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

Percentage Accurate: 86.0% → 98.1%

Time: 9.7s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.9%

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

   1. *-commutative 82.9%

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

   2. associate-/l* 96.8%

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

   3. associate-/r/ 99.2%

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

3. Applied egg-rr 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13500:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-115}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+90}:\\ \;\;\;\;x + \frac{y}{-\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -13500.0)
   (+ x y)
   (if (<= z 1.58e-115)
     (+ x (* y (/ t a)))
     (if (<= z 1.95e+90) (+ x (/ y (- (/ z t)))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -13500.0) {
		tmp = x + y;
	} else if (z <= 1.58e-115) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.95e+90) {
		tmp = x + (y / -(z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-13500.0d0)) then
        tmp = x + y
    else if (z <= 1.58d-115) then
        tmp = x + (y * (t / a))
    else if (z <= 1.95d+90) then
        tmp = x + (y / -(z / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -13500.0) {
		tmp = x + y;
	} else if (z <= 1.58e-115) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.95e+90) {
		tmp = x + (y / -(z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -13500.0:
		tmp = x + y
	elif z <= 1.58e-115:
		tmp = x + (y * (t / a))
	elif z <= 1.95e+90:
		tmp = x + (y / -(z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -13500.0)
		tmp = Float64(x + y);
	elseif (z <= 1.58e-115)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.95e+90)
		tmp = Float64(x + Float64(y / Float64(-Float64(z / t))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -13500.0)
		tmp = x + y;
	elseif (z <= 1.58e-115)
		tmp = x + (y * (t / a));
	elseif (z <= 1.95e+90)
		tmp = x + (y / -(z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -13500.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.58e-115], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+90], N[(x + N[(y / (-N[(z / t), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -13500 or 1.9500000000000001e90 < z

   1. Initial program 69.1%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 77.7%

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

      1. +-commutative 77.7%

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

   6. Simplified 77.7%

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

   if -13500 < z < 1.58e-115

   1. Initial program 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-/l* 95.5%

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

      3. associate-/r/ 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in z around 0 89.0%

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

   if 1.58e-115 < z < 1.9500000000000001e90

   1. Initial program 98.0%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in a around 0 74.8%

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

      1. +-commutative 74.8%

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

      2. associate-/l* 76.7%

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

   6. Simplified 76.7%

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

   7. Taylor expanded in z around 0 76.8%

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

      1. associate-*r/ 76.8%

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

      2. neg-mul-1 76.8%

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

   9. Simplified 76.8%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13500:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-115}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+90}:\\ \;\;\;\;x + \frac{y}{-\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-115}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+84}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e-5)
   (+ x y)
   (if (<= z 1.58e-115)
     (+ x (* y (/ t a)))
     (if (<= z 3.3e+84) (- x (* t (/ y z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e-5) {
		tmp = x + y;
	} else if (z <= 1.58e-115) {
		tmp = x + (y * (t / a));
	} else if (z <= 3.3e+84) {
		tmp = x - (t * (y / 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 (z <= (-8.5d-5)) then
        tmp = x + y
    else if (z <= 1.58d-115) then
        tmp = x + (y * (t / a))
    else if (z <= 3.3d+84) then
        tmp = x - (t * (y / 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 (z <= -8.5e-5) {
		tmp = x + y;
	} else if (z <= 1.58e-115) {
		tmp = x + (y * (t / a));
	} else if (z <= 3.3e+84) {
		tmp = x - (t * (y / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e-5:
		tmp = x + y
	elif z <= 1.58e-115:
		tmp = x + (y * (t / a))
	elif z <= 3.3e+84:
		tmp = x - (t * (y / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e-5)
		tmp = Float64(x + y);
	elseif (z <= 1.58e-115)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 3.3e+84)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e-5)
		tmp = x + y;
	elseif (z <= 1.58e-115)
		tmp = x + (y * (t / a));
	elseif (z <= 3.3e+84)
		tmp = x - (t * (y / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e-5], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.58e-115], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+84], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.500000000000001e-5 or 3.30000000000000017e84 < z

   1. Initial program 69.1%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 77.7%

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

      1. +-commutative 77.7%

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

   6. Simplified 77.7%

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

   if -8.500000000000001e-5 < z < 1.58e-115

   1. Initial program 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-/l* 95.5%

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

      3. associate-/r/ 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in z around 0 89.0%

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

   if 1.58e-115 < z < 3.30000000000000017e84

   1. Initial program 98.0%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in t around inf 85.9%

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

      1. associate-/l* 87.7%

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

      2. associate-*r/ 87.7%

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

      3. neg-mul-1 87.7%

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

   6. Simplified 87.7%

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

      1. div-inv 87.7%

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

      2. /-rgt-identity 87.7%

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

      3. cancel-sign-sub-inv 87.7%

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

      4. /-rgt-identity 87.7%

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

      5. clear-num 87.7%

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

   8. Applied egg-rr 87.7%

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

   9. Taylor expanded in z around inf 74.9%

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

       1. *-lft-identity 74.9%

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

       2. times-frac 76.8%

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

       3. /-rgt-identity 76.8%

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

   11. Simplified 76.8%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-115}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+84}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 76.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1150000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-115}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+82}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1150000.0)
   (+ x y)
   (if (<= z 1.58e-115)
     (+ x (* y (/ t a)))
     (if (<= z 2.15e+82) (- x (/ t (/ z y))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1150000.0) {
		tmp = x + y;
	} else if (z <= 1.58e-115) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.15e+82) {
		tmp = x - (t / (z / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1150000.0d0)) then
        tmp = x + y
    else if (z <= 1.58d-115) then
        tmp = x + (y * (t / a))
    else if (z <= 2.15d+82) then
        tmp = x - (t / (z / y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1150000.0) {
		tmp = x + y;
	} else if (z <= 1.58e-115) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.15e+82) {
		tmp = x - (t / (z / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1150000.0:
		tmp = x + y
	elif z <= 1.58e-115:
		tmp = x + (y * (t / a))
	elif z <= 2.15e+82:
		tmp = x - (t / (z / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1150000.0)
		tmp = Float64(x + y);
	elseif (z <= 1.58e-115)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 2.15e+82)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1150000.0)
		tmp = x + y;
	elseif (z <= 1.58e-115)
		tmp = x + (y * (t / a));
	elseif (z <= 2.15e+82)
		tmp = x - (t / (z / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1150000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.58e-115], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+82], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e6 or 2.15000000000000007e82 < z

   1. Initial program 69.1%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 77.7%

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

      1. +-commutative 77.7%

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

   6. Simplified 77.7%

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

   if -1.15e6 < z < 1.58e-115

   1. Initial program 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-/l* 95.5%

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

      3. associate-/r/ 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in z around 0 89.0%

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

   if 1.58e-115 < z < 2.15000000000000007e82

   1. Initial program 98.0%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in t around inf 85.9%

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

      1. associate-/l* 87.7%

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

      2. associate-*r/ 87.7%

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

      3. neg-mul-1 87.7%

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

   6. Simplified 87.7%

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

      1. div-inv 87.7%

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

      2. /-rgt-identity 87.7%

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

      3. cancel-sign-sub-inv 87.7%

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

      4. /-rgt-identity 87.7%

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

      5. clear-num 87.7%

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

   8. Applied egg-rr 87.7%

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

   9. Taylor expanded in z around inf 74.9%

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

       1. associate-/l* 76.8%

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

   11. Simplified 76.8%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1150000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-115}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+82}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 80.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-8} \lor \neg \left(z \leq 1.58 \cdot 10^{-115}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5e-8) (not (<= z 1.58e-115)))
   (+ x (* (- z t) (/ y z)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5e-8) || !(z <= 1.58e-115)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y * (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 <= (-5d-8)) .or. (.not. (z <= 1.58d-115))) then
        tmp = x + ((z - t) * (y / z))
    else
        tmp = x + (y * (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 <= -5e-8) || !(z <= 1.58e-115)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5e-8) or not (z <= 1.58e-115):
		tmp = x + ((z - t) * (y / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5e-8) || !(z <= 1.58e-115))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5e-8) || ~((z <= 1.58e-115)))
		tmp = x + ((z - t) * (y / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5e-8], N[Not[LessEqual[z, 1.58e-115]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999998e-8 or 1.58e-115 < z

   1. Initial program 77.0%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around inf 82.8%

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

   if -4.9999999999999998e-8 < z < 1.58e-115

   1. Initial program 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-/l* 95.5%

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

      3. associate-/r/ 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in z around 0 89.0%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-8} \lor \neg \left(z \leq 1.58 \cdot 10^{-115}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 6: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-9} \lor \neg \left(z \leq 1.58 \cdot 10^{-115}\right):\\ \;\;\;\;x + \left(y - \frac{t}{\frac{z}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.6e-9) (not (<= z 1.58e-115)))
   (+ x (- y (/ t (/ z y))))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.6e-9) || !(z <= 1.58e-115)) {
		tmp = x + (y - (t / (z / y)));
	} else {
		tmp = x + (y * (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 <= (-6.6d-9)) .or. (.not. (z <= 1.58d-115))) then
        tmp = x + (y - (t / (z / y)))
    else
        tmp = x + (y * (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 <= -6.6e-9) || !(z <= 1.58e-115)) {
		tmp = x + (y - (t / (z / y)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.6e-9) or not (z <= 1.58e-115):
		tmp = x + (y - (t / (z / y)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.6e-9) || !(z <= 1.58e-115))
		tmp = Float64(x + Float64(y - Float64(t / Float64(z / y))));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.6e-9) || ~((z <= 1.58e-115)))
		tmp = x + (y - (t / (z / y)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.6e-9], N[Not[LessEqual[z, 1.58e-115]], $MachinePrecision]], N[(x + N[(y - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.60000000000000037e-9 or 1.58e-115 < z

   1. Initial program 77.0%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around inf 82.8%

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

      1. *-commutative 82.8%

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

      2. clear-num 82.6%

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

      3. un-div-inv 82.7%

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

      4. div-sub 82.1%

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

      5. un-div-inv 82.0%

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

      6. clear-num 82.3%

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

      7. div-inv 82.2%

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

      8. *-commutative 82.2%

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

      9. associate-*r* 83.8%

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

      10. div-inv 83.9%

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

      11. *-inverses 83.9%

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

      12. *-lft-identity 83.9%

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

   6. Applied egg-rr 83.9%

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

   if -6.60000000000000037e-9 < z < 1.58e-115

   1. Initial program 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-/l* 95.5%

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

      3. associate-/r/ 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in z around 0 89.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-9} \lor \neg \left(z \leq 1.58 \cdot 10^{-115}\right):\\ \;\;\;\;x + \left(y - \frac{t}{\frac{z}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 7: 81.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.017:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-115}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.017)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 1.58e-115) (+ x (* y (/ t a))) (+ x (- y (/ t (/ z y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.017) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 1.58e-115) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y - (t / (z / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-0.017d0)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 1.58d-115) then
        tmp = x + (y * (t / a))
    else
        tmp = x + (y - (t / (z / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.017) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 1.58e-115) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y - (t / (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.017:
		tmp = x + (y / (z / (z - t)))
	elif z <= 1.58e-115:
		tmp = x + (y * (t / a))
	else:
		tmp = x + (y - (t / (z / y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.017)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 1.58e-115)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + Float64(y - Float64(t / Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.017)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 1.58e-115)
		tmp = x + (y * (t / a));
	else
		tmp = x + (y - (t / (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.017], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.58e-115], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.017000000000000001

   1. Initial program 80.6%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in a around 0 68.5%

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

      1. +-commutative 68.5%

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

      2. associate-/l* 87.8%

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

   6. Simplified 87.8%

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

   if -0.017000000000000001 < z < 1.58e-115

   1. Initial program 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-/l* 95.5%

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

      3. associate-/r/ 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in z around 0 89.0%

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

   if 1.58e-115 < z

   1. Initial program 74.6%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around inf 81.3%

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

      1. *-commutative 81.3%

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

      2. clear-num 80.9%

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

      3. un-div-inv 81.0%

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

      4. div-sub 80.0%

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

      5. un-div-inv 80.0%

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

      6. clear-num 80.3%

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

      7. div-inv 80.3%

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

      8. *-commutative 80.3%

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

      9. associate-*r* 82.3%

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

      10. div-inv 82.3%

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

      11. *-inverses 82.3%

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

      12. *-lft-identity 82.3%

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

   6. Applied egg-rr 82.3%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.017:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-115}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{\frac{z}{y}}\right)\\ \end{array} \]

Alternative 8: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+54}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.6e+24)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 5.8e+54) (- x (* t (/ y (- z a)))) (+ x (- y (/ t (/ z y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.6e+24) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 5.8e+54) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (y - (t / (z / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.6d+24)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 5.8d+54) then
        tmp = x - (t * (y / (z - a)))
    else
        tmp = x + (y - (t / (z / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.6e+24) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 5.8e+54) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (y - (t / (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.6e+24:
		tmp = x + (y / (z / (z - t)))
	elif z <= 5.8e+54:
		tmp = x - (t * (y / (z - a)))
	else:
		tmp = x + (y - (t / (z / y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.6e+24)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 5.8e+54)
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y - Float64(t / Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.6e+24)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 5.8e+54)
		tmp = x - (t * (y / (z - a)));
	else
		tmp = x + (y - (t / (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.6e+24], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+54], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.59999999999999975e24

   1. Initial program 78.1%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in a around 0 67.0%

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

      1. +-commutative 67.0%

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

      2. associate-/l* 88.8%

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

   6. Simplified 88.8%

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

   if -8.59999999999999975e24 < z < 5.7999999999999997e54

   1. Initial program 96.1%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around inf 90.1%

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

      1. associate-/l* 91.7%

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

      2. associate-*r/ 91.7%

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

      3. neg-mul-1 91.7%

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

   6. Simplified 91.7%

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

      1. div-inv 91.0%

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

      2. /-rgt-identity 91.0%

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

      3. cancel-sign-sub-inv 91.0%

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

      4. /-rgt-identity 91.0%

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

      5. clear-num 91.1%

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

   8. Applied egg-rr 91.1%

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

   if 5.7999999999999997e54 < z

   1. Initial program 61.7%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around inf 87.8%

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

      1. *-commutative 87.8%

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

      2. clear-num 87.3%

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

      3. un-div-inv 87.4%

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

      4. div-sub 87.4%

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

      5. un-div-inv 87.3%

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

      6. clear-num 87.8%

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

      7. div-inv 87.8%

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

      8. *-commutative 87.8%

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

      9. associate-*r* 89.3%

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

      10. div-inv 89.3%

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

      11. *-inverses 89.3%

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

      12. *-lft-identity 89.3%

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

   6. Applied egg-rr 89.3%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+54}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{\frac{z}{y}}\right)\\ \end{array} \]

Alternative 9: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+54}:\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.1e+26)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 4.5e+54) (- x (/ t (/ (- z a) y))) (+ x (- y (/ t (/ z y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+26) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 4.5e+54) {
		tmp = x - (t / ((z - a) / y));
	} else {
		tmp = x + (y - (t / (z / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.1d+26)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 4.5d+54) then
        tmp = x - (t / ((z - a) / y))
    else
        tmp = x + (y - (t / (z / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+26) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 4.5e+54) {
		tmp = x - (t / ((z - a) / y));
	} else {
		tmp = x + (y - (t / (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.1e+26:
		tmp = x + (y / (z / (z - t)))
	elif z <= 4.5e+54:
		tmp = x - (t / ((z - a) / y))
	else:
		tmp = x + (y - (t / (z / y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.1e+26)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 4.5e+54)
		tmp = Float64(x - Float64(t / Float64(Float64(z - a) / y)));
	else
		tmp = Float64(x + Float64(y - Float64(t / Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.1e+26)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 4.5e+54)
		tmp = x - (t / ((z - a) / y));
	else
		tmp = x + (y - (t / (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.1e+26], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+54], N[(x - N[(t / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1e26

   1. Initial program 78.1%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in a around 0 67.0%

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

      1. +-commutative 67.0%

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

      2. associate-/l* 88.8%

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

   6. Simplified 88.8%

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

   if -3.1e26 < z < 4.49999999999999984e54

   1. Initial program 96.1%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around inf 90.1%

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

      1. associate-/l* 91.7%

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

      2. associate-*r/ 91.7%

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

      3. neg-mul-1 91.7%

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

   6. Simplified 91.7%

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

   if 4.49999999999999984e54 < z

   1. Initial program 61.7%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around inf 87.8%

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

      1. *-commutative 87.8%

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

      2. clear-num 87.3%

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

      3. un-div-inv 87.4%

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

      4. div-sub 87.4%

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

      5. un-div-inv 87.3%

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

      6. clear-num 87.8%

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

      7. div-inv 87.8%

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

      8. *-commutative 87.8%

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

      9. associate-*r* 89.3%

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

      10. div-inv 89.3%

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

      11. *-inverses 89.3%

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

      12. *-lft-identity 89.3%

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

   6. Applied egg-rr 89.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+54}:\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{\frac{z}{y}}\right)\\ \end{array} \]

Alternative 10: 77.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -36000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -36000000.0)
   (+ x y)
   (if (<= z 2.1e+58) (+ x (* y (/ t a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -36000000.0) {
		tmp = x + y;
	} else if (z <= 2.1e+58) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-36000000.0d0)) then
        tmp = x + y
    else if (z <= 2.1d+58) then
        tmp = x + (y * (t / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -36000000.0) {
		tmp = x + y;
	} else if (z <= 2.1e+58) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -36000000.0:
		tmp = x + y
	elif z <= 2.1e+58:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -36000000.0)
		tmp = Float64(x + y);
	elseif (z <= 2.1e+58)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -36000000.0)
		tmp = x + y;
	elseif (z <= 2.1e+58)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -36000000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.1e+58], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e7 or 2.10000000000000012e58 < z

   1. Initial program 71.0%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in z around inf 76.6%

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

      1. +-commutative 76.6%

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

   6. Simplified 76.6%

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

   if -3.6e7 < z < 2.10000000000000012e58

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

      2. associate-/l* 96.7%

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

      3. associate-/r/ 98.4%

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

   3. Applied egg-rr 98.4%

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

   4. Taylor expanded in z around 0 81.8%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -36000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.9%

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

   1. associate-*l/ 96.6%

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

3. Simplified 96.6%

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

4. Final simplification 96.6%

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

Alternative 12: 63.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e-16) (+ x y) (if (<= z 8e+51) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e-16) {
		tmp = x + y;
	} else if (z <= 8e+51) {
		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 (z <= (-1.7d-16)) then
        tmp = x + y
    else if (z <= 8d+51) 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 (z <= -1.7e-16) {
		tmp = x + y;
	} else if (z <= 8e+51) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e-16:
		tmp = x + y
	elif z <= 8e+51:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e-16)
		tmp = Float64(x + y);
	elseif (z <= 8e+51)
		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 (z <= -1.7e-16)
		tmp = x + y;
	elseif (z <= 8e+51)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e-16], N[(x + y), $MachinePrecision], If[LessEqual[z, 8e+51], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e-16 or 8e51 < z

   1. Initial program 71.4%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in z around inf 75.6%

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

      1. +-commutative 75.6%

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

   6. Simplified 75.6%

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

   if -1.7e-16 < z < 8e51

   1. Initial program 95.8%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in x around inf 53.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13: 50.9% 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 82.9%

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

   1. associate-*l/ 96.6%

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

3. Simplified 96.6%

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

4. Taylor expanded in x around inf 52.0%

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

5. Final simplification 52.0%

   \[\leadsto x \]

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

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

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

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