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

Percentage Accurate: 84.3% → 96.9%

Time: 7.4s

Alternatives: 9

Speedup: 1.0×

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: 84.3% 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: 96.9% accurate, 1.0× speedup

Math

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

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(x * Float64(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[(x * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.4%

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

   1. associate-*r/ 97.4%

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

3. Simplified 97.4%

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

4. Final simplification 97.4%

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

Alternative 2: 60.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.08e-14)
   x
   (if (<= z 4.5e-68) (* x (/ y t)) (if (<= z 1.85e+99) (* x (/ (- y) z)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.08e-14) {
		tmp = x;
	} else if (z <= 4.5e-68) {
		tmp = x * (y / t);
	} else if (z <= 1.85e+99) {
		tmp = x * (-y / 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 <= (-1.08d-14)) then
        tmp = x
    else if (z <= 4.5d-68) then
        tmp = x * (y / t)
    else if (z <= 1.85d+99) then
        tmp = x * (-y / 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 <= -1.08e-14) {
		tmp = x;
	} else if (z <= 4.5e-68) {
		tmp = x * (y / t);
	} else if (z <= 1.85e+99) {
		tmp = x * (-y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.08e-14:
		tmp = x
	elif z <= 4.5e-68:
		tmp = x * (y / t)
	elif z <= 1.85e+99:
		tmp = x * (-y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.08e-14)
		tmp = x;
	elseif (z <= 4.5e-68)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 1.85e+99)
		tmp = Float64(x * Float64(Float64(-y) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.08e-14)
		tmp = x;
	elseif (z <= 4.5e-68)
		tmp = x * (y / t);
	elseif (z <= 1.85e+99)
		tmp = x * (-y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.08e-14], x, If[LessEqual[z, 4.5e-68], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+99], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.08000000000000004e-14 or 1.85000000000000005e99 < z

   1. Initial program 72.1%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 67.2%

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

   if -1.08000000000000004e-14 < z < 4.49999999999999999e-68

   1. Initial program 93.3%

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

      1. associate-*r/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around 0 72.6%

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

   if 4.49999999999999999e-68 < z < 1.85000000000000005e99

   1. Initial program 91.6%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 60.3%

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

   5. Taylor expanded in t around 0 48.8%

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

      1. associate-*r/ 48.8%

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

      2. neg-mul-1 48.8%

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

   7. Simplified 48.8%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.5e-14)
   x
   (if (<= z 3.45e-68) (* x (/ y t)) (if (<= z 1.5e+99) (* y (/ (- x) z)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e-14) {
		tmp = x;
	} else if (z <= 3.45e-68) {
		tmp = x * (y / t);
	} else if (z <= 1.5e+99) {
		tmp = y * (-x / 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 <= (-2.5d-14)) then
        tmp = x
    else if (z <= 3.45d-68) then
        tmp = x * (y / t)
    else if (z <= 1.5d+99) then
        tmp = y * (-x / 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 <= -2.5e-14) {
		tmp = x;
	} else if (z <= 3.45e-68) {
		tmp = x * (y / t);
	} else if (z <= 1.5e+99) {
		tmp = y * (-x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.5e-14:
		tmp = x
	elif z <= 3.45e-68:
		tmp = x * (y / t)
	elif z <= 1.5e+99:
		tmp = y * (-x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.5e-14)
		tmp = x;
	elseif (z <= 3.45e-68)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 1.5e+99)
		tmp = Float64(y * Float64(Float64(-x) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.5e-14)
		tmp = x;
	elseif (z <= 3.45e-68)
		tmp = x * (y / t);
	elseif (z <= 1.5e+99)
		tmp = y * (-x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.5e-14], x, If[LessEqual[z, 3.45e-68], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+99], N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5000000000000001e-14 or 1.50000000000000007e99 < z

   1. Initial program 72.1%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 67.2%

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

   if -2.5000000000000001e-14 < z < 3.45000000000000016e-68

   1. Initial program 93.3%

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

      1. associate-*r/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around 0 72.6%

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

   if 3.45000000000000016e-68 < z < 1.50000000000000007e99

   1. Initial program 91.6%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 60.3%

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

   5. Taylor expanded in t around 0 46.2%

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

      1. mul-1-neg 46.2%

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

      2. associate-*r/ 48.8%

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

      3. distribute-rgt-neg-in 48.8%

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

   7. Simplified 48.8%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{\frac{-z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.02e-14)
   x
   (if (<= z 4.2e-68) (* x (/ y t)) (if (<= z 1.6e+99) (/ x (/ (- z) y)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.02e-14) {
		tmp = x;
	} else if (z <= 4.2e-68) {
		tmp = x * (y / t);
	} else if (z <= 1.6e+99) {
		tmp = x / (-z / 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 <= (-1.02d-14)) then
        tmp = x
    else if (z <= 4.2d-68) then
        tmp = x * (y / t)
    else if (z <= 1.6d+99) then
        tmp = x / (-z / 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 <= -1.02e-14) {
		tmp = x;
	} else if (z <= 4.2e-68) {
		tmp = x * (y / t);
	} else if (z <= 1.6e+99) {
		tmp = x / (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.02e-14:
		tmp = x
	elif z <= 4.2e-68:
		tmp = x * (y / t)
	elif z <= 1.6e+99:
		tmp = x / (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.02e-14)
		tmp = x;
	elseif (z <= 4.2e-68)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 1.6e+99)
		tmp = Float64(x / Float64(Float64(-z) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.02e-14)
		tmp = x;
	elseif (z <= 4.2e-68)
		tmp = x * (y / t);
	elseif (z <= 1.6e+99)
		tmp = x / (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.02e-14], x, If[LessEqual[z, 4.2e-68], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+99], N[(x / N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.02e-14 or 1.6e99 < z

   1. Initial program 72.1%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 67.2%

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

   if -1.02e-14 < z < 4.20000000000000016e-68

   1. Initial program 93.3%

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

      1. associate-*r/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around 0 72.6%

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

   if 4.20000000000000016e-68 < z < 1.6e99

   1. Initial program 91.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 59.9%

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

      1. neg-mul-1 59.9%

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

      2. distribute-neg-frac 59.9%

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

   6. Simplified 59.9%

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

   7. Taylor expanded in z around 0 48.9%

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

      1. associate-*r/ 48.9%

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

      2. mul-1-neg 48.9%

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

   9. Simplified 48.9%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{\frac{-z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 72.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+116} \lor \neg \left(z \leq 7.2 \cdot 10^{+92}\right):\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.8e+116) (not (<= z 7.2e+92)))
   (- x (* y (/ x z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+116) || !(z <= 7.2e+92)) {
		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 <= (-3.8d+116)) .or. (.not. (z <= 7.2d+92))) 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 <= -3.8e+116) || !(z <= 7.2e+92)) {
		tmp = x - (y * (x / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.8e+116) or not (z <= 7.2e+92):
		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 <= -3.8e+116) || !(z <= 7.2e+92))
		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 <= -3.8e+116) || ~((z <= 7.2e+92)))
		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, -3.8e+116], N[Not[LessEqual[z, 7.2e+92]], $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 < -3.7999999999999999e116 or 7.2e92 < z

   1. Initial program 69.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 88.4%

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

      1. neg-mul-1 88.4%

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

      2. distribute-neg-frac 88.4%

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

   6. Simplified 88.4%

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

   7. Taylor expanded in z around 0 78.4%

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

      1. +-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. associate-*r/ 83.1%

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

   9. Simplified 83.1%

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

   if -3.7999999999999999e116 < z < 7.2e92

   1. Initial program 93.3%

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

      1. associate-*r/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in y around inf 79.5%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+116} \lor \neg \left(z \leq 7.2 \cdot 10^{+92}\right):\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 6: 73.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+116} \lor \neg \left(z \leq 6.4 \cdot 10^{+94}\right):\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.8e+116) (not (<= z 6.4e+94)))
   (- x (/ x (/ z y)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+116) || !(z <= 6.4e+94)) {
		tmp = x - (x / (z / y));
	} 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 <= (-3.8d+116)) .or. (.not. (z <= 6.4d+94))) then
        tmp = x - (x / (z / y))
    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 <= -3.8e+116) || !(z <= 6.4e+94)) {
		tmp = x - (x / (z / y));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.8e+116) or not (z <= 6.4e+94):
		tmp = x - (x / (z / y))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.8e+116) || !(z <= 6.4e+94))
		tmp = Float64(x - Float64(x / Float64(z / y)));
	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 <= -3.8e+116) || ~((z <= 6.4e+94)))
		tmp = x - (x / (z / y));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.8e+116], N[Not[LessEqual[z, 6.4e+94]], $MachinePrecision]], N[(x - N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999999e116 or 6.40000000000000028e94 < z

   1. Initial program 69.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 88.4%

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

      1. neg-mul-1 88.4%

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

      2. distribute-neg-frac 88.4%

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

   6. Simplified 88.4%

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

   7. Taylor expanded in z around 0 78.4%

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

      1. +-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. associate-*r/ 83.1%

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

   9. Simplified 83.1%

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

   10. Taylor expanded in y around 0 78.4%

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

       1. *-commutative 78.4%

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

       2. associate-/l* 88.4%

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

   12. Simplified 88.4%

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

   if -3.7999999999999999e116 < z < 6.40000000000000028e94

   1. Initial program 93.3%

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

      1. associate-*r/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in y around inf 79.5%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+116} \lor \neg \left(z \leq 6.4 \cdot 10^{+94}\right):\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 7: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.7e+131) x (if (<= z 1.8e+99) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.7e+131) {
		tmp = x;
	} else if (z <= 1.8e+99) {
		tmp = x * (y / (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 <= (-5.7d+131)) then
        tmp = x
    else if (z <= 1.8d+99) then
        tmp = x * (y / (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 <= -5.7e+131) {
		tmp = x;
	} else if (z <= 1.8e+99) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.7e+131:
		tmp = x
	elif z <= 1.8e+99:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.7e+131)
		tmp = x;
	elseif (z <= 1.8e+99)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.7e+131)
		tmp = x;
	elseif (z <= 1.8e+99)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.7e+131], x, If[LessEqual[z, 1.8e+99], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7e131 or 1.8000000000000001e99 < z

   1. Initial program 67.6%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 73.4%

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

   if -5.7e131 < z < 1.8000000000000001e99

   1. Initial program 93.5%

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

      1. associate-*r/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in y around inf 78.9%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e-14) x (if (<= z 7.2e+92) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-14) {
		tmp = x;
	} else if (z <= 7.2e+92) {
		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 <= (-1.6d-14)) then
        tmp = x
    else if (z <= 7.2d+92) 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 <= -1.6e-14) {
		tmp = x;
	} else if (z <= 7.2e+92) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e-14:
		tmp = x
	elif z <= 7.2e+92:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e-14)
		tmp = x;
	elseif (z <= 7.2e+92)
		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 <= -1.6e-14)
		tmp = x;
	elseif (z <= 7.2e+92)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e-14], x, If[LessEqual[z, 7.2e+92], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6000000000000001e-14 or 7.2e92 < z

   1. Initial program 72.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 66.8%

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

   if -1.6000000000000001e-14 < z < 7.2e92

   1. Initial program 92.8%

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

      1. associate-*r/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around 0 63.7%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 35.5% 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 84.4%

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

   1. associate-*r/ 97.4%

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

3. Simplified 97.4%

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

4. Taylor expanded in z around inf 34.0%

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

5. Final simplification 34.0%

   \[\leadsto x \]

Developer target: 96.9% 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 2023240 
(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)))