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

Percentage Accurate: 97.0% → 99.6%

Time: 10.0s

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: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.8%

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

   1. associate-/r/ 99.2%

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

3. Simplified 99.2%

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

   1. clear-num 99.2%

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

   2. associate-*l/ 99.2%

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

   3. *-lft-identity 99.2%

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

   4. associate-+l- 99.2%

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

   5. sub-neg 99.2%

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

   6. metadata-eval 99.2%

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

5. Applied egg-rr 99.2%

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

6. Final simplification 99.2%

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

Alternative 2: 86.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{+18} \lor \neg \left(z \leq 2.5 \cdot 10^{-10}\right):\\ \;\;\;\;x - z \cdot \frac{a}{-1 + \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.3e+18) (not (<= z 2.5e-10)))
   (- x (* z (/ a (+ -1.0 (- z t)))))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.3e+18) || !(z <= 2.5e-10)) {
		tmp = x - (z * (a / (-1.0 + (z - t))));
	} else {
		tmp = x - (a * (y / (t + 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 <= (-8.3d+18)) .or. (.not. (z <= 2.5d-10))) then
        tmp = x - (z * (a / ((-1.0d0) + (z - t))))
    else
        tmp = x - (a * (y / (t + 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 <= -8.3e+18) || !(z <= 2.5e-10)) {
		tmp = x - (z * (a / (-1.0 + (z - t))));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.3e+18) or not (z <= 2.5e-10):
		tmp = x - (z * (a / (-1.0 + (z - t))))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.3e+18) || !(z <= 2.5e-10))
		tmp = Float64(x - Float64(z * Float64(a / Float64(-1.0 + Float64(z - t)))));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.3e+18) || ~((z <= 2.5e-10)))
		tmp = x - (z * (a / (-1.0 + (z - t))));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.3e+18], N[Not[LessEqual[z, 2.5e-10]], $MachinePrecision]], N[(x - N[(z * N[(a / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.3e18 or 2.50000000000000016e-10 < z

   1. Initial program 93.0%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 68.0%

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

      1. associate-/l* 85.5%

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

      2. associate-*r/ 85.5%

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

      3. neg-mul-1 85.5%

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

      4. associate--l+ 85.5%

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

   6. Simplified 85.5%

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

      1. associate-/r/ 80.9%

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

      2. frac-2neg 80.9%

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

      3. remove-double-neg 80.9%

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

      4. neg-sub0 80.9%

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

      5. associate--r+ 80.9%

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

      6. metadata-eval 80.9%

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

   8. Applied egg-rr 80.9%

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

   if -8.3e18 < z < 2.50000000000000016e-10

   1. Initial program 96.9%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 95.4%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{+18} \lor \neg \left(z \leq 2.5 \cdot 10^{-10}\right):\\ \;\;\;\;x - z \cdot \frac{a}{-1 + \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 3: 88.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+26} \lor \neg \left(y \leq 4 \cdot 10^{+92}\right):\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{a}{-1 + \left(z - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.1e+26) (not (<= y 4e+92)))
   (- x (* a (/ y (- (+ t 1.0) z))))
   (- x (* z (/ a (+ -1.0 (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.1e+26) || !(y <= 4e+92)) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x - (z * (a / (-1.0 + (z - 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 ((y <= (-4.1d+26)) .or. (.not. (y <= 4d+92))) then
        tmp = x - (a * (y / ((t + 1.0d0) - z)))
    else
        tmp = x - (z * (a / ((-1.0d0) + (z - 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 ((y <= -4.1e+26) || !(y <= 4e+92)) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x - (z * (a / (-1.0 + (z - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.1e+26) or not (y <= 4e+92):
		tmp = x - (a * (y / ((t + 1.0) - z)))
	else:
		tmp = x - (z * (a / (-1.0 + (z - t))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.1e+26) || !(y <= 4e+92))
		tmp = Float64(x - Float64(a * Float64(y / Float64(Float64(t + 1.0) - z))));
	else
		tmp = Float64(x - Float64(z * Float64(a / Float64(-1.0 + Float64(z - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.1e+26) || ~((y <= 4e+92)))
		tmp = x - (a * (y / ((t + 1.0) - z)));
	else
		tmp = x - (z * (a / (-1.0 + (z - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.1e+26], N[Not[LessEqual[y, 4e+92]], $MachinePrecision]], N[(x - N[(a * N[(y / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(a / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.09999999999999983e26 or 4.0000000000000002e92 < y

   1. Initial program 92.9%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 88.5%

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

   if -4.09999999999999983e26 < y < 4.0000000000000002e92

   1. Initial program 96.3%

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

      1. associate-/r/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in y around 0 84.9%

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

      1. associate-/l* 93.9%

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

      2. associate-*r/ 93.9%

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

      3. neg-mul-1 93.9%

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

      4. associate--l+ 93.9%

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

   6. Simplified 93.9%

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

      1. associate-/r/ 91.0%

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

      2. frac-2neg 91.0%

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

      3. remove-double-neg 91.0%

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

      4. neg-sub0 91.0%

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

      5. associate--r+ 91.0%

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

      6. metadata-eval 91.0%

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

   8. Applied egg-rr 91.0%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+26} \lor \neg \left(y \leq 4 \cdot 10^{+92}\right):\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{a}{-1 + \left(z - t\right)}\\ \end{array} \]

Alternative 4: 89.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -480:\\ \;\;\;\;x - z \cdot \frac{a}{-1 + \left(z - t\right)}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+72}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -480.0)
   (- x (* z (/ a (+ -1.0 (- z t)))))
   (if (<= t 4.8e+72)
     (- x (* a (/ (- y z) (- 1.0 z))))
     (- x (/ a (/ t (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -480.0) {
		tmp = x - (z * (a / (-1.0 + (z - t))));
	} else if (t <= 4.8e+72) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else {
		tmp = x - (a / (t / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-480.0d0)) then
        tmp = x - (z * (a / ((-1.0d0) + (z - t))))
    else if (t <= 4.8d+72) then
        tmp = x - (a * ((y - z) / (1.0d0 - z)))
    else
        tmp = x - (a / (t / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -480.0) {
		tmp = x - (z * (a / (-1.0 + (z - t))));
	} else if (t <= 4.8e+72) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else {
		tmp = x - (a / (t / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -480.0:
		tmp = x - (z * (a / (-1.0 + (z - t))))
	elif t <= 4.8e+72:
		tmp = x - (a * ((y - z) / (1.0 - z)))
	else:
		tmp = x - (a / (t / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -480.0)
		tmp = Float64(x - Float64(z * Float64(a / Float64(-1.0 + Float64(z - t)))));
	elseif (t <= 4.8e+72)
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(1.0 - z))));
	else
		tmp = Float64(x - Float64(a / Float64(t / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -480.0)
		tmp = x - (z * (a / (-1.0 + (z - t))));
	elseif (t <= 4.8e+72)
		tmp = x - (a * ((y - z) / (1.0 - z)));
	else
		tmp = x - (a / (t / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -480.0], N[(x - N[(z * N[(a / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+72], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -480

   1. Initial program 96.2%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 73.9%

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

      1. associate-/l* 87.6%

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

      2. associate-*r/ 87.6%

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

      3. neg-mul-1 87.6%

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

      4. associate--l+ 87.6%

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

   6. Simplified 87.6%

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

      1. associate-/r/ 86.8%

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

      2. frac-2neg 86.8%

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

      3. remove-double-neg 86.8%

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

      4. neg-sub0 86.8%

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

      5. associate--r+ 86.8%

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

      6. metadata-eval 86.8%

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

   8. Applied egg-rr 86.8%

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

   if -480 < t < 4.8000000000000002e72

   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. Taylor expanded in t around 0 97.3%

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

   if 4.8000000000000002e72 < t

   1. Initial program 90.5%

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

      1. associate-/r/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around inf 77.8%

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

      1. associate-/l* 89.5%

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

   6. Simplified 89.5%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -480:\\ \;\;\;\;x - z \cdot \frac{a}{-1 + \left(z - t\right)}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+72}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \end{array} \]

Alternative 5: 90.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1250:\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+72}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1250.0)
   (+ x (/ a (/ (+ (- t z) 1.0) z)))
   (if (<= t 5e+72)
     (+ x (* a (/ (- z y) (- 1.0 z))))
     (- x (/ a (/ t (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1250.0) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else if (t <= 5e+72) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else {
		tmp = x - (a / (t / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1250.0d0)) then
        tmp = x + (a / (((t - z) + 1.0d0) / z))
    else if (t <= 5d+72) then
        tmp = x + (a * ((z - y) / (1.0d0 - z)))
    else
        tmp = x - (a / (t / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1250.0) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else if (t <= 5e+72) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else {
		tmp = x - (a / (t / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1250.0:
		tmp = x + (a / (((t - z) + 1.0) / z))
	elif t <= 5e+72:
		tmp = x + (a * ((z - y) / (1.0 - z)))
	else:
		tmp = x - (a / (t / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1250.0)
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t - z) + 1.0) / z)));
	elseif (t <= 5e+72)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	else
		tmp = Float64(x - Float64(a / Float64(t / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1250.0)
		tmp = x + (a / (((t - z) + 1.0) / z));
	elseif (t <= 5e+72)
		tmp = x + (a * ((z - y) / (1.0 - z)));
	else
		tmp = x - (a / (t / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1250.0], N[(x + N[(a / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+72], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1250

   1. Initial program 96.2%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 73.9%

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

      1. associate-/l* 87.6%

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

      2. associate-*r/ 87.6%

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

      3. neg-mul-1 87.6%

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

      4. associate--l+ 87.6%

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

   6. Simplified 87.6%

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

   if -1250 < t < 4.99999999999999992e72

   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. Taylor expanded in t around 0 97.3%

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

   if 4.99999999999999992e72 < t

   1. Initial program 90.5%

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

      1. associate-/r/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around inf 77.8%

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

      1. associate-/l* 89.5%

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

   6. Simplified 89.5%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1250:\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+72}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \end{array} \]

Alternative 6: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot y\\ \mathbf{if}\;z \leq -0.000185:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-188}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a y))))
   (if (<= z -0.000185)
     (- x a)
     (if (<= z 5.4e-251)
       t_1
       (if (<= z 2.75e-188)
         (- x (* a (/ y t)))
         (if (<= z 3.3e+22) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * y);
	double tmp;
	if (z <= -0.000185) {
		tmp = x - a;
	} else if (z <= 5.4e-251) {
		tmp = t_1;
	} else if (z <= 2.75e-188) {
		tmp = x - (a * (y / t));
	} else if (z <= 3.3e+22) {
		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 * y)
    if (z <= (-0.000185d0)) then
        tmp = x - a
    else if (z <= 5.4d-251) then
        tmp = t_1
    else if (z <= 2.75d-188) then
        tmp = x - (a * (y / t))
    else if (z <= 3.3d+22) 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 * y);
	double tmp;
	if (z <= -0.000185) {
		tmp = x - a;
	} else if (z <= 5.4e-251) {
		tmp = t_1;
	} else if (z <= 2.75e-188) {
		tmp = x - (a * (y / t));
	} else if (z <= 3.3e+22) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * y)
	tmp = 0
	if z <= -0.000185:
		tmp = x - a
	elif z <= 5.4e-251:
		tmp = t_1
	elif z <= 2.75e-188:
		tmp = x - (a * (y / t))
	elif z <= 3.3e+22:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * y))
	tmp = 0.0
	if (z <= -0.000185)
		tmp = Float64(x - a);
	elseif (z <= 5.4e-251)
		tmp = t_1;
	elseif (z <= 2.75e-188)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= 3.3e+22)
		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 * y);
	tmp = 0.0;
	if (z <= -0.000185)
		tmp = x - a;
	elseif (z <= 5.4e-251)
		tmp = t_1;
	elseif (z <= 2.75e-188)
		tmp = x - (a * (y / t));
	elseif (z <= 3.3e+22)
		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 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.000185], N[(x - a), $MachinePrecision], If[LessEqual[z, 5.4e-251], t$95$1, If[LessEqual[z, 2.75e-188], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+22], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.85e-4 or 3.2999999999999998e22 < z

   1. Initial program 92.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 74.0%

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

   if -1.85e-4 < z < 5.4000000000000002e-251 or 2.7500000000000001e-188 < z < 3.2999999999999998e22

   1. Initial program 97.6%

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

      1. associate-/r/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 89.6%

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

      1. associate-/l* 92.0%

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

   6. Simplified 92.0%

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

   7. Taylor expanded in t around 0 76.5%

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

   if 5.4000000000000002e-251 < z < 2.7500000000000001e-188

   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. Taylor expanded in t around inf 93.1%

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

   5. Taylor expanded in y around inf 93.1%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.000185:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-251}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-188}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+22}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot y\\ \mathbf{if}\;z \leq -0.0002:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-187}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a y))))
   (if (<= z -0.0002)
     (- x a)
     (if (<= z 1.65e-250)
       t_1
       (if (<= z 3.7e-187)
         (- x (/ a (/ t y)))
         (if (<= z 3.05e+22) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * y);
	double tmp;
	if (z <= -0.0002) {
		tmp = x - a;
	} else if (z <= 1.65e-250) {
		tmp = t_1;
	} else if (z <= 3.7e-187) {
		tmp = x - (a / (t / y));
	} else if (z <= 3.05e+22) {
		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 * y)
    if (z <= (-0.0002d0)) then
        tmp = x - a
    else if (z <= 1.65d-250) then
        tmp = t_1
    else if (z <= 3.7d-187) then
        tmp = x - (a / (t / y))
    else if (z <= 3.05d+22) 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 * y);
	double tmp;
	if (z <= -0.0002) {
		tmp = x - a;
	} else if (z <= 1.65e-250) {
		tmp = t_1;
	} else if (z <= 3.7e-187) {
		tmp = x - (a / (t / y));
	} else if (z <= 3.05e+22) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * y)
	tmp = 0
	if z <= -0.0002:
		tmp = x - a
	elif z <= 1.65e-250:
		tmp = t_1
	elif z <= 3.7e-187:
		tmp = x - (a / (t / y))
	elif z <= 3.05e+22:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * y))
	tmp = 0.0
	if (z <= -0.0002)
		tmp = Float64(x - a);
	elseif (z <= 1.65e-250)
		tmp = t_1;
	elseif (z <= 3.7e-187)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (z <= 3.05e+22)
		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 * y);
	tmp = 0.0;
	if (z <= -0.0002)
		tmp = x - a;
	elseif (z <= 1.65e-250)
		tmp = t_1;
	elseif (z <= 3.7e-187)
		tmp = x - (a / (t / y));
	elseif (z <= 3.05e+22)
		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 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0002], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.65e-250], t$95$1, If[LessEqual[z, 3.7e-187], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.05e+22], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0000000000000001e-4 or 3.0499999999999999e22 < z

   1. Initial program 92.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 74.0%

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

   if -2.0000000000000001e-4 < z < 1.65e-250 or 3.7000000000000001e-187 < z < 3.0499999999999999e22

   1. Initial program 97.6%

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

      1. associate-/r/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 89.6%

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

      1. associate-/l* 92.0%

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

   6. Simplified 92.0%

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

   7. Taylor expanded in t around 0 76.5%

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

   if 1.65e-250 < z < 3.7000000000000001e-187

   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. Taylor expanded in t around inf 93.1%

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

   5. Taylor expanded in y around inf 93.3%

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

      1. associate-/l* 93.3%

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

   7. Simplified 93.3%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0002:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-250}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-187}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+22}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 8: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot y\\ \mathbf{if}\;z \leq -0.00025:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-188}:\\ \;\;\;\;x - \frac{a \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a y))))
   (if (<= z -0.00025)
     (- x a)
     (if (<= z 4.9e-269)
       t_1
       (if (<= z 3.2e-188)
         (- x (/ (* a y) t))
         (if (<= z 3.9e+22) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * y);
	double tmp;
	if (z <= -0.00025) {
		tmp = x - a;
	} else if (z <= 4.9e-269) {
		tmp = t_1;
	} else if (z <= 3.2e-188) {
		tmp = x - ((a * y) / t);
	} else if (z <= 3.9e+22) {
		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 * y)
    if (z <= (-0.00025d0)) then
        tmp = x - a
    else if (z <= 4.9d-269) then
        tmp = t_1
    else if (z <= 3.2d-188) then
        tmp = x - ((a * y) / t)
    else if (z <= 3.9d+22) 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 * y);
	double tmp;
	if (z <= -0.00025) {
		tmp = x - a;
	} else if (z <= 4.9e-269) {
		tmp = t_1;
	} else if (z <= 3.2e-188) {
		tmp = x - ((a * y) / t);
	} else if (z <= 3.9e+22) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * y)
	tmp = 0
	if z <= -0.00025:
		tmp = x - a
	elif z <= 4.9e-269:
		tmp = t_1
	elif z <= 3.2e-188:
		tmp = x - ((a * y) / t)
	elif z <= 3.9e+22:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * y))
	tmp = 0.0
	if (z <= -0.00025)
		tmp = Float64(x - a);
	elseif (z <= 4.9e-269)
		tmp = t_1;
	elseif (z <= 3.2e-188)
		tmp = Float64(x - Float64(Float64(a * y) / t));
	elseif (z <= 3.9e+22)
		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 * y);
	tmp = 0.0;
	if (z <= -0.00025)
		tmp = x - a;
	elseif (z <= 4.9e-269)
		tmp = t_1;
	elseif (z <= 3.2e-188)
		tmp = x - ((a * y) / t);
	elseif (z <= 3.9e+22)
		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 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.00025], N[(x - a), $MachinePrecision], If[LessEqual[z, 4.9e-269], t$95$1, If[LessEqual[z, 3.2e-188], N[(x - N[(N[(a * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+22], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5000000000000001e-4 or 3.90000000000000021e22 < z

   1. Initial program 92.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 74.0%

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

   if -2.5000000000000001e-4 < z < 4.89999999999999999e-269 or 3.20000000000000022e-188 < z < 3.90000000000000021e22

   1. Initial program 97.5%

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

      1. associate-/r/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 89.3%

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

      1. associate-/l* 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in t around 0 77.5%

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

   if 4.89999999999999999e-269 < z < 3.20000000000000022e-188

   1. Initial program 94.4%

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

      1. associate-/r/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in t around inf 83.1%

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

   5. Taylor expanded in y around inf 88.5%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00025:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-269}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-188}:\\ \;\;\;\;x - \frac{a \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+22}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 9: 83.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+173} \lor \neg \left(z \leq 2.15 \cdot 10^{+24}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+173) (not (<= z 2.15e+24)))
   (- x a)
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+173) || !(z <= 2.15e+24)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / (t + 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 <= (-1.45d+173)) .or. (.not. (z <= 2.15d+24))) then
        tmp = x - a
    else
        tmp = x - (a * (y / (t + 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 <= -1.45e+173) || !(z <= 2.15e+24)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+173) or not (z <= 2.15e+24):
		tmp = x - a
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+173) || !(z <= 2.15e+24))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.45e+173) || ~((z <= 2.15e+24)))
		tmp = x - a;
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+173], N[Not[LessEqual[z, 2.15e+24]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45000000000000003e173 or 2.14999999999999994e24 < z

   1. Initial program 91.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.8%

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

   if -1.45000000000000003e173 < z < 2.14999999999999994e24

   1. Initial program 96.6%

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

      1. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 86.2%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+173} \lor \neg \left(z \leq 2.15 \cdot 10^{+24}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 10: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+173}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+25}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e+173)
   (- x a)
   (if (<= z 1.12e+25) (- x (/ a (/ (+ t 1.0) y))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e+173) {
		tmp = x - a;
	} else if (z <= 1.12e+25) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.65d+173)) then
        tmp = x - a
    else if (z <= 1.12d+25) then
        tmp = x - (a / ((t + 1.0d0) / y))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e+173) {
		tmp = x - a;
	} else if (z <= 1.12e+25) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.65e+173:
		tmp = x - a
	elif z <= 1.12e+25:
		tmp = x - (a / ((t + 1.0) / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.65e+173)
		tmp = Float64(x - a);
	elseif (z <= 1.12e+25)
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.65e+173)
		tmp = x - a;
	elseif (z <= 1.12e+25)
		tmp = x - (a / ((t + 1.0) / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.65e+173], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.12e+25], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.64999999999999998e173 or 1.1200000000000001e25 < z

   1. Initial program 91.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.8%

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

   if -1.64999999999999998e173 < z < 1.1200000000000001e25

   1. Initial program 96.6%

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

      1. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 82.9%

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

      1. associate-/l* 86.3%

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

   6. Simplified 86.3%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+173}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+25}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 11: 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 94.8%

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

   1. associate-/r/ 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 12: 72.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00028:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+22}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.00028) (- x a) (if (<= z 3.6e+22) (- x (* a y)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.00028) {
		tmp = x - a;
	} else if (z <= 3.6e+22) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-0.00028d0)) then
        tmp = x - a
    else if (z <= 3.6d+22) then
        tmp = x - (a * y)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.00028) {
		tmp = x - a;
	} else if (z <= 3.6e+22) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.00028:
		tmp = x - a
	elif z <= 3.6e+22:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.00028)
		tmp = Float64(x - a);
	elseif (z <= 3.6e+22)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.00028)
		tmp = x - a;
	elseif (z <= 3.6e+22)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.00028], N[(x - a), $MachinePrecision], If[LessEqual[z, 3.6e+22], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999998e-4 or 3.6e22 < z

   1. Initial program 92.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 74.0%

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

   if -2.7999999999999998e-4 < z < 3.6e22

   1. Initial program 97.1%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in z around 0 90.7%

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

      1. associate-/l* 92.9%

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

   6. Simplified 92.9%

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

   7. Taylor expanded in t around 0 74.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00028:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+22}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 13: 66.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -25:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -25.0) (- x a) (if (<= z 2.5e+23) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -25.0) {
		tmp = x - a;
	} else if (z <= 2.5e+23) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-25.0d0)) then
        tmp = x - a
    else if (z <= 2.5d+23) then
        tmp = x
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -25.0) {
		tmp = x - a;
	} else if (z <= 2.5e+23) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -25.0:
		tmp = x - a
	elif z <= 2.5e+23:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -25.0)
		tmp = Float64(x - a);
	elseif (z <= 2.5e+23)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -25.0)
		tmp = x - a;
	elseif (z <= 2.5e+23)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -25.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.5e+23], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -25 or 2.5e23 < z

   1. Initial program 92.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 74.5%

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

   if -25 < z < 2.5e23

   1. Initial program 97.1%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around inf 92.9%

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

   5. Taylor expanded in x around inf 63.9%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -25:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 14: 53.8% 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 94.8%

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

   1. associate-/r/ 99.2%

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

3. Simplified 99.2%

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

4. Taylor expanded in y around inf 77.5%

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

5. Taylor expanded in x around inf 56.5%

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

6. Final simplification 56.5%

   \[\leadsto x \]

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 2023297 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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