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

Percentage Accurate: 98.2% → 98.2%

Time: 10.6s

Alternatives: 10

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: 98.2% 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]

Alternative 1: 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 99.1%

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

3. Final simplification 99.1%

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

Alternative 2: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+41}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-127}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-14} \lor \neg \left(z \leq 2.3 \cdot 10^{+45}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ t z)))))
   (if (<= z -9.5e+41)
     (+ x y)
     (if (<= z -1.25e-24)
       t_1
       (if (<= z 1.05e-127)
         (+ x (* y (/ t a)))
         (if (or (<= z 1.6e-14) (not (<= z 2.3e+45))) (+ x y) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (t / z));
	double tmp;
	if (z <= -9.5e+41) {
		tmp = x + y;
	} else if (z <= -1.25e-24) {
		tmp = t_1;
	} else if (z <= 1.05e-127) {
		tmp = x + (y * (t / a));
	} else if ((z <= 1.6e-14) || !(z <= 2.3e+45)) {
		tmp = x + y;
	} 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 * (t / z))
    if (z <= (-9.5d+41)) then
        tmp = x + y
    else if (z <= (-1.25d-24)) then
        tmp = t_1
    else if (z <= 1.05d-127) then
        tmp = x + (y * (t / a))
    else if ((z <= 1.6d-14) .or. (.not. (z <= 2.3d+45))) then
        tmp = x + y
    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 * (t / z));
	double tmp;
	if (z <= -9.5e+41) {
		tmp = x + y;
	} else if (z <= -1.25e-24) {
		tmp = t_1;
	} else if (z <= 1.05e-127) {
		tmp = x + (y * (t / a));
	} else if ((z <= 1.6e-14) || !(z <= 2.3e+45)) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (t / z))
	tmp = 0
	if z <= -9.5e+41:
		tmp = x + y
	elif z <= -1.25e-24:
		tmp = t_1
	elif z <= 1.05e-127:
		tmp = x + (y * (t / a))
	elif (z <= 1.6e-14) or not (z <= 2.3e+45):
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(t / z)))
	tmp = 0.0
	if (z <= -9.5e+41)
		tmp = Float64(x + y);
	elseif (z <= -1.25e-24)
		tmp = t_1;
	elseif (z <= 1.05e-127)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif ((z <= 1.6e-14) || !(z <= 2.3e+45))
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (t / z));
	tmp = 0.0;
	if (z <= -9.5e+41)
		tmp = x + y;
	elseif (z <= -1.25e-24)
		tmp = t_1;
	elseif (z <= 1.05e-127)
		tmp = x + (y * (t / a));
	elseif ((z <= 1.6e-14) || ~((z <= 2.3e+45)))
		tmp = x + y;
	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[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+41], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.25e-24], t$95$1, If[LessEqual[z, 1.05e-127], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.6e-14], N[Not[LessEqual[z, 2.3e+45]], $MachinePrecision]], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999996e41 or 1.05000000000000005e-127 < z < 1.6000000000000001e-14 or 2.30000000000000012e45 < z

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 79.0%

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

   if -9.4999999999999996e41 < z < -1.24999999999999995e-24 or 1.6000000000000001e-14 < z < 2.30000000000000012e45

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 90.5%

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

      1. neg-mul-1 90.5%

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

      2. distribute-neg-frac 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in z around inf 85.4%

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

      1. associate-*r/ 85.4%

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

      2. neg-mul-1 85.4%

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

   8. Simplified 85.4%

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

   if -1.24999999999999995e-24 < z < 1.05000000000000005e-127

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 83.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+41}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-24}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-127}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-14} \lor \neg \left(z \leq 2.3 \cdot 10^{+45}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-26}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-196}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))))
   (if (<= z -1.5e+37)
     t_1
     (if (<= z -7.2e-26)
       (- x (* t (/ y z)))
       (if (<= z 5.5e-196) (+ x (/ y (/ a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -1.5e+37) {
		tmp = t_1;
	} else if (z <= -7.2e-26) {
		tmp = x - (t * (y / z));
	} else if (z <= 5.5e-196) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / (z - a)))
    if (z <= (-1.5d+37)) then
        tmp = t_1
    else if (z <= (-7.2d-26)) then
        tmp = x - (t * (y / z))
    else if (z <= 5.5d-196) then
        tmp = x + (y / (a / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -1.5e+37) {
		tmp = t_1;
	} else if (z <= -7.2e-26) {
		tmp = x - (t * (y / z));
	} else if (z <= 5.5e-196) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	tmp = 0
	if z <= -1.5e+37:
		tmp = t_1
	elif z <= -7.2e-26:
		tmp = x - (t * (y / z))
	elif z <= 5.5e-196:
		tmp = x + (y / (a / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(z - a))))
	tmp = 0.0
	if (z <= -1.5e+37)
		tmp = t_1;
	elseif (z <= -7.2e-26)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 5.5e-196)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (z - a)));
	tmp = 0.0;
	if (z <= -1.5e+37)
		tmp = t_1;
	elseif (z <= -7.2e-26)
		tmp = x - (t * (y / z));
	elseif (z <= 5.5e-196)
		tmp = x + (y / (a / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+37], t$95$1, If[LessEqual[z, -7.2e-26], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-196], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.50000000000000011e37 or 5.50000000000000014e-196 < z

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0 85.0%

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

   if -1.50000000000000011e37 < z < -7.2000000000000003e-26

   1. Initial program 99.9%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. associate-/l* 98.9%

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

      3. distribute-neg-frac 98.9%

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

   9. Simplified 98.9%

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

   10. Taylor expanded in z around inf 97.9%

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

       1. mul-1-neg 97.9%

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

       2. associate-*r/ 97.9%

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

       3. *-commutative 97.9%

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

       4. distribute-rgt-neg-in 97.9%

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

   12. Simplified 97.9%

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

   if -7.2000000000000003e-26 < z < 5.50000000000000014e-196

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 87.0%

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

      1. clear-num 87.0%

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

      2. un-div-inv 87.1%

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

   5. Applied egg-rr 87.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+37}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-26}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-196}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-26}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-196}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+39)
   (+ x (/ y (/ (- z a) z)))
   (if (<= z -6.2e-26)
     (- x (* t (/ y z)))
     (if (<= z 5.5e-196) (+ x (/ y (/ a t))) (+ x (* y (/ z (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+39) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= -6.2e-26) {
		tmp = x - (t * (y / z));
	} else if (z <= 5.5e-196) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y * (z / (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 <= (-2.6d+39)) then
        tmp = x + (y / ((z - a) / z))
    else if (z <= (-6.2d-26)) then
        tmp = x - (t * (y / z))
    else if (z <= 5.5d-196) then
        tmp = x + (y / (a / t))
    else
        tmp = x + (y * (z / (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 <= -2.6e+39) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= -6.2e-26) {
		tmp = x - (t * (y / z));
	} else if (z <= 5.5e-196) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+39:
		tmp = x + (y / ((z - a) / z))
	elif z <= -6.2e-26:
		tmp = x - (t * (y / z))
	elif z <= 5.5e-196:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+39)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	elseif (z <= -6.2e-26)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 5.5e-196)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+39)
		tmp = x + (y / ((z - a) / z));
	elseif (z <= -6.2e-26)
		tmp = x - (t * (y / z));
	elseif (z <= 5.5e-196)
		tmp = x + (y / (a / t));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+39], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-26], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-196], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e39

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 87.4%

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

      1. associate-/l* 93.7%

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

   5. Simplified 93.7%

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

   if -2.6e39 < z < -6.19999999999999966e-26

   1. Initial program 99.9%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. associate-/l* 98.9%

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

      3. distribute-neg-frac 98.9%

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

   9. Simplified 98.9%

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

   10. Taylor expanded in z around inf 97.9%

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

       1. mul-1-neg 97.9%

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

       2. associate-*r/ 97.9%

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

       3. *-commutative 97.9%

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

       4. distribute-rgt-neg-in 97.9%

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

   12. Simplified 97.9%

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

   if -6.19999999999999966e-26 < z < 5.50000000000000014e-196

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 87.0%

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

      1. clear-num 87.0%

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

      2. un-div-inv 87.1%

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

   5. Applied egg-rr 87.1%

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

   if 5.50000000000000014e-196 < z

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 80.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-26}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-196}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+40}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-24}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-127}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+40)
   (+ x y)
   (if (<= z -3.9e-24)
     (- x (* t (/ y z)))
     (if (<= z 1.05e-127) (+ x (* y (/ t a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+40) {
		tmp = x + y;
	} else if (z <= -3.9e-24) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.05e-127) {
		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 <= (-1.5d+40)) then
        tmp = x + y
    else if (z <= (-3.9d-24)) then
        tmp = x - (t * (y / z))
    else if (z <= 1.05d-127) 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 <= -1.5e+40) {
		tmp = x + y;
	} else if (z <= -3.9e-24) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.05e-127) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.5e+40:
		tmp = x + y
	elif z <= -3.9e-24:
		tmp = x - (t * (y / z))
	elif z <= 1.05e-127:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+40)
		tmp = Float64(x + y);
	elseif (z <= -3.9e-24)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 1.05e-127)
		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 <= -1.5e+40)
		tmp = x + y;
	elseif (z <= -3.9e-24)
		tmp = x - (t * (y / z));
	elseif (z <= 1.05e-127)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+40], N[(x + y), $MachinePrecision], If[LessEqual[z, -3.9e-24], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-127], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5000000000000001e40 or 1.05000000000000005e-127 < z

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 75.3%

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

   if -1.5000000000000001e40 < z < -3.9e-24

   1. Initial program 99.9%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. associate-/l* 98.9%

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

      3. distribute-neg-frac 98.9%

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

   9. Simplified 98.9%

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

   10. Taylor expanded in z around inf 97.9%

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

       1. mul-1-neg 97.9%

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

       2. associate-*r/ 97.9%

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

       3. *-commutative 97.9%

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

       4. distribute-rgt-neg-in 97.9%

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

   12. Simplified 97.9%

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

   if -3.9e-24 < z < 1.05000000000000005e-127

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 83.5%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+40}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-24}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-127}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-67} \lor \neg \left(t \leq 4.6 \cdot 10^{+86}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2e-67) (not (<= t 4.6e+86)))
   (- x (* y (/ t (- z a))))
   (+ x (/ y (/ (- z a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e-67) || !(t <= 4.6e+86)) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2d-67)) .or. (.not. (t <= 4.6d+86))) then
        tmp = x - (y * (t / (z - a)))
    else
        tmp = x + (y / ((z - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e-67) || !(t <= 4.6e+86)) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2e-67) or not (t <= 4.6e+86):
		tmp = x - (y * (t / (z - a)))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2e-67) || !(t <= 4.6e+86))
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2e-67) || ~((t <= 4.6e+86)))
		tmp = x - (y * (t / (z - a)));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2e-67], N[Not[LessEqual[t, 4.6e+86]], $MachinePrecision]], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.99999999999999989e-67 or 4.59999999999999979e86 < t

   1. Initial program 98.1%

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

   3. Taylor expanded in t around inf 89.1%

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

      1. neg-mul-1 89.1%

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

      2. distribute-neg-frac 89.1%

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

   5. Simplified 89.1%

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

   if -1.99999999999999989e-67 < t < 4.59999999999999979e86

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 79.1%

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

      1. associate-/l* 90.8%

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

   5. Simplified 90.8%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-67} \lor \neg \left(t \leq 4.6 \cdot 10^{+86}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-68} \lor \neg \left(t \leq 6.2 \cdot 10^{+86}\right):\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.5e-68) (not (<= t 6.2e+86)))
   (- x (/ t (/ (- z a) y)))
   (+ x (/ y (/ (- z a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e-68) || !(t <= 6.2e+86)) {
		tmp = x - (t / ((z - a) / y));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.5d-68)) .or. (.not. (t <= 6.2d+86))) then
        tmp = x - (t / ((z - a) / y))
    else
        tmp = x + (y / ((z - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e-68) || !(t <= 6.2e+86)) {
		tmp = x - (t / ((z - a) / y));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.5e-68) or not (t <= 6.2e+86):
		tmp = x - (t / ((z - a) / y))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.5e-68) || !(t <= 6.2e+86))
		tmp = Float64(x - Float64(t / Float64(Float64(z - a) / y)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.5e-68) || ~((t <= 6.2e+86)))
		tmp = x - (t / ((z - a) / y));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.5e-68], N[Not[LessEqual[t, 6.2e+86]], $MachinePrecision]], N[(x - N[(t / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.49999999999999986e-68 or 6.2000000000000004e86 < t

   1. Initial program 98.1%

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

      1. associate-*r/ 84.7%

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

   3. Simplified 84.7%

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

      1. associate-/l* 98.1%

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

      2. associate-/r/ 98.9%

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

   6. Applied egg-rr 98.9%

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

   7. Taylor expanded in t around inf 81.7%

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

      1. mul-1-neg 81.7%

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

      2. associate-/l* 90.9%

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

      3. distribute-neg-frac 90.9%

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

   9. Simplified 90.9%

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

   if -2.49999999999999986e-68 < t < 6.2000000000000004e86

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 79.1%

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

      1. associate-/l* 90.8%

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

   5. Simplified 90.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-68} \lor \neg \left(t \leq 6.2 \cdot 10^{+86}\right):\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-13} \lor \neg \left(z \leq 1.05 \cdot 10^{-127}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3e-13) (not (<= z 1.05e-127))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e-13) || !(z <= 1.05e-127)) {
		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 <= (-3d-13)) .or. (.not. (z <= 1.05d-127))) 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 <= -3e-13) || !(z <= 1.05e-127)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3e-13) or not (z <= 1.05e-127):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3e-13) || !(z <= 1.05e-127))
		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 <= -3e-13) || ~((z <= 1.05e-127)))
		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, -3e-13], N[Not[LessEqual[z, 1.05e-127]], $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 < -2.99999999999999984e-13 or 1.05000000000000005e-127 < z

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 73.7%

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

   if -2.99999999999999984e-13 < z < 1.05000000000000005e-127

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 81.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-13} \lor \neg \left(z \leq 1.05 \cdot 10^{-127}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.85e+44) x (if (<= a 1.1e+33) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.85e+44) {
		tmp = x;
	} else if (a <= 1.1e+33) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.85d+44)) then
        tmp = x
    else if (a <= 1.1d+33) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.85e+44) {
		tmp = x;
	} else if (a <= 1.1e+33) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.85e+44:
		tmp = x
	elif a <= 1.1e+33:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.85e+44)
		tmp = x;
	elseif (a <= 1.1e+33)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.85e+44)
		tmp = x;
	elseif (a <= 1.1e+33)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.85e+44], x, If[LessEqual[a, 1.1e+33], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8500000000000001e44 or 1.09999999999999997e33 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 82.6%

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

   4. Taylor expanded in x around inf 65.3%

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

   if -2.8500000000000001e44 < a < 1.09999999999999997e33

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf 62.5%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.3% 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 z around 0 60.4%

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

4. Taylor expanded in x around inf 50.7%

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

5. Final simplification 50.7%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 98.4% 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 2024020 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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