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

Percentage Accurate: 97.4% → 99.6%

Time: 16.6s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.4% 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 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. Final simplification 99.9%

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

Alternative 2: 71.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13500:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-192}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-80}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 14:\\ \;\;\;\;x + z \cdot a\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+183}:\\ \;\;\;\;x + \frac{y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -13500.0)
   (- x a)
   (if (<= z -8e-192)
     (- x (* a (/ y t)))
     (if (<= z 1.6e-80)
       (- x (* y a))
       (if (<= z 14.0)
         (+ x (* z a))
         (if (<= z 2.45e+183) (+ x (/ y (/ z a))) (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -13500.0) {
		tmp = x - a;
	} else if (z <= -8e-192) {
		tmp = x - (a * (y / t));
	} else if (z <= 1.6e-80) {
		tmp = x - (y * a);
	} else if (z <= 14.0) {
		tmp = x + (z * a);
	} else if (z <= 2.45e+183) {
		tmp = x + (y / (z / 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 <= (-13500.0d0)) then
        tmp = x - a
    else if (z <= (-8d-192)) then
        tmp = x - (a * (y / t))
    else if (z <= 1.6d-80) then
        tmp = x - (y * a)
    else if (z <= 14.0d0) then
        tmp = x + (z * a)
    else if (z <= 2.45d+183) then
        tmp = x + (y / (z / 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 <= -13500.0) {
		tmp = x - a;
	} else if (z <= -8e-192) {
		tmp = x - (a * (y / t));
	} else if (z <= 1.6e-80) {
		tmp = x - (y * a);
	} else if (z <= 14.0) {
		tmp = x + (z * a);
	} else if (z <= 2.45e+183) {
		tmp = x + (y / (z / a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -13500.0:
		tmp = x - a
	elif z <= -8e-192:
		tmp = x - (a * (y / t))
	elif z <= 1.6e-80:
		tmp = x - (y * a)
	elif z <= 14.0:
		tmp = x + (z * a)
	elif z <= 2.45e+183:
		tmp = x + (y / (z / a))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -13500.0)
		tmp = Float64(x - a);
	elseif (z <= -8e-192)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= 1.6e-80)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 14.0)
		tmp = Float64(x + Float64(z * a));
	elseif (z <= 2.45e+183)
		tmp = Float64(x + Float64(y / Float64(z / 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 <= -13500.0)
		tmp = x - a;
	elseif (z <= -8e-192)
		tmp = x - (a * (y / t));
	elseif (z <= 1.6e-80)
		tmp = x - (y * a);
	elseif (z <= 14.0)
		tmp = x + (z * a);
	elseif (z <= 2.45e+183)
		tmp = x + (y / (z / a));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -13500.0], N[(x - a), $MachinePrecision], If[LessEqual[z, -8e-192], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-80], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 14.0], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+183], N[(x + N[(y / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -13500 or 2.44999999999999986e183 < z

   1. Initial program 95.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 81.7%

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

   if -13500 < z < -8.0000000000000008e-192

   1. Initial program 99.1%

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

      1. associate-/r/ 99.8%

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

   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 78.8%

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

   6. Taylor expanded in y around inf 81.5%

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

   if -8.0000000000000008e-192 < z < 1.5999999999999999e-80

   1. Initial program 98.7%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 92.7%

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

   8. Taylor expanded in t around 0 77.9%

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

   if 1.5999999999999999e-80 < z < 14

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 82.6%

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

      1. neg-mul-1 82.6%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in z around 0 78.8%

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

      1. mul-1-neg 78.8%

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

      2. distribute-neg-frac2 78.8%

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

      3. distribute-neg-in 78.8%

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

      4. metadata-eval 78.8%

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

      5. unsub-neg 78.8%

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

   8. Simplified 78.8%

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

   9. Taylor expanded in t around 0 79.2%

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

       1. associate-*r* 79.2%

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

       2. neg-mul-1 79.2%

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

       3. cancel-sign-sub 79.2%

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

   11. Simplified 79.2%

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

   if 14 < z < 2.44999999999999986e183

   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 80.1%

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

      1. associate-*r/ 80.1%

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

      2. neg-mul-1 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in y around inf 72.8%

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{-z}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13500:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-192}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-80}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 14:\\ \;\;\;\;x + z \cdot a\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+183}:\\ \;\;\;\;x + \frac{y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6800:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-192}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-81}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-7}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6800.0)
   (- x a)
   (if (<= z -1.45e-192)
     (- x (* a (/ y t)))
     (if (<= z 4.5e-81)
       (- x (* y a))
       (if (<= z 4.2e-7) (+ x (* z a)) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6800.0) {
		tmp = x - a;
	} else if (z <= -1.45e-192) {
		tmp = x - (a * (y / t));
	} else if (z <= 4.5e-81) {
		tmp = x - (y * a);
	} else if (z <= 4.2e-7) {
		tmp = x + (z * 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 <= (-6800.0d0)) then
        tmp = x - a
    else if (z <= (-1.45d-192)) then
        tmp = x - (a * (y / t))
    else if (z <= 4.5d-81) then
        tmp = x - (y * a)
    else if (z <= 4.2d-7) then
        tmp = x + (z * 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 <= -6800.0) {
		tmp = x - a;
	} else if (z <= -1.45e-192) {
		tmp = x - (a * (y / t));
	} else if (z <= 4.5e-81) {
		tmp = x - (y * a);
	} else if (z <= 4.2e-7) {
		tmp = x + (z * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6800.0:
		tmp = x - a
	elif z <= -1.45e-192:
		tmp = x - (a * (y / t))
	elif z <= 4.5e-81:
		tmp = x - (y * a)
	elif z <= 4.2e-7:
		tmp = x + (z * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6800.0)
		tmp = Float64(x - a);
	elseif (z <= -1.45e-192)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= 4.5e-81)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 4.2e-7)
		tmp = Float64(x + Float64(z * 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 <= -6800.0)
		tmp = x - a;
	elseif (z <= -1.45e-192)
		tmp = x - (a * (y / t));
	elseif (z <= 4.5e-81)
		tmp = x - (y * a);
	elseif (z <= 4.2e-7)
		tmp = x + (z * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6800.0], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.45e-192], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-81], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-7], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6800 or 4.2e-7 < z

   1. Initial program 96.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 75.1%

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

   if -6800 < z < -1.45000000000000008e-192

   1. Initial program 99.1%

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

      1. associate-/r/ 99.8%

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

   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 78.8%

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

   6. Taylor expanded in y around inf 81.5%

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

   if -1.45000000000000008e-192 < z < 4.5e-81

   1. Initial program 98.7%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 92.7%

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

   8. Taylor expanded in t around 0 77.9%

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

   if 4.5e-81 < z < 4.2e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 90.4%

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

      1. neg-mul-1 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in z around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. distribute-neg-frac2 86.2%

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

      3. distribute-neg-in 86.2%

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

      4. metadata-eval 86.2%

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

      5. unsub-neg 86.2%

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

   8. Simplified 86.2%

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

   9. Taylor expanded in t around 0 86.6%

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

       1. associate-*r* 86.6%

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

       2. neg-mul-1 86.6%

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

       3. cancel-sign-sub 86.6%

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

   11. Simplified 86.6%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6800:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-192}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-81}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-7}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{if}\;z \leq -18000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-74}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{z}{\frac{1 - z}{a}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ z a)))))
   (if (<= z -18000.0)
     t_1
     (if (<= z 3.8e-74)
       (+ x (* a (/ y (- -1.0 t))))
       (if (<= z 3.2e+55) (+ x (/ z (/ (- 1.0 z) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (z / a));
	double tmp;
	if (z <= -18000.0) {
		tmp = t_1;
	} else if (z <= 3.8e-74) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 3.2e+55) {
		tmp = x + (z / ((1.0 - z) / 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 + ((y - z) / (z / a))
    if (z <= (-18000.0d0)) then
        tmp = t_1
    else if (z <= 3.8d-74) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else if (z <= 3.2d+55) then
        tmp = x + (z / ((1.0d0 - z) / 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 + ((y - z) / (z / a));
	double tmp;
	if (z <= -18000.0) {
		tmp = t_1;
	} else if (z <= 3.8e-74) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 3.2e+55) {
		tmp = x + (z / ((1.0 - z) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / (z / a))
	tmp = 0
	if z <= -18000.0:
		tmp = t_1
	elif z <= 3.8e-74:
		tmp = x + (a * (y / (-1.0 - t)))
	elif z <= 3.2e+55:
		tmp = x + (z / ((1.0 - z) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(z / a)))
	tmp = 0.0
	if (z <= -18000.0)
		tmp = t_1;
	elseif (z <= 3.8e-74)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	elseif (z <= 3.2e+55)
		tmp = Float64(x + Float64(z / Float64(Float64(1.0 - z) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / (z / a));
	tmp = 0.0;
	if (z <= -18000.0)
		tmp = t_1;
	elseif (z <= 3.8e-74)
		tmp = x + (a * (y / (-1.0 - t)));
	elseif (z <= 3.2e+55)
		tmp = x + (z / ((1.0 - z) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -18000.0], t$95$1, If[LessEqual[z, 3.8e-74], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+55], N[(x + N[(z / N[(N[(1.0 - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -18000 or 3.2000000000000003e55 < z

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf 85.5%

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

      1. associate-*r/ 85.5%

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

      2. neg-mul-1 85.5%

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

   5. Simplified 85.5%

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

   if -18000 < z < 3.7999999999999996e-74

   1. Initial program 98.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 97.5%

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

   if 3.7999999999999996e-74 < z < 3.2000000000000003e55

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 90.7%

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

      1. neg-mul-1 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in t around 0 85.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -18000:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-74}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{z}{\frac{1 - z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -820000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+182}:\\ \;\;\;\;x + \frac{y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -820000000000.0)
   (- x a)
   (if (<= z 8.8e+55)
     (+ x (* a (/ y (- -1.0 t))))
     (if (<= z 7.5e+182) (+ x (/ y (/ z a))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -820000000000.0) {
		tmp = x - a;
	} else if (z <= 8.8e+55) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 7.5e+182) {
		tmp = x + (y / (z / 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 <= (-820000000000.0d0)) then
        tmp = x - a
    else if (z <= 8.8d+55) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else if (z <= 7.5d+182) then
        tmp = x + (y / (z / 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 <= -820000000000.0) {
		tmp = x - a;
	} else if (z <= 8.8e+55) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 7.5e+182) {
		tmp = x + (y / (z / a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -820000000000.0:
		tmp = x - a
	elif z <= 8.8e+55:
		tmp = x + (a * (y / (-1.0 - t)))
	elif z <= 7.5e+182:
		tmp = x + (y / (z / a))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -820000000000.0)
		tmp = Float64(x - a);
	elseif (z <= 8.8e+55)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	elseif (z <= 7.5e+182)
		tmp = Float64(x + Float64(y / Float64(z / 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 <= -820000000000.0)
		tmp = x - a;
	elseif (z <= 8.8e+55)
		tmp = x + (a * (y / (-1.0 - t)));
	elseif (z <= 7.5e+182)
		tmp = x + (y / (z / a));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -820000000000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 8.8e+55], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+182], N[(x + N[(y / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2e11 or 7.49999999999999989e182 < z

   1. Initial program 95.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 82.5%

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

   if -8.2e11 < z < 8.80000000000000042e55

   1. Initial program 99.0%

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

      1. associate-/r/ 99.9%

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

   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 91.5%

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

   if 8.80000000000000042e55 < z < 7.49999999999999989e182

   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 79.5%

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

      1. associate-*r/ 79.5%

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

      2. neg-mul-1 79.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in y around inf 75.7%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -820000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+182}:\\ \;\;\;\;x + \frac{y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -17000 \lor \neg \left(z \leq 5.7 \cdot 10^{+62}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -17000.0) (not (<= z 5.7e+62)))
   (+ x (/ (- y z) (/ z a)))
   (+ x (/ (- y z) (/ (- -1.0 t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -17000.0) || !(z <= 5.7e+62)) {
		tmp = x + ((y - z) / (z / a));
	} else {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-17000.0d0)) .or. (.not. (z <= 5.7d+62))) then
        tmp = x + ((y - z) / (z / a))
    else
        tmp = x + ((y - z) / (((-1.0d0) - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -17000.0) || !(z <= 5.7e+62)) {
		tmp = x + ((y - z) / (z / a));
	} else {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -17000.0) or not (z <= 5.7e+62):
		tmp = x + ((y - z) / (z / a))
	else:
		tmp = x + ((y - z) / ((-1.0 - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -17000.0) || !(z <= 5.7e+62))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(-1.0 - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -17000.0) || ~((z <= 5.7e+62)))
		tmp = x + ((y - z) / (z / a));
	else
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -17000.0], N[Not[LessEqual[z, 5.7e+62]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(-1.0 - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -17000 or 5.69999999999999998e62 < z

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf 86.9%

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

      1. associate-*r/ 86.9%

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

      2. neg-mul-1 86.9%

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

   5. Simplified 86.9%

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

   if -17000 < z < 5.69999999999999998e62

   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 96.2%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17000 \lor \neg \left(z \leq 5.7 \cdot 10^{+62}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15200:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-73}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -15200.0)
   (+ x (/ (- y z) (/ z a)))
   (if (<= z 9e-73)
     (+ x (* a (/ y (- -1.0 t))))
     (+ x (* a (/ z (+ (- t z) 1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -15200.0) {
		tmp = x + ((y - z) / (z / a));
	} else if (z <= 9e-73) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-15200.0d0)) then
        tmp = x + ((y - z) / (z / a))
    else if (z <= 9d-73) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x + (a * (z / ((t - z) + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -15200.0) {
		tmp = x + ((y - z) / (z / a));
	} else if (z <= 9e-73) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -15200.0:
		tmp = x + ((y - z) / (z / a))
	elif z <= 9e-73:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x + (a * (z / ((t - z) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -15200.0)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	elseif (z <= 9e-73)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t - z) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -15200.0)
		tmp = x + ((y - z) / (z / a));
	elseif (z <= 9e-73)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x + (a * (z / ((t - z) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -15200.0], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-73], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -15200

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf 87.6%

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

      1. associate-*r/ 87.6%

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

      2. neg-mul-1 87.6%

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

   5. Simplified 87.6%

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

   if -15200 < z < 9e-73

   1. Initial program 98.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 97.5%

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

   if 9e-73 < z

   1. Initial program 98.5%

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

      1. sub-neg 98.5%

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

      2. +-commutative 98.5%

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

      3. associate-/r/ 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. associate-*l/ 75.6%

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

      6. associate-/l* 98.6%

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

      7. fma-define 98.6%

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

      8. distribute-frac-neg 98.6%

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

      9. distribute-neg-frac2 98.6%

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

      10. distribute-neg-in 98.6%

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

      11. sub-neg 98.6%

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

      12. distribute-neg-in 98.6%

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

      13. remove-double-neg 98.6%

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

      14. +-commutative 98.6%

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

      15. sub-neg 98.6%

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

      16. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in y around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. unsub-neg 63.8%

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

      3. associate-/l* 82.8%

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

      4. associate--r+ 82.8%

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

      5. sub-neg 82.8%

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

      6. metadata-eval 82.8%

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

      7. +-commutative 82.8%

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

      8. associate--l+ 82.8%

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

   7. Simplified 82.8%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15200:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-73}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2150000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-80}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2150000000.0)
   (- x a)
   (if (<= z 1.65e-80)
     (- x (* y a))
     (if (<= z 8.2e-5) (+ x (* z a)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2150000000.0) {
		tmp = x - a;
	} else if (z <= 1.65e-80) {
		tmp = x - (y * a);
	} else if (z <= 8.2e-5) {
		tmp = x + (z * 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 <= (-2150000000.0d0)) then
        tmp = x - a
    else if (z <= 1.65d-80) then
        tmp = x - (y * a)
    else if (z <= 8.2d-5) then
        tmp = x + (z * 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 <= -2150000000.0) {
		tmp = x - a;
	} else if (z <= 1.65e-80) {
		tmp = x - (y * a);
	} else if (z <= 8.2e-5) {
		tmp = x + (z * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2150000000.0:
		tmp = x - a
	elif z <= 1.65e-80:
		tmp = x - (y * a)
	elif z <= 8.2e-5:
		tmp = x + (z * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2150000000.0)
		tmp = Float64(x - a);
	elseif (z <= 1.65e-80)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 8.2e-5)
		tmp = Float64(x + Float64(z * 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 <= -2150000000.0)
		tmp = x - a;
	elseif (z <= 1.65e-80)
		tmp = x - (y * a);
	elseif (z <= 8.2e-5)
		tmp = x + (z * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2150000000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.65e-80], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-5], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.15e9 or 8.20000000000000009e-5 < z

   1. Initial program 96.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 75.7%

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

   if -2.15e9 < z < 1.65e-80

   1. Initial program 98.8%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 92.0%

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

   8. Taylor expanded in t around 0 71.9%

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

   if 1.65e-80 < z < 8.20000000000000009e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 90.4%

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

      1. neg-mul-1 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in z around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. distribute-neg-frac2 86.2%

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

      3. distribute-neg-in 86.2%

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

      4. metadata-eval 86.2%

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

      5. unsub-neg 86.2%

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

   8. Simplified 86.2%

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

   9. Taylor expanded in t around 0 86.6%

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

       1. associate-*r* 86.6%

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

       2. neg-mul-1 86.6%

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

       3. cancel-sign-sub 86.6%

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

   11. Simplified 86.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2150000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-80}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -820000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-73}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{1 - z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -820000000000.0)
   (- x a)
   (if (<= z 9e-73) (+ x (* a (/ y (- -1.0 t)))) (+ x (/ z (/ (- 1.0 z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -820000000000.0) {
		tmp = x - a;
	} else if (z <= 9e-73) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (z / ((1.0 - z) / 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 <= (-820000000000.0d0)) then
        tmp = x - a
    else if (z <= 9d-73) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x + (z / ((1.0d0 - z) / 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 <= -820000000000.0) {
		tmp = x - a;
	} else if (z <= 9e-73) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (z / ((1.0 - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -820000000000.0:
		tmp = x - a
	elif z <= 9e-73:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x + (z / ((1.0 - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -820000000000.0)
		tmp = Float64(x - a);
	elseif (z <= 9e-73)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(z / Float64(Float64(1.0 - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -820000000000.0)
		tmp = x - a;
	elseif (z <= 9e-73)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x + (z / ((1.0 - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -820000000000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 9e-73], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(N[(1.0 - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2e11

   1. Initial program 95.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 81.3%

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

   if -8.2e11 < z < 9e-73

   1. Initial program 98.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 96.8%

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

   if 9e-73 < z

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 82.8%

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

      1. neg-mul-1 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in t around 0 73.3%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -820000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-73}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{1 - z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -18500 \lor \neg \left(z \leq 5.9 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -18500.0) (not (<= z 5.9e-5))) (- x a) (+ x (* z a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -18500.0) || !(z <= 5.9e-5)) {
		tmp = x - a;
	} else {
		tmp = x + (z * 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 <= (-18500.0d0)) .or. (.not. (z <= 5.9d-5))) then
        tmp = x - a
    else
        tmp = x + (z * 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 <= -18500.0) || !(z <= 5.9e-5)) {
		tmp = x - a;
	} else {
		tmp = x + (z * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -18500.0) or not (z <= 5.9e-5):
		tmp = x - a
	else:
		tmp = x + (z * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -18500.0) || !(z <= 5.9e-5))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(z * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -18500.0) || ~((z <= 5.9e-5)))
		tmp = x - a;
	else
		tmp = x + (z * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -18500.0], N[Not[LessEqual[z, 5.9e-5]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -18500 or 5.8999999999999998e-5 < z

   1. Initial program 96.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 75.7%

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

   if -18500 < z < 5.8999999999999998e-5

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 61.4%

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

      1. neg-mul-1 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in z around 0 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-neg-frac2 61.1%

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

      3. distribute-neg-in 61.1%

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

      4. metadata-eval 61.1%

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

      5. unsub-neg 61.1%

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

   8. Simplified 61.1%

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

   9. Taylor expanded in t around 0 59.8%

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

       1. associate-*r* 59.8%

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

       2. neg-mul-1 59.8%

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

       3. cancel-sign-sub 59.8%

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

   11. Simplified 59.8%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -18500 \lor \neg \left(z \leq 5.9 \cdot 10^{-5}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -12000 \lor \neg \left(z \leq 20000000000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -12000.0) (not (<= z 20000000000000.0))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -12000.0) || !(z <= 20000000000000.0)) {
		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 <= (-12000.0d0)) .or. (.not. (z <= 20000000000000.0d0))) 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 <= -12000.0) || !(z <= 20000000000000.0)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -12000.0) or not (z <= 20000000000000.0):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -12000.0) || !(z <= 20000000000000.0))
		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 <= -12000.0) || ~((z <= 20000000000000.0)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -12000.0], N[Not[LessEqual[z, 20000000000000.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -12000 or 2e13 < 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 75.5%

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

   if -12000 < z < 2e13

   1. Initial program 98.9%

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

      1. sub-neg 98.9%

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

      2. +-commutative 98.9%

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

      3. associate-/r/ 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. associate-*l/ 94.9%

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

      6. associate-/l* 99.1%

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

      7. fma-define 99.1%

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

      8. distribute-frac-neg 99.1%

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

      9. distribute-neg-frac2 99.1%

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

      10. distribute-neg-in 99.1%

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

      11. sub-neg 99.1%

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

      12. distribute-neg-in 99.1%

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

      13. remove-double-neg 99.1%

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

      14. +-commutative 99.1%

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

      15. sub-neg 99.1%

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

      16. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in a around 0 56.1%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12000 \lor \neg \left(z \leq 20000000000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{+140}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -7.4e+140) (- a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.4e+140) {
		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 (a <= (-7.4d+140)) 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 (a <= -7.4e+140) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.4e+140:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.4e+140)
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.4e+140)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.4e+140], (-a), x]

Derivation

1. Split input into 2 regimes

2. if a < -7.40000000000000006e140

   1. Initial program 99.8%

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

      1. associate-/r/ 99.9%

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

   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 37.0%

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

   6. Taylor expanded in x around 0 31.3%

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

      1. neg-mul-1 31.3%

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

   8. Simplified 31.3%

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

   if -7.40000000000000006e140 < a

   1. Initial program 97.5%

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

      1. sub-neg 97.5%

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

      2. +-commutative 97.5%

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

      3. associate-/r/ 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. associate-*l/ 88.9%

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

      6. associate-/l* 97.6%

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

      7. fma-define 97.6%

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

      8. distribute-frac-neg 97.6%

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

      9. distribute-neg-frac2 97.6%

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

      10. distribute-neg-in 97.6%

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

      11. sub-neg 97.6%

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

      12. distribute-neg-in 97.6%

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

      13. remove-double-neg 97.6%

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

      14. +-commutative 97.6%

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

      15. sub-neg 97.6%

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

      16. metadata-eval 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in a around 0 61.0%

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

Alternative 13: 53.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

   1. sub-neg 97.9%

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

   2. +-commutative 97.9%

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

   3. associate-/r/ 99.9%

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

   4. distribute-rgt-neg-in 99.9%

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

   5. associate-*l/ 84.5%

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

   6. associate-/l* 98.0%

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

   7. fma-define 98.0%

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

   8. distribute-frac-neg 98.0%

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

   9. distribute-neg-frac2 98.0%

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

   10. distribute-neg-in 98.0%

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

   11. sub-neg 98.0%

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

   12. distribute-neg-in 98.0%

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

   13. remove-double-neg 98.0%

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

   14. +-commutative 98.0%

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

   15. sub-neg 98.0%

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

   16. metadata-eval 98.0%

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

3. Simplified 98.0%

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

5. Taylor expanded in a around 0 53.1%

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

Alternative 14: 3.2% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 inf 58.8%

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

6. Taylor expanded in x around 0 15.7%

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

   1. neg-mul-1 15.7%

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

8. Simplified 15.7%

   \[\leadsto \color{blue}{-a} \]
9. Step-by-step derivation

   1. neg-sub0 15.7%

      \[\leadsto \color{blue}{0 - a} \]

   2. sub-neg 15.7%

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

   3. add-sqr-sqrt 7.7%

      \[\leadsto 0 + \color{blue}{\sqrt{-a} \cdot \sqrt{-a}} \]

   4. sqrt-unprod 9.5%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \]

   5. sqr-neg 9.5%

      \[\leadsto 0 + \sqrt{\color{blue}{a \cdot a}} \]

   6. sqrt-unprod 1.9%

      \[\leadsto 0 + \color{blue}{\sqrt{a} \cdot \sqrt{a}} \]

   7. add-sqr-sqrt 3.5%

      \[\leadsto 0 + \color{blue}{a} \]

10. Applied egg-rr 3.5%

    \[\leadsto \color{blue}{0 + a} \]
11. Step-by-step derivation

    1. +-lft-identity 3.5%

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

12. Simplified 3.5%

    \[\leadsto \color{blue}{a} \]
13. Add Preprocessing

Developer Target 1: 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 2024157 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (/ (- y z) (+ (- t z) 1)) a)))

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