Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 96.7% → 99.6%

Time: 9.4s

Alternatives: 12

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / 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) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / 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) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{z - y}{-1 + \left(z - t\right)} \cdot a \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (* (/ (- z y) (+ -1.0 (- z t))) a)))

C

double code(double x, double y, double z, double t, double a) {
	return x - (((z - y) / (-1.0 + (z - t))) * a);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - (((z - y) / ((-1.0d0) + (z - t))) * a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - (((z - y) / (-1.0 + (z - t))) * a);
}

Python

def code(x, y, z, t, a):
	return x - (((z - y) / (-1.0 + (z - t))) * a)

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(Float64(z - y) / Float64(-1.0 + Float64(z - t))) * a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - (((z - y) / (-1.0 + (z - t))) * a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(N[(z - y), $MachinePrecision] / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.1%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Step-by-step derivation

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

   \[\leadsto x - \frac{z - y}{-1 + \left(z - t\right)} \cdot a \]
6. Add Preprocessing

Alternative 2: 70.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-255}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ a (/ t y)))))
   (if (<= t -2.9e+48)
     t_1
     (if (<= t -1.9e-255) (- x a) (if (<= t 1.0) (- x (* y a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a / (t / y));
	double tmp;
	if (t <= -2.9e+48) {
		tmp = t_1;
	} else if (t <= -1.9e-255) {
		tmp = x - a;
	} else if (t <= 1.0) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a / (t / y))
    if (t <= (-2.9d+48)) then
        tmp = t_1
    else if (t <= (-1.9d-255)) then
        tmp = x - a
    else if (t <= 1.0d0) then
        tmp = x - (y * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a / (t / y));
	double tmp;
	if (t <= -2.9e+48) {
		tmp = t_1;
	} else if (t <= -1.9e-255) {
		tmp = x - a;
	} else if (t <= 1.0) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a / (t / y))
	tmp = 0
	if t <= -2.9e+48:
		tmp = t_1
	elif t <= -1.9e-255:
		tmp = x - a
	elif t <= 1.0:
		tmp = x - (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a / Float64(t / y)))
	tmp = 0.0
	if (t <= -2.9e+48)
		tmp = t_1;
	elseif (t <= -1.9e-255)
		tmp = Float64(x - a);
	elseif (t <= 1.0)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a / (t / y));
	tmp = 0.0;
	if (t <= -2.9e+48)
		tmp = t_1;
	elseif (t <= -1.9e-255)
		tmp = x - a;
	elseif (t <= 1.0)
		tmp = x - (y * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+48], t$95$1, If[LessEqual[t, -1.9e-255], N[(x - a), $MachinePrecision], If[LessEqual[t, 1.0], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8999999999999999e48 or 1 < t

   1. Initial program 99.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 84.7%

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

   6. Taylor expanded in y around inf 81.6%

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

      1. *-commutative 81.6%

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

      2. clear-num 81.6%

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

      3. un-div-inv 81.7%

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

   8. Applied egg-rr 81.7%

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

   if -2.8999999999999999e48 < t < -1.9e-255

   1. Initial program 94.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 72.4%

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

   if -1.9e-255 < t < 1

   1. Initial program 97.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 98.9%

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

   8. Taylor expanded in z around 0 72.5%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-255}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-255}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y t)))))
   (if (<= t -3.5e+47)
     t_1
     (if (<= t -4.1e-255) (- x a) (if (<= t 1.0) (- x (* y a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / t));
	double tmp;
	if (t <= -3.5e+47) {
		tmp = t_1;
	} else if (t <= -4.1e-255) {
		tmp = x - a;
	} else if (t <= 1.0) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a * (y / t))
    if (t <= (-3.5d+47)) then
        tmp = t_1
    else if (t <= (-4.1d-255)) then
        tmp = x - a
    else if (t <= 1.0d0) then
        tmp = x - (y * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / t));
	double tmp;
	if (t <= -3.5e+47) {
		tmp = t_1;
	} else if (t <= -4.1e-255) {
		tmp = x - a;
	} else if (t <= 1.0) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / t))
	tmp = 0
	if t <= -3.5e+47:
		tmp = t_1
	elif t <= -4.1e-255:
		tmp = x - a
	elif t <= 1.0:
		tmp = x - (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / t)))
	tmp = 0.0
	if (t <= -3.5e+47)
		tmp = t_1;
	elseif (t <= -4.1e-255)
		tmp = Float64(x - a);
	elseif (t <= 1.0)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (y / t));
	tmp = 0.0;
	if (t <= -3.5e+47)
		tmp = t_1;
	elseif (t <= -4.1e-255)
		tmp = x - a;
	elseif (t <= 1.0)
		tmp = x - (y * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+47], t$95$1, If[LessEqual[t, -4.1e-255], N[(x - a), $MachinePrecision], If[LessEqual[t, 1.0], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.50000000000000015e47 or 1 < t

   1. Initial program 99.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 84.7%

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

   6. Taylor expanded in y around inf 81.6%

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

   if -3.50000000000000015e47 < t < -4.1e-255

   1. Initial program 94.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 72.4%

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

   if -4.1e-255 < t < 1

   1. Initial program 97.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 98.9%

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

   8. Taylor expanded in z around 0 72.5%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+47}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-255}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -700000000000 \lor \neg \left(y \leq 1.12 \cdot 10^{-39}\right):\\ \;\;\;\;x + y \cdot \frac{a}{-1 + \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{a}{\left(t + 1\right) - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -700000000000.0) (not (<= y 1.12e-39)))
   (+ x (* y (/ a (+ -1.0 (- z t)))))
   (+ x (* z (/ a (- (+ t 1.0) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -700000000000.0) || !(y <= 1.12e-39)) {
		tmp = x + (y * (a / (-1.0 + (z - t))));
	} else {
		tmp = x + (z * (a / ((t + 1.0) - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-700000000000.0d0)) .or. (.not. (y <= 1.12d-39))) then
        tmp = x + (y * (a / ((-1.0d0) + (z - t))))
    else
        tmp = x + (z * (a / ((t + 1.0d0) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -700000000000.0) || !(y <= 1.12e-39)) {
		tmp = x + (y * (a / (-1.0 + (z - t))));
	} else {
		tmp = x + (z * (a / ((t + 1.0) - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -700000000000.0) or not (y <= 1.12e-39):
		tmp = x + (y * (a / (-1.0 + (z - t))))
	else:
		tmp = x + (z * (a / ((t + 1.0) - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -700000000000.0) || !(y <= 1.12e-39))
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 + Float64(z - t)))));
	else
		tmp = Float64(x + Float64(z * Float64(a / Float64(Float64(t + 1.0) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -700000000000.0) || ~((y <= 1.12e-39)))
		tmp = x + (y * (a / (-1.0 + (z - t))));
	else
		tmp = x + (z * (a / ((t + 1.0) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -700000000000.0], N[Not[LessEqual[y, 1.12e-39]], $MachinePrecision]], N[(x + N[(y * N[(a / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(a / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7e11 or 1.12e-39 < y

   1. Initial program 96.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 85.6%

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

      1. *-commutative 85.6%

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

      2. associate--l+ 85.6%

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

      3. +-commutative 85.6%

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

      4. associate-*r/ 91.5%

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

      5. +-commutative 91.5%

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

      6. associate--l+ 91.5%

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

      7. associate--l+ 91.5%

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

   7. Simplified 91.5%

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

   if -7e11 < y < 1.12e-39

   1. Initial program 98.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. *-commutative 77.5%

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

      3. associate--l+ 77.5%

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

      4. +-commutative 77.5%

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

      5. associate-*r/ 94.3%

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

      6. distribute-rgt-neg-in 94.3%

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

      7. distribute-neg-frac2 94.3%

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

      8. +-commutative 94.3%

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

      9. distribute-neg-in 94.3%

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

      10. metadata-eval 94.3%

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

      11. unsub-neg 94.3%

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

      12. associate--r- 94.3%

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

   7. Simplified 94.3%

      \[\leadsto x - \color{blue}{z \cdot \frac{a}{\left(-1 - t\right) + z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -700000000000 \lor \neg \left(y \leq 1.12 \cdot 10^{-39}\right):\\ \;\;\;\;x + y \cdot \frac{a}{-1 + \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{a}{\left(t + 1\right) - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+46}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 + \left(z - t\right)}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+46}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.6e+46)
   (+ x (* y (/ a (+ -1.0 (- z t)))))
   (if (<= t 3.1e+46)
     (+ x (* a (/ (- y z) (+ z -1.0))))
     (- x (/ (- y z) (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.6e+46) {
		tmp = x + (y * (a / (-1.0 + (z - t))));
	} else if (t <= 3.1e+46) {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	} else {
		tmp = x - ((y - z) / (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 (t <= (-7.6d+46)) then
        tmp = x + (y * (a / ((-1.0d0) + (z - t))))
    else if (t <= 3.1d+46) then
        tmp = x + (a * ((y - z) / (z + (-1.0d0))))
    else
        tmp = x - ((y - z) / (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 (t <= -7.6e+46) {
		tmp = x + (y * (a / (-1.0 + (z - t))));
	} else if (t <= 3.1e+46) {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	} else {
		tmp = x - ((y - z) / (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.6e+46:
		tmp = x + (y * (a / (-1.0 + (z - t))))
	elif t <= 3.1e+46:
		tmp = x + (a * ((y - z) / (z + -1.0)))
	else:
		tmp = x - ((y - z) / (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.6e+46)
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 + Float64(z - t)))));
	elseif (t <= 3.1e+46)
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / Float64(z + -1.0))));
	else
		tmp = Float64(x - Float64(Float64(y - z) / Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.6e+46)
		tmp = x + (y * (a / (-1.0 + (z - t))));
	elseif (t <= 3.1e+46)
		tmp = x + (a * ((y - z) / (z + -1.0)));
	else
		tmp = x - ((y - z) / (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.6e+46], N[(x + N[(y * N[(a / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e+46], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5999999999999998e46

   1. Initial program 97.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 74.2%

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

      1. *-commutative 74.2%

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

      2. associate--l+ 74.2%

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

      3. +-commutative 74.2%

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

      4. associate-*r/ 82.6%

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

      5. +-commutative 82.6%

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

      6. associate--l+ 82.6%

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

      7. associate--l+ 82.6%

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

   7. Simplified 82.6%

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

   if -7.5999999999999998e46 < t < 3.09999999999999975e46

   1. Initial program 95.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 98.2%

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

   if 3.09999999999999975e46 < t

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 93.1%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+46}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 + \left(z - t\right)}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+46}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+117}:\\ \;\;\;\;x - \left(a - y \cdot \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+106}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 + \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{\frac{z}{a}} - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+117)
   (- x (- a (* y (/ a z))))
   (if (<= z 3.8e+106)
     (+ x (* y (/ a (+ -1.0 (- z t)))))
     (+ x (- (/ y (/ z a)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+117) {
		tmp = x - (a - (y * (a / z)));
	} else if (z <= 3.8e+106) {
		tmp = x + (y * (a / (-1.0 + (z - t))));
	} else {
		tmp = x + ((y / (z / a)) - a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.5d+117)) then
        tmp = x - (a - (y * (a / z)))
    else if (z <= 3.8d+106) then
        tmp = x + (y * (a / ((-1.0d0) + (z - t))))
    else
        tmp = x + ((y / (z / a)) - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+117) {
		tmp = x - (a - (y * (a / z)));
	} else if (z <= 3.8e+106) {
		tmp = x + (y * (a / (-1.0 + (z - t))));
	} else {
		tmp = x + ((y / (z / a)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.5e+117:
		tmp = x - (a - (y * (a / z)))
	elif z <= 3.8e+106:
		tmp = x + (y * (a / (-1.0 + (z - t))))
	else:
		tmp = x + ((y / (z / a)) - a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+117)
		tmp = Float64(x - Float64(a - Float64(y * Float64(a / z))));
	elseif (z <= 3.8e+106)
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 + Float64(z - t)))));
	else
		tmp = Float64(x + Float64(Float64(y / Float64(z / a)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.5e+117)
		tmp = x - (a - (y * (a / z)));
	elseif (z <= 3.8e+106)
		tmp = x + (y * (a / (-1.0 + (z - t))));
	else
		tmp = x + ((y / (z / a)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+117], N[(x - N[(a - N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+106], N[(x + N[(y * N[(a / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / N[(z / a), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e117

   1. Initial program 90.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.9%

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

      1. mul-1-neg 83.9%

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

      2. distribute-neg-frac2 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in y around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. unsub-neg 86.2%

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

      3. *-commutative 86.2%

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

      4. associate-*r/ 88.4%

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

   8. Simplified 88.4%

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

   if -1.5e117 < z < 3.7999999999999998e106

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 87.5%

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

      1. *-commutative 87.5%

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

      2. associate--l+ 87.5%

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

      3. +-commutative 87.5%

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

      4. associate-*r/ 91.1%

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

      5. +-commutative 91.1%

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

      6. associate--l+ 91.1%

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

      7. associate--l+ 91.1%

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

   7. Simplified 91.1%

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

   if 3.7999999999999998e106 < z

   1. Initial program 96.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 91.3%

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

      1. mul-1-neg 91.3%

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

      2. distribute-neg-frac2 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in y around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. unsub-neg 79.2%

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

      3. *-commutative 79.2%

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

      4. associate-*r/ 91.2%

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

   8. Simplified 91.2%

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

      1. clear-num 91.2%

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

      2. un-div-inv 91.3%

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

   10. Applied egg-rr 91.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+117}:\\ \;\;\;\;x - \left(a - y \cdot \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+106}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 + \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{\frac{z}{a}} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+79} \lor \neg \left(z \leq 1.7 \cdot 10^{+22}\right):\\ \;\;\;\;x + \left(\frac{y}{\frac{z}{a}} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.6e+79) (not (<= z 1.7e+22)))
   (+ x (- (/ y (/ z a)) a))
   (+ x (* y (/ a (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.6e+79) || !(z <= 1.7e+22)) {
		tmp = x + ((y / (z / a)) - a);
	} else {
		tmp = x + (y * (a / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.6d+79)) .or. (.not. (z <= 1.7d+22))) then
        tmp = x + ((y / (z / a)) - a)
    else
        tmp = x + (y * (a / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.6e+79) || !(z <= 1.7e+22)) {
		tmp = x + ((y / (z / a)) - a);
	} else {
		tmp = x + (y * (a / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.6e+79) or not (z <= 1.7e+22):
		tmp = x + ((y / (z / a)) - a)
	else:
		tmp = x + (y * (a / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.6e+79) || !(z <= 1.7e+22))
		tmp = Float64(x + Float64(Float64(y / Float64(z / a)) - a));
	else
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.6e+79) || ~((z <= 1.7e+22)))
		tmp = x + ((y / (z / a)) - a);
	else
		tmp = x + (y * (a / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.6e+79], N[Not[LessEqual[z, 1.7e+22]], $MachinePrecision]], N[(x + N[(N[(y / N[(z / a), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(a / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6000000000000003e79 or 1.7e22 < z

   1. Initial program 92.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 81.5%

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

      1. mul-1-neg 81.5%

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

      2. distribute-neg-frac2 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in y around 0 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. *-commutative 80.0%

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

      4. associate-*r/ 83.7%

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

   8. Simplified 83.7%

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

      1. clear-num 83.7%

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

      2. un-div-inv 83.8%

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

   10. Applied egg-rr 83.8%

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

   if -6.6000000000000003e79 < z < 1.7e22

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-/l* 91.6%

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

   7. Simplified 91.6%

      \[\leadsto x - \color{blue}{y \cdot \frac{a}{1 + t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+79} \lor \neg \left(z \leq 1.7 \cdot 10^{+22}\right):\\ \;\;\;\;x + \left(\frac{y}{\frac{z}{a}} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+79} \lor \neg \left(z \leq 1.8 \cdot 10^{+22}\right):\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+79) (not (<= z 1.8e+22)))
   (+ x (- (* y (/ a z)) a))
   (+ x (* y (/ a (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+79) || !(z <= 1.8e+22)) {
		tmp = x + ((y * (a / z)) - a);
	} else {
		tmp = x + (y * (a / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.2d+79)) .or. (.not. (z <= 1.8d+22))) then
        tmp = x + ((y * (a / z)) - a)
    else
        tmp = x + (y * (a / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+79) || !(z <= 1.8e+22)) {
		tmp = x + ((y * (a / z)) - a);
	} else {
		tmp = x + (y * (a / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e+79) or not (z <= 1.8e+22):
		tmp = x + ((y * (a / z)) - a)
	else:
		tmp = x + (y * (a / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e+79) || !(z <= 1.8e+22))
		tmp = Float64(x + Float64(Float64(y * Float64(a / z)) - a));
	else
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.2e+79) || ~((z <= 1.8e+22)))
		tmp = x + ((y * (a / z)) - a);
	else
		tmp = x + (y * (a / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.2e+79], N[Not[LessEqual[z, 1.8e+22]], $MachinePrecision]], N[(x + N[(N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(a / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000003e79 or 1.8e22 < z

   1. Initial program 92.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 81.5%

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

      1. mul-1-neg 81.5%

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

      2. distribute-neg-frac2 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in y around 0 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. *-commutative 80.0%

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

      4. associate-*r/ 83.7%

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

   8. Simplified 83.7%

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

   if -3.20000000000000003e79 < z < 1.8e22

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-/l* 91.6%

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

   7. Simplified 91.6%

      \[\leadsto x - \color{blue}{y \cdot \frac{a}{1 + t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+79} \lor \neg \left(z \leq 1.8 \cdot 10^{+22}\right):\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.75 \cdot 10^{+118} \lor \neg \left(z \leq 3.5 \cdot 10^{+106}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.75e+118) (not (<= z 3.5e+106)))
   (- x a)
   (+ x (* y (/ a (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.75e+118) || !(z <= 3.5e+106)) {
		tmp = x - a;
	} else {
		tmp = x + (y * (a / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.75d+118)) .or. (.not. (z <= 3.5d+106))) then
        tmp = x - a
    else
        tmp = x + (y * (a / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.75e+118) || !(z <= 3.5e+106)) {
		tmp = x - a;
	} else {
		tmp = x + (y * (a / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.75e+118) or not (z <= 3.5e+106):
		tmp = x - a
	else:
		tmp = x + (y * (a / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.75e+118) || !(z <= 3.5e+106))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.75e+118) || ~((z <= 3.5e+106)))
		tmp = x - a;
	else
		tmp = x + (y * (a / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.75e+118], N[Not[LessEqual[z, 3.5e+106]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(y * N[(a / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.75000000000000001e118 or 3.49999999999999981e106 < z

   1. Initial program 93.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.6%

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

   if -3.75000000000000001e118 < z < 3.49999999999999981e106

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 83.1%

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

      1. *-commutative 83.1%

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

      2. associate-/l* 87.2%

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

   7. Simplified 87.2%

      \[\leadsto x - \color{blue}{y \cdot \frac{a}{1 + t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.75 \cdot 10^{+118} \lor \neg \left(z \leq 3.5 \cdot 10^{+106}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+32} \lor \neg \left(z \leq 7.5 \cdot 10^{-8}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.6e+32) (not (<= z 7.5e-8))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.6e+32) || !(z <= 7.5e-8)) {
		tmp = x - a;
	} else {
		tmp = x - (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 <= (-4.6d+32)) .or. (.not. (z <= 7.5d-8))) then
        tmp = x - a
    else
        tmp = x - (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 <= -4.6e+32) || !(z <= 7.5e-8)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.6e+32) or not (z <= 7.5e-8):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.6e+32) || !(z <= 7.5e-8))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.6e+32) || ~((z <= 7.5e-8)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.6e+32], N[Not[LessEqual[z, 7.5e-8]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5999999999999999e32 or 7.4999999999999997e-8 < z

   1. Initial program 94.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 71.0%

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

   if -4.5999999999999999e32 < z < 7.4999999999999997e-8

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 77.5%

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

   8. Taylor expanded in z around 0 72.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+32} \lor \neg \left(z \leq 7.5 \cdot 10^{-8}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+117} \lor \neg \left(z \leq 3.1 \cdot 10^{-68}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+117) (not (<= z 3.1e-68))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+117) || !(z <= 3.1e-68)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.5d+117)) .or. (.not. (z <= 3.1d-68))) then
        tmp = x - a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+117) || !(z <= 3.1e-68)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+117) or not (z <= 3.1e-68):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+117) || !(z <= 3.1e-68))
		tmp = Float64(x - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.5e+117) || ~((z <= 3.1e-68)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+117], N[Not[LessEqual[z, 3.1e-68]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e117 or 3.0999999999999999e-68 < z

   1. Initial program 94.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 72.9%

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

   if -1.5e117 < z < 3.0999999999999999e-68

   1. Initial program 99.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 60.7%

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

   6. Taylor expanded in x around inf 57.0%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+117} \lor \neg \left(z \leq 3.1 \cdot 10^{-68}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.4% accurate, 13.0× 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 97.1%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Step-by-step derivation

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in t around inf 50.6%

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

6. Taylor expanded in x around inf 54.4%

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

Developer target: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\left(t - z\right) + 1} \cdot a \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (* (/ (- y z) (+ (- t z) 1.0)) a)))

C

double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * 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) + 1.0d0)) * a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * a);
}

Python

def code(x, y, z, t, a):
	return x - (((y - z) / ((t - z) + 1.0)) * a)

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(Float64(y - z) / Float64(Float64(t - z) + 1.0)) * a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - (((y - z) / ((t - z) + 1.0)) * a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(N[(y - z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024106 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))