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

Percentage Accurate: 97.3% → 99.6%

Time: 10.4s

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: 97.3% 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

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

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 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. Add Preprocessing

5. Final simplification 99.9%

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

Alternative 2: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{a}{t}\\ t_2 := x + \frac{a}{\frac{z}{y - z}}\\ \mathbf{if}\;z \leq -5 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-77}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 7200000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ a t)))) (t_2 (+ x (/ a (/ z (- y z))))))
   (if (<= z -5e-5)
     t_2
     (if (<= z 5.2e-258)
       t_1
       (if (<= z 2.65e-77) (- x (* y a)) (if (<= z 7200000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * (a / t));
	double t_2 = x + (a / (z / (y - z)));
	double tmp;
	if (z <= -5e-5) {
		tmp = t_2;
	} else if (z <= 5.2e-258) {
		tmp = t_1;
	} else if (z <= 2.65e-77) {
		tmp = x - (y * a);
	} else if (z <= 7200000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((y - z) * (a / t))
    t_2 = x + (a / (z / (y - z)))
    if (z <= (-5d-5)) then
        tmp = t_2
    else if (z <= 5.2d-258) then
        tmp = t_1
    else if (z <= 2.65d-77) then
        tmp = x - (y * a)
    else if (z <= 7200000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * (a / t));
	double t_2 = x + (a / (z / (y - z)));
	double tmp;
	if (z <= -5e-5) {
		tmp = t_2;
	} else if (z <= 5.2e-258) {
		tmp = t_1;
	} else if (z <= 2.65e-77) {
		tmp = x - (y * a);
	} else if (z <= 7200000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) * (a / t))
	t_2 = x + (a / (z / (y - z)))
	tmp = 0
	if z <= -5e-5:
		tmp = t_2
	elif z <= 5.2e-258:
		tmp = t_1
	elif z <= 2.65e-77:
		tmp = x - (y * a)
	elif z <= 7200000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(a / t)))
	t_2 = Float64(x + Float64(a / Float64(z / Float64(y - z))))
	tmp = 0.0
	if (z <= -5e-5)
		tmp = t_2;
	elseif (z <= 5.2e-258)
		tmp = t_1;
	elseif (z <= 2.65e-77)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 7200000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) * (a / t));
	t_2 = x + (a / (z / (y - z)));
	tmp = 0.0;
	if (z <= -5e-5)
		tmp = t_2;
	elseif (z <= 5.2e-258)
		tmp = t_1;
	elseif (z <= 2.65e-77)
		tmp = x - (y * a);
	elseif (z <= 7200000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y - z), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e-5], t$95$2, If[LessEqual[z, 5.2e-258], t$95$1, If[LessEqual[z, 2.65e-77], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7200000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000024e-5 or 7.2e9 < z

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. distribute-neg-frac 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in x around 0 63.3%

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

      1. +-commutative 63.3%

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

      2. associate-/l* 87.4%

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

   8. Simplified 87.4%

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

   if -5.00000000000000024e-5 < z < 5.20000000000000036e-258 or 2.65000000000000007e-77 < z < 7.2e9

   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 t around inf 72.4%

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

      1. associate-/l* 77.5%

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

      2. associate-/r/ 76.5%

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

   7. Simplified 76.5%

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

   if 5.20000000000000036e-258 < z < 2.65000000000000007e-77

   1. Initial program 97.2%

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

   5. Taylor expanded in z around 0 94.5%

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

      1. associate-/l* 97.2%

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

   7. Simplified 97.2%

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

   8. Taylor expanded in t around 0 80.4%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-258}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-77}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 7200000000:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{\frac{z}{y - z}}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-258}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-77}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 29000000000:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (/ z (- y z))))))
   (if (<= z -4.8e-5)
     t_1
     (if (<= z 5.7e-258)
       (- x (* (- y z) (/ a t)))
       (if (<= z 6.1e-77)
         (- x (* y a))
         (if (<= z 29000000000.0) (+ x (* a (/ (- z y) t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / (z / (y - z)));
	double tmp;
	if (z <= -4.8e-5) {
		tmp = t_1;
	} else if (z <= 5.7e-258) {
		tmp = x - ((y - z) * (a / t));
	} else if (z <= 6.1e-77) {
		tmp = x - (y * a);
	} else if (z <= 29000000000.0) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a / (z / (y - z)))
    if (z <= (-4.8d-5)) then
        tmp = t_1
    else if (z <= 5.7d-258) then
        tmp = x - ((y - z) * (a / t))
    else if (z <= 6.1d-77) then
        tmp = x - (y * a)
    else if (z <= 29000000000.0d0) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / (z / (y - z)));
	double tmp;
	if (z <= -4.8e-5) {
		tmp = t_1;
	} else if (z <= 5.7e-258) {
		tmp = x - ((y - z) * (a / t));
	} else if (z <= 6.1e-77) {
		tmp = x - (y * a);
	} else if (z <= 29000000000.0) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a / (z / (y - z)))
	tmp = 0
	if z <= -4.8e-5:
		tmp = t_1
	elif z <= 5.7e-258:
		tmp = x - ((y - z) * (a / t))
	elif z <= 6.1e-77:
		tmp = x - (y * a)
	elif z <= 29000000000.0:
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a / Float64(z / Float64(y - z))))
	tmp = 0.0
	if (z <= -4.8e-5)
		tmp = t_1;
	elseif (z <= 5.7e-258)
		tmp = Float64(x - Float64(Float64(y - z) * Float64(a / t)));
	elseif (z <= 6.1e-77)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 29000000000.0)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a / (z / (y - z)));
	tmp = 0.0;
	if (z <= -4.8e-5)
		tmp = t_1;
	elseif (z <= 5.7e-258)
		tmp = x - ((y - z) * (a / t));
	elseif (z <= 6.1e-77)
		tmp = x - (y * a);
	elseif (z <= 29000000000.0)
		tmp = x + (a * ((z - y) / t));
	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[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-5], t$95$1, If[LessEqual[z, 5.7e-258], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.1e-77], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 29000000000.0], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8000000000000001e-5 or 2.9e10 < z

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. distribute-neg-frac 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in x around 0 63.3%

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

      1. +-commutative 63.3%

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

      2. associate-/l* 87.4%

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

   8. Simplified 87.4%

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

   if -4.8000000000000001e-5 < z < 5.7000000000000002e-258

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around inf 73.2%

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

      1. associate-/l* 79.6%

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

      2. associate-/r/ 78.4%

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

   7. Simplified 78.4%

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

   if 5.7000000000000002e-258 < z < 6.1000000000000002e-77

   1. Initial program 97.2%

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

   5. Taylor expanded in z around 0 94.5%

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

      1. associate-/l* 97.2%

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

   7. Simplified 97.2%

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

   8. Taylor expanded in t around 0 80.4%

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

   if 6.1000000000000002e-77 < z < 2.9e10

   1. Initial program 99.6%

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

      1. associate-/r/ 99.8%

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

   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 69.5%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-258}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-77}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 29000000000:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{\frac{z}{y - z}}\\ \mathbf{if}\;z \leq -0.000205:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-254}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.15:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (/ z (- y z))))))
   (if (<= z -0.000205)
     t_1
     (if (<= z 8.4e-254)
       (- x (/ a (/ t y)))
       (if (<= z 1.15) (- x (* y a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / (z / (y - z)));
	double tmp;
	if (z <= -0.000205) {
		tmp = t_1;
	} else if (z <= 8.4e-254) {
		tmp = x - (a / (t / y));
	} else if (z <= 1.15) {
		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 / (z / (y - z)))
    if (z <= (-0.000205d0)) then
        tmp = t_1
    else if (z <= 8.4d-254) then
        tmp = x - (a / (t / y))
    else if (z <= 1.15d0) 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 / (z / (y - z)));
	double tmp;
	if (z <= -0.000205) {
		tmp = t_1;
	} else if (z <= 8.4e-254) {
		tmp = x - (a / (t / y));
	} else if (z <= 1.15) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a / (z / (y - z)))
	tmp = 0
	if z <= -0.000205:
		tmp = t_1
	elif z <= 8.4e-254:
		tmp = x - (a / (t / y))
	elif z <= 1.15:
		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(z / Float64(y - z))))
	tmp = 0.0
	if (z <= -0.000205)
		tmp = t_1;
	elseif (z <= 8.4e-254)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (z <= 1.15)
		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 / (z / (y - z)));
	tmp = 0.0;
	if (z <= -0.000205)
		tmp = t_1;
	elseif (z <= 8.4e-254)
		tmp = x - (a / (t / y));
	elseif (z <= 1.15)
		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[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.000205], t$95$1, If[LessEqual[z, 8.4e-254], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05e-4 or 1.1499999999999999 < z

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-neg-frac 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in x around 0 62.0%

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

      1. +-commutative 62.0%

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

      2. associate-/l* 85.7%

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

   8. Simplified 85.7%

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

   if -2.05e-4 < z < 8.39999999999999987e-254

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 84.3%

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

      1. associate-/l* 91.9%

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

   7. Simplified 91.9%

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

   8. Taylor expanded in t around inf 71.9%

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

      1. associate-/l* 77.0%

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

   10. Simplified 77.0%

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

   if 8.39999999999999987e-254 < z < 1.1499999999999999

   1. Initial program 97.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 87.0%

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

      1. associate-/l* 88.8%

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

   7. Simplified 88.8%

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

   8. Taylor expanded in t around 0 71.5%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.000205:\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-254}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.15:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+25}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+55}:\\ \;\;\;\;x - \frac{a}{\frac{z + -1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6e+25)
   (+ x (* a (/ (- z y) t)))
   (if (<= t -1e-80)
     (+ x (/ a (/ z (- y z))))
     (if (<= t 1.8e+55)
       (- x (/ a (/ (+ z -1.0) z)))
       (- x (* (- y z) (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e+25) {
		tmp = x + (a * ((z - y) / t));
	} else if (t <= -1e-80) {
		tmp = x + (a / (z / (y - z)));
	} else if (t <= 1.8e+55) {
		tmp = x - (a / ((z + -1.0) / z));
	} else {
		tmp = x - ((y - z) * (a / 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 (t <= (-6d+25)) then
        tmp = x + (a * ((z - y) / t))
    else if (t <= (-1d-80)) then
        tmp = x + (a / (z / (y - z)))
    else if (t <= 1.8d+55) then
        tmp = x - (a / ((z + (-1.0d0)) / z))
    else
        tmp = x - ((y - z) * (a / 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 (t <= -6e+25) {
		tmp = x + (a * ((z - y) / t));
	} else if (t <= -1e-80) {
		tmp = x + (a / (z / (y - z)));
	} else if (t <= 1.8e+55) {
		tmp = x - (a / ((z + -1.0) / z));
	} else {
		tmp = x - ((y - z) * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6e+25:
		tmp = x + (a * ((z - y) / t))
	elif t <= -1e-80:
		tmp = x + (a / (z / (y - z)))
	elif t <= 1.8e+55:
		tmp = x - (a / ((z + -1.0) / z))
	else:
		tmp = x - ((y - z) * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6e+25)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	elseif (t <= -1e-80)
		tmp = Float64(x + Float64(a / Float64(z / Float64(y - z))));
	elseif (t <= 1.8e+55)
		tmp = Float64(x - Float64(a / Float64(Float64(z + -1.0) / z)));
	else
		tmp = Float64(x - Float64(Float64(y - z) * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6e+25)
		tmp = x + (a * ((z - y) / t));
	elseif (t <= -1e-80)
		tmp = x + (a / (z / (y - z)));
	elseif (t <= 1.8e+55)
		tmp = x - (a / ((z + -1.0) / z));
	else
		tmp = x - ((y - z) * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6e+25], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1e-80], N[(x + N[(a / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+55], N[(x - N[(a / N[(N[(z + -1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.00000000000000011e25

   1. Initial program 99.2%

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

      1. associate-/r/ 99.9%

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

   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 86.0%

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

   if -6.00000000000000011e25 < t < -9.99999999999999961e-81

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. distribute-neg-frac 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in x around 0 58.2%

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

      1. +-commutative 58.2%

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

      2. associate-/l* 74.3%

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

   8. Simplified 74.3%

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

   if -9.99999999999999961e-81 < t < 1.79999999999999994e55

   1. Initial program 97.4%

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

   5. Taylor expanded in t around 0 82.4%

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

      1. associate-/l* 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in y around 0 81.8%

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

      1. associate-*r/ 81.8%

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

      2. neg-mul-1 81.8%

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

      3. neg-sub0 81.8%

         \[\leadsto x - \frac{a}{\frac{\color{blue}{0 - \left(1 - z\right)}}{z}} \]

      4. associate--r- 81.8%

         \[\leadsto x - \frac{a}{\frac{\color{blue}{\left(0 - 1\right) + z}}{z}} \]

      5. metadata-eval 81.8%

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

   10. Simplified 81.8%

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

   if 1.79999999999999994e55 < t

   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 t around inf 74.6%

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

      1. associate-/l* 84.0%

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

      2. associate-/r/ 85.4%

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

   7. Simplified 85.4%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+25}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+55}:\\ \;\;\;\;x - \frac{a}{\frac{z + -1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+26}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+53}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.5e+26)
   (+ x (* a (/ (- z y) t)))
   (if (<= t 2e+53)
     (- x (* a (/ (- y z) (- 1.0 z))))
     (- x (* (- y z) (/ a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+26) {
		tmp = x + (a * ((z - y) / t));
	} else if (t <= 2e+53) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else {
		tmp = x - ((y - z) * (a / 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 (t <= (-2.5d+26)) then
        tmp = x + (a * ((z - y) / t))
    else if (t <= 2d+53) then
        tmp = x - (a * ((y - z) / (1.0d0 - z)))
    else
        tmp = x - ((y - z) * (a / 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 (t <= -2.5e+26) {
		tmp = x + (a * ((z - y) / t));
	} else if (t <= 2e+53) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else {
		tmp = x - ((y - z) * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.5e+26:
		tmp = x + (a * ((z - y) / t))
	elif t <= 2e+53:
		tmp = x - (a * ((y - z) / (1.0 - z)))
	else:
		tmp = x - ((y - z) * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.5e+26)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	elseif (t <= 2e+53)
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(1.0 - z))));
	else
		tmp = Float64(x - Float64(Float64(y - z) * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.5e+26)
		tmp = x + (a * ((z - y) / t));
	elseif (t <= 2e+53)
		tmp = x - (a * ((y - z) / (1.0 - z)));
	else
		tmp = x - ((y - z) * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.5e+26], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+53], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5e26

   1. Initial program 99.2%

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

      1. associate-/r/ 99.9%

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

   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 86.0%

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

   if -2.5e26 < t < 2e53

   1. Initial program 97.6%

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

      1. associate-/r/ 99.9%

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

   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 97.5%

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

   if 2e53 < t

   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 t around inf 74.6%

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

      1. associate-/l* 84.0%

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

      2. associate-/r/ 85.4%

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

   7. Simplified 85.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+26}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+53}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -46000000000000:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{elif}\;z \leq 4000000000:\\ \;\;\;\;x - \frac{y - z}{\frac{t + 1}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -46000000000000.0)
   (- x (* a (/ (- y z) (- 1.0 z))))
   (if (<= z 4000000000.0)
     (- x (/ (- y z) (/ (+ t 1.0) a)))
     (- x (/ a (/ (- 1.0 z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -46000000000000.0) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else if (z <= 4000000000.0) {
		tmp = x - ((y - z) / ((t + 1.0) / a));
	} else {
		tmp = x - (a / ((1.0 - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-46000000000000.0d0)) then
        tmp = x - (a * ((y - z) / (1.0d0 - z)))
    else if (z <= 4000000000.0d0) then
        tmp = x - ((y - z) / ((t + 1.0d0) / a))
    else
        tmp = x - (a / ((1.0d0 - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -46000000000000.0) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else if (z <= 4000000000.0) {
		tmp = x - ((y - z) / ((t + 1.0) / a));
	} else {
		tmp = x - (a / ((1.0 - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -46000000000000.0:
		tmp = x - (a * ((y - z) / (1.0 - z)))
	elif z <= 4000000000.0:
		tmp = x - ((y - z) / ((t + 1.0) / a))
	else:
		tmp = x - (a / ((1.0 - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -46000000000000.0)
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(1.0 - z))));
	elseif (z <= 4000000000.0)
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(t + 1.0) / a)));
	else
		tmp = Float64(x - Float64(a / Float64(Float64(1.0 - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -46000000000000.0)
		tmp = x - (a * ((y - z) / (1.0 - z)));
	elseif (z <= 4000000000.0)
		tmp = x - ((y - z) / ((t + 1.0) / a));
	else
		tmp = x - (a / ((1.0 - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -46000000000000.0], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4000000000.0], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(t + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(N[(1.0 - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e13

   1. Initial program 96.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 87.7%

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

   if -4.6e13 < z < 4e9

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 97.4%

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

   if 4e9 < z

   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 t around 0 58.9%

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

      1. associate-/l* 89.1%

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

   7. Simplified 89.1%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -46000000000000:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{elif}\;z \leq 4000000000:\\ \;\;\;\;x - \frac{y - z}{\frac{t + 1}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+92}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-258}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 205:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.7e+92)
   (- x a)
   (if (<= z -1.36e-6)
     (+ x (* y (/ a z)))
     (if (<= z 6.5e-258)
       (+ x (/ a (/ t z)))
       (if (<= z 205.0) (- x (* y a)) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e+92) {
		tmp = x - a;
	} else if (z <= -1.36e-6) {
		tmp = x + (y * (a / z));
	} else if (z <= 6.5e-258) {
		tmp = x + (a / (t / z));
	} else if (z <= 205.0) {
		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 <= (-4.7d+92)) then
        tmp = x - a
    else if (z <= (-1.36d-6)) then
        tmp = x + (y * (a / z))
    else if (z <= 6.5d-258) then
        tmp = x + (a / (t / z))
    else if (z <= 205.0d0) 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 <= -4.7e+92) {
		tmp = x - a;
	} else if (z <= -1.36e-6) {
		tmp = x + (y * (a / z));
	} else if (z <= 6.5e-258) {
		tmp = x + (a / (t / z));
	} else if (z <= 205.0) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.7e+92:
		tmp = x - a
	elif z <= -1.36e-6:
		tmp = x + (y * (a / z))
	elif z <= 6.5e-258:
		tmp = x + (a / (t / z))
	elif z <= 205.0:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.7e+92)
		tmp = Float64(x - a);
	elseif (z <= -1.36e-6)
		tmp = Float64(x + Float64(y * Float64(a / z)));
	elseif (z <= 6.5e-258)
		tmp = Float64(x + Float64(a / Float64(t / z)));
	elseif (z <= 205.0)
		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 <= -4.7e+92)
		tmp = x - a;
	elseif (z <= -1.36e-6)
		tmp = x + (y * (a / z));
	elseif (z <= 6.5e-258)
		tmp = x + (a / (t / z));
	elseif (z <= 205.0)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.7e+92], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.36e-6], N[(x + N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-258], N[(x + N[(a / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 205.0], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.7e92 or 205 < z

   1. Initial program 96.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 76.7%

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

   if -4.7e92 < z < -1.3599999999999999e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. distribute-neg-frac 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in y around inf 75.3%

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

      1. mul-1-neg 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-*r/ 81.9%

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

      4. distribute-rgt-neg-in 81.9%

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

      5. distribute-neg-frac 81.9%

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

   8. Simplified 81.9%

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

      1. *-commutative 81.9%

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

      2. distribute-frac-neg 81.9%

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

      3. cancel-sign-sub 81.9%

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

      4. *-commutative 81.9%

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

      5. add-sqr-sqrt 32.6%

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

      6. sqrt-unprod 62.3%

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

      7. sqr-neg 62.3%

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

      8. distribute-frac-neg 62.3%

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

      9. distribute-frac-neg 62.3%

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

      10. sqrt-unprod 37.2%

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

      11. add-sqr-sqrt 66.2%

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

      12. +-commutative 66.2%

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

   10. Applied egg-rr 81.9%

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

   if -1.3599999999999999e-6 < z < 6.5000000000000002e-258

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around inf 78.3%

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

   6. Taylor expanded in y around 0 65.5%

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

      1. sub-neg 65.5%

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

      2. mul-1-neg 65.5%

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

      3. remove-double-neg 65.5%

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

      4. associate-/l* 65.3%

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

   8. Simplified 65.3%

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

   if 6.5000000000000002e-258 < z < 205

   1. Initial program 97.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 87.0%

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

      1. associate-/l* 88.8%

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

   7. Simplified 88.8%

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

   8. Taylor expanded in t around 0 71.5%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+92}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-258}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 205:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+93}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-257}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 0.0225:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+93)
   (- x a)
   (if (<= z -2.5e-11)
     (+ x (* y (/ a z)))
     (if (<= z 5.8e-257)
       (- x (* a (/ y t)))
       (if (<= z 0.0225) (- x (* y a)) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+93) {
		tmp = x - a;
	} else if (z <= -2.5e-11) {
		tmp = x + (y * (a / z));
	} else if (z <= 5.8e-257) {
		tmp = x - (a * (y / t));
	} else if (z <= 0.0225) {
		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 <= (-1.9d+93)) then
        tmp = x - a
    else if (z <= (-2.5d-11)) then
        tmp = x + (y * (a / z))
    else if (z <= 5.8d-257) then
        tmp = x - (a * (y / t))
    else if (z <= 0.0225d0) 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 <= -1.9e+93) {
		tmp = x - a;
	} else if (z <= -2.5e-11) {
		tmp = x + (y * (a / z));
	} else if (z <= 5.8e-257) {
		tmp = x - (a * (y / t));
	} else if (z <= 0.0225) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+93:
		tmp = x - a
	elif z <= -2.5e-11:
		tmp = x + (y * (a / z))
	elif z <= 5.8e-257:
		tmp = x - (a * (y / t))
	elif z <= 0.0225:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+93)
		tmp = Float64(x - a);
	elseif (z <= -2.5e-11)
		tmp = Float64(x + Float64(y * Float64(a / z)));
	elseif (z <= 5.8e-257)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= 0.0225)
		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 <= -1.9e+93)
		tmp = x - a;
	elseif (z <= -2.5e-11)
		tmp = x + (y * (a / z));
	elseif (z <= 5.8e-257)
		tmp = x - (a * (y / t));
	elseif (z <= 0.0225)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+93], N[(x - a), $MachinePrecision], If[LessEqual[z, -2.5e-11], N[(x + N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-257], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0225], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8999999999999999e93 or 0.022499999999999999 < z

   1. Initial program 96.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 76.7%

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

   if -1.8999999999999999e93 < z < -2.50000000000000009e-11

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. distribute-neg-frac 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in y around inf 72.8%

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

      1. mul-1-neg 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*r/ 79.2%

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

      4. distribute-rgt-neg-in 79.2%

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

      5. distribute-neg-frac 79.2%

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

   8. Simplified 79.2%

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

      1. *-commutative 79.2%

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

      2. distribute-frac-neg 79.2%

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

      3. cancel-sign-sub 79.2%

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

      4. *-commutative 79.2%

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

      5. add-sqr-sqrt 31.6%

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

      6. sqrt-unprod 60.3%

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

      7. sqr-neg 60.3%

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

      8. distribute-frac-neg 60.3%

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

      9. distribute-frac-neg 60.3%

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

      10. sqrt-unprod 35.8%

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

      11. add-sqr-sqrt 63.9%

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

      12. +-commutative 63.9%

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

   10. Applied egg-rr 79.2%

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

   if -2.50000000000000009e-11 < z < 5.8000000000000003e-257

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around inf 78.0%

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

   6. Taylor expanded in y around inf 76.4%

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

   if 5.8000000000000003e-257 < z < 0.022499999999999999

   1. Initial program 97.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 87.0%

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

      1. associate-/l* 88.8%

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

   7. Simplified 88.8%

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

   8. Taylor expanded in t around 0 71.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+93}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-257}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 0.0225:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+99}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-256}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 0.185:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+99)
   (- x a)
   (if (<= z -6.5e-13)
     (+ x (* y (/ a z)))
     (if (<= z 2.55e-256)
       (- x (/ a (/ t y)))
       (if (<= z 0.185) (- x (* y a)) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+99) {
		tmp = x - a;
	} else if (z <= -6.5e-13) {
		tmp = x + (y * (a / z));
	} else if (z <= 2.55e-256) {
		tmp = x - (a / (t / y));
	} else if (z <= 0.185) {
		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 <= (-1.15d+99)) then
        tmp = x - a
    else if (z <= (-6.5d-13)) then
        tmp = x + (y * (a / z))
    else if (z <= 2.55d-256) then
        tmp = x - (a / (t / y))
    else if (z <= 0.185d0) 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 <= -1.15e+99) {
		tmp = x - a;
	} else if (z <= -6.5e-13) {
		tmp = x + (y * (a / z));
	} else if (z <= 2.55e-256) {
		tmp = x - (a / (t / y));
	} else if (z <= 0.185) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+99:
		tmp = x - a
	elif z <= -6.5e-13:
		tmp = x + (y * (a / z))
	elif z <= 2.55e-256:
		tmp = x - (a / (t / y))
	elif z <= 0.185:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+99)
		tmp = Float64(x - a);
	elseif (z <= -6.5e-13)
		tmp = Float64(x + Float64(y * Float64(a / z)));
	elseif (z <= 2.55e-256)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (z <= 0.185)
		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 <= -1.15e+99)
		tmp = x - a;
	elseif (z <= -6.5e-13)
		tmp = x + (y * (a / z));
	elseif (z <= 2.55e-256)
		tmp = x - (a / (t / y));
	elseif (z <= 0.185)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+99], N[(x - a), $MachinePrecision], If[LessEqual[z, -6.5e-13], N[(x + N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.55e-256], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.185], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1500000000000001e99 or 0.185 < z

   1. Initial program 96.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 76.7%

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

   if -1.1500000000000001e99 < z < -6.49999999999999957e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. distribute-neg-frac 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in y around inf 72.8%

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

      1. mul-1-neg 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*r/ 79.2%

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

      4. distribute-rgt-neg-in 79.2%

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

      5. distribute-neg-frac 79.2%

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

   8. Simplified 79.2%

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

      1. *-commutative 79.2%

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

      2. distribute-frac-neg 79.2%

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

      3. cancel-sign-sub 79.2%

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

      4. *-commutative 79.2%

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

      5. add-sqr-sqrt 31.6%

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

      6. sqrt-unprod 60.3%

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

      7. sqr-neg 60.3%

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

      8. distribute-frac-neg 60.3%

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

      9. distribute-frac-neg 60.3%

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

      10. sqrt-unprod 35.8%

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

      11. add-sqr-sqrt 63.9%

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

      12. +-commutative 63.9%

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

   10. Applied egg-rr 79.2%

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

   if -6.49999999999999957e-13 < z < 2.55000000000000005e-256

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 85.3%

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

      1. associate-/l* 93.1%

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

   7. Simplified 93.1%

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

   8. Taylor expanded in t around inf 72.5%

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

      1. associate-/l* 77.7%

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

   10. Simplified 77.7%

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

   if 2.55000000000000005e-256 < z < 0.185

   1. Initial program 97.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 87.0%

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

      1. associate-/l* 88.8%

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

   7. Simplified 88.8%

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

   8. Taylor expanded in t around 0 71.5%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+99}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-256}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 0.185:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+20} \lor \neg \left(z \leq 1400000000\right):\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+20) (not (<= z 1400000000.0)))
   (+ x (/ a (/ z (- y z))))
   (- x (/ a (/ (+ t 1.0) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+20) || !(z <= 1400000000.0)) {
		tmp = x + (a / (z / (y - z)));
	} else {
		tmp = x - (a / ((t + 1.0) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.5d+20)) .or. (.not. (z <= 1400000000.0d0))) then
        tmp = x + (a / (z / (y - z)))
    else
        tmp = x - (a / ((t + 1.0d0) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+20) || !(z <= 1400000000.0)) {
		tmp = x + (a / (z / (y - z)));
	} else {
		tmp = x - (a / ((t + 1.0) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e+20) or not (z <= 1400000000.0):
		tmp = x + (a / (z / (y - z)))
	else:
		tmp = x - (a / ((t + 1.0) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+20) || !(z <= 1400000000.0))
		tmp = Float64(x + Float64(a / Float64(z / Float64(y - z))));
	else
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.5e+20) || ~((z <= 1400000000.0)))
		tmp = x + (a / (z / (y - z)));
	else
		tmp = x - (a / ((t + 1.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+20], N[Not[LessEqual[z, 1400000000.0]], $MachinePrecision]], N[(x + N[(a / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5e20 or 1.4e9 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. distribute-neg-frac 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in x around 0 62.2%

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

      1. +-commutative 62.2%

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

      2. associate-/l* 87.9%

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

   8. Simplified 87.9%

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

   if -9.5e20 < z < 1.4e9

   1. Initial program 99.2%

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

      1. associate-/r/ 99.9%

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

   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 84.4%

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

      1. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+20} \lor \neg \left(z \leq 1400000000\right):\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+64} \lor \neg \left(z \leq 0.00033\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e+64) (not (<= z 0.00033))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+64) || !(z <= 0.00033)) {
		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 <= (-8.8d+64)) .or. (.not. (z <= 0.00033d0))) 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 <= -8.8e+64) || !(z <= 0.00033)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.8e+64) or not (z <= 0.00033):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.8e+64) || !(z <= 0.00033))
		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 <= -8.8e+64) || ~((z <= 0.00033)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.8e+64], N[Not[LessEqual[z, 0.00033]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.80000000000000007e64 or 3.3e-4 < z

   1. Initial program 96.8%

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

   5. Taylor expanded in z around inf 74.7%

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

   if -8.80000000000000007e64 < z < 3.3e-4

   1. Initial program 99.2%

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

      1. associate-/r/ 99.9%

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

   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 84.8%

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

      1. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in t around 0 67.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+64} \lor \neg \left(z \leq 0.00033\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+22} \lor \neg \left(z \leq 3400\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e+22) (not (<= z 3400.0))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+22) || !(z <= 3400.0)) {
		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 <= (-1.2d+22)) .or. (.not. (z <= 3400.0d0))) 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 <= -1.2e+22) || !(z <= 3400.0)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e+22) or not (z <= 3400.0):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e+22) || !(z <= 3400.0))
		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 <= -1.2e+22) || ~((z <= 3400.0)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e+22], N[Not[LessEqual[z, 3400.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e22 or 3400 < z

   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 z around inf 74.2%

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

   if -1.2e22 < z < 3400

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 37.9%

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

      1. mul-1-neg 37.9%

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

      2. distribute-neg-frac 37.9%

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

   5. Simplified 37.9%

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

   6. Taylor expanded in x around inf 63.1%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+22} \lor \neg \left(z \leq 3400\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.1% 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 98.2%

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

3. Taylor expanded in z around inf 60.5%

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

   1. mul-1-neg 60.5%

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

   2. distribute-neg-frac 60.5%

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

5. Simplified 60.5%

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

6. Taylor expanded in x around inf 54.7%

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

7. Final simplification 54.7%

   \[\leadsto x \]
8. 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 2024011 
(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))))