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

Percentage Accurate: 96.9% → 99.6%

Time: 16.9s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.9% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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. Final simplification 99.8%

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

Alternative 2: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+57}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-204}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 0.0185:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (- z y)))))
   (if (<= z -8.2e+57)
     (- x a)
     (if (<= z 1.8e-269)
       t_1
       (if (<= z 6e-204)
         (- x (* a (/ y t)))
         (if (<= z 0.0185) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z - y));
	double tmp;
	if (z <= -8.2e+57) {
		tmp = x - a;
	} else if (z <= 1.8e-269) {
		tmp = t_1;
	} else if (z <= 6e-204) {
		tmp = x - (a * (y / t));
	} else if (z <= 0.0185) {
		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 * (z - y))
    if (z <= (-8.2d+57)) then
        tmp = x - a
    else if (z <= 1.8d-269) then
        tmp = t_1
    else if (z <= 6d-204) then
        tmp = x - (a * (y / t))
    else if (z <= 0.0185d0) 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 * (z - y));
	double tmp;
	if (z <= -8.2e+57) {
		tmp = x - a;
	} else if (z <= 1.8e-269) {
		tmp = t_1;
	} else if (z <= 6e-204) {
		tmp = x - (a * (y / t));
	} else if (z <= 0.0185) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * (z - y))
	tmp = 0
	if z <= -8.2e+57:
		tmp = x - a
	elif z <= 1.8e-269:
		tmp = t_1
	elif z <= 6e-204:
		tmp = x - (a * (y / t))
	elif z <= 0.0185:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(z - y)))
	tmp = 0.0
	if (z <= -8.2e+57)
		tmp = Float64(x - a);
	elseif (z <= 1.8e-269)
		tmp = t_1;
	elseif (z <= 6e-204)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= 0.0185)
		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 * (z - y));
	tmp = 0.0;
	if (z <= -8.2e+57)
		tmp = x - a;
	elseif (z <= 1.8e-269)
		tmp = t_1;
	elseif (z <= 6e-204)
		tmp = x - (a * (y / t));
	elseif (z <= 0.0185)
		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[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+57], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.8e-269], t$95$1, If[LessEqual[z, 6e-204], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0185], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2e57 or 0.0184999999999999991 < z

   1. Initial program 92.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.3%

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

   if -8.2e57 < z < 1.79999999999999999e-269 or 5.9999999999999997e-204 < z < 0.0184999999999999991

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 98.1%

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

   4. Taylor expanded in t around 0 81.9%

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

   if 1.79999999999999999e-269 < z < 5.9999999999999997e-204

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 99.9%

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

   6. Taylor expanded in t around inf 83.0%

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

      1. associate-/l* 83.0%

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

   8. Simplified 83.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+57}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-269}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-204}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 0.0185:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+57}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 0.019:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (- z y)))))
   (if (<= z -8.2e+57)
     (- x a)
     (if (<= z 1.8e-269)
       t_1
       (if (<= z 1.25e-203)
         (- x (/ (* y a) t))
         (if (<= z 0.019) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z - y));
	double tmp;
	if (z <= -8.2e+57) {
		tmp = x - a;
	} else if (z <= 1.8e-269) {
		tmp = t_1;
	} else if (z <= 1.25e-203) {
		tmp = x - ((y * a) / t);
	} else if (z <= 0.019) {
		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 * (z - y))
    if (z <= (-8.2d+57)) then
        tmp = x - a
    else if (z <= 1.8d-269) then
        tmp = t_1
    else if (z <= 1.25d-203) then
        tmp = x - ((y * a) / t)
    else if (z <= 0.019d0) 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 * (z - y));
	double tmp;
	if (z <= -8.2e+57) {
		tmp = x - a;
	} else if (z <= 1.8e-269) {
		tmp = t_1;
	} else if (z <= 1.25e-203) {
		tmp = x - ((y * a) / t);
	} else if (z <= 0.019) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * (z - y))
	tmp = 0
	if z <= -8.2e+57:
		tmp = x - a
	elif z <= 1.8e-269:
		tmp = t_1
	elif z <= 1.25e-203:
		tmp = x - ((y * a) / t)
	elif z <= 0.019:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(z - y)))
	tmp = 0.0
	if (z <= -8.2e+57)
		tmp = Float64(x - a);
	elseif (z <= 1.8e-269)
		tmp = t_1;
	elseif (z <= 1.25e-203)
		tmp = Float64(x - Float64(Float64(y * a) / t));
	elseif (z <= 0.019)
		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 * (z - y));
	tmp = 0.0;
	if (z <= -8.2e+57)
		tmp = x - a;
	elseif (z <= 1.8e-269)
		tmp = t_1;
	elseif (z <= 1.25e-203)
		tmp = x - ((y * a) / t);
	elseif (z <= 0.019)
		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[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+57], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.8e-269], t$95$1, If[LessEqual[z, 1.25e-203], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.019], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2e57 or 0.0189999999999999995 < z

   1. Initial program 92.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.3%

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

   if -8.2e57 < z < 1.79999999999999999e-269 or 1.25e-203 < z < 0.0189999999999999995

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 98.1%

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

   4. Taylor expanded in t around 0 81.9%

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

   if 1.79999999999999999e-269 < z < 1.25e-203

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 99.9%

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

   6. Taylor expanded in t around inf 83.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+57}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-269}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 0.019:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot a\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 0.019:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z a))))
   (if (<= z -1.6e-25)
     (- x a)
     (if (<= z 3e-207)
       t_1
       (if (<= z 1.6e-179) (* y (- a)) (if (<= z 0.019) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * a);
	double tmp;
	if (z <= -1.6e-25) {
		tmp = x - a;
	} else if (z <= 3e-207) {
		tmp = t_1;
	} else if (z <= 1.6e-179) {
		tmp = y * -a;
	} else if (z <= 0.019) {
		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 + (z * a)
    if (z <= (-1.6d-25)) then
        tmp = x - a
    else if (z <= 3d-207) then
        tmp = t_1
    else if (z <= 1.6d-179) then
        tmp = y * -a
    else if (z <= 0.019d0) 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 + (z * a);
	double tmp;
	if (z <= -1.6e-25) {
		tmp = x - a;
	} else if (z <= 3e-207) {
		tmp = t_1;
	} else if (z <= 1.6e-179) {
		tmp = y * -a;
	} else if (z <= 0.019) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * a)
	tmp = 0
	if z <= -1.6e-25:
		tmp = x - a
	elif z <= 3e-207:
		tmp = t_1
	elif z <= 1.6e-179:
		tmp = y * -a
	elif z <= 0.019:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * a))
	tmp = 0.0
	if (z <= -1.6e-25)
		tmp = Float64(x - a);
	elseif (z <= 3e-207)
		tmp = t_1;
	elseif (z <= 1.6e-179)
		tmp = Float64(y * Float64(-a));
	elseif (z <= 0.019)
		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 + (z * a);
	tmp = 0.0;
	if (z <= -1.6e-25)
		tmp = x - a;
	elseif (z <= 3e-207)
		tmp = t_1;
	elseif (z <= 1.6e-179)
		tmp = y * -a;
	elseif (z <= 0.019)
		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[(z * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e-25], N[(x - a), $MachinePrecision], If[LessEqual[z, 3e-207], t$95$1, If[LessEqual[z, 1.6e-179], N[(y * (-a)), $MachinePrecision], If[LessEqual[z, 0.019], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6000000000000001e-25 or 0.0189999999999999995 < z

   1. Initial program 93.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 76.7%

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

   if -1.6000000000000001e-25 < z < 2.9999999999999999e-207 or 1.6e-179 < z < 0.0189999999999999995

   1. Initial program 99.0%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 78.6%

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

   6. Taylor expanded in y around 0 58.3%

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

      1. sub-neg 58.3%

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

      2. mul-1-neg 58.3%

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

      3. remove-double-neg 58.3%

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

   8. Simplified 58.3%

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

   9. Taylor expanded in z around 0 58.3%

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

   if 2.9999999999999999e-207 < z < 1.6e-179

   1. Initial program 99.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around 0 85.2%

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

   6. Taylor expanded in x around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. neg-mul-1 70.6%

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

      3. distribute-rgt-neg-out 70.6%

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

      4. distribute-neg-frac2 70.6%

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

   8. Simplified 70.6%

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

   9. Taylor expanded in z around 0 70.7%

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

       1. associate-*r* 70.7%

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

       2. mul-1-neg 70.7%

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

   11. Simplified 70.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-207}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 0.019:\\ \;\;\;\;x + z \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+100} \lor \neg \left(z \leq 8.2 \cdot 10^{+18}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e+100) (not (<= z 8.2e+18)))
   (- x (/ (- z y) (/ z a)))
   (+ x (* a (/ (- y z) (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+100) || !(z <= 8.2e+18)) {
		tmp = x - ((z - y) / (z / a));
	} else {
		tmp = x + (a * ((y - z) / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8d+100)) .or. (.not. (z <= 8.2d+18))) then
        tmp = x - ((z - y) / (z / a))
    else
        tmp = x + (a * ((y - z) / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+100) || !(z <= 8.2e+18)) {
		tmp = x - ((z - y) / (z / a));
	} else {
		tmp = x + (a * ((y - z) / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e+100) or not (z <= 8.2e+18):
		tmp = x - ((z - y) / (z / a))
	else:
		tmp = x + (a * ((y - z) / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e+100) || !(z <= 8.2e+18))
		tmp = Float64(x - Float64(Float64(z - y) / Float64(z / a)));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e+100) || ~((z <= 8.2e+18)))
		tmp = x - ((z - y) / (z / a));
	else
		tmp = x + (a * ((y - z) / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e+100], N[Not[LessEqual[z, 8.2e+18]], $MachinePrecision]], N[(x - N[(N[(z - y), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000013e100 or 8.2e18 < z

   1. Initial program 92.7%

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

   3. Taylor expanded in z around inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. distribute-neg-frac2 89.7%

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

   5. Simplified 89.7%

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

   if -8.00000000000000013e100 < z < 8.2e18

   1. Initial program 98.6%

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

   3. Taylor expanded in z around 0 97.2%

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

      1. associate-/r/ 98.4%

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

   5. Applied egg-rr 98.4%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+100} \lor \neg \left(z \leq 8.2 \cdot 10^{+18}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-38}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-207}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.75e-38)
   (- x a)
   (if (<= z 2.6e-207) x (if (<= z 3.6e-178) (* y (- a)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e-38) {
		tmp = x - a;
	} else if (z <= 2.6e-207) {
		tmp = x;
	} else if (z <= 3.6e-178) {
		tmp = 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 <= (-1.75d-38)) then
        tmp = x - a
    else if (z <= 2.6d-207) then
        tmp = x
    else if (z <= 3.6d-178) then
        tmp = 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 <= -1.75e-38) {
		tmp = x - a;
	} else if (z <= 2.6e-207) {
		tmp = x;
	} else if (z <= 3.6e-178) {
		tmp = y * -a;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.75e-38:
		tmp = x - a
	elif z <= 2.6e-207:
		tmp = x
	elif z <= 3.6e-178:
		tmp = y * -a
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.75e-38)
		tmp = Float64(x - a);
	elseif (z <= 2.6e-207)
		tmp = x;
	elseif (z <= 3.6e-178)
		tmp = Float64(y * Float64(-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 <= -1.75e-38)
		tmp = x - a;
	elseif (z <= 2.6e-207)
		tmp = x;
	elseif (z <= 3.6e-178)
		tmp = y * -a;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.75e-38], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.6e-207], x, If[LessEqual[z, 3.6e-178], N[(y * (-a)), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7500000000000001e-38 or 3.59999999999999994e-178 < 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. Add Preprocessing

   5. Taylor expanded in z around inf 68.6%

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

   if -1.7500000000000001e-38 < z < 2.5999999999999999e-207

   1. Initial program 98.6%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 95.8%

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

      1. *-commutative 95.8%

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

      2. associate--l+ 95.8%

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

      3. +-commutative 95.8%

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

      4. associate-*r/ 97.0%

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

      5. +-commutative 97.0%

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

      6. associate--l+ 97.0%

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

      7. associate--l+ 97.0%

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

   7. Simplified 97.0%

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

   8. Taylor expanded in x around inf 60.0%

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

   if 2.5999999999999999e-207 < z < 3.59999999999999994e-178

   1. Initial program 99.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around 0 85.2%

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

   6. Taylor expanded in x around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. neg-mul-1 70.6%

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

      3. distribute-rgt-neg-out 70.6%

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

      4. distribute-neg-frac2 70.6%

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

   8. Simplified 70.6%

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

   9. Taylor expanded in z around 0 70.7%

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

       1. associate-*r* 70.7%

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

       2. mul-1-neg 70.7%

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

   11. Simplified 70.7%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-38}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-207}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+97} \lor \neg \left(z \leq 1.1 \cdot 10^{+19}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.3e+97) (not (<= z 1.1e+19)))
   (- x a)
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.3e+97) || !(z <= 1.1e+19)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.3d+97)) .or. (.not. (z <= 1.1d+19))) then
        tmp = x - a
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.3e+97) || !(z <= 1.1e+19)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.3e+97) or not (z <= 1.1e+19):
		tmp = x - a
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.3e+97) || !(z <= 1.1e+19))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.3e+97) || ~((z <= 1.1e+19)))
		tmp = x - a;
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.3e+97], N[Not[LessEqual[z, 1.1e+19]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3000000000000003e97 or 1.1e19 < z

   1. Initial program 92.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 80.8%

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

   if -5.3000000000000003e97 < z < 1.1e19

   1. Initial program 98.6%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 93.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+97} \lor \neg \left(z \leq 1.1 \cdot 10^{+19}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+95} \lor \neg \left(z \leq 7.2 \cdot 10^{+18}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.6e+95) (not (<= z 7.2e+18)))
   (- x (/ (- z y) (/ z a)))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.6e+95) || !(z <= 7.2e+18)) {
		tmp = x - ((z - y) / (z / a));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7.6d+95)) .or. (.not. (z <= 7.2d+18))) then
        tmp = x - ((z - y) / (z / a))
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.6e+95) || !(z <= 7.2e+18)) {
		tmp = x - ((z - y) / (z / a));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.6e+95) or not (z <= 7.2e+18):
		tmp = x - ((z - y) / (z / a))
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.6e+95) || !(z <= 7.2e+18))
		tmp = Float64(x - Float64(Float64(z - y) / Float64(z / a)));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.6e+95) || ~((z <= 7.2e+18)))
		tmp = x - ((z - y) / (z / a));
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.6e+95], N[Not[LessEqual[z, 7.2e+18]], $MachinePrecision]], N[(x - N[(N[(z - y), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5999999999999999e95 or 7.2e18 < z

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf 89.0%

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

      1. mul-1-neg 89.0%

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

      2. distribute-neg-frac2 89.0%

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

   5. Simplified 89.0%

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

   if -7.5999999999999999e95 < z < 7.2e18

   1. Initial program 98.6%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 93.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+95} \lor \neg \left(z \leq 7.2 \cdot 10^{+18}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+57} \lor \neg \left(z \leq 0.019\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.2e+57) (not (<= z 0.019))) (- x a) (+ x (* a (- z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.2e+57) || !(z <= 0.019)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (z - 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 <= (-8.2d+57)) .or. (.not. (z <= 0.019d0))) then
        tmp = x - a
    else
        tmp = x + (a * (z - 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 <= -8.2e+57) || !(z <= 0.019)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.2e+57) or not (z <= 0.019):
		tmp = x - a
	else:
		tmp = x + (a * (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.2e+57) || !(z <= 0.019))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.2e+57) || ~((z <= 0.019)))
		tmp = x - a;
	else
		tmp = x + (a * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.2e+57], N[Not[LessEqual[z, 0.019]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2e57 or 0.0189999999999999995 < z

   1. Initial program 92.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.3%

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

   if -8.2e57 < z < 0.0189999999999999995

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 98.3%

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

   4. Taylor expanded in t around 0 78.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+57} \lor \neg \left(z \leq 0.019\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+58} \lor \neg \left(z \leq 0.019\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1e+58) (not (<= z 0.019))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e+58) || !(z <= 0.019)) {
		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 <= (-1d+58)) .or. (.not. (z <= 0.019d0))) 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 <= -1e+58) || !(z <= 0.019)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1e+58) or not (z <= 0.019):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1e+58) || !(z <= 0.019))
		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 <= -1e+58) || ~((z <= 0.019)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1e+58], N[Not[LessEqual[z, 0.019]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999944e57 or 0.0189999999999999995 < z

   1. Initial program 92.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.3%

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

   if -9.99999999999999944e57 < z < 0.0189999999999999995

   1. Initial program 99.1%

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

   5. Taylor expanded in z around 0 91.4%

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

   6. Taylor expanded in t around 0 75.3%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+58} \lor \neg \left(z \leq 0.019\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-38} \lor \neg \left(z \leq 2.2 \cdot 10^{+45}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e-38) (not (<= z 2.2e+45))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e-38) || !(z <= 2.2e+45)) {
		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 <= (-1.15d-38)) .or. (.not. (z <= 2.2d+45))) 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 <= -1.15e-38) || !(z <= 2.2e+45)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e-38) or not (z <= 2.2e+45):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e-38) || !(z <= 2.2e+45))
		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 <= -1.15e-38) || ~((z <= 2.2e+45)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e-38], N[Not[LessEqual[z, 2.2e+45]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000001e-38 or 2.2e45 < z

   1. Initial program 93.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 76.1%

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

   if -1.15000000000000001e-38 < z < 2.2e45

   1. Initial program 99.1%

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

   5. Taylor expanded in y around inf 92.6%

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

      1. *-commutative 92.6%

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

      2. associate--l+ 92.6%

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

      3. +-commutative 92.6%

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

      4. associate-*r/ 94.6%

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

      5. +-commutative 94.6%

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

      6. associate--l+ 94.6%

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

      7. associate--l+ 94.6%

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

   7. Simplified 94.6%

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

   8. Taylor expanded in x around inf 53.6%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-38} \lor \neg \left(z \leq 2.2 \cdot 10^{+45}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-117}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -9e-160) x (if (<= x 4.3e-117) (- a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9e-160) {
		tmp = x;
	} else if (x <= 4.3e-117) {
		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 <= (-9d-160)) then
        tmp = x
    else if (x <= 4.3d-117) 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 <= -9e-160) {
		tmp = x;
	} else if (x <= 4.3e-117) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -9e-160:
		tmp = x
	elif x <= 4.3e-117:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -9e-160)
		tmp = x;
	elseif (x <= 4.3e-117)
		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 <= -9e-160)
		tmp = x;
	elseif (x <= 4.3e-117)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -9e-160], x, If[LessEqual[x, 4.3e-117], (-a), x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.00000000000000053e-160 or 4.3e-117 < 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/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 87.6%

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

      1. *-commutative 87.6%

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

      2. associate--l+ 87.6%

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

      3. +-commutative 87.6%

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

      4. associate-*r/ 90.2%

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

      5. +-commutative 90.2%

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

      6. associate--l+ 90.2%

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

      7. associate--l+ 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in x around inf 67.3%

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

   if -9.00000000000000053e-160 < x < 4.3e-117

   1. Initial program 87.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 59.6%

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

   6. Taylor expanded in x around 0 49.8%

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

      1. associate-*r/ 64.5%

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

      2. neg-mul-1 64.5%

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

      3. distribute-rgt-neg-out 64.5%

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

      4. distribute-neg-frac2 64.5%

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

   8. Simplified 64.5%

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

   9. Taylor expanded in z around inf 31.0%

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

       1. mul-1-neg 31.0%

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

   11. Simplified 31.0%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-117}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.5% 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 96.3%

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

   1. associate-/r/ 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around inf 79.0%

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

   1. *-commutative 79.0%

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

   2. associate--l+ 79.0%

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

   3. +-commutative 79.0%

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

   4. associate-*r/ 81.7%

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

   5. +-commutative 81.7%

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

   6. associate--l+ 81.7%

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

   7. associate--l+ 81.7%

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

7. Simplified 81.7%

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

8. Taylor expanded in x around inf 52.8%

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

9. Final simplification 52.8%

   \[\leadsto x \]
10. 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 2024076 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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