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

Percentage Accurate: 85.8% → 98.3%

Time: 10.1s

Alternatives: 15

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: 85.8% 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: 98.3% 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]

Derivation

1. Initial program 87.4%

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

   1. associate-/l* 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 2: 81.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-81}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (- 1.0 (/ a z))))))
   (if (<= z -6.4e+100)
     t_1
     (if (<= z -1.8e-133)
       (+ x (* (- z t) (/ y z)))
       (if (<= z 5.6e-81) (+ x (* y (/ t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (1.0 - (a / z)));
	double tmp;
	if (z <= -6.4e+100) {
		tmp = t_1;
	} else if (z <= -1.8e-133) {
		tmp = x + ((z - t) * (y / z));
	} else if (z <= 5.6e-81) {
		tmp = x + (y * (t / a));
	} 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 / (1.0d0 - (a / z)))
    if (z <= (-6.4d+100)) then
        tmp = t_1
    else if (z <= (-1.8d-133)) then
        tmp = x + ((z - t) * (y / z))
    else if (z <= 5.6d-81) then
        tmp = x + (y * (t / a))
    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 / (1.0 - (a / z)));
	double tmp;
	if (z <= -6.4e+100) {
		tmp = t_1;
	} else if (z <= -1.8e-133) {
		tmp = x + ((z - t) * (y / z));
	} else if (z <= 5.6e-81) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (1.0 - (a / z)))
	tmp = 0
	if z <= -6.4e+100:
		tmp = t_1
	elif z <= -1.8e-133:
		tmp = x + ((z - t) * (y / z))
	elif z <= 5.6e-81:
		tmp = x + (y * (t / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))))
	tmp = 0.0
	if (z <= -6.4e+100)
		tmp = t_1;
	elseif (z <= -1.8e-133)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	elseif (z <= 5.6e-81)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (1.0 - (a / z)));
	tmp = 0.0;
	if (z <= -6.4e+100)
		tmp = t_1;
	elseif (z <= -1.8e-133)
		tmp = x + ((z - t) * (y / z));
	elseif (z <= 5.6e-81)
		tmp = x + (y * (t / a));
	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[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e+100], t$95$1, If[LessEqual[z, -1.8e-133], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-81], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.3999999999999998e100 or 5.5999999999999998e-81 < z

   1. Initial program 79.9%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in t around 0 73.7%

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

      1. associate-/l* 87.5%

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

      2. div-sub 87.5%

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

      3. *-inverses 87.5%

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

   6. Simplified 87.5%

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

   if -6.3999999999999998e100 < z < -1.8000000000000002e-133

   1. Initial program 95.3%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 87.4%

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

   if -1.8000000000000002e-133 < z < 5.5999999999999998e-81

   1. Initial program 95.4%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in z around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. associate-/l* 78.5%

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

   6. Simplified 78.5%

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

      1. associate-/r/ 79.8%

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

   8. Applied egg-rr 79.8%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-81}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]

Alternative 3: 76.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-59}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+101)
   (+ x y)
   (if (<= z -4.6e-59)
     (- x (* y (/ t z)))
     (if (<= z 2e+42) (+ x (* y (/ t a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+101) {
		tmp = x + y;
	} else if (z <= -4.6e-59) {
		tmp = x - (y * (t / z));
	} else if (z <= 2e+42) {
		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 <= (-4.2d+101)) then
        tmp = x + y
    else if (z <= (-4.6d-59)) then
        tmp = x - (y * (t / z))
    else if (z <= 2d+42) 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 <= -4.2e+101) {
		tmp = x + y;
	} else if (z <= -4.6e-59) {
		tmp = x - (y * (t / z));
	} else if (z <= 2e+42) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+101:
		tmp = x + y
	elif z <= -4.6e-59:
		tmp = x - (y * (t / z))
	elif z <= 2e+42:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+101)
		tmp = Float64(x + y);
	elseif (z <= -4.6e-59)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= 2e+42)
		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 <= -4.2e+101)
		tmp = x + y;
	elseif (z <= -4.6e-59)
		tmp = x - (y * (t / z));
	elseif (z <= 2e+42)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+101], N[(x + y), $MachinePrecision], If[LessEqual[z, -4.6e-59], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+42], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e101 or 2.00000000000000009e42 < z

   1. Initial program 75.4%

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

      1. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in z around inf 77.2%

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

      1. +-commutative 77.2%

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

   6. Simplified 77.2%

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

   if -4.2e101 < z < -4.59999999999999959e-59

   1. Initial program 94.1%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 87.3%

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

   5. Taylor expanded in z around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-lft-neg-out 76.9%

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

      3. *-commutative 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in x around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. associate-*l/ 76.9%

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

      3. *-commutative 76.9%

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

      4. sub-neg 76.9%

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

   10. Simplified 76.9%

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

   if -4.59999999999999959e-59 < z < 2.00000000000000009e42

   1. Initial program 96.0%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-/l* 77.1%

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

   6. Simplified 77.1%

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

      1. associate-/r/ 78.0%

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

   8. Applied egg-rr 78.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-59}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.02 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-133}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+38}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.02e+101)
   (+ x y)
   (if (<= z -1.66e-133)
     (- x (/ (* y t) z))
     (if (<= z 2.6e+38) (+ x (* y (/ t a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.02e+101) {
		tmp = x + y;
	} else if (z <= -1.66e-133) {
		tmp = x - ((y * t) / z);
	} else if (z <= 2.6e+38) {
		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 <= (-2.02d+101)) then
        tmp = x + y
    else if (z <= (-1.66d-133)) then
        tmp = x - ((y * t) / z)
    else if (z <= 2.6d+38) 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 <= -2.02e+101) {
		tmp = x + y;
	} else if (z <= -1.66e-133) {
		tmp = x - ((y * t) / z);
	} else if (z <= 2.6e+38) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.02e+101:
		tmp = x + y
	elif z <= -1.66e-133:
		tmp = x - ((y * t) / z)
	elif z <= 2.6e+38:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.02e+101)
		tmp = Float64(x + y);
	elseif (z <= -1.66e-133)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	elseif (z <= 2.6e+38)
		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 <= -2.02e+101)
		tmp = x + y;
	elseif (z <= -1.66e-133)
		tmp = x - ((y * t) / z);
	elseif (z <= 2.6e+38)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.02e+101], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.66e-133], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+38], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.02000000000000015e101 or 2.5999999999999999e38 < z

   1. Initial program 75.4%

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

      1. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in z around inf 77.2%

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

      1. +-commutative 77.2%

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

   6. Simplified 77.2%

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

   if -2.02000000000000015e101 < z < -1.66e-133

   1. Initial program 93.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 85.3%

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

   5. Taylor expanded in z around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. distribute-lft-neg-out 77.3%

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

      3. *-commutative 77.3%

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

   7. Simplified 77.3%

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

   if -1.66e-133 < z < 2.5999999999999999e38

   1. Initial program 96.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 0 78.5%

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

      1. +-commutative 78.5%

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

      2. associate-/l* 77.7%

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

   6. Simplified 77.7%

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

      1. associate-/r/ 78.6%

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

   8. Applied egg-rr 78.6%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.02 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-133}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+38}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-58} \lor \neg \left(z \leq 6 \cdot 10^{+34}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e-58) (not (<= z 6e+34)))
   (+ x (* y (/ (- z t) z)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e-58) || !(z <= 6e+34)) {
		tmp = x + (y * ((z - t) / 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 <= (-1.15d-58)) .or. (.not. (z <= 6d+34))) then
        tmp = x + (y * ((z - t) / 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 <= -1.15e-58) || !(z <= 6e+34)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e-58) or not (z <= 6e+34):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e-58) || !(z <= 6e+34))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / 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 <= -1.15e-58) || ~((z <= 6e+34)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e-58], N[Not[LessEqual[z, 6e+34]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1499999999999999e-58 or 6.00000000000000037e34 < z

   1. Initial program 79.9%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in x around 0 79.9%

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

      1. associate-*r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-udef 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in a around 0 70.9%

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

      1. associate-*r/ 86.2%

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

   9. Simplified 86.2%

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

   if -1.1499999999999999e-58 < z < 6.00000000000000037e34

   1. Initial program 96.0%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-/l* 77.1%

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

   6. Simplified 77.1%

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

      1. associate-/r/ 78.0%

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

   8. Applied egg-rr 78.0%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-58} \lor \neg \left(z \leq 6 \cdot 10^{+34}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 6: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+98} \lor \neg \left(z \leq 1.8 \cdot 10^{+25}\right):\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e+98) (not (<= z 1.8e+25)))
   (+ x (/ y (- 1.0 (/ a z))))
   (- x (* t (/ y (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+98) || !(z <= 1.8e+25)) {
		tmp = x + (y / (1.0 - (a / z)));
	} else {
		tmp = x - (t * (y / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.85d+98)) .or. (.not. (z <= 1.8d+25))) then
        tmp = x + (y / (1.0d0 - (a / z)))
    else
        tmp = x - (t * (y / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+98) || !(z <= 1.8e+25)) {
		tmp = x + (y / (1.0 - (a / z)));
	} else {
		tmp = x - (t * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e+98) or not (z <= 1.8e+25):
		tmp = x + (y / (1.0 - (a / z)))
	else:
		tmp = x - (t * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e+98) || !(z <= 1.8e+25))
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	else
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.85e+98) || ~((z <= 1.8e+25)))
		tmp = x + (y / (1.0 - (a / z)));
	else
		tmp = x - (t * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e+98], N[Not[LessEqual[z, 1.8e+25]], $MachinePrecision]], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8499999999999999e98 or 1.80000000000000008e25 < z

   1. Initial program 76.3%

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

      1. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in t around 0 73.2%

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

      1. associate-/l* 89.4%

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

      2. div-sub 89.4%

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

      3. *-inverses 89.4%

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

   6. Simplified 89.4%

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

   if -1.8499999999999999e98 < z < 1.80000000000000008e25

   1. Initial program 96.0%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around inf 89.2%

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

      1. associate-*r/ 89.2%

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

      2. mul-1-neg 89.2%

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

      3. distribute-lft-neg-out 89.2%

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

      4. associate-*r/ 90.5%

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

      5. *-commutative 90.5%

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

   6. Simplified 90.5%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+98} \lor \neg \left(z \leq 1.8 \cdot 10^{+25}\right):\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 7: 62.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+250} \lor \neg \left(y \leq 1.2 \cdot 10^{+37}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.3e+250) (not (<= y 1.2e+37))) (* y (- 1.0 (/ t z))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.3e+250) || !(y <= 1.2e+37)) {
		tmp = y * (1.0 - (t / 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 ((y <= (-1.3d+250)) .or. (.not. (y <= 1.2d+37))) then
        tmp = y * (1.0d0 - (t / 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 ((y <= -1.3e+250) || !(y <= 1.2e+37)) {
		tmp = y * (1.0 - (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.3e+250) or not (y <= 1.2e+37):
		tmp = y * (1.0 - (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.3e+250) || !(y <= 1.2e+37))
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.3e+250) || ~((y <= 1.2e+37)))
		tmp = y * (1.0 - (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.3e+250], N[Not[LessEqual[y, 1.2e+37]], $MachinePrecision]], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.30000000000000006e250 or 1.2e37 < y

   1. Initial program 76.1%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in a around 0 49.2%

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

   5. Taylor expanded in x around 0 40.1%

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

      1. associate-*r/ 57.5%

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

      2. div-sub 57.5%

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

      3. *-inverses 57.5%

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

   7. Simplified 57.5%

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

   if -1.30000000000000006e250 < y < 1.2e37

   1. Initial program 90.8%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around inf 68.3%

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

      1. +-commutative 68.3%

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

   6. Simplified 68.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+250} \lor \neg \left(y \leq 1.2 \cdot 10^{+37}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+101} \lor \neg \left(z \leq 1.56 \cdot 10^{+37}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e+101) (not (<= z 1.56e+37))) (+ x y) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+101) || !(z <= 1.56e+37)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.6d+101)) .or. (.not. (z <= 1.56d+37))) then
        tmp = x + y
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+101) || !(z <= 1.56e+37)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.6e+101) or not (z <= 1.56e+37):
		tmp = x + y
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e+101) || !(z <= 1.56e+37))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.6e+101) || ~((z <= 1.56e+37)))
		tmp = x + y;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e+101], N[Not[LessEqual[z, 1.56e+37]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000003e101 or 1.56000000000000008e37 < z

   1. Initial program 75.4%

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

      1. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in z around inf 77.2%

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

      1. +-commutative 77.2%

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

   6. Simplified 77.2%

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

   if -1.60000000000000003e101 < z < 1.56000000000000008e37

   1. Initial program 95.6%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in z around 0 74.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+101} \lor \neg \left(z \leq 1.56 \cdot 10^{+37}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 9: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+101} \lor \neg \left(z \leq 8.6 \cdot 10^{+43}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.7e+101) (not (<= z 8.6e+43))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.7e+101) || !(z <= 8.6e+43)) {
		tmp = x + 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 <= (-3.7d+101)) .or. (.not. (z <= 8.6d+43))) then
        tmp = x + 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 <= -3.7e+101) || !(z <= 8.6e+43)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.7e+101) or not (z <= 8.6e+43):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.7e+101) || !(z <= 8.6e+43))
		tmp = Float64(x + 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 <= -3.7e+101) || ~((z <= 8.6e+43)))
		tmp = x + y;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.7e+101], N[Not[LessEqual[z, 8.6e+43]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6999999999999997e101 or 8.6e43 < z

   1. Initial program 75.4%

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

      1. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in z around inf 77.2%

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

      1. +-commutative 77.2%

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

   6. Simplified 77.2%

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

   if -3.6999999999999997e101 < z < 8.6e43

   1. Initial program 95.6%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around 0 72.7%

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

      1. +-commutative 72.7%

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

      2. associate-/l* 73.3%

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

   6. Simplified 73.3%

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

      1. associate-/r/ 74.0%

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

   8. Applied egg-rr 74.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+101} \lor \neg \left(z \leq 8.6 \cdot 10^{+43}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 10: 62.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+249}:\\ \;\;\;\;y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+36}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.65e+249)
   (* y (/ (- z t) z))
   (if (<= y 8.6e+36) (+ x y) (* y (- 1.0 (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.65e+249) {
		tmp = y * ((z - t) / z);
	} else if (y <= 8.6e+36) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.65d+249)) then
        tmp = y * ((z - t) / z)
    else if (y <= 8.6d+36) then
        tmp = x + y
    else
        tmp = y * (1.0d0 - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.65e+249) {
		tmp = y * ((z - t) / z);
	} else if (y <= 8.6e+36) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.65e+249:
		tmp = y * ((z - t) / z)
	elif y <= 8.6e+36:
		tmp = x + y
	else:
		tmp = y * (1.0 - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.65e+249)
		tmp = Float64(y * Float64(Float64(z - t) / z));
	elseif (y <= 8.6e+36)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.65e+249)
		tmp = y * ((z - t) / z);
	elseif (y <= 8.6e+36)
		tmp = x + y;
	else
		tmp = y * (1.0 - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.65e+249], N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e+36], N[(x + y), $MachinePrecision], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.65000000000000019e249

   1. Initial program 57.2%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 33.3%

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

   5. Taylor expanded in x around 0 29.5%

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

      1. associate-*r/ 64.5%

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

   7. Simplified 64.5%

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

   if -2.65000000000000019e249 < y < 8.6000000000000001e36

   1. Initial program 90.8%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around inf 68.3%

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

      1. +-commutative 68.3%

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

   6. Simplified 68.3%

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

   if 8.6000000000000001e36 < y

   1. Initial program 81.4%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in a around 0 53.7%

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

   5. Taylor expanded in x around 0 43.1%

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

      1. associate-*r/ 55.6%

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

      2. div-sub 55.6%

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

      3. *-inverses 55.6%

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

   7. Simplified 55.6%

      \[\leadsto \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+249}:\\ \;\;\;\;y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+36}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]

Alternative 11: 95.8% 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 87.4%

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

   1. associate-*l/ 94.6%

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

3. Simplified 94.6%

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

4. Final simplification 94.6%

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

Alternative 12: 98.2% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 87.4%

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

   1. associate-/l* 98.0%

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

3. Simplified 98.0%

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

   1. clear-num 97.9%

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

   2. associate-/r/ 97.6%

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

   3. clear-num 97.7%

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

5. Applied egg-rr 97.7%

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

6. Final simplification 97.7%

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

Alternative 13: 64.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-58} \lor \neg \left(z \leq 2.8 \cdot 10^{+34}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.25e-58) (not (<= z 2.8e+34))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e-58) || !(z <= 2.8e+34)) {
		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 ((z <= (-1.25d-58)) .or. (.not. (z <= 2.8d+34))) 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 ((z <= -1.25e-58) || !(z <= 2.8e+34)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.25e-58) or not (z <= 2.8e+34):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.25e-58) || !(z <= 2.8e+34))
		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 ((z <= -1.25e-58) || ~((z <= 2.8e+34)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.25e-58], N[Not[LessEqual[z, 2.8e+34]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.24999999999999994e-58 or 2.80000000000000008e34 < z

   1. Initial program 80.0%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around inf 71.9%

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

      1. +-commutative 71.9%

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

   6. Simplified 71.9%

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

   if -1.24999999999999994e-58 < z < 2.80000000000000008e34

   1. Initial program 96.0%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around inf 56.0%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-58} \lor \neg \left(z \leq 2.8 \cdot 10^{+34}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 52.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-195}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -7e-195) x (if (<= x 6e-95) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7e-195) {
		tmp = x;
	} else if (x <= 6e-95) {
		tmp = 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 (x <= (-7d-195)) then
        tmp = x
    else if (x <= 6d-95) then
        tmp = 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 (x <= -7e-195) {
		tmp = x;
	} else if (x <= 6e-95) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -7e-195:
		tmp = x
	elif x <= 6e-95:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -7e-195)
		tmp = x;
	elseif (x <= 6e-95)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -7e-195)
		tmp = x;
	elseif (x <= 6e-95)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -7e-195], x, If[LessEqual[x, 6e-95], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.00000000000000028e-195 or 6e-95 < x

   1. Initial program 90.3%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 70.4%

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

   if -7.00000000000000028e-195 < x < 6e-95

   1. Initial program 80.9%

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

      1. associate-*l/ 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in a around 0 46.6%

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

   5. Taylor expanded in x around 0 41.8%

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

      1. associate-*r/ 55.2%

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

      2. div-sub 55.2%

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

      3. *-inverses 55.2%

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

   7. Simplified 55.2%

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

   8. Taylor expanded in t around 0 39.2%

      \[\leadsto y \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-195}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 51.1% 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 87.4%

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

   1. associate-*l/ 94.6%

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

3. Simplified 94.6%

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

4. Taylor expanded in x around inf 53.4%

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

5. Final simplification 53.4%

   \[\leadsto x \]

Developer target: 98.3% 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 2023318 
(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))))