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

Percentage Accurate: 98.1% → 98.3%

Time: 10.0s

Alternatives: 12

Speedup: 1.0×

Specification

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]

Initial Program: 98.1% 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]

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) / (t - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. clear-num 99.1%

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

   2. un-div-inv 99.1%

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

4. Applied egg-rr 99.1%

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

5. Final simplification 99.1%

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

Alternative 2: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-80}:\\ \;\;\;\;x - y \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-54}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e-80)
   (- x (* y (/ z (- a z))))
   (if (<= z 1.4e-54)
     (+ x (* y (/ t a)))
     (if (<= z 1.8e+52) (+ x (* z (/ y (- z a)))) (+ x (* y (/ (- z t) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e-80) {
		tmp = x - (y * (z / (a - z)));
	} else if (z <= 1.4e-54) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.8e+52) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = x + (y * ((z - 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 (z <= (-1.2d-80)) then
        tmp = x - (y * (z / (a - z)))
    else if (z <= 1.4d-54) then
        tmp = x + (y * (t / a))
    else if (z <= 1.8d+52) then
        tmp = x + (z * (y / (z - a)))
    else
        tmp = x + (y * ((z - 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 (z <= -1.2e-80) {
		tmp = x - (y * (z / (a - z)));
	} else if (z <= 1.4e-54) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.8e+52) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e-80:
		tmp = x - (y * (z / (a - z)))
	elif z <= 1.4e-54:
		tmp = x + (y * (t / a))
	elif z <= 1.8e+52:
		tmp = x + (z * (y / (z - a)))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e-80)
		tmp = Float64(x - Float64(y * Float64(z / Float64(a - z))));
	elseif (z <= 1.4e-54)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.8e+52)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e-80)
		tmp = x - (y * (z / (a - z)));
	elseif (z <= 1.4e-54)
		tmp = x + (y * (t / a));
	elseif (z <= 1.8e+52)
		tmp = x + (z * (y / (z - a)));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e-80], N[(x - N[(y * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-54], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+52], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2e-80

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-/l* 89.4%

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

   5. Simplified 89.4%

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

   if -1.2e-80 < z < 1.4000000000000001e-54

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0 83.2%

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

      1. *-commutative 83.2%

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

      2. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

   if 1.4000000000000001e-54 < z < 1.8e52

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 91.0%

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

      1. *-lft-identity 91.0%

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

      2. associate-*l/ 91.0%

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

      3. associate-*r* 99.9%

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

      4. associate-/r/ 99.9%

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

      5. associate-*l/ 99.9%

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

      6. *-lft-identity 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around 0 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-*r/ 82.2%

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

   8. Simplified 82.2%

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

   if 1.8e52 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 98.4%

      \[\leadsto x + y \cdot \color{blue}{\frac{z - t}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-80}:\\ \;\;\;\;x - y \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-54}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{z}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-52}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+51}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) z)))))
   (if (<= z -1.45e-85)
     t_1
     (if (<= z 2.5e-52)
       (+ x (* y (/ t a)))
       (if (<= z 1.5e+51) (+ x (* z (/ y (- z a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -1.45e-85) {
		tmp = t_1;
	} else if (z <= 2.5e-52) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.5e+51) {
		tmp = x + (z * (y / (z - 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 * ((z - t) / z))
    if (z <= (-1.45d-85)) then
        tmp = t_1
    else if (z <= 2.5d-52) then
        tmp = x + (y * (t / a))
    else if (z <= 1.5d+51) then
        tmp = x + (z * (y / (z - 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 * ((z - t) / z));
	double tmp;
	if (z <= -1.45e-85) {
		tmp = t_1;
	} else if (z <= 2.5e-52) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.5e+51) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / z))
	tmp = 0
	if z <= -1.45e-85:
		tmp = t_1
	elif z <= 2.5e-52:
		tmp = x + (y * (t / a))
	elif z <= 1.5e+51:
		tmp = x + (z * (y / (z - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / z)))
	tmp = 0.0
	if (z <= -1.45e-85)
		tmp = t_1;
	elseif (z <= 2.5e-52)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.5e+51)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / z));
	tmp = 0.0;
	if (z <= -1.45e-85)
		tmp = t_1;
	elseif (z <= 2.5e-52)
		tmp = x + (y * (t / a));
	elseif (z <= 1.5e+51)
		tmp = x + (z * (y / (z - 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[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e-85], t$95$1, If[LessEqual[z, 2.5e-52], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+51], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4500000000000001e-85 or 1.5e51 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 91.6%

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

   if -1.4500000000000001e-85 < z < 2.5e-52

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0 83.1%

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

      1. *-commutative 83.1%

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

      2. associate-/l* 86.5%

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

   5. Simplified 86.5%

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

   if 2.5e-52 < z < 1.5e51

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 91.0%

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

      1. *-lft-identity 91.0%

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

      2. associate-*l/ 91.0%

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

      3. associate-*r* 99.9%

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

      4. associate-/r/ 99.9%

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

      5. associate-*l/ 99.9%

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

      6. *-lft-identity 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around 0 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-*r/ 82.2%

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

   8. Simplified 82.2%

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

Alternative 4: 76.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 92000000000000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+48}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.1e-70)
   (+ x y)
   (if (<= z 92000000000000.0)
     (+ x (* y (/ t a)))
     (if (<= z 2.5e+48) (- x (* z (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e-70) {
		tmp = x + y;
	} else if (z <= 92000000000000.0) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.5e+48) {
		tmp = x - (z * (y / 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 <= (-3.1d-70)) then
        tmp = x + y
    else if (z <= 92000000000000.0d0) then
        tmp = x + (y * (t / a))
    else if (z <= 2.5d+48) then
        tmp = x - (z * (y / 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 <= -3.1e-70) {
		tmp = x + y;
	} else if (z <= 92000000000000.0) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.5e+48) {
		tmp = x - (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.1e-70:
		tmp = x + y
	elif z <= 92000000000000.0:
		tmp = x + (y * (t / a))
	elif z <= 2.5e+48:
		tmp = x - (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.1e-70)
		tmp = Float64(x + y);
	elseif (z <= 92000000000000.0)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 2.5e+48)
		tmp = Float64(x - Float64(z * Float64(y / 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 <= -3.1e-70)
		tmp = x + y;
	elseif (z <= 92000000000000.0)
		tmp = x + (y * (t / a));
	elseif (z <= 2.5e+48)
		tmp = x - (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.1e-70], N[(x + y), $MachinePrecision], If[LessEqual[z, 92000000000000.0], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+48], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1e-70 or 2.49999999999999987e48 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 82.4%

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

      1. +-commutative 82.4%

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

   5. Simplified 82.4%

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

   if -3.1e-70 < z < 9.2e13

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 81.4%

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

      1. *-commutative 81.4%

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

      2. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

   if 9.2e13 < z < 2.49999999999999987e48

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. associate-/l* 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in z around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

      3. associate-/l* 84.0%

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

   8. Simplified 84.0%

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

      1. clear-num 84.0%

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

      2. un-div-inv 84.0%

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

   10. Applied egg-rr 84.0%

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

       1. associate-/r/ 84.0%

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

   12. Simplified 84.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 92000000000000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+48}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-69}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+14}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+48}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.16e-69)
   (+ x y)
   (if (<= z 1.02e+14)
     (+ x (* y (/ t a)))
     (if (<= z 8e+48) (- x (* y (/ z a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.16e-69) {
		tmp = x + y;
	} else if (z <= 1.02e+14) {
		tmp = x + (y * (t / a));
	} else if (z <= 8e+48) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.16d-69)) then
        tmp = x + y
    else if (z <= 1.02d+14) then
        tmp = x + (y * (t / a))
    else if (z <= 8d+48) then
        tmp = x - (y * (z / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.16e-69) {
		tmp = x + y;
	} else if (z <= 1.02e+14) {
		tmp = x + (y * (t / a));
	} else if (z <= 8e+48) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.16e-69:
		tmp = x + y
	elif z <= 1.02e+14:
		tmp = x + (y * (t / a))
	elif z <= 8e+48:
		tmp = x - (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.16e-69)
		tmp = Float64(x + y);
	elseif (z <= 1.02e+14)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 8e+48)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.16e-69)
		tmp = x + y;
	elseif (z <= 1.02e+14)
		tmp = x + (y * (t / a));
	elseif (z <= 8e+48)
		tmp = x - (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.16e-69], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.02e+14], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+48], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15999999999999989e-69 or 8.00000000000000035e48 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 82.4%

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

      1. +-commutative 82.4%

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

   5. Simplified 82.4%

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

   if -1.15999999999999989e-69 < z < 1.02e14

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 81.4%

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

      1. *-commutative 81.4%

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

      2. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

   if 1.02e14 < z < 8.00000000000000035e48

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. associate-/l* 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in z around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

      3. associate-/l* 84.0%

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

   8. Simplified 84.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-69}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+14}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+48}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-85} \lor \neg \left(z \leq 4 \cdot 10^{-15}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.46e-85) (not (<= z 4e-15)))
   (+ 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 <= -1.46e-85) || !(z <= 4e-15)) {
		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 <= (-1.46d-85)) .or. (.not. (z <= 4d-15))) 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 <= -1.46e-85) || !(z <= 4e-15)) {
		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 <= -1.46e-85) or not (z <= 4e-15):
		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 <= -1.46e-85) || !(z <= 4e-15))
		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 <= -1.46e-85) || ~((z <= 4e-15)))
		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, -1.46e-85], N[Not[LessEqual[z, 4e-15]], $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 < -1.46e-85 or 4.0000000000000003e-15 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 87.1%

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

   if -1.46e-85 < z < 4.0000000000000003e-15

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-/l* 86.3%

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

   5. Simplified 86.3%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-85} \lor \neg \left(z \leq 4 \cdot 10^{-15}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-65}:\\ \;\;\;\;x - y \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e-65)
   (- x (* y (/ z (- a z))))
   (if (<= z 3.6e+48) (- x (/ y (/ (- z a) t))) (+ x (* y (/ (- z t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e-65) {
		tmp = x - (y * (z / (a - z)));
	} else if (z <= 3.6e+48) {
		tmp = x - (y / ((z - a) / t));
	} else {
		tmp = x + (y * ((z - 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 (z <= (-8d-65)) then
        tmp = x - (y * (z / (a - z)))
    else if (z <= 3.6d+48) then
        tmp = x - (y / ((z - a) / t))
    else
        tmp = x + (y * ((z - 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 (z <= -8e-65) {
		tmp = x - (y * (z / (a - z)));
	} else if (z <= 3.6e+48) {
		tmp = x - (y / ((z - a) / t));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e-65:
		tmp = x - (y * (z / (a - z)))
	elif z <= 3.6e+48:
		tmp = x - (y / ((z - a) / t))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e-65)
		tmp = Float64(x - Float64(y * Float64(z / Float64(a - z))));
	elseif (z <= 3.6e+48)
		tmp = Float64(x - Float64(y / Float64(Float64(z - a) / t)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e-65)
		tmp = x - (y * (z / (a - z)));
	elseif (z <= 3.6e+48)
		tmp = x - (y / ((z - a) / t));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e-65], N[(x - N[(y * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+48], N[(x - N[(y / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.99999999999999939e-65

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 71.5%

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

      1. +-commutative 71.5%

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

      2. associate-/l* 90.5%

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

   5. Simplified 90.5%

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

   if -7.99999999999999939e-65 < z < 3.59999999999999983e48

   1. Initial program 98.5%

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

      1. clear-num 98.4%

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

      2. un-div-inv 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in t around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. distribute-neg-frac2 90.2%

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

   7. Simplified 90.2%

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

   if 3.59999999999999983e48 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 98.4%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-65}:\\ \;\;\;\;x - y \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-64}:\\ \;\;\;\;x - y \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+48}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e-64)
   (- x (* y (/ z (- a z))))
   (if (<= z 6e+48) (+ x (* t (/ y (- a z)))) (+ x (* y (/ (- z t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e-64) {
		tmp = x - (y * (z / (a - z)));
	} else if (z <= 6e+48) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * ((z - 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 (z <= (-1.35d-64)) then
        tmp = x - (y * (z / (a - z)))
    else if (z <= 6d+48) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (y * ((z - 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 (z <= -1.35e-64) {
		tmp = x - (y * (z / (a - z)));
	} else if (z <= 6e+48) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e-64:
		tmp = x - (y * (z / (a - z)))
	elif z <= 6e+48:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e-64)
		tmp = Float64(x - Float64(y * Float64(z / Float64(a - z))));
	elseif (z <= 6e+48)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e-64)
		tmp = x - (y * (z / (a - z)));
	elseif (z <= 6e+48)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e-64], N[(x - N[(y * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+48], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.34999999999999993e-64

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 71.5%

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

      1. +-commutative 71.5%

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

      2. associate-/l* 90.5%

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

   5. Simplified 90.5%

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

   if -1.34999999999999993e-64 < z < 5.9999999999999999e48

   1. Initial program 98.5%

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

      1. clear-num 98.4%

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

      2. un-div-inv 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in t around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. distribute-neg-frac2 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in x around 0 86.8%

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

      1. associate-*r/ 87.9%

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

      2. neg-mul-1 87.9%

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

      3. distribute-lft-neg-in 87.9%

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

      4. cancel-sign-sub-inv 87.9%

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

   10. Simplified 87.9%

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

   if 5.9999999999999999e48 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 98.4%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-64}:\\ \;\;\;\;x - y \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+48}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-69} \lor \neg \left(z \leq 10^{-54}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e-69) (not (<= z 1e-54))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e-69) || !(z <= 1e-54)) {
		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 <= (-1.85d-69)) .or. (.not. (z <= 1d-54))) 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 <= -1.85e-69) || !(z <= 1e-54)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e-69) or not (z <= 1e-54):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e-69) || !(z <= 1e-54))
		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 <= -1.85e-69) || ~((z <= 1e-54)))
		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, -1.85e-69], N[Not[LessEqual[z, 1e-54]], $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 < -1.8500000000000001e-69 or 1e-54 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.6%

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

      1. +-commutative 78.6%

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

   5. Simplified 78.6%

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

   if -1.8500000000000001e-69 < z < 1e-54

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0 83.2%

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

      1. *-commutative 83.2%

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

      2. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-69} \lor \neg \left(z \leq 10^{-54}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-66} \lor \neg \left(z \leq 3.6 \cdot 10^{-54}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.6e-66) (not (<= z 3.6e-54))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.6e-66) || !(z <= 3.6e-54)) {
		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 <= (-3.6d-66)) .or. (.not. (z <= 3.6d-54))) 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 <= -3.6e-66) || !(z <= 3.6e-54)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.6e-66) or not (z <= 3.6e-54):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.6e-66) || !(z <= 3.6e-54))
		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 <= -3.6e-66) || ~((z <= 3.6e-54)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.6e-66], N[Not[LessEqual[z, 3.6e-54]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.60000000000000012e-66 or 3.59999999999999976e-54 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 79.1%

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

      1. +-commutative 79.1%

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

   5. Simplified 79.1%

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

   if -3.60000000000000012e-66 < z < 3.59999999999999976e-54

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf 59.2%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-66} \lor \neg \left(z \leq 3.6 \cdot 10^{-54}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.1% 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 99.1%

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

Alternative 12: 51.5% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 99.1%

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

3. Taylor expanded in x around inf 55.6%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

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 2024091 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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