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

Percentage Accurate: 84.0% → 97.3%

Time: 7.3s

Alternatives: 8

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: 84.0% 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: 97.3% 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 86.3%

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

   1. associate-*r/ 96.4%

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

3. Simplified 96.4%

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

4. Final simplification 96.4%

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

Alternative 2: 69.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-81}:\\ \;\;\;\;\frac{-z}{\frac{t - z}{x}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;y \leq 28000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.6e-52)
   (/ x (/ (- t z) y))
   (if (<= y 5.4e-81)
     (/ (- z) (/ (- t z) x))
     (if (<= y 6.2e-27)
       (/ (- y z) (/ t x))
       (if (<= y 28000000.0) x (* x (/ y (- t z))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.6e-52) {
		tmp = x / ((t - z) / y);
	} else if (y <= 5.4e-81) {
		tmp = -z / ((t - z) / x);
	} else if (y <= 6.2e-27) {
		tmp = (y - z) / (t / x);
	} else if (y <= 28000000.0) {
		tmp = x;
	} 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 (y <= (-3.6d-52)) then
        tmp = x / ((t - z) / y)
    else if (y <= 5.4d-81) then
        tmp = -z / ((t - z) / x)
    else if (y <= 6.2d-27) then
        tmp = (y - z) / (t / x)
    else if (y <= 28000000.0d0) then
        tmp = x
    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 (y <= -3.6e-52) {
		tmp = x / ((t - z) / y);
	} else if (y <= 5.4e-81) {
		tmp = -z / ((t - z) / x);
	} else if (y <= 6.2e-27) {
		tmp = (y - z) / (t / x);
	} else if (y <= 28000000.0) {
		tmp = x;
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.6e-52:
		tmp = x / ((t - z) / y)
	elif y <= 5.4e-81:
		tmp = -z / ((t - z) / x)
	elif y <= 6.2e-27:
		tmp = (y - z) / (t / x)
	elif y <= 28000000.0:
		tmp = x
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.6e-52)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (y <= 5.4e-81)
		tmp = Float64(Float64(-z) / Float64(Float64(t - z) / x));
	elseif (y <= 6.2e-27)
		tmp = Float64(Float64(y - z) / Float64(t / x));
	elseif (y <= 28000000.0)
		tmp = x;
	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 (y <= -3.6e-52)
		tmp = x / ((t - z) / y);
	elseif (y <= 5.4e-81)
		tmp = -z / ((t - z) / x);
	elseif (y <= 6.2e-27)
		tmp = (y - z) / (t / x);
	elseif (y <= 28000000.0)
		tmp = x;
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.6e-52], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-81], N[((-z) / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-27], N[(N[(y - z), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 28000000.0], x, N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.59999999999999988e-52

   1. Initial program 86.7%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in y around inf 76.6%

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

   if -3.59999999999999988e-52 < y < 5.39999999999999979e-81

   1. Initial program 85.0%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

      1. associate-/l* 85.0%

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

      2. clear-num 84.9%

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

      3. associate-/r/ 84.9%

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

   5. Applied egg-rr 84.9%

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

   6. Taylor expanded in y around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. associate-/l* 73.6%

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

   8. Simplified 73.6%

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

   if 5.39999999999999979e-81 < y < 6.1999999999999997e-27

   1. Initial program 99.6%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around inf 72.8%

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

      1. associate-/l* 73.0%

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

   6. Simplified 73.0%

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

   if 6.1999999999999997e-27 < y < 2.8e7

   1. Initial program 86.2%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 72.4%

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

   if 2.8e7 < y

   1. Initial program 86.1%

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

      1. associate-*r/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around inf 84.5%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-81}:\\ \;\;\;\;\frac{-z}{\frac{t - z}{x}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;y \leq 28000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 3: 68.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.15e+105)
   x
   (if (<= z 1.6e-165)
     (* x (/ y (- t z)))
     (if (<= z 2.6e+23) (/ (* x (- y z)) t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.15e+105) {
		tmp = x;
	} else if (z <= 1.6e-165) {
		tmp = x * (y / (t - z));
	} else if (z <= 2.6e+23) {
		tmp = (x * (y - 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 <= (-1.15d+105)) then
        tmp = x
    else if (z <= 1.6d-165) then
        tmp = x * (y / (t - z))
    else if (z <= 2.6d+23) then
        tmp = (x * (y - 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 <= -1.15e+105) {
		tmp = x;
	} else if (z <= 1.6e-165) {
		tmp = x * (y / (t - z));
	} else if (z <= 2.6e+23) {
		tmp = (x * (y - z)) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.15e+105:
		tmp = x
	elif z <= 1.6e-165:
		tmp = x * (y / (t - z))
	elif z <= 2.6e+23:
		tmp = (x * (y - z)) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.15e+105)
		tmp = x;
	elseif (z <= 1.6e-165)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 2.6e+23)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.15e+105)
		tmp = x;
	elseif (z <= 1.6e-165)
		tmp = x * (y / (t - z));
	elseif (z <= 2.6e+23)
		tmp = (x * (y - z)) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.15e+105], x, If[LessEqual[z, 1.6e-165], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+23], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1499999999999999e105 or 2.59999999999999992e23 < z

   1. Initial program 77.9%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 66.8%

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

   if -1.1499999999999999e105 < z < 1.60000000000000006e-165

   1. Initial program 89.5%

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

      1. associate-*r/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around inf 78.5%

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

   if 1.60000000000000006e-165 < z < 2.59999999999999992e23

   1. Initial program 97.3%

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

      1. associate-*r/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in t around inf 78.3%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.6e+102)
   x
   (if (<= z 3.4e-236)
     (* x (/ y (- t z)))
     (if (<= z 1.5e+20) (/ (- y z) (/ t x)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.6e+102) {
		tmp = x;
	} else if (z <= 3.4e-236) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.5e+20) {
		tmp = (y - z) / (t / x);
	} 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 <= (-5.6d+102)) then
        tmp = x
    else if (z <= 3.4d-236) then
        tmp = x * (y / (t - z))
    else if (z <= 1.5d+20) then
        tmp = (y - z) / (t / x)
    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 <= -5.6e+102) {
		tmp = x;
	} else if (z <= 3.4e-236) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.5e+20) {
		tmp = (y - z) / (t / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.6e+102:
		tmp = x
	elif z <= 3.4e-236:
		tmp = x * (y / (t - z))
	elif z <= 1.5e+20:
		tmp = (y - z) / (t / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.6e+102)
		tmp = x;
	elseif (z <= 3.4e-236)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 1.5e+20)
		tmp = Float64(Float64(y - z) / Float64(t / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.6e+102)
		tmp = x;
	elseif (z <= 3.4e-236)
		tmp = x * (y / (t - z));
	elseif (z <= 1.5e+20)
		tmp = (y - z) / (t / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.6e+102], x, If[LessEqual[z, 3.4e-236], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+20], N[(N[(y - z), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.60000000000000037e102 or 1.5e20 < z

   1. Initial program 77.9%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 66.8%

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

   if -5.60000000000000037e102 < z < 3.3999999999999998e-236

   1. Initial program 90.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 76.5%

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

   if 3.3999999999999998e-236 < z < 1.5e20

   1. Initial program 93.5%

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

      1. associate-*r/ 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in t around inf 78.5%

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

      1. associate-/l* 83.2%

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

   6. Simplified 83.2%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 75.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{-z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.7e-46)
   (/ x (/ (- t z) y))
   (if (<= y 1.26e+23) (* x (/ (- z) (- t z))) (* x (/ y (- t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e-46) {
		tmp = x / ((t - z) / y);
	} else if (y <= 1.26e+23) {
		tmp = x * (-z / (t - 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 (y <= (-2.7d-46)) then
        tmp = x / ((t - z) / y)
    else if (y <= 1.26d+23) then
        tmp = x * (-z / (t - 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 (y <= -2.7e-46) {
		tmp = x / ((t - z) / y);
	} else if (y <= 1.26e+23) {
		tmp = x * (-z / (t - z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.7e-46:
		tmp = x / ((t - z) / y)
	elif y <= 1.26e+23:
		tmp = x * (-z / (t - z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.7e-46)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (y <= 1.26e+23)
		tmp = Float64(x * Float64(Float64(-z) / Float64(t - 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 (y <= -2.7e-46)
		tmp = x / ((t - z) / y);
	elseif (y <= 1.26e+23)
		tmp = x * (-z / (t - z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.7e-46], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+23], N[(x * N[((-z) / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e-46

   1. Initial program 86.7%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in y around inf 76.6%

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

   if -2.7e-46 < y < 1.26000000000000004e23

   1. Initial program 86.5%

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

      1. associate-*r/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around 0 80.4%

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

      1. neg-mul-1 80.4%

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

      2. distribute-neg-frac 80.4%

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

   6. Simplified 80.4%

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

   if 1.26000000000000004e23 < y

   1. Initial program 85.6%

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

      1. associate-*r/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around inf 85.6%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{-z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 6: 70.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1e+105) x (if (<= z 3e+99) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e+105) {
		tmp = x;
	} else if (z <= 3e+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 <= (-1.1d+105)) then
        tmp = x
    else if (z <= 3d+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 <= -1.1e+105) {
		tmp = x;
	} else if (z <= 3e+99) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.1e+105:
		tmp = x
	elif z <= 3e+99:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.1e+105)
		tmp = x;
	elseif (z <= 3e+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 <= -1.1e+105)
		tmp = x;
	elseif (z <= 3e+99)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.1e+105], x, If[LessEqual[z, 3e+99], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.10000000000000003e105 or 3.00000000000000014e99 < z

   1. Initial program 75.8%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 70.4%

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

   if -1.10000000000000003e105 < z < 3.00000000000000014e99

   1. Initial program 91.3%

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

      1. associate-*r/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around inf 72.8%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.1e+96) x (if (<= z 5.4e+17) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.1e+96) {
		tmp = x;
	} else if (z <= 5.4e+17) {
		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 <= (-4.1d+96)) then
        tmp = x
    else if (z <= 5.4d+17) 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 <= -4.1e+96) {
		tmp = x;
	} else if (z <= 5.4e+17) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.1e+96:
		tmp = x
	elif z <= 5.4e+17:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.1e+96)
		tmp = x;
	elseif (z <= 5.4e+17)
		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 <= -4.1e+96)
		tmp = x;
	elseif (z <= 5.4e+17)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.1e+96], x, If[LessEqual[z, 5.4e+17], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.09999999999999998e96 or 5.4e17 < z

   1. Initial program 78.1%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 66.2%

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

   if -4.09999999999999998e96 < z < 5.4e17

   1. Initial program 91.2%

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

      1. associate-*r/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around 0 67.9%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 34.8% 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 86.3%

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

   1. associate-*r/ 96.4%

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

3. Simplified 96.4%

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

4. Taylor expanded in z around inf 34.5%

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

5. Final simplification 34.5%

   \[\leadsto x \]

Developer target: 97.3% 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 2023187 
(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)))