Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.1% → 95.7%

Time: 9.0s

Alternatives: 16

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{-120}:\\ \;\;\;\;\frac{y - z}{\frac{t - z}{x}}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.9e-120)
   (/ (- y z) (/ (- t z) x))
   (if (<= x 9.2e-20) (/ (* x (- y z)) (- t z)) (* (- y z) (/ x (- t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.9e-120) {
		tmp = (y - z) / ((t - z) / x);
	} else if (x <= 9.2e-20) {
		tmp = (x * (y - z)) / (t - z);
	} else {
		tmp = (y - z) * (x / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-5.9d-120)) then
        tmp = (y - z) / ((t - z) / x)
    else if (x <= 9.2d-20) then
        tmp = (x * (y - z)) / (t - z)
    else
        tmp = (y - z) * (x / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.9e-120) {
		tmp = (y - z) / ((t - z) / x);
	} else if (x <= 9.2e-20) {
		tmp = (x * (y - z)) / (t - z);
	} else {
		tmp = (y - z) * (x / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.9e-120:
		tmp = (y - z) / ((t - z) / x)
	elif x <= 9.2e-20:
		tmp = (x * (y - z)) / (t - z)
	else:
		tmp = (y - z) * (x / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.9e-120)
		tmp = Float64(Float64(y - z) / Float64(Float64(t - z) / x));
	elseif (x <= 9.2e-20)
		tmp = Float64(Float64(x * Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.9e-120)
		tmp = (y - z) / ((t - z) / x);
	elseif (x <= 9.2e-20)
		tmp = (x * (y - z)) / (t - z);
	else
		tmp = (y - z) * (x / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.9e-120], N[(N[(y - z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e-20], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.89999999999999979e-120

   1. Initial program 80.8%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

      1. *-commutative 96.7%

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

      2. clear-num 96.7%

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

      3. un-div-inv 97.1%

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

   5. Applied egg-rr 97.1%

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

   if -5.89999999999999979e-120 < x < 9.1999999999999997e-20

   1. Initial program 95.8%

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

   if 9.1999999999999997e-20 < x

   1. Initial program 71.7%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{-120}:\\ \;\;\;\;\frac{y - z}{\frac{t - z}{x}}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \]

Alternative 2: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.4e+17)
   x
   (if (<= z 1.15e-84)
     (* y (/ x (- t z)))
     (if (<= z 9.5e+156) (* z (/ x (- z t))) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.4e+17) {
		tmp = x;
	} else if (z <= 1.15e-84) {
		tmp = y * (x / (t - z));
	} else if (z <= 9.5e+156) {
		tmp = z * (x / (z - t));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.4d+17)) then
        tmp = x
    else if (z <= 1.15d-84) then
        tmp = y * (x / (t - z))
    else if (z <= 9.5d+156) then
        tmp = z * (x / (z - t))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.4e+17) {
		tmp = x;
	} else if (z <= 1.15e-84) {
		tmp = y * (x / (t - z));
	} else if (z <= 9.5e+156) {
		tmp = z * (x / (z - t));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.4e+17:
		tmp = x
	elif z <= 1.15e-84:
		tmp = y * (x / (t - z))
	elif z <= 9.5e+156:
		tmp = z * (x / (z - t))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.4e+17)
		tmp = x;
	elseif (z <= 1.15e-84)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	elseif (z <= 9.5e+156)
		tmp = Float64(z * Float64(x / Float64(z - t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.4e+17)
		tmp = x;
	elseif (z <= 1.15e-84)
		tmp = y * (x / (t - z));
	elseif (z <= 9.5e+156)
		tmp = z * (x / (z - t));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.4e+17], x, If[LessEqual[z, 1.15e-84], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+156], N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4e17 or 9.5000000000000002e156 < z

   1. Initial program 72.5%

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

      1. associate-*l/ 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in z around inf 66.5%

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

   if -4.4e17 < z < 1.1499999999999999e-84

   1. Initial program 92.1%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around inf 80.0%

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

      1. associate-*l/ 81.4%

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

      2. *-commutative 81.4%

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

   6. Simplified 81.4%

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

   if 1.1499999999999999e-84 < z < 9.5000000000000002e156

   1. Initial program 83.2%

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

      1. associate-*l/ 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in y around 0 50.9%

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

      1. associate-*r/ 50.9%

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

      2. mul-1-neg 50.9%

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

      3. distribute-rgt-neg-out 50.9%

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

      4. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

      1. frac-2neg 63.0%

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

      2. remove-double-neg 63.0%

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

      3. associate-/r/ 56.3%

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

      4. sub-neg 56.3%

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

      5. distribute-neg-in 56.3%

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

      6. remove-double-neg 56.3%

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

   8. Applied egg-rr 56.3%

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

      1. *-commutative 56.3%

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

      2. +-commutative 56.3%

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

      3. unsub-neg 56.3%

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

   10. Simplified 56.3%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+163}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.32e+163)
   x
   (if (<= z 8e+19)
     (* x (/ y (- t z)))
     (if (<= z 9.5e+156) (* z (/ x (- z t))) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.32e+163) {
		tmp = x;
	} else if (z <= 8e+19) {
		tmp = x * (y / (t - z));
	} else if (z <= 9.5e+156) {
		tmp = z * (x / (z - t));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.32d+163)) then
        tmp = x
    else if (z <= 8d+19) then
        tmp = x * (y / (t - z))
    else if (z <= 9.5d+156) then
        tmp = z * (x / (z - t))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.32e+163) {
		tmp = x;
	} else if (z <= 8e+19) {
		tmp = x * (y / (t - z));
	} else if (z <= 9.5e+156) {
		tmp = z * (x / (z - t));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.32e+163:
		tmp = x
	elif z <= 8e+19:
		tmp = x * (y / (t - z))
	elif z <= 9.5e+156:
		tmp = z * (x / (z - t))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.32e+163)
		tmp = x;
	elseif (z <= 8e+19)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 9.5e+156)
		tmp = Float64(z * Float64(x / Float64(z - t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.32e+163)
		tmp = x;
	elseif (z <= 8e+19)
		tmp = x * (y / (t - z));
	elseif (z <= 9.5e+156)
		tmp = z * (x / (z - t));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.32e+163], x, If[LessEqual[z, 8e+19], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+156], N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.31999999999999995e163 or 9.5000000000000002e156 < z

   1. Initial program 66.0%

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

      1. associate-*l/ 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in z around inf 80.1%

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

   if -1.31999999999999995e163 < z < 8e19

   1. Initial program 92.1%

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

      1. associate-*l/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in y around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-/l* 69.5%

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

      3. associate-/r/ 72.7%

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

   6. Simplified 72.7%

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

   if 8e19 < z < 9.5000000000000002e156

   1. Initial program 70.0%

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

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in y around 0 48.5%

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

      1. associate-*r/ 48.5%

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

      2. mul-1-neg 48.5%

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

      3. distribute-rgt-neg-out 48.5%

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

      4. associate-/l* 70.2%

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

   6. Simplified 70.2%

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

      1. frac-2neg 70.2%

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

      2. remove-double-neg 70.2%

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

      3. associate-/r/ 61.2%

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

      4. sub-neg 61.2%

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

      5. distribute-neg-in 61.2%

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

      6. remove-double-neg 61.2%

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

   8. Applied egg-rr 61.2%

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

      1. *-commutative 61.2%

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

      2. +-commutative 61.2%

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

      3. unsub-neg 61.2%

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

   10. Simplified 61.2%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+163}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 90.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+139} \lor \neg \left(z \leq 1.35 \cdot 10^{+156}\right):\\ \;\;\;\;\frac{-x}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.9e+139) (not (<= z 1.35e+156)))
   (/ (- x) (/ z (- y z)))
   (* (- y z) (/ x (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+139) || !(z <= 1.35e+156)) {
		tmp = -x / (z / (y - z));
	} else {
		tmp = (y - z) * (x / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.9d+139)) .or. (.not. (z <= 1.35d+156))) then
        tmp = -x / (z / (y - z))
    else
        tmp = (y - z) * (x / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+139) || !(z <= 1.35e+156)) {
		tmp = -x / (z / (y - z));
	} else {
		tmp = (y - z) * (x / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.9e+139) or not (z <= 1.35e+156):
		tmp = -x / (z / (y - z))
	else:
		tmp = (y - z) * (x / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.9e+139) || !(z <= 1.35e+156))
		tmp = Float64(Float64(-x) / Float64(z / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.9e+139) || ~((z <= 1.35e+156)))
		tmp = -x / (z / (y - z));
	else
		tmp = (y - z) * (x / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.9e+139], N[Not[LessEqual[z, 1.35e+156]], $MachinePrecision]], N[((-x) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8999999999999999e139 or 1.35e156 < z

   1. Initial program 67.3%

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

      1. associate-*l/ 62.0%

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

   3. Simplified 62.0%

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

   4. Taylor expanded in t around 0 62.9%

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

      1. mul-1-neg 62.9%

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

      2. associate-/l* 93.8%

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

      3. distribute-neg-frac 93.8%

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

   6. Simplified 93.8%

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

   if -2.8999999999999999e139 < z < 1.35e156

   1. Initial program 89.0%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+139} \lor \neg \left(z \leq 1.35 \cdot 10^{+156}\right):\\ \;\;\;\;\frac{-x}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \]

Alternative 5: 95.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-120} \lor \neg \left(x \leq 3 \cdot 10^{-20}\right):\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6e-120) (not (<= x 3e-20)))
   (* (- y z) (/ x (- t z)))
   (/ (* x (- y z)) (- t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6e-120) || !(x <= 3e-20)) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = (x * (y - z)) / (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-6d-120)) .or. (.not. (x <= 3d-20))) then
        tmp = (y - z) * (x / (t - z))
    else
        tmp = (x * (y - z)) / (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6e-120) || !(x <= 3e-20)) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = (x * (y - z)) / (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6e-120) or not (x <= 3e-20):
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = (x * (y - z)) / (t - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6e-120) || !(x <= 3e-20))
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	else
		tmp = Float64(Float64(x * Float64(y - z)) / Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -6e-120) || ~((x <= 3e-20)))
		tmp = (y - z) * (x / (t - z));
	else
		tmp = (x * (y - z)) / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6e-120], N[Not[LessEqual[x, 3e-20]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.00000000000000022e-120 or 3.00000000000000029e-20 < x

   1. Initial program 77.2%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   if -6.00000000000000022e-120 < x < 3.00000000000000029e-20

   1. Initial program 95.8%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-120} \lor \neg \left(x \leq 3 \cdot 10^{-20}\right):\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array} \]

Alternative 6: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-38} \lor \neg \left(z \leq 2.9 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{-x}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.85e-38) (not (<= z 2.9e+20)))
   (/ (- x) (/ z (- y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.85e-38) || !(z <= 2.9e+20)) {
		tmp = -x / (z / (y - z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.85d-38)) .or. (.not. (z <= 2.9d+20))) then
        tmp = -x / (z / (y - z))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.85e-38) || !(z <= 2.9e+20)) {
		tmp = -x / (z / (y - z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.85e-38) or not (z <= 2.9e+20):
		tmp = -x / (z / (y - z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.85e-38) || !(z <= 2.9e+20))
		tmp = Float64(Float64(-x) / Float64(z / Float64(y - z)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.85e-38) || ~((z <= 2.9e+20)))
		tmp = -x / (z / (y - z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.85e-38], N[Not[LessEqual[z, 2.9e+20]], $MachinePrecision]], N[((-x) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e-38 or 2.9e20 < z

   1. Initial program 75.8%

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

      1. associate-*l/ 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in t around 0 60.5%

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

      1. mul-1-neg 60.5%

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

      2. associate-/l* 79.2%

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

      3. distribute-neg-frac 79.2%

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

   6. Simplified 79.2%

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

   if -1.85e-38 < z < 2.9e20

   1. Initial program 92.0%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in y around inf 77.3%

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

      1. *-commutative 77.3%

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

      2. associate-/l* 77.2%

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

      3. associate-/r/ 79.3%

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

   6. Simplified 79.3%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-38} \lor \neg \left(z \leq 2.9 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{-x}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 7: 61.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e+22)
   x
   (if (<= z -6.5e-46) (* y (/ (- x) z)) (if (<= z 3.5e+20) (/ x (/ t y)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+22) {
		tmp = x;
	} else if (z <= -6.5e-46) {
		tmp = y * (-x / z);
	} else if (z <= 3.5e+20) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.7d+22)) then
        tmp = x
    else if (z <= (-6.5d-46)) then
        tmp = y * (-x / z)
    else if (z <= 3.5d+20) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+22) {
		tmp = x;
	} else if (z <= -6.5e-46) {
		tmp = y * (-x / z);
	} else if (z <= 3.5e+20) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e+22:
		tmp = x
	elif z <= -6.5e-46:
		tmp = y * (-x / z)
	elif z <= 3.5e+20:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e+22)
		tmp = x;
	elseif (z <= -6.5e-46)
		tmp = Float64(y * Float64(Float64(-x) / z));
	elseif (z <= 3.5e+20)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.7e+22)
		tmp = x;
	elseif (z <= -6.5e-46)
		tmp = y * (-x / z);
	elseif (z <= 3.5e+20)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e+22], x, If[LessEqual[z, -6.5e-46], N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+20], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7000000000000002e22 or 3.5e20 < z

   1. Initial program 72.4%

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

      1. associate-*l/ 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in z around inf 60.1%

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

   if -2.7000000000000002e22 < z < -6.49999999999999966e-46

   1. Initial program 99.8%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 66.3%

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

      1. associate-*l/ 66.0%

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

      2. *-commutative 66.0%

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

   6. Simplified 66.0%

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

   7. Taylor expanded in t around 0 62.9%

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

      1. associate-*r/ 62.9%

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

      2. neg-mul-1 62.9%

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

   9. Simplified 62.9%

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

   if -6.49999999999999966e-46 < z < 3.5e20

   1. Initial program 91.9%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in z around 0 64.3%

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

      1. associate-/l* 67.1%

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

   6. Simplified 67.1%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-45}:\\ \;\;\;\;\left(-x\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.26e+14)
   x
   (if (<= z -4.2e-45) (* (- x) (/ y z)) (if (<= z 3.4e+20) (/ x (/ t y)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.26e+14) {
		tmp = x;
	} else if (z <= -4.2e-45) {
		tmp = -x * (y / z);
	} else if (z <= 3.4e+20) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.26d+14)) then
        tmp = x
    else if (z <= (-4.2d-45)) then
        tmp = -x * (y / z)
    else if (z <= 3.4d+20) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.26e+14) {
		tmp = x;
	} else if (z <= -4.2e-45) {
		tmp = -x * (y / z);
	} else if (z <= 3.4e+20) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.26e+14:
		tmp = x
	elif z <= -4.2e-45:
		tmp = -x * (y / z)
	elif z <= 3.4e+20:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.26e+14)
		tmp = x;
	elseif (z <= -4.2e-45)
		tmp = Float64(Float64(-x) * Float64(y / z));
	elseif (z <= 3.4e+20)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.26e+14)
		tmp = x;
	elseif (z <= -4.2e-45)
		tmp = -x * (y / z);
	elseif (z <= 3.4e+20)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.26e+14], x, If[LessEqual[z, -4.2e-45], N[((-x) * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+20], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.26e14 or 3.4e20 < z

   1. Initial program 72.4%

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

      1. associate-*l/ 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in z around inf 60.1%

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

   if -1.26e14 < z < -4.1999999999999999e-45

   1. Initial program 99.8%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 66.3%

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

      1. associate-*l/ 66.0%

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

      2. *-commutative 66.0%

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

   6. Simplified 66.0%

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

   7. Taylor expanded in t around 0 63.1%

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

      1. mul-1-neg 63.1%

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

      2. associate-/l* 63.2%

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

      3. distribute-neg-frac 63.2%

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

   9. Simplified 63.2%

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

   10. Taylor expanded in x around 0 63.1%

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

       1. associate-*r/ 63.1%

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

       2. associate-*r* 63.1%

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

       3. *-commutative 63.1%

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

       4. associate-*r* 63.1%

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

       5. *-commutative 63.1%

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

       6. mul-1-neg 63.1%

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

   12. Simplified 63.1%

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

   if -4.1999999999999999e-45 < z < 3.4e20

   1. Initial program 91.9%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in z around 0 64.3%

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

      1. associate-/l* 67.1%

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

   6. Simplified 67.1%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-45}:\\ \;\;\;\;\left(-x\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10600000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -10600000000000.0)
   x
   (if (<= z -3.2e-45) (/ (- x) (/ z y)) (if (<= z 3.8e+20) (/ x (/ t y)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -10600000000000.0) {
		tmp = x;
	} else if (z <= -3.2e-45) {
		tmp = -x / (z / y);
	} else if (z <= 3.8e+20) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-10600000000000.0d0)) then
        tmp = x
    else if (z <= (-3.2d-45)) then
        tmp = -x / (z / y)
    else if (z <= 3.8d+20) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -10600000000000.0) {
		tmp = x;
	} else if (z <= -3.2e-45) {
		tmp = -x / (z / y);
	} else if (z <= 3.8e+20) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -10600000000000.0:
		tmp = x
	elif z <= -3.2e-45:
		tmp = -x / (z / y)
	elif z <= 3.8e+20:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -10600000000000.0)
		tmp = x;
	elseif (z <= -3.2e-45)
		tmp = Float64(Float64(-x) / Float64(z / y));
	elseif (z <= 3.8e+20)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -10600000000000.0)
		tmp = x;
	elseif (z <= -3.2e-45)
		tmp = -x / (z / y);
	elseif (z <= 3.8e+20)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -10600000000000.0], x, If[LessEqual[z, -3.2e-45], N[((-x) / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+20], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.06e13 or 3.8e20 < z

   1. Initial program 72.4%

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

      1. associate-*l/ 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in z around inf 60.1%

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

   if -1.06e13 < z < -3.20000000000000007e-45

   1. Initial program 99.8%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 66.3%

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

      1. associate-*l/ 66.0%

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

      2. *-commutative 66.0%

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

   6. Simplified 66.0%

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

   7. Taylor expanded in t around 0 63.1%

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

      1. mul-1-neg 63.1%

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

      2. associate-/l* 63.2%

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

      3. distribute-neg-frac 63.2%

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

   9. Simplified 63.2%

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

   if -3.20000000000000007e-45 < z < 3.8e20

   1. Initial program 91.9%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in z around 0 64.3%

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

      1. associate-/l* 67.1%

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

   6. Simplified 67.1%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10600000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-38} \lor \neg \left(z \leq 3 \cdot 10^{+20}\right):\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.4e-38) (not (<= z 3e+20)))
   (- x (* y (/ x z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e-38) || !(z <= 3e+20)) {
		tmp = x - (y * (x / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.4d-38)) .or. (.not. (z <= 3d+20))) then
        tmp = x - (y * (x / z))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e-38) || !(z <= 3e+20)) {
		tmp = x - (y * (x / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.4e-38) or not (z <= 3e+20):
		tmp = x - (y * (x / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.4e-38) || !(z <= 3e+20))
		tmp = Float64(x - Float64(y * Float64(x / z)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.4e-38) || ~((z <= 3e+20)))
		tmp = x - (y * (x / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.4e-38], N[Not[LessEqual[z, 3e+20]], $MachinePrecision]], N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e-38 or 3e20 < z

   1. Initial program 75.8%

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

      1. associate-*l/ 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in t around 0 58.2%

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

      1. associate-*r/ 22.5%

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

      2. neg-mul-1 22.5%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in z around 0 72.8%

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

      1. mul-1-neg 72.8%

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

      2. unsub-neg 72.8%

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

      3. associate-*l/ 74.2%

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

      4. *-commutative 74.2%

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

   9. Simplified 74.2%

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

   if -1.4e-38 < z < 3e20

   1. Initial program 92.0%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in y around inf 77.3%

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

      1. *-commutative 77.3%

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

      2. associate-/l* 77.2%

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

      3. associate-/r/ 79.3%

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

   6. Simplified 79.3%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-38} \lor \neg \left(z \leq 3 \cdot 10^{+20}\right):\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 11: 68.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.5e+21) x (if (<= z 5.5e+31) (* y (/ x (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e+21) {
		tmp = x;
	} else if (z <= 5.5e+31) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.5d+21)) then
        tmp = x
    else if (z <= 5.5d+31) then
        tmp = y * (x / (t - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e+21) {
		tmp = x;
	} else if (z <= 5.5e+31) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.5e+21:
		tmp = x
	elif z <= 5.5e+31:
		tmp = y * (x / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.5e+21)
		tmp = x;
	elseif (z <= 5.5e+31)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.5e+21)
		tmp = x;
	elseif (z <= 5.5e+31)
		tmp = y * (x / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.5e+21], x, If[LessEqual[z, 5.5e+31], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e21 or 5.50000000000000002e31 < z

   1. Initial program 71.4%

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

      1. associate-*l/ 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in z around inf 61.2%

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

   if -6.5e21 < z < 5.50000000000000002e31

   1. Initial program 93.0%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in y around inf 74.9%

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

      1. associate-*l/ 74.8%

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

      2. *-commutative 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-38}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2e-38)
   (- x (* y (/ x z)))
   (if (<= z 3.6e+19) (* x (/ y (- t z))) (/ x (/ (- z t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e-38) {
		tmp = x - (y * (x / z));
	} else if (z <= 3.6e+19) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / ((z - t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2d-38)) then
        tmp = x - (y * (x / z))
    else if (z <= 3.6d+19) then
        tmp = x * (y / (t - z))
    else
        tmp = x / ((z - t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e-38) {
		tmp = x - (y * (x / z));
	} else if (z <= 3.6e+19) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / ((z - t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2e-38:
		tmp = x - (y * (x / z))
	elif z <= 3.6e+19:
		tmp = x * (y / (t - z))
	else:
		tmp = x / ((z - t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2e-38)
		tmp = Float64(x - Float64(y * Float64(x / z)));
	elseif (z <= 3.6e+19)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(z - t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2e-38)
		tmp = x - (y * (x / z));
	elseif (z <= 3.6e+19)
		tmp = x * (y / (t - z));
	else
		tmp = x / ((z - t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2e-38], N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+19], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9999999999999999e-38

   1. Initial program 78.8%

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

      1. associate-*l/ 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in t around 0 60.4%

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

      1. associate-*r/ 25.9%

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

      2. neg-mul-1 25.9%

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

   6. Simplified 60.4%

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

   7. Taylor expanded in z around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. unsub-neg 75.8%

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

      3. associate-*l/ 76.0%

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

      4. *-commutative 76.0%

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

   9. Simplified 76.0%

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

   if -1.9999999999999999e-38 < z < 3.6e19

   1. Initial program 92.6%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in y around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. associate-/l* 77.8%

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

      3. associate-/r/ 79.8%

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

   6. Simplified 79.8%

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

   if 3.6e19 < z

   1. Initial program 70.9%

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

      1. associate-*l/ 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in y around 0 53.5%

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

      1. associate-*r/ 53.5%

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

      2. mul-1-neg 53.5%

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

      3. distribute-rgt-neg-out 53.5%

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

      4. associate-/l* 74.6%

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

   6. Simplified 74.6%

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

      1. frac-2neg 74.6%

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

      2. div-inv 74.4%

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

      3. sub-neg 74.4%

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

      4. distribute-neg-in 74.4%

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

      5. remove-double-neg 74.4%

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

      6. remove-double-neg 74.4%

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

   8. Applied egg-rr 74.4%

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

      1. associate-*r/ 74.6%

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

      2. *-rgt-identity 74.6%

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

      3. +-commutative 74.6%

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

      4. unsub-neg 74.6%

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

   10. Simplified 74.6%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-38}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \end{array} \]

Alternative 13: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.4e-38) x (if (<= z 2.35e+20) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.4e-38) {
		tmp = x;
	} else if (z <= 2.35e+20) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.4d-38)) then
        tmp = x
    else if (z <= 2.35d+20) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.4e-38) {
		tmp = x;
	} else if (z <= 2.35e+20) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.4e-38:
		tmp = x
	elif z <= 2.35e+20:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.4e-38)
		tmp = x;
	elseif (z <= 2.35e+20)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.4e-38)
		tmp = x;
	elseif (z <= 2.35e+20)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.4e-38], x, If[LessEqual[z, 2.35e+20], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e-38 or 2.35e20 < z

   1. Initial program 75.8%

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

      1. associate-*l/ 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in z around inf 55.5%

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

   if -1.4e-38 < z < 2.35e20

   1. Initial program 92.0%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in z around 0 64.1%

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

      1. associate-/l* 66.8%

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

      2. associate-/r/ 63.3%

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

   6. Simplified 63.3%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.02 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.02e-38) x (if (<= z 3.2e+20) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.02e-38) {
		tmp = x;
	} else if (z <= 3.2e+20) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.02d-38)) then
        tmp = x
    else if (z <= 3.2d+20) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.02e-38) {
		tmp = x;
	} else if (z <= 3.2e+20) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.02e-38:
		tmp = x
	elif z <= 3.2e+20:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.02e-38)
		tmp = x;
	elseif (z <= 3.2e+20)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.02e-38)
		tmp = x;
	elseif (z <= 3.2e+20)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.02e-38], x, If[LessEqual[z, 3.2e+20], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.02000000000000007e-38 or 3.2e20 < z

   1. Initial program 75.8%

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

      1. associate-*l/ 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in z around inf 55.5%

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

   if -2.02000000000000007e-38 < z < 3.2e20

   1. Initial program 92.0%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

      1. *-commutative 92.0%

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

      2. clear-num 92.0%

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

      3. un-div-inv 92.3%

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

   5. Applied egg-rr 92.3%

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

   6. Taylor expanded in z around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-*l/ 66.8%

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

   8. Simplified 66.8%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.02 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.02 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.02e-38) x (if (<= z 3.3e+20) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.02e-38) {
		tmp = x;
	} else if (z <= 3.3e+20) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.02d-38)) then
        tmp = x
    else if (z <= 3.3d+20) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.02e-38) {
		tmp = x;
	} else if (z <= 3.3e+20) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.02e-38:
		tmp = x
	elif z <= 3.3e+20:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.02e-38)
		tmp = x;
	elseif (z <= 3.3e+20)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.02e-38)
		tmp = x;
	elseif (z <= 3.3e+20)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.02e-38], x, If[LessEqual[z, 3.3e+20], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.02000000000000007e-38 or 3.3e20 < z

   1. Initial program 75.8%

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

      1. associate-*l/ 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in z around inf 55.5%

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

   if -2.02000000000000007e-38 < z < 3.3e20

   1. Initial program 92.0%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in z around 0 64.1%

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

      1. associate-/l* 66.8%

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

   6. Simplified 66.8%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.02 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 35.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.3%

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

   1. associate-*l/ 84.2%

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

3. Simplified 84.2%

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

4. Taylor expanded in z around inf 32.3%

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

5. Final simplification 32.3%

   \[\leadsto x \]

Developer target: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{t - z}{y - z}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))