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

Percentage Accurate: 97.1% → 99.7%

Time: 10.6s

Alternatives: 14

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: 97.1% 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: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (a * ((z - y) / ((t - z) + 1.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. associate-/r/ 99.7%

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

3. Simplified 99.7%

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

4. Final simplification 99.7%

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

Alternative 2: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y - z}{-z}\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 24000000000:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ (- y z) (- z))))))
   (if (<= z -1.26e+134)
     t_1
     (if (<= z -4.6e-17)
       (+ x (/ (- z y) (/ t a)))
       (if (<= z 24000000000.0) (- x (/ a (/ (+ t 1.0) y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * ((y - z) / -z));
	double tmp;
	if (z <= -1.26e+134) {
		tmp = t_1;
	} else if (z <= -4.6e-17) {
		tmp = x + ((z - y) / (t / a));
	} else if (z <= 24000000000.0) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a * ((y - z) / -z))
    if (z <= (-1.26d+134)) then
        tmp = t_1
    else if (z <= (-4.6d-17)) then
        tmp = x + ((z - y) / (t / a))
    else if (z <= 24000000000.0d0) then
        tmp = x - (a / ((t + 1.0d0) / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * ((y - z) / -z));
	double tmp;
	if (z <= -1.26e+134) {
		tmp = t_1;
	} else if (z <= -4.6e-17) {
		tmp = x + ((z - y) / (t / a));
	} else if (z <= 24000000000.0) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * ((y - z) / -z))
	tmp = 0
	if z <= -1.26e+134:
		tmp = t_1
	elif z <= -4.6e-17:
		tmp = x + ((z - y) / (t / a))
	elif z <= 24000000000.0:
		tmp = x - (a / ((t + 1.0) / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(-z))))
	tmp = 0.0
	if (z <= -1.26e+134)
		tmp = t_1;
	elseif (z <= -4.6e-17)
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	elseif (z <= 24000000000.0)
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * ((y - z) / -z));
	tmp = 0.0;
	if (z <= -1.26e+134)
		tmp = t_1;
	elseif (z <= -4.6e-17)
		tmp = x + ((z - y) / (t / a));
	elseif (z <= 24000000000.0)
		tmp = x - (a / ((t + 1.0) / y));
	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[(N[(y - z), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.26e+134], t$95$1, If[LessEqual[z, -4.6e-17], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 24000000000.0], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2600000000000001e134 or 2.4e10 < z

   1. Initial program 95.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 87.8%

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

      1. mul-1-neg 87.8%

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

   6. Simplified 87.8%

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

   if -1.2600000000000001e134 < z < -4.60000000000000018e-17

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 78.4%

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

   if -4.60000000000000018e-17 < z < 2.4e10

   1. Initial program 99.2%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 89.7%

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

      1. associate-/l* 92.6%

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

   6. Simplified 92.6%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+134}:\\ \;\;\;\;x - a \cdot \frac{y - z}{-z}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 24000000000:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{-z}\\ \end{array} \]

Alternative 3: 69.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+134}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-172}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ a (/ t y)))))
   (if (<= z -1.4e+134)
     (- x a)
     (if (<= z -8.6e-257)
       t_1
       (if (<= z 3.1e-172) (- x (* y a)) (if (<= z 5.8e+142) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a / (t / y));
	double tmp;
	if (z <= -1.4e+134) {
		tmp = x - a;
	} else if (z <= -8.6e-257) {
		tmp = t_1;
	} else if (z <= 3.1e-172) {
		tmp = x - (y * a);
	} else if (z <= 5.8e+142) {
		tmp = t_1;
	} else {
		tmp = x - 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 = x - (a / (t / y))
    if (z <= (-1.4d+134)) then
        tmp = x - a
    else if (z <= (-8.6d-257)) then
        tmp = t_1
    else if (z <= 3.1d-172) then
        tmp = x - (y * a)
    else if (z <= 5.8d+142) then
        tmp = t_1
    else
        tmp = x - 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 = x - (a / (t / y));
	double tmp;
	if (z <= -1.4e+134) {
		tmp = x - a;
	} else if (z <= -8.6e-257) {
		tmp = t_1;
	} else if (z <= 3.1e-172) {
		tmp = x - (y * a);
	} else if (z <= 5.8e+142) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a / (t / y))
	tmp = 0
	if z <= -1.4e+134:
		tmp = x - a
	elif z <= -8.6e-257:
		tmp = t_1
	elif z <= 3.1e-172:
		tmp = x - (y * a)
	elif z <= 5.8e+142:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a / Float64(t / y)))
	tmp = 0.0
	if (z <= -1.4e+134)
		tmp = Float64(x - a);
	elseif (z <= -8.6e-257)
		tmp = t_1;
	elseif (z <= 3.1e-172)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 5.8e+142)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a / (t / y));
	tmp = 0.0;
	if (z <= -1.4e+134)
		tmp = x - a;
	elseif (z <= -8.6e-257)
		tmp = t_1;
	elseif (z <= 3.1e-172)
		tmp = x - (y * a);
	elseif (z <= 5.8e+142)
		tmp = t_1;
	else
		tmp = x - a;
	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[z, -1.4e+134], N[(x - a), $MachinePrecision], If[LessEqual[z, -8.6e-257], t$95$1, If[LessEqual[z, 3.1e-172], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+142], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3999999999999999e134 or 5.80000000000000027e142 < z

   1. Initial program 93.4%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 87.9%

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

   if -1.3999999999999999e134 < z < -8.59999999999999995e-257 or 3.1000000000000003e-172 < z < 5.80000000000000027e142

   1. Initial program 99.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around 0 77.3%

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

      1. associate-/l* 81.9%

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

   6. Simplified 81.9%

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

   7. Taylor expanded in t around inf 68.8%

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

      1. *-commutative 68.8%

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

      2. associate-/l* 72.7%

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

   9. Simplified 72.7%

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

   if -8.59999999999999995e-257 < z < 3.1000000000000003e-172

   1. Initial program 99.8%

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

      1. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in t around 0 77.7%

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

   5. Taylor expanded in z around 0 75.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+134}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-257}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-172}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+142}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 4: 81.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+134}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+142}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+134)
   (- x a)
   (if (<= z -7e-18)
     (- x (/ a (/ t (- y z))))
     (if (<= z 5.8e+142) (- x (/ a (/ (+ t 1.0) y))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+134) {
		tmp = x - a;
	} else if (z <= -7e-18) {
		tmp = x - (a / (t / (y - z)));
	} else if (z <= 5.8e+142) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x - 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 <= (-1.3d+134)) then
        tmp = x - a
    else if (z <= (-7d-18)) then
        tmp = x - (a / (t / (y - z)))
    else if (z <= 5.8d+142) then
        tmp = x - (a / ((t + 1.0d0) / y))
    else
        tmp = x - 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 <= -1.3e+134) {
		tmp = x - a;
	} else if (z <= -7e-18) {
		tmp = x - (a / (t / (y - z)));
	} else if (z <= 5.8e+142) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+134:
		tmp = x - a
	elif z <= -7e-18:
		tmp = x - (a / (t / (y - z)))
	elif z <= 5.8e+142:
		tmp = x - (a / ((t + 1.0) / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+134)
		tmp = Float64(x - a);
	elseif (z <= -7e-18)
		tmp = Float64(x - Float64(a / Float64(t / Float64(y - z))));
	elseif (z <= 5.8e+142)
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+134)
		tmp = x - a;
	elseif (z <= -7e-18)
		tmp = x - (a / (t / (y - z)));
	elseif (z <= 5.8e+142)
		tmp = x - (a / ((t + 1.0) / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+134], N[(x - a), $MachinePrecision], If[LessEqual[z, -7e-18], N[(x - N[(a / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+142], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3000000000000001e134 or 5.80000000000000027e142 < z

   1. Initial program 93.4%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 87.9%

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

   if -1.3000000000000001e134 < z < -6.9999999999999997e-18

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around inf 75.6%

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

      1. associate-/l* 78.4%

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

   6. Simplified 78.4%

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

   if -6.9999999999999997e-18 < z < 5.80000000000000027e142

   1. Initial program 99.3%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 84.6%

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

      1. associate-/l* 88.5%

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

   6. Simplified 88.5%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+134}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+142}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 5: 81.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+134}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+142}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.55e+134)
   (- x a)
   (if (<= z -7e-18)
     (+ x (/ (- z y) (/ t a)))
     (if (<= z 5.8e+142) (- x (/ a (/ (+ t 1.0) y))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e+134) {
		tmp = x - a;
	} else if (z <= -7e-18) {
		tmp = x + ((z - y) / (t / a));
	} else if (z <= 5.8e+142) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x - 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 <= (-1.55d+134)) then
        tmp = x - a
    else if (z <= (-7d-18)) then
        tmp = x + ((z - y) / (t / a))
    else if (z <= 5.8d+142) then
        tmp = x - (a / ((t + 1.0d0) / y))
    else
        tmp = x - 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 <= -1.55e+134) {
		tmp = x - a;
	} else if (z <= -7e-18) {
		tmp = x + ((z - y) / (t / a));
	} else if (z <= 5.8e+142) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.55e+134:
		tmp = x - a
	elif z <= -7e-18:
		tmp = x + ((z - y) / (t / a))
	elif z <= 5.8e+142:
		tmp = x - (a / ((t + 1.0) / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.55e+134)
		tmp = Float64(x - a);
	elseif (z <= -7e-18)
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	elseif (z <= 5.8e+142)
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.55e+134)
		tmp = x - a;
	elseif (z <= -7e-18)
		tmp = x + ((z - y) / (t / a));
	elseif (z <= 5.8e+142)
		tmp = x - (a / ((t + 1.0) / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.55e+134], N[(x - a), $MachinePrecision], If[LessEqual[z, -7e-18], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+142], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.54999999999999991e134 or 5.80000000000000027e142 < z

   1. Initial program 93.4%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 87.9%

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

   if -1.54999999999999991e134 < z < -6.9999999999999997e-18

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 78.4%

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

   if -6.9999999999999997e-18 < z < 5.80000000000000027e142

   1. Initial program 99.3%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 84.6%

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

      1. associate-/l* 88.5%

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

   6. Simplified 88.5%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+134}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+142}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 6: 88.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+135} \lor \neg \left(z \leq 1.25 \cdot 10^{+138}\right):\\ \;\;\;\;x - a \cdot \frac{y - z}{-z}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.7e+135) (not (<= z 1.25e+138)))
   (- x (* a (/ (- y z) (- z))))
   (- x (* a (/ y (- (+ t 1.0) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.7e+135) || !(z <= 1.25e+138)) {
		tmp = x - (a * ((y - z) / -z));
	} else {
		tmp = x - (a * (y / ((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 ((z <= (-3.7d+135)) .or. (.not. (z <= 1.25d+138))) then
        tmp = x - (a * ((y - z) / -z))
    else
        tmp = x - (a * (y / ((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 ((z <= -3.7e+135) || !(z <= 1.25e+138)) {
		tmp = x - (a * ((y - z) / -z));
	} else {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.7e+135) or not (z <= 1.25e+138):
		tmp = x - (a * ((y - z) / -z))
	else:
		tmp = x - (a * (y / ((t + 1.0) - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.7e+135) || !(z <= 1.25e+138))
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(-z))));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(Float64(t + 1.0) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.7e+135) || ~((z <= 1.25e+138)))
		tmp = x - (a * ((y - z) / -z));
	else
		tmp = x - (a * (y / ((t + 1.0) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.7e+135], N[Not[LessEqual[z, 1.25e+138]], $MachinePrecision]], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.69999999999999997e135 or 1.25000000000000004e138 < z

   1. Initial program 93.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 93.3%

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

      1. mul-1-neg 93.3%

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

   6. Simplified 93.3%

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

   if -3.69999999999999997e135 < z < 1.25000000000000004e138

   1. Initial program 99.4%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 89.0%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+135} \lor \neg \left(z \leq 1.25 \cdot 10^{+138}\right):\\ \;\;\;\;x - a \cdot \frac{y - z}{-z}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \end{array} \]

Alternative 7: 90.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -165000 \lor \neg \left(y \leq 68000000000000\right):\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{t - \left(z + -1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -165000.0) (not (<= y 68000000000000.0)))
   (- x (* a (/ y (- (+ t 1.0) z))))
   (+ x (* a (/ z (- t (+ z -1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -165000.0) || !(y <= 68000000000000.0)) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x + (a * (z / (t - (z + -1.0))));
	}
	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 <= (-165000.0d0)) .or. (.not. (y <= 68000000000000.0d0))) then
        tmp = x - (a * (y / ((t + 1.0d0) - z)))
    else
        tmp = x + (a * (z / (t - (z + (-1.0d0)))))
    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 <= -165000.0) || !(y <= 68000000000000.0)) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x + (a * (z / (t - (z + -1.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -165000.0) or not (y <= 68000000000000.0):
		tmp = x - (a * (y / ((t + 1.0) - z)))
	else:
		tmp = x + (a * (z / (t - (z + -1.0))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -165000.0) || !(y <= 68000000000000.0))
		tmp = Float64(x - Float64(a * Float64(y / Float64(Float64(t + 1.0) - z))));
	else
		tmp = Float64(x + Float64(a * Float64(z / Float64(t - Float64(z + -1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -165000.0) || ~((y <= 68000000000000.0)))
		tmp = x - (a * (y / ((t + 1.0) - z)));
	else
		tmp = x + (a * (z / (t - (z + -1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -165000.0], N[Not[LessEqual[y, 68000000000000.0]], $MachinePrecision]], N[(x - N[(a * N[(y / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(z / N[(t - N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -165000 or 6.8e13 < y

   1. Initial program 97.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in y around inf 89.6%

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

   if -165000 < y < 6.8e13

   1. Initial program 97.8%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 96.2%

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

      1. associate-*r/ 96.2%

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

      2. mul-1-neg 96.2%

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

      3. associate--l+ 96.2%

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

      4. +-commutative 96.2%

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

      5. metadata-eval 96.2%

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

      6. sub-neg 96.2%

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

      7. associate--r+ 96.2%

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

      8. +-commutative 96.2%

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

   6. Simplified 96.2%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -165000 \lor \neg \left(y \leq 68000000000000\right):\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{t - \left(z + -1\right)}\\ \end{array} \]

Alternative 8: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -31 \lor \neg \left(t \leq 2.95 \cdot 10^{-8}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -31.0) (not (<= t 2.95e-8)))
   (+ x (* a (/ (- z y) t)))
   (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -31.0) || !(t <= 2.95e-8)) {
		tmp = x + (a * ((z - y) / t));
	} 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 ((t <= (-31.0d0)) .or. (.not. (t <= 2.95d-8))) then
        tmp = x + (a * ((z - y) / t))
    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 ((t <= -31.0) || !(t <= 2.95e-8)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -31.0) or not (t <= 2.95e-8):
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -31.0) || !(t <= 2.95e-8))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	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 ((t <= -31.0) || ~((t <= 2.95e-8)))
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -31.0], N[Not[LessEqual[t, 2.95e-8]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -31 or 2.9499999999999999e-8 < t

   1. Initial program 97.3%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 85.7%

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

   if -31 < t < 2.9499999999999999e-8

   1. Initial program 98.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around 0 86.0%

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

   5. Taylor expanded in z around 0 70.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -31 \lor \neg \left(t \leq 2.95 \cdot 10^{-8}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]

Alternative 9: 71.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+118}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 1250000000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+118)
   (- x a)
   (if (<= z -8.5e-17)
     (+ x (/ a (/ t z)))
     (if (<= z 1250000000.0) (- x (* y a)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+118) {
		tmp = x - a;
	} else if (z <= -8.5e-17) {
		tmp = x + (a / (t / z));
	} else if (z <= 1250000000.0) {
		tmp = x - (y * a);
	} else {
		tmp = x - 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 <= (-8d+118)) then
        tmp = x - a
    else if (z <= (-8.5d-17)) then
        tmp = x + (a / (t / z))
    else if (z <= 1250000000.0d0) then
        tmp = x - (y * a)
    else
        tmp = x - 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 <= -8e+118) {
		tmp = x - a;
	} else if (z <= -8.5e-17) {
		tmp = x + (a / (t / z));
	} else if (z <= 1250000000.0) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+118:
		tmp = x - a
	elif z <= -8.5e-17:
		tmp = x + (a / (t / z))
	elif z <= 1250000000.0:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+118)
		tmp = Float64(x - a);
	elseif (z <= -8.5e-17)
		tmp = Float64(x + Float64(a / Float64(t / z)));
	elseif (z <= 1250000000.0)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+118)
		tmp = x - a;
	elseif (z <= -8.5e-17)
		tmp = x + (a / (t / z));
	elseif (z <= 1250000000.0)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+118], N[(x - a), $MachinePrecision], If[LessEqual[z, -8.5e-17], N[(x + N[(a / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1250000000.0], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.99999999999999973e118 or 1.25e9 < z

   1. Initial program 95.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 78.9%

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

   if -7.99999999999999973e118 < z < -8.5e-17

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around inf 74.6%

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

   5. Taylor expanded in y around 0 65.3%

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

      1. cancel-sign-sub-inv 65.3%

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

      2. metadata-eval 65.3%

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

      3. *-lft-identity 65.3%

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

      4. +-commutative 65.3%

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

      5. associate-/l* 65.2%

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

   7. Simplified 65.2%

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

   if -8.5e-17 < z < 1.25e9

   1. Initial program 99.2%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around 0 71.9%

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

   5. Taylor expanded in z around 0 70.5%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+118}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 1250000000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 10: 71.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+118}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{z \cdot a}{t}\\ \mathbf{elif}\;z \leq 1500000000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.8e+118)
   (- x a)
   (if (<= z -7e-17)
     (+ x (/ (* z a) t))
     (if (<= z 1500000000.0) (- x (* y a)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.8e+118) {
		tmp = x - a;
	} else if (z <= -7e-17) {
		tmp = x + ((z * a) / t);
	} else if (z <= 1500000000.0) {
		tmp = x - (y * a);
	} else {
		tmp = x - 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 <= (-7.8d+118)) then
        tmp = x - a
    else if (z <= (-7d-17)) then
        tmp = x + ((z * a) / t)
    else if (z <= 1500000000.0d0) then
        tmp = x - (y * a)
    else
        tmp = x - 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 <= -7.8e+118) {
		tmp = x - a;
	} else if (z <= -7e-17) {
		tmp = x + ((z * a) / t);
	} else if (z <= 1500000000.0) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.8e+118:
		tmp = x - a
	elif z <= -7e-17:
		tmp = x + ((z * a) / t)
	elif z <= 1500000000.0:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.8e+118)
		tmp = Float64(x - a);
	elseif (z <= -7e-17)
		tmp = Float64(x + Float64(Float64(z * a) / t));
	elseif (z <= 1500000000.0)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.8e+118)
		tmp = x - a;
	elseif (z <= -7e-17)
		tmp = x + ((z * a) / t);
	elseif (z <= 1500000000.0)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.8e+118], N[(x - a), $MachinePrecision], If[LessEqual[z, -7e-17], N[(x + N[(N[(z * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1500000000.0], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8e118 or 1.5e9 < z

   1. Initial program 95.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 78.9%

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

   if -7.8e118 < z < -7.0000000000000003e-17

   1. Initial program 99.8%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. distribute-neg-frac 75.1%

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

   8. Simplified 75.1%

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

   9. Taylor expanded in t around inf 65.3%

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

   if -7.0000000000000003e-17 < z < 1.5e9

   1. Initial program 99.2%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around 0 71.9%

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

   5. Taylor expanded in z around 0 70.5%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+118}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{z \cdot a}{t}\\ \mathbf{elif}\;z \leq 1500000000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 11: 73.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+18}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4100000000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e+18) (- x a) (if (<= z 4100000000.0) (- x (* y a)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+18) {
		tmp = x - a;
	} else if (z <= 4100000000.0) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3d+18)) then
        tmp = x - a
    else if (z <= 4100000000.0d0) then
        tmp = x - (y * a)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+18) {
		tmp = x - a;
	} else if (z <= 4100000000.0) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e+18:
		tmp = x - a
	elif z <= 4100000000.0:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e+18)
		tmp = Float64(x - a);
	elseif (z <= 4100000000.0)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e+18)
		tmp = x - a;
	elseif (z <= 4100000000.0)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e+18], N[(x - a), $MachinePrecision], If[LessEqual[z, 4100000000.0], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3e18 or 4.1e9 < z

   1. Initial program 95.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 75.2%

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

   if -3e18 < z < 4.1e9

   1. Initial program 99.2%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around 0 71.5%

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

   5. Taylor expanded in z around 0 68.3%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+18}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4100000000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 12: 66.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -270000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -270000000000.0) (- x a) (if (<= z 3.2e-11) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -270000000000.0) {
		tmp = x - a;
	} else if (z <= 3.2e-11) {
		tmp = x;
	} else {
		tmp = x - 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 <= (-270000000000.0d0)) then
        tmp = x - a
    else if (z <= 3.2d-11) then
        tmp = x
    else
        tmp = x - 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 <= -270000000000.0) {
		tmp = x - a;
	} else if (z <= 3.2e-11) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -270000000000.0:
		tmp = x - a
	elif z <= 3.2e-11:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -270000000000.0)
		tmp = Float64(x - a);
	elseif (z <= 3.2e-11)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -270000000000.0)
		tmp = x - a;
	elseif (z <= 3.2e-11)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -270000000000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 3.2e-11], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e11 or 3.19999999999999994e-11 < z

   1. Initial program 96.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 72.3%

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

   if -2.7e11 < z < 3.19999999999999994e-11

   1. Initial program 99.2%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 36.2%

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

      1. mul-1-neg 36.2%

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

   6. Simplified 36.2%

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

   7. Taylor expanded in x around inf 60.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -270000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 13: 55.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-242}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-169}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5.4e-242) x (if (<= x 3.2e-169) (- a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.4e-242) {
		tmp = x;
	} else if (x <= 3.2e-169) {
		tmp = -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 (x <= (-5.4d-242)) then
        tmp = x
    else if (x <= 3.2d-169) then
        tmp = -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 (x <= -5.4e-242) {
		tmp = x;
	} else if (x <= 3.2e-169) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5.4e-242:
		tmp = x
	elif x <= 3.2e-169:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5.4e-242)
		tmp = x;
	elseif (x <= 3.2e-169)
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5.4e-242)
		tmp = x;
	elseif (x <= 3.2e-169)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5.4e-242], x, If[LessEqual[x, 3.2e-169], (-a), x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4e-242 or 3.19999999999999995e-169 < x

   1. Initial program 99.5%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 61.7%

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

      1. mul-1-neg 61.7%

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

   6. Simplified 61.7%

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

   7. Taylor expanded in x around inf 66.1%

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

   if -5.4e-242 < x < 3.19999999999999995e-169

   1. Initial program 90.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around 0 54.0%

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

   5. Taylor expanded in y around 0 28.1%

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

      1. associate-*r/ 28.1%

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

      2. associate-*r* 28.1%

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

      3. neg-mul-1 28.1%

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

   7. Simplified 28.1%

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

   8. Taylor expanded in x around 0 23.0%

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

   9. Taylor expanded in z around inf 27.9%

      \[\leadsto \color{blue}{-1 \cdot a} \]
   10. Step-by-step derivation

       1. neg-mul-1 27.9%

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

   11. Simplified 27.9%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-242}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-169}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 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 97.7%

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

   1. associate-/r/ 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in z around inf 57.9%

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

   1. mul-1-neg 57.9%

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

6. Simplified 57.9%

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

7. Taylor expanded in x around inf 55.6%

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

8. Final simplification 55.6%

   \[\leadsto x \]

Developer target: 99.7% 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 2023224 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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