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

Percentage Accurate: 98.0% → 96.7%

Time: 12.6s

Alternatives: 17

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: 98.0% 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: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := x + t \cdot \frac{y}{a - z}\\ \mathbf{if}\;t\_1 \leq -50000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.1:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+43}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))) (t_2 (+ x (* t (/ y (- a z))))))
   (if (<= t_1 -50000000000.0)
     t_2
     (if (<= t_1 0.1)
       (+ x (* y (/ (- t z) a)))
       (if (<= t_1 5e+43) (- x (* y (/ (- t z) z))) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = x + (t * (y / (a - z)));
	double tmp;
	if (t_1 <= -50000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.1) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 5e+43) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (z - t) / (z - a)
    t_2 = x + (t * (y / (a - z)))
    if (t_1 <= (-50000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.1d0) then
        tmp = x + (y * ((t - z) / a))
    else if (t_1 <= 5d+43) then
        tmp = x - (y * ((t - z) / z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = x + (t * (y / (a - z)));
	double tmp;
	if (t_1 <= -50000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.1) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 5e+43) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	t_2 = x + (t * (y / (a - z)))
	tmp = 0
	if t_1 <= -50000000000.0:
		tmp = t_2
	elif t_1 <= 0.1:
		tmp = x + (y * ((t - z) / a))
	elif t_1 <= 5e+43:
		tmp = x - (y * ((t - z) / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = Float64(x + Float64(t * Float64(y / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -50000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.1)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	elseif (t_1 <= 5e+43)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	t_2 = x + (t * (y / (a - z)));
	tmp = 0.0;
	if (t_1 <= -50000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.1)
		tmp = x + (y * ((t - z) / a));
	elseif (t_1 <= 5e+43)
		tmp = x - (y * ((t - z) / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -50000000000.0], t$95$2, If[LessEqual[t$95$1, 0.1], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+43], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5e10 or 5.0000000000000004e43 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 95.1%

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

   3. Taylor expanded in t around inf 91.0%

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

      1. mul-1-neg 91.0%

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

      2. associate-/l* 99.4%

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

   5. Simplified 99.4%

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

   if -5e10 < (/.f64 (-.f64 z t) (-.f64 z a)) < 0.10000000000000001

   1. Initial program 99.6%

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

   3. Taylor expanded in a around inf 86.4%

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

      1. mul-1-neg 86.4%

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

      2. associate-/l* 98.2%

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

      3. distribute-rgt-neg-in 98.2%

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

      4. distribute-neg-frac2 98.2%

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

   5. Simplified 98.2%

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

   if 0.10000000000000001 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5.0000000000000004e43

   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 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -50000000000:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 0.1:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 5 \cdot 10^{+43}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. +-commutative 98.4%

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

   2. fma-define 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

   \[\leadsto \mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right) \]
6. Add Preprocessing

Alternative 3: 82.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 0.1:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+111}:\\ \;\;\;\;y \cdot t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{+204}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -5e+17)
     (- x (* t (/ y z)))
     (if (<= t_1 0.1)
       (+ x (* t (/ y a)))
       (if (<= t_1 2.0)
         (- x (* y (/ (- t z) z)))
         (if (<= t_1 1e+111)
           (* y t_1)
           (if (<= t_1 1e+204) (- x (/ y (/ z t))) (* t (/ y (- a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 0.1) {
		tmp = x + (t * (y / a));
	} else if (t_1 <= 2.0) {
		tmp = x - (y * ((t - z) / z));
	} else if (t_1 <= 1e+111) {
		tmp = y * t_1;
	} else if (t_1 <= 1e+204) {
		tmp = x - (y / (z / t));
	} else {
		tmp = t * (y / (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) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (z - a)
    if (t_1 <= (-5d+17)) then
        tmp = x - (t * (y / z))
    else if (t_1 <= 0.1d0) then
        tmp = x + (t * (y / a))
    else if (t_1 <= 2.0d0) then
        tmp = x - (y * ((t - z) / z))
    else if (t_1 <= 1d+111) then
        tmp = y * t_1
    else if (t_1 <= 1d+204) then
        tmp = x - (y / (z / t))
    else
        tmp = t * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 0.1) {
		tmp = x + (t * (y / a));
	} else if (t_1 <= 2.0) {
		tmp = x - (y * ((t - z) / z));
	} else if (t_1 <= 1e+111) {
		tmp = y * t_1;
	} else if (t_1 <= 1e+204) {
		tmp = x - (y / (z / t));
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -5e+17:
		tmp = x - (t * (y / z))
	elif t_1 <= 0.1:
		tmp = x + (t * (y / a))
	elif t_1 <= 2.0:
		tmp = x - (y * ((t - z) / z))
	elif t_1 <= 1e+111:
		tmp = y * t_1
	elif t_1 <= 1e+204:
		tmp = x - (y / (z / t))
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+17)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (t_1 <= 0.1)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (t_1 <= 2.0)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	elseif (t_1 <= 1e+111)
		tmp = Float64(y * t_1);
	elseif (t_1 <= 1e+204)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	tmp = 0.0;
	if (t_1 <= -5e+17)
		tmp = x - (t * (y / z));
	elseif (t_1 <= 0.1)
		tmp = x + (t * (y / a));
	elseif (t_1 <= 2.0)
		tmp = x - (y * ((t - z) / z));
	elseif (t_1 <= 1e+111)
		tmp = y * t_1;
	elseif (t_1 <= 1e+204)
		tmp = x - (y / (z / t));
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+17], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.1], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+111], N[(y * t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 1e+204], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5e17

   1. Initial program 97.0%

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

   3. Taylor expanded in t around inf 88.6%

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

      1. mul-1-neg 88.6%

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

      2. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. sub-neg 68.5%

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

      3. associate-/l* 77.0%

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

   8. Simplified 77.0%

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

   if -5e17 < (/.f64 (-.f64 z t) (-.f64 z a)) < 0.10000000000000001

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. associate-/l* 83.2%

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

   5. Simplified 83.2%

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

   if 0.10000000000000001 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 99.9%

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

   if 2 < (/.f64 (-.f64 z t) (-.f64 z a)) < 9.99999999999999957e110

   1. Initial program 99.7%

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

      1. add-cube-cbrt 98.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot \frac{z - t}{z - a}} \cdot \sqrt[3]{x + y \cdot \frac{z - t}{z - a}}\right) \cdot \sqrt[3]{x + y \cdot \frac{z - t}{z - a}}} \]

      2. pow3 98.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot \frac{z - t}{z - a}}\right)}^{3}} \]

      3. +-commutative 98.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \frac{z - t}{z - a} + x}}\right)}^{3} \]

      4. fma-undefine 98.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around inf 89.1%

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

      1. div-sub 89.1%

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

   7. Simplified 89.1%

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

   if 9.99999999999999957e110 < (/.f64 (-.f64 z t) (-.f64 z a)) < 9.99999999999999989e203

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 75.8%

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

      1. clear-num 75.6%

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

      2. un-div-inv 87.7%

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

   5. Applied egg-rr 87.7%

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

   6. Taylor expanded in z around 0 87.7%

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

      1. associate-*r/ 87.7%

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

      2. neg-mul-1 87.7%

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

   8. Simplified 87.7%

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

   if 9.99999999999999989e203 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 84.3%

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

      1. add-cube-cbrt 83.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot \frac{z - t}{z - a}} \cdot \sqrt[3]{x + y \cdot \frac{z - t}{z - a}}\right) \cdot \sqrt[3]{x + y \cdot \frac{z - t}{z - a}}} \]

      2. pow3 83.8%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot \frac{z - t}{z - a}}\right)}^{3}} \]

      3. +-commutative 83.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \frac{z - t}{z - a} + x}}\right)}^{3} \]

      4. fma-undefine 83.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 83.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in t around inf 93.3%

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

      1. neg-mul-1 93.3%

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

      2. distribute-frac-neg2 93.3%

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

      3. associate-/l* 93.3%

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

   7. Simplified 93.3%

      \[\leadsto \color{blue}{t \cdot \frac{y}{-\left(z - a\right)}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 0.1:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 2:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+111}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+204}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 0.1:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+111}:\\ \;\;\;\;y \cdot t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{+204}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -5e+17)
     (- x (* t (/ y z)))
     (if (<= t_1 0.1)
       (+ x (* (/ y a) (- t z)))
       (if (<= t_1 2.0)
         (- x (* y (/ (- t z) z)))
         (if (<= t_1 1e+111)
           (* y t_1)
           (if (<= t_1 1e+204) (- x (/ y (/ z t))) (* t (/ y (- a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 0.1) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 2.0) {
		tmp = x - (y * ((t - z) / z));
	} else if (t_1 <= 1e+111) {
		tmp = y * t_1;
	} else if (t_1 <= 1e+204) {
		tmp = x - (y / (z / t));
	} else {
		tmp = t * (y / (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) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (z - a)
    if (t_1 <= (-5d+17)) then
        tmp = x - (t * (y / z))
    else if (t_1 <= 0.1d0) then
        tmp = x + ((y / a) * (t - z))
    else if (t_1 <= 2.0d0) then
        tmp = x - (y * ((t - z) / z))
    else if (t_1 <= 1d+111) then
        tmp = y * t_1
    else if (t_1 <= 1d+204) then
        tmp = x - (y / (z / t))
    else
        tmp = t * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 0.1) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 2.0) {
		tmp = x - (y * ((t - z) / z));
	} else if (t_1 <= 1e+111) {
		tmp = y * t_1;
	} else if (t_1 <= 1e+204) {
		tmp = x - (y / (z / t));
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -5e+17:
		tmp = x - (t * (y / z))
	elif t_1 <= 0.1:
		tmp = x + ((y / a) * (t - z))
	elif t_1 <= 2.0:
		tmp = x - (y * ((t - z) / z))
	elif t_1 <= 1e+111:
		tmp = y * t_1
	elif t_1 <= 1e+204:
		tmp = x - (y / (z / t))
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+17)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (t_1 <= 0.1)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	elseif (t_1 <= 2.0)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	elseif (t_1 <= 1e+111)
		tmp = Float64(y * t_1);
	elseif (t_1 <= 1e+204)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	tmp = 0.0;
	if (t_1 <= -5e+17)
		tmp = x - (t * (y / z));
	elseif (t_1 <= 0.1)
		tmp = x + ((y / a) * (t - z));
	elseif (t_1 <= 2.0)
		tmp = x - (y * ((t - z) / z));
	elseif (t_1 <= 1e+111)
		tmp = y * t_1;
	elseif (t_1 <= 1e+204)
		tmp = x - (y / (z / t));
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+17], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.1], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+111], N[(y * t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 1e+204], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5e17

   1. Initial program 97.0%

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

   3. Taylor expanded in t around inf 88.6%

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

      1. mul-1-neg 88.6%

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

      2. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. sub-neg 68.5%

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

      3. associate-/l* 77.0%

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

   8. Simplified 77.0%

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

   if -5e17 < (/.f64 (-.f64 z t) (-.f64 z a)) < 0.10000000000000001

   1. Initial program 99.6%

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

   3. Taylor expanded in a around inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

      3. *-commutative 85.7%

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

      4. associate-/l* 94.1%

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

   5. Simplified 94.1%

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

   if 0.10000000000000001 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 99.9%

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

   if 2 < (/.f64 (-.f64 z t) (-.f64 z a)) < 9.99999999999999957e110

   1. Initial program 99.7%

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

      1. add-cube-cbrt 98.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot \frac{z - t}{z - a}} \cdot \sqrt[3]{x + y \cdot \frac{z - t}{z - a}}\right) \cdot \sqrt[3]{x + y \cdot \frac{z - t}{z - a}}} \]

      2. pow3 98.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot \frac{z - t}{z - a}}\right)}^{3}} \]

      3. +-commutative 98.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \frac{z - t}{z - a} + x}}\right)}^{3} \]

      4. fma-undefine 98.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around inf 89.1%

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

      1. div-sub 89.1%

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

   7. Simplified 89.1%

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

   if 9.99999999999999957e110 < (/.f64 (-.f64 z t) (-.f64 z a)) < 9.99999999999999989e203

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 75.8%

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

      1. clear-num 75.6%

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

      2. un-div-inv 87.7%

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

   5. Applied egg-rr 87.7%

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

   6. Taylor expanded in z around 0 87.7%

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

      1. associate-*r/ 87.7%

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

      2. neg-mul-1 87.7%

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

   8. Simplified 87.7%

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

   if 9.99999999999999989e203 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 84.3%

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

      1. add-cube-cbrt 83.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot \frac{z - t}{z - a}} \cdot \sqrt[3]{x + y \cdot \frac{z - t}{z - a}}\right) \cdot \sqrt[3]{x + y \cdot \frac{z - t}{z - a}}} \]

      2. pow3 83.8%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot \frac{z - t}{z - a}}\right)}^{3}} \]

      3. +-commutative 83.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \frac{z - t}{z - a} + x}}\right)}^{3} \]

      4. fma-undefine 83.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 83.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in t around inf 93.3%

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

      1. neg-mul-1 93.3%

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

      2. distribute-frac-neg2 93.3%

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

      3. associate-/l* 93.3%

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

   7. Simplified 93.3%

      \[\leadsto \color{blue}{t \cdot \frac{y}{-\left(z - a\right)}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 0.1:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 2:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+111}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+204}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 0.1:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -5e+17)
     (- x (* t (/ y z)))
     (if (<= t_1 0.1)
       (+ x (* t (/ y a)))
       (if (<= t_1 2.0) (+ y x) (* y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 0.1) {
		tmp = x + (t * (y / a));
	} else if (t_1 <= 2.0) {
		tmp = y + x;
	} else {
		tmp = y * 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 = (z - t) / (z - a)
    if (t_1 <= (-5d+17)) then
        tmp = x - (t * (y / z))
    else if (t_1 <= 0.1d0) then
        tmp = x + (t * (y / a))
    else if (t_1 <= 2.0d0) then
        tmp = y + x
    else
        tmp = y * 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 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 0.1) {
		tmp = x + (t * (y / a));
	} else if (t_1 <= 2.0) {
		tmp = y + x;
	} else {
		tmp = y * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -5e+17:
		tmp = x - (t * (y / z))
	elif t_1 <= 0.1:
		tmp = x + (t * (y / a))
	elif t_1 <= 2.0:
		tmp = y + x
	else:
		tmp = y * t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+17)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (t_1 <= 0.1)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (t_1 <= 2.0)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	tmp = 0.0;
	if (t_1 <= -5e+17)
		tmp = x - (t * (y / z));
	elseif (t_1 <= 0.1)
		tmp = x + (t * (y / a));
	elseif (t_1 <= 2.0)
		tmp = y + x;
	else
		tmp = y * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+17], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.1], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(y + x), $MachinePrecision], N[(y * t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5e17

   1. Initial program 97.0%

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

   3. Taylor expanded in t around inf 88.6%

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

      1. mul-1-neg 88.6%

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

      2. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. sub-neg 68.5%

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

      3. associate-/l* 77.0%

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

   8. Simplified 77.0%

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

   if -5e17 < (/.f64 (-.f64 z t) (-.f64 z a)) < 0.10000000000000001

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. associate-/l* 83.2%

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

   5. Simplified 83.2%

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

   if 0.10000000000000001 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.2%

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

      1. +-commutative 99.2%

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

   5. Simplified 99.2%

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

   if 2 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 93.7%

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

      1. add-cube-cbrt 92.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot \frac{z - t}{z - a}} \cdot \sqrt[3]{x + y \cdot \frac{z - t}{z - a}}\right) \cdot \sqrt[3]{x + y \cdot \frac{z - t}{z - a}}} \]

      2. pow3 92.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot \frac{z - t}{z - a}}\right)}^{3}} \]

      3. +-commutative 92.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \frac{z - t}{z - a} + x}}\right)}^{3} \]

      4. fma-undefine 92.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 92.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around inf 78.0%

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

      1. div-sub 78.0%

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

   7. Simplified 78.0%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 0.1:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 2:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := x + t \cdot \frac{y}{a - z}\\ \mathbf{if}\;t\_1 \leq -50000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.1:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+43}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))) (t_2 (+ x (* t (/ y (- a z))))))
   (if (<= t_1 -50000000000.0)
     t_2
     (if (<= t_1 0.1)
       (+ x (* (/ y a) (- t z)))
       (if (<= t_1 5e+43) (- x (* y (/ (- t z) z))) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = x + (t * (y / (a - z)));
	double tmp;
	if (t_1 <= -50000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.1) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 5e+43) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (z - t) / (z - a)
    t_2 = x + (t * (y / (a - z)))
    if (t_1 <= (-50000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.1d0) then
        tmp = x + ((y / a) * (t - z))
    else if (t_1 <= 5d+43) then
        tmp = x - (y * ((t - z) / z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = x + (t * (y / (a - z)));
	double tmp;
	if (t_1 <= -50000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.1) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 5e+43) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	t_2 = x + (t * (y / (a - z)))
	tmp = 0
	if t_1 <= -50000000000.0:
		tmp = t_2
	elif t_1 <= 0.1:
		tmp = x + ((y / a) * (t - z))
	elif t_1 <= 5e+43:
		tmp = x - (y * ((t - z) / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = Float64(x + Float64(t * Float64(y / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -50000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.1)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	elseif (t_1 <= 5e+43)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	t_2 = x + (t * (y / (a - z)));
	tmp = 0.0;
	if (t_1 <= -50000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.1)
		tmp = x + ((y / a) * (t - z));
	elseif (t_1 <= 5e+43)
		tmp = x - (y * ((t - z) / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -50000000000.0], t$95$2, If[LessEqual[t$95$1, 0.1], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+43], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5e10 or 5.0000000000000004e43 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 95.1%

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

   3. Taylor expanded in t around inf 91.0%

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

      1. mul-1-neg 91.0%

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

      2. associate-/l* 99.4%

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

   5. Simplified 99.4%

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

   if -5e10 < (/.f64 (-.f64 z t) (-.f64 z a)) < 0.10000000000000001

   1. Initial program 99.6%

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

   3. Taylor expanded in a around inf 86.4%

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

      1. mul-1-neg 86.4%

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

      2. unsub-neg 86.4%

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

      3. *-commutative 86.4%

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

      4. associate-/l* 95.1%

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

   5. Simplified 95.1%

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

   if 0.10000000000000001 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5.0000000000000004e43

   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 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -50000000000:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 0.1:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 5 \cdot 10^{+43}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -5e+17)
     (- x (* t (/ y z)))
     (if (<= t_1 2.0) (+ x (* y (/ z (- z a)))) (* y t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 2.0) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = y * 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 = (z - t) / (z - a)
    if (t_1 <= (-5d+17)) then
        tmp = x - (t * (y / z))
    else if (t_1 <= 2.0d0) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = y * 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 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 2.0) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = y * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -5e+17:
		tmp = x - (t * (y / z))
	elif t_1 <= 2.0:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = y * t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+17)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (t_1 <= 2.0)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(y * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	tmp = 0.0;
	if (t_1 <= -5e+17)
		tmp = x - (t * (y / z));
	elseif (t_1 <= 2.0)
		tmp = x + (y * (z / (z - a)));
	else
		tmp = y * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+17], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5e17

   1. Initial program 97.0%

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

   3. Taylor expanded in t around inf 88.6%

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

      1. mul-1-neg 88.6%

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

      2. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. sub-neg 68.5%

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

      3. associate-/l* 77.0%

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

   8. Simplified 77.0%

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

   if -5e17 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 74.9%

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

      1. +-commutative 74.9%

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

      2. associate-/l* 92.2%

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

   5. Simplified 92.2%

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

   if 2 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 93.7%

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

      1. add-cube-cbrt 92.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot \frac{z - t}{z - a}} \cdot \sqrt[3]{x + y \cdot \frac{z - t}{z - a}}\right) \cdot \sqrt[3]{x + y \cdot \frac{z - t}{z - a}}} \]

      2. pow3 92.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot \frac{z - t}{z - a}}\right)}^{3}} \]

      3. +-commutative 92.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \frac{z - t}{z - a} + x}}\right)}^{3} \]

      4. fma-undefine 92.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 92.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around inf 78.0%

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

      1. div-sub 78.0%

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

   7. Simplified 78.0%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 2:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-40}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 700000000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+142} \lor \neg \left(z \leq 1.2 \cdot 10^{+181}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e-40)
   (+ y x)
   (if (<= z 700000000.0)
     (+ x (* t (/ y a)))
     (if (or (<= z 4.7e+142) (not (<= z 1.2e+181)))
       (+ y x)
       (- x (* t (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e-40) {
		tmp = y + x;
	} else if (z <= 700000000.0) {
		tmp = x + (t * (y / a));
	} else if ((z <= 4.7e+142) || !(z <= 1.2e+181)) {
		tmp = y + x;
	} else {
		tmp = x - (t * (y / 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 <= (-9.5d-40)) then
        tmp = y + x
    else if (z <= 700000000.0d0) then
        tmp = x + (t * (y / a))
    else if ((z <= 4.7d+142) .or. (.not. (z <= 1.2d+181))) then
        tmp = y + x
    else
        tmp = x - (t * (y / 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 <= -9.5e-40) {
		tmp = y + x;
	} else if (z <= 700000000.0) {
		tmp = x + (t * (y / a));
	} else if ((z <= 4.7e+142) || !(z <= 1.2e+181)) {
		tmp = y + x;
	} else {
		tmp = x - (t * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e-40:
		tmp = y + x
	elif z <= 700000000.0:
		tmp = x + (t * (y / a))
	elif (z <= 4.7e+142) or not (z <= 1.2e+181):
		tmp = y + x
	else:
		tmp = x - (t * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e-40)
		tmp = Float64(y + x);
	elseif (z <= 700000000.0)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif ((z <= 4.7e+142) || !(z <= 1.2e+181))
		tmp = Float64(y + x);
	else
		tmp = Float64(x - Float64(t * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e-40)
		tmp = y + x;
	elseif (z <= 700000000.0)
		tmp = x + (t * (y / a));
	elseif ((z <= 4.7e+142) || ~((z <= 1.2e+181)))
		tmp = y + x;
	else
		tmp = x - (t * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e-40], N[(y + x), $MachinePrecision], If[LessEqual[z, 700000000.0], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.7e+142], N[Not[LessEqual[z, 1.2e+181]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000006e-40 or 7e8 < z < 4.7e142 or 1.20000000000000001e181 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -9.5000000000000006e-40 < z < 7e8

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. +-commutative 71.8%

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

      2. associate-/l* 72.3%

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

   5. Simplified 72.3%

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

   if 4.7e142 < z < 1.20000000000000001e181

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in z around inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. sub-neg 70.3%

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

      3. associate-/l* 86.6%

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

   8. Simplified 86.6%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-40}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 700000000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+142} \lor \neg \left(z \leq 1.2 \cdot 10^{+181}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot \left(-t\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+182}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+278}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y z) (- t))))
   (if (<= t -4.5e+185)
     t_1
     (if (<= t 1.8e+182)
       (+ y x)
       (if (<= t 1.15e+273) t_1 (if (<= t 5.4e+278) (+ y x) (/ (* y t) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / z) * -t;
	double tmp;
	if (t <= -4.5e+185) {
		tmp = t_1;
	} else if (t <= 1.8e+182) {
		tmp = y + x;
	} else if (t <= 1.15e+273) {
		tmp = t_1;
	} else if (t <= 5.4e+278) {
		tmp = y + x;
	} else {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = (y / z) * -t
    if (t <= (-4.5d+185)) then
        tmp = t_1
    else if (t <= 1.8d+182) then
        tmp = y + x
    else if (t <= 1.15d+273) then
        tmp = t_1
    else if (t <= 5.4d+278) then
        tmp = y + x
    else
        tmp = (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 t_1 = (y / z) * -t;
	double tmp;
	if (t <= -4.5e+185) {
		tmp = t_1;
	} else if (t <= 1.8e+182) {
		tmp = y + x;
	} else if (t <= 1.15e+273) {
		tmp = t_1;
	} else if (t <= 5.4e+278) {
		tmp = y + x;
	} else {
		tmp = (y * t) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / z) * -t
	tmp = 0
	if t <= -4.5e+185:
		tmp = t_1
	elif t <= 1.8e+182:
		tmp = y + x
	elif t <= 1.15e+273:
		tmp = t_1
	elif t <= 5.4e+278:
		tmp = y + x
	else:
		tmp = (y * t) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / z) * Float64(-t))
	tmp = 0.0
	if (t <= -4.5e+185)
		tmp = t_1;
	elseif (t <= 1.8e+182)
		tmp = Float64(y + x);
	elseif (t <= 1.15e+273)
		tmp = t_1;
	elseif (t <= 5.4e+278)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(y * t) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / z) * -t;
	tmp = 0.0;
	if (t <= -4.5e+185)
		tmp = t_1;
	elseif (t <= 1.8e+182)
		tmp = y + x;
	elseif (t <= 1.15e+273)
		tmp = t_1;
	elseif (t <= 5.4e+278)
		tmp = y + x;
	else
		tmp = (y * t) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * (-t)), $MachinePrecision]}, If[LessEqual[t, -4.5e+185], t$95$1, If[LessEqual[t, 1.8e+182], N[(y + x), $MachinePrecision], If[LessEqual[t, 1.15e+273], t$95$1, If[LessEqual[t, 5.4e+278], N[(y + x), $MachinePrecision], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5000000000000002e185 or 1.8e182 < t < 1.15e273

   1. Initial program 93.8%

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

   3. Taylor expanded in y around inf 87.0%

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

      1. associate--l+ 87.0%

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

      2. div-sub 87.0%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in t around inf 71.0%

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

      1. associate-*r/ 71.0%

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

      2. neg-mul-1 71.0%

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

   8. Simplified 71.0%

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

   9. Taylor expanded in z around inf 51.0%

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

       1. mul-1-neg 51.0%

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

       2. associate-*r/ 57.4%

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

       3. distribute-rgt-neg-in 57.4%

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

       4. distribute-frac-neg2 57.4%

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

   11. Simplified 57.4%

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

   if -4.5000000000000002e185 < t < 1.8e182 or 1.15e273 < t < 5.40000000000000021e278

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 71.0%

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

      1. +-commutative 71.0%

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

   5. Simplified 71.0%

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

   if 5.40000000000000021e278 < t

   1. Initial program 86.1%

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

   3. Taylor expanded in y around inf 86.1%

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

      1. associate--l+ 86.1%

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

      2. div-sub 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in t around inf 72.6%

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

      1. associate-*r/ 72.6%

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

      2. neg-mul-1 72.6%

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

   8. Simplified 72.6%

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

   9. Taylor expanded in z around 0 44.3%

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

       1. associate-*r/ 57.9%

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

   11. Applied egg-rr 57.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+185}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+182}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+273}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+278}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+184} \lor \neg \left(t \leq 4.8 \cdot 10^{+164}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.6e+184) (not (<= t 4.8e+164)))
   (* y (- 1.0 (/ t z)))
   (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e+184) || !(t <= 4.8e+164)) {
		tmp = y * (1.0 - (t / z));
	} else {
		tmp = y + 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 ((t <= (-2.6d+184)) .or. (.not. (t <= 4.8d+164))) then
        tmp = y * (1.0d0 - (t / z))
    else
        tmp = y + 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 ((t <= -2.6e+184) || !(t <= 4.8e+164)) {
		tmp = y * (1.0 - (t / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.6e+184) or not (t <= 4.8e+164):
		tmp = y * (1.0 - (t / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.6e+184) || !(t <= 4.8e+164))
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.6e+184) || ~((t <= 4.8e+164)))
		tmp = y * (1.0 - (t / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.6e+184], N[Not[LessEqual[t, 4.8e+164]], $MachinePrecision]], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.59999999999999993e184 or 4.80000000000000021e164 < t

   1. Initial program 94.0%

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

   3. Taylor expanded in a around 0 69.5%

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

   4. Taylor expanded in y around inf 53.8%

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

   if -2.59999999999999993e184 < t < 4.80000000000000021e164

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 71.8%

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

      1. +-commutative 71.8%

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

   5. Simplified 71.8%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+184} \lor \neg \left(t \leq 4.8 \cdot 10^{+164}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-41} \lor \neg \left(z \leq 2.3 \cdot 10^{+25}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e-41) (not (<= z 2.3e+25))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e-41) || !(z <= 2.3e+25)) {
		tmp = y + x;
	} 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 <= (-7.2d-41)) .or. (.not. (z <= 2.3d+25))) then
        tmp = y + x
    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 <= -7.2e-41) || !(z <= 2.3e+25)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e-41) or not (z <= 2.3e+25):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e-41) || !(z <= 2.3e+25))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.2e-41) || ~((z <= 2.3e+25)))
		tmp = y + x;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e-41], N[Not[LessEqual[z, 2.3e+25]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e-41 or 2.2999999999999998e25 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 76.3%

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

      1. +-commutative 76.3%

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

   5. Simplified 76.3%

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

   if -7.2e-41 < z < 2.2999999999999998e25

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0 71.5%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-41} \lor \neg \left(z \leq 2.3 \cdot 10^{+25}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-40} \lor \neg \left(z \leq 130\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.6e-40) (not (<= z 130.0))) (+ y x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.6e-40) || !(z <= 130.0)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / 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 <= (-8.6d-40)) .or. (.not. (z <= 130.0d0))) then
        tmp = y + x
    else
        tmp = x + (t * (y / 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 <= -8.6e-40) || !(z <= 130.0)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.6e-40) or not (z <= 130.0):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.6e-40) || !(z <= 130.0))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.6e-40) || ~((z <= 130.0)))
		tmp = y + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.6e-40], N[Not[LessEqual[z, 130.0]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.6000000000000005e-40 or 130 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

   if -8.6000000000000005e-40 < z < 130

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. +-commutative 71.8%

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

      2. associate-/l* 72.3%

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

   5. Simplified 72.3%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-40} \lor \neg \left(z \leq 130\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 98.0% 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 98.4%

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

3. Final simplification 98.4%

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

Alternative 14: 60.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+246}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.6e+246) (* y (/ t a)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.6e+246) {
		tmp = y * (t / a);
	} else {
		tmp = y + 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 (t <= (-6.6d+246)) then
        tmp = y * (t / a)
    else
        tmp = y + 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 (t <= -6.6e+246) {
		tmp = y * (t / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.6e+246:
		tmp = y * (t / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.6e+246)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.6e+246)
		tmp = y * (t / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.6e+246], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.6e246

   1. Initial program 90.4%

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

   3. Taylor expanded in y around inf 81.0%

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

      1. associate--l+ 81.0%

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

      2. div-sub 81.0%

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

   5. Simplified 81.0%

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

   6. Taylor expanded in t around inf 80.6%

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

      1. associate-*r/ 80.6%

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

      2. neg-mul-1 80.6%

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

   8. Simplified 80.6%

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

   9. Taylor expanded in z around 0 70.6%

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

   if -6.6e246 < t

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 63.6%

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

      1. +-commutative 63.6%

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

   5. Simplified 63.6%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+246}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+249}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2e+249) (/ (* y t) a) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2e+249) {
		tmp = (y * t) / a;
	} else {
		tmp = y + 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 (t <= (-2d+249)) then
        tmp = (y * t) / a
    else
        tmp = y + 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 (t <= -2e+249) {
		tmp = (y * t) / a;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2e+249:
		tmp = (y * t) / a
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2e+249)
		tmp = Float64(Float64(y * t) / a);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2e+249)
		tmp = (y * t) / a;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2e+249], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9999999999999998e249

   1. Initial program 90.4%

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

   3. Taylor expanded in y around inf 81.0%

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

      1. associate--l+ 81.0%

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

      2. div-sub 81.0%

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

   5. Simplified 81.0%

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

   6. Taylor expanded in t around inf 80.6%

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

      1. associate-*r/ 80.6%

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

      2. neg-mul-1 80.6%

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

   8. Simplified 80.6%

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

   9. Taylor expanded in z around 0 70.6%

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

       1. associate-*r/ 73.8%

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

   11. Applied egg-rr 73.8%

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

   if -1.9999999999999998e249 < t

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 63.6%

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

      1. +-commutative 63.6%

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

   5. Simplified 63.6%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+249}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 60.1% accurate, 3.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return y + 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 = y + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(y + x), $MachinePrecision]

Derivation

1. Initial program 98.4%

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

3. Taylor expanded in z around inf 61.6%

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

   1. +-commutative 61.6%

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

5. Simplified 61.6%

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

6. Final simplification 61.6%

   \[\leadsto y + x \]
7. Add Preprocessing

Alternative 17: 49.9% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Taylor expanded in x around inf 47.1%

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

4. Final simplification 47.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(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)))))