (t <= 0.041) {
		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 <= (-1.8d+80)) then
        tmp = x + y
    else if (t <= (-9.6d-61)) then
        tmp = x - (y * (z / t))
    else if (t <= 0.041d0) 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 <= -1.8e+80) {
		tmp = x + y;
	} else if (t <= -9.6e-61) {
		tmp = x - (y * (z / t));
	} else if (t <= 0.041) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.8e+80:
		tmp = x + y
	elif t <= -9.6e-61:
		tmp = x - (y * (z / t))
	elif t <= 0.041:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.8e+80)
		tmp = Float64(x + y);
	elseif (t <= -9.6e-61)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 0.041)
		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 <= -1.8e+80)
		tmp = x + y;
	elseif (t <= -9.6e-61)
		tmp = x - (y * (z / t));
	elseif (t <= 0.041)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e+80], N[(x + y), $MachinePrecision], If[LessEqual[t, -9.6e-61], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.041], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.79999999999999997e80 or 0.0410000000000000017 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 78.0%

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

   if -1.79999999999999997e80 < t < -9.6000000000000004e-61

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 71.6%

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

      1. associate-/l* 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in a around 0 62.2%

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

      1. +-commutative 62.2%

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

      2. mul-1-neg 62.2%

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

      3. unsub-neg 62.2%

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

      4. associate-/l* 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in y around 0 62.2%

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

      1. associate-/l* 65.0%

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

      2. *-rgt-identity 65.0%

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

      3. associate-*r/ 65.0%

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

      4. associate-/r/ 64.9%

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

      5. associate-*l/ 65.0%

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

      6. *-lft-identity 65.0%

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

   10. Simplified 65.0%

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

   if -9.6000000000000004e-61 < t < 0.0410000000000000017

   1. Initial program 97.8%

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

   2. Taylor expanded in t around 0 81.8%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+80}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-61}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 0.041:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+79}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-61}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 450:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.1e+79)
   (+ x y)
   (if (<= t -2.95e-61)
     (- x (* z (/ y t)))
     (if (<= t 450.0) (+ x (* y (/ z a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e+79) {
		tmp = x + y;
	} else if (t <= -2.95e-61) {
		tmp = x - (z * (y / t));
	} else if (t <= 450.0) {
		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 <= (-3.1d+79)) then
        tmp = x + y
    else if (t <= (-2.95d-61)) then
        tmp = x - (z * (y / t))
    else if (t <= 450.0d0) 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 <= -3.1e+79) {
		tmp = x + y;
	} else if (t <= -2.95e-61) {
		tmp = x - (z * (y / t));
	} else if (t <= 450.0) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.1e+79:
		tmp = x + y
	elif t <= -2.95e-61:
		tmp = x - (z * (y / t))
	elif t <= 450.0:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.1e+79)
		tmp = Float64(x + y);
	elseif (t <= -2.95e-61)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	elseif (t <= 450.0)
		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 <= -3.1e+79)
		tmp = x + y;
	elseif (t <= -2.95e-61)
		tmp = x - (z * (y / t));
	elseif (t <= 450.0)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.1e+79], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.95e-61], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 450.0], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.0999999999999999e79 or 450 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 78.0%

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

   if -3.0999999999999999e79 < t < -2.94999999999999986e-61

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 71.6%

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

      1. associate-/l* 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in a around 0 62.2%

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

      1. +-commutative 62.2%

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

      2. mul-1-neg 62.2%

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

      3. unsub-neg 62.2%

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

      4. associate-/l* 65.0%

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

   7. Simplified 65.0%

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

      1. associate-/r/ 65.1%

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

   9. Applied egg-rr 65.1%

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

   if -2.94999999999999986e-61 < t < 450

   1. Initial program 97.8%

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

   2. Taylor expanded in t around 0 81.8%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+79}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-61}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 450:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+149} \lor \neg \left(t \leq 2.6 \cdot 10^{+104}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.3e+149) (not (<= t 2.6e+104)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e+149) || !(t <= 2.6e+104)) {
		tmp = x + y;
	} 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 <= (-2.3d+149)) .or. (.not. (t <= 2.6d+104))) then
        tmp = x + y
    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 <= -2.3e+149) || !(t <= 2.6e+104)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.3e+149) or not (t <= 2.6e+104):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.3e+149) || !(t <= 2.6e+104))
		tmp = Float64(x + y);
	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 <= -2.3e+149) || ~((t <= 2.6e+104)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.3e+149], N[Not[LessEqual[t, 2.6e+104]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2999999999999998e149 or 2.6e104 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 82.8%

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

   if -2.2999999999999998e149 < t < 2.6e104

   1. Initial program 98.6%

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

   2. Taylor expanded in z around inf 81.1%

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

      1. associate-/l* 87.1%

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

   4. Simplified 87.1%

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

      1. associate-/r/ 85.5%

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

   6. Applied egg-rr 85.5%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+149} \lor \neg \left(t \leq 2.6 \cdot 10^{+104}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 6: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.95 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.95e-22)
   (+ x (* y (/ (- z t) a)))
   (if (<= a 3.5e-5) (+ x (- y (/ y (/ t z)))) (+ x (* z (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.95e-22) {
		tmp = x + (y * ((z - t) / a));
	} else if (a <= 3.5e-5) {
		tmp = x + (y - (y / (t / z)));
	} 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 (a <= (-3.95d-22)) then
        tmp = x + (y * ((z - t) / a))
    else if (a <= 3.5d-5) then
        tmp = x + (y - (y / (t / z)))
    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 (a <= -3.95e-22) {
		tmp = x + (y * ((z - t) / a));
	} else if (a <= 3.5e-5) {
		tmp = x + (y - (y / (t / z)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.95e-22:
		tmp = x + (y * ((z - t) / a))
	elif a <= 3.5e-5:
		tmp = x + (y - (y / (t / z)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.95e-22)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (a <= 3.5e-5)
		tmp = Float64(x + Float64(y - Float64(y / Float64(t / z))));
	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 (a <= -3.95e-22)
		tmp = x + (y * ((z - t) / a));
	elseif (a <= 3.5e-5)
		tmp = x + (y - (y / (t / z)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.95e-22], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-5], N[(x + N[(y - N[(y / N[(t / z), $MachinePrecision]), $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 a < -3.9499999999999999e-22

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 90.5%

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

   if -3.9499999999999999e-22 < a < 3.4999999999999997e-5

   1. Initial program 98.4%

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

   2. Taylor expanded in a around 0 86.4%

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

      1. associate-*r/ 86.4%

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

      2. neg-mul-1 86.4%

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

      3. neg-sub0 86.4%

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

      4. associate--r- 86.4%

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

      5. neg-sub0 86.4%

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

   4. Simplified 86.4%

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

   5. Taylor expanded in z around 0 81.8%

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

      1. +-commutative 81.8%

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

      2. mul-1-neg 81.8%

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

      3. unsub-neg 81.8%

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

      4. associate-/l* 86.4%

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

   7. Simplified 86.4%

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

   if 3.4999999999999997e-5 < a

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 76.2%

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

      1. associate-/l* 85.4%

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

   4. Simplified 85.4%

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

      1. associate-/r/ 85.4%

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

   6. Applied egg-rr 85.4%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.95 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 7: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+17}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.8e-22)
   (+ x (* y (/ (- z t) a)))
   (if (<= a 9.2e+17) (+ x (- y (/ y (/ t z)))) (+ x (/ (- z t) (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e-22) {
		tmp = x + (y * ((z - t) / a));
	} else if (a <= 9.2e+17) {
		tmp = x + (y - (y / (t / z)));
	} else {
		tmp = x + ((z - t) / (a / 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 <= (-5.8d-22)) then
        tmp = x + (y * ((z - t) / a))
    else if (a <= 9.2d+17) then
        tmp = x + (y - (y / (t / z)))
    else
        tmp = x + ((z - t) / (a / 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 <= -5.8e-22) {
		tmp = x + (y * ((z - t) / a));
	} else if (a <= 9.2e+17) {
		tmp = x + (y - (y / (t / z)));
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.8e-22:
		tmp = x + (y * ((z - t) / a))
	elif a <= 9.2e+17:
		tmp = x + (y - (y / (t / z)))
	else:
		tmp = x + ((z - t) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.8e-22)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (a <= 9.2e+17)
		tmp = Float64(x + Float64(y - Float64(y / Float64(t / z))));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.8e-22)
		tmp = x + (y * ((z - t) / a));
	elseif (a <= 9.2e+17)
		tmp = x + (y - (y / (t / z)));
	else
		tmp = x + ((z - t) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.8e-22], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e+17], N[(x + N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.8000000000000003e-22

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 90.5%

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

   if -5.8000000000000003e-22 < a < 9.2e17

   1. Initial program 98.5%

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

   2. Taylor expanded in a around 0 86.0%

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

      1. associate-*r/ 86.0%

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

      2. neg-mul-1 86.0%

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

      3. neg-sub0 86.0%

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

      4. associate--r- 86.0%

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

      5. neg-sub0 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in z around 0 81.6%

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

      1. +-commutative 81.6%

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

      2. mul-1-neg 81.6%

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

      3. unsub-neg 81.6%

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

      4. associate-/l* 86.0%

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

   7. Simplified 86.0%

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

   if 9.2e17 < a

   1. Initial program 99.2%

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

      1. associate-*r/ 83.4%

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

   3. Simplified 83.4%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in a around inf 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-/l* 86.8%

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

   8. Simplified 86.8%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+17}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.95e-22)
   (+ x (* y (/ (- z t) a)))
   (if (<= a 1.02e+18) (+ x (* y (/ (- t z) t))) (+ x (/ (- z t) (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e-22) {
		tmp = x + (y * ((z - t) / a));
	} else if (a <= 1.02e+18) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + ((z - t) / (a / 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 <= (-1.95d-22)) then
        tmp = x + (y * ((z - t) / a))
    else if (a <= 1.02d+18) then
        tmp = x + (y * ((t - z) / t))
    else
        tmp = x + ((z - t) / (a / 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 <= -1.95e-22) {
		tmp = x + (y * ((z - t) / a));
	} else if (a <= 1.02e+18) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.95e-22:
		tmp = x + (y * ((z - t) / a))
	elif a <= 1.02e+18:
		tmp = x + (y * ((t - z) / t))
	else:
		tmp = x + ((z - t) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.95e-22)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (a <= 1.02e+18)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.95e-22)
		tmp = x + (y * ((z - t) / a));
	elseif (a <= 1.02e+18)
		tmp = x + (y * ((t - z) / t));
	else
		tmp = x + ((z - t) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.95e-22], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+18], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.94999999999999999e-22

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 90.5%

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

   if -1.94999999999999999e-22 < a < 1.02e18

   1. Initial program 98.5%

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

   2. Taylor expanded in a around 0 86.0%

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

      1. associate-*r/ 86.0%

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

      2. neg-mul-1 86.0%

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

      3. neg-sub0 86.0%

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

      4. associate--r- 86.0%

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

      5. neg-sub0 86.0%

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

   4. Simplified 86.0%

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

   if 1.02e18 < a

   1. Initial program 99.2%

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

      1. associate-*r/ 83.4%

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

   3. Simplified 83.4%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in a around inf 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-/l* 86.8%

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

   8. Simplified 86.8%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.1 \cdot 10^{+145}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+104}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.1e+145)
   (+ x (- y (/ y (/ t z))))
   (if (<= t 1.9e+104) (+ x (/ y (/ (- a t) z))) (- x (* t (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.1e+145) {
		tmp = x + (y - (y / (t / z)));
	} else if (t <= 1.9e+104) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x - (t * (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 <= (-8.1d+145)) then
        tmp = x + (y - (y / (t / z)))
    else if (t <= 1.9d+104) then
        tmp = x + (y / ((a - t) / z))
    else
        tmp = x - (t * (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 <= -8.1e+145) {
		tmp = x + (y - (y / (t / z)));
	} else if (t <= 1.9e+104) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x - (t * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.1e+145:
		tmp = x + (y - (y / (t / z)))
	elif t <= 1.9e+104:
		tmp = x + (y / ((a - t) / z))
	else:
		tmp = x - (t * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.1e+145)
		tmp = Float64(x + Float64(y - Float64(y / Float64(t / z))));
	elseif (t <= 1.9e+104)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(x - Float64(t * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.1e+145)
		tmp = x + (y - (y / (t / z)));
	elseif (t <= 1.9e+104)
		tmp = x + (y / ((a - t) / z));
	else
		tmp = x - (t * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.1e+145], N[(x + N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+104], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.1000000000000001e145

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 89.5%

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

      1. associate-*r/ 89.5%

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

      2. neg-mul-1 89.5%

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

      3. neg-sub0 89.5%

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

      4. associate--r- 89.5%

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

      5. neg-sub0 89.5%

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

   4. Simplified 89.5%

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

   5. Taylor expanded in z around 0 86.7%

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

      1. +-commutative 86.7%

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

      2. mul-1-neg 86.7%

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

      3. unsub-neg 86.7%

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

      4. associate-/l* 89.5%

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

   7. Simplified 89.5%

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

   if -8.1000000000000001e145 < t < 1.89999999999999984e104

   1. Initial program 98.6%

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

   2. Taylor expanded in z around inf 81.1%

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

      1. associate-/l* 87.1%

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

   4. Simplified 87.1%

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

   if 1.89999999999999984e104 < t

   1. Initial program 99.9%

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

      1. associate-*r/ 51.1%

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

   3. Simplified 51.1%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in z around 0 50.9%

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

      1. associate-*r/ 50.9%

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

      2. mul-1-neg 50.9%

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

      3. distribute-rgt-neg-out 50.9%

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

      4. associate-*l/ 89.0%

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

   8. Simplified 89.0%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.1 \cdot 10^{+145}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+104}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 10: 77.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 850:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e-5) (+ x y) (if (<= t 850.0) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-5) {
		tmp = x + y;
	} else if (t <= 850.0) {
		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 <= (-1.15d-5)) then
        tmp = x + y
    else if (t <= 850.0d0) 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 <= -1.15e-5) {
		tmp = x + y;
	} else if (t <= 850.0) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e-5:
		tmp = x + y
	elif t <= 850.0:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e-5)
		tmp = Float64(x + y);
	elseif (t <= 850.0)
		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 <= -1.15e-5)
		tmp = x + y;
	elseif (t <= 850.0)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e-5], N[(x + y), $MachinePrecision], If[LessEqual[t, 850.0], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15e-5 or 850 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 74.4%

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

   if -1.15e-5 < t < 850

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0 77.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 850:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 60.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3.9 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 3.9e+14) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 3.9e+14) {
		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 <= 3.9d+14) 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 <= 3.9e+14) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 3.9e+14:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 3.9e+14)
		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 <= 3.9e+14)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 3.9e+14], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 3.9e14

   1. Initial program 99.0%

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

   2. Taylor expanded in t around inf 60.4%

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

   if 3.9e14 < a

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 63.4%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.9 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 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 99.0%

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

2. Taylor expanded in x around inf 49.4%

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

3. Final simplification 49.4%

   \[\leadsto x \]

Developer target: 99.4% 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 2023185 
(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)))))