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

Percentage Accurate: 84.8% → 96.8%

Time: 11.1s

Alternatives: 10

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: 84.8% 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: 96.8% 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 84.9%

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

   1. *-commutative 84.9%

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

   2. associate-*l/ 97.4%

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

   3. *-commutative 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. Add Preprocessing

5. Final simplification 97.4%

   \[\leadsto x \cdot \frac{y - z}{t - z} \]
6. Add Preprocessing

Alternative 2: 69.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-13}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -6e+75)
     x
     (if (<= z 9.8e-107)
       t_1
       (if (<= z 1.12e-13) (* (- y z) (/ x t)) (if (<= z 7.1e+142) t_1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -6e+75) {
		tmp = x;
	} else if (z <= 9.8e-107) {
		tmp = t_1;
	} else if (z <= 1.12e-13) {
		tmp = (y - z) * (x / t);
	} else if (z <= 7.1e+142) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (z <= (-6d+75)) then
        tmp = x
    else if (z <= 9.8d-107) then
        tmp = t_1
    else if (z <= 1.12d-13) then
        tmp = (y - z) * (x / t)
    else if (z <= 7.1d+142) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -6e+75) {
		tmp = x;
	} else if (z <= 9.8e-107) {
		tmp = t_1;
	} else if (z <= 1.12e-13) {
		tmp = (y - z) * (x / t);
	} else if (z <= 7.1e+142) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -6e+75:
		tmp = x
	elif z <= 9.8e-107:
		tmp = t_1
	elif z <= 1.12e-13:
		tmp = (y - z) * (x / t)
	elif z <= 7.1e+142:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -6e+75)
		tmp = x;
	elseif (z <= 9.8e-107)
		tmp = t_1;
	elseif (z <= 1.12e-13)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 7.1e+142)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -6e+75)
		tmp = x;
	elseif (z <= 9.8e-107)
		tmp = t_1;
	elseif (z <= 1.12e-13)
		tmp = (y - z) * (x / t);
	elseif (z <= 7.1e+142)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+75], x, If[LessEqual[z, 9.8e-107], t$95$1, If[LessEqual[z, 1.12e-13], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.1e+142], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e75 or 7.1e142 < z

   1. Initial program 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 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. Add Preprocessing

   5. Taylor expanded in z around inf 71.3%

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

   if -6e75 < z < 9.79999999999999959e-107 or 1.12e-13 < z < 7.1e142

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

      2. associate-*l/ 96.3%

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

      3. *-commutative 96.3%

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

   3. Simplified 96.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 78.0%

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

   if 9.79999999999999959e-107 < z < 1.12e-13

   1. Initial program 99.8%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 79.3%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-13}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -0.023:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e+87)
   x
   (if (<= z -0.023) (/ (* x (- y)) z) (if (<= z 2.1e+118) (/ x (/ t y)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+87) {
		tmp = x;
	} else if (z <= -0.023) {
		tmp = (x * -y) / z;
	} else if (z <= 2.1e+118) {
		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+87)) then
        tmp = x
    else if (z <= (-0.023d0)) then
        tmp = (x * -y) / z
    else if (z <= 2.1d+118) 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+87) {
		tmp = x;
	} else if (z <= -0.023) {
		tmp = (x * -y) / z;
	} else if (z <= 2.1e+118) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e+87:
		tmp = x
	elif z <= -0.023:
		tmp = (x * -y) / z
	elif z <= 2.1e+118:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e+87)
		tmp = x;
	elseif (z <= -0.023)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	elseif (z <= 2.1e+118)
		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+87)
		tmp = x;
	elseif (z <= -0.023)
		tmp = (x * -y) / z;
	elseif (z <= 2.1e+118)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e+87], x, If[LessEqual[z, -0.023], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.1e+118], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.70000000000000007e87 or 2.1e118 < z

   1. Initial program 66.3%

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

      1. *-commutative 66.3%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 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. Add Preprocessing

   5. Taylor expanded in z around inf 70.9%

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

   if -2.70000000000000007e87 < z < -0.023

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 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. Add Preprocessing

   5. Taylor expanded in y around inf 53.2%

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

   6. Taylor expanded in t around 0 44.9%

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

      1. mul-1-neg 44.9%

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

   8. Simplified 44.9%

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

   if -0.023 < z < 2.1e118

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*l/ 95.5%

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

      3. *-commutative 95.5%

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

   3. Simplified 95.5%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 67.0%

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

      1. associate-/l* 68.9%

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

   7. Simplified 68.9%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -0.023:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+24} \lor \neg \left(y \leq 1.02 \cdot 10^{-56}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e+24) (not (<= y 1.02e-56)))
   (* x (/ y (- t z)))
   (* z (/ x (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+24) || !(y <= 1.02e-56)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = z * (x / (z - t));
	}
	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 <= (-3.8d+24)) .or. (.not. (y <= 1.02d-56))) then
        tmp = x * (y / (t - z))
    else
        tmp = z * (x / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+24) || !(y <= 1.02e-56)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = z * (x / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.8e+24) or not (y <= 1.02e-56):
		tmp = x * (y / (t - z))
	else:
		tmp = z * (x / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e+24) || !(y <= 1.02e-56))
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(z * Float64(x / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.8e+24) || ~((y <= 1.02e-56)))
		tmp = x * (y / (t - z));
	else
		tmp = z * (x / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.8e+24], N[Not[LessEqual[y, 1.02e-56]], $MachinePrecision]], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000015e24 or 1.02e-56 < y

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-*l/ 98.4%

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

      3. *-commutative 98.4%

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

   3. Simplified 98.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 76.2%

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

   if -3.80000000000000015e24 < y < 1.02e-56

   1. Initial program 82.9%

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

      1. *-commutative 82.9%

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

      2. associate-*l/ 96.2%

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

      3. *-commutative 96.2%

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

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.7%

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

      1. associate-*r/ 67.7%

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

      2. mul-1-neg 67.7%

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

      3. distribute-rgt-neg-out 67.7%

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

      4. associate-*l/ 79.2%

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

   7. Simplified 79.2%

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

      1. associate-*l/ 67.7%

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

      2. frac-2neg 67.7%

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

      3. add-sqr-sqrt 35.4%

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

      4. sqrt-unprod 35.2%

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

      5. sqr-neg 35.2%

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

      6. sqrt-unprod 10.3%

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

      7. add-sqr-sqrt 17.4%

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

      8. distribute-rgt-neg-out 17.4%

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

      9. add-sqr-sqrt 7.1%

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

      10. sqrt-unprod 33.2%

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

      11. sqr-neg 33.2%

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

      12. sqrt-unprod 32.0%

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

      13. add-sqr-sqrt 67.7%

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

      14. sub-neg 67.7%

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

      15. distribute-neg-in 67.7%

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

      16. add-sqr-sqrt 35.5%

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

      17. sqrt-unprod 43.9%

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

      18. sqr-neg 43.9%

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

      19. sqrt-unprod 19.2%

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

      20. add-sqr-sqrt 36.9%

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

      21. add-sqr-sqrt 17.7%

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

      22. sqrt-unprod 43.1%

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

      23. sqr-neg 43.1%

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

   9. Applied egg-rr 67.7%

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

       1. associate-/l* 81.4%

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

       2. +-commutative 81.4%

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

       3. unsub-neg 81.4%

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

   11. Simplified 81.4%

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

       1. associate-/r/ 79.2%

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

   13. Applied egg-rr 79.2%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+24} \lor \neg \left(y \leq 1.02 \cdot 10^{-56}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+24} \lor \neg \left(y \leq 3.2 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4e+24) (not (<= y 3.2e-52)))
   (* x (/ y (- t z)))
   (* x (/ z (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4e+24) || !(y <= 3.2e-52)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	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 <= (-4d+24)) .or. (.not. (y <= 3.2d-52))) then
        tmp = x * (y / (t - z))
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4e+24) || !(y <= 3.2e-52)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4e+24) or not (y <= 3.2e-52):
		tmp = x * (y / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4e+24) || !(y <= 3.2e-52))
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4e+24) || ~((y <= 3.2e-52)))
		tmp = x * (y / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4e+24], N[Not[LessEqual[y, 3.2e-52]], $MachinePrecision]], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9999999999999999e24 or 3.2000000000000001e-52 < y

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-*l/ 98.4%

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

      3. *-commutative 98.4%

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

   3. Simplified 98.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 76.2%

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

   if -3.9999999999999999e24 < y < 3.2000000000000001e-52

   1. Initial program 82.9%

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

      1. *-commutative 82.9%

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

      2. associate-*l/ 96.2%

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

      3. *-commutative 96.2%

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

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.7%

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

      1. associate-*r/ 67.7%

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

      2. mul-1-neg 67.7%

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

      3. distribute-rgt-neg-out 67.7%

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

      4. associate-*l/ 79.2%

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

   7. Simplified 79.2%

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

      1. associate-*l/ 67.7%

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

      2. frac-2neg 67.7%

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

      3. add-sqr-sqrt 35.4%

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

      4. sqrt-unprod 35.2%

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

      5. sqr-neg 35.2%

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

      6. sqrt-unprod 10.3%

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

      7. add-sqr-sqrt 17.4%

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

      8. distribute-rgt-neg-out 17.4%

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

      9. add-sqr-sqrt 7.1%

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

      10. sqrt-unprod 33.2%

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

      11. sqr-neg 33.2%

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

      12. sqrt-unprod 32.0%

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

      13. add-sqr-sqrt 67.7%

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

      14. sub-neg 67.7%

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

      15. distribute-neg-in 67.7%

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

      16. add-sqr-sqrt 35.5%

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

      17. sqrt-unprod 43.9%

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

      18. sqr-neg 43.9%

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

      19. sqrt-unprod 19.2%

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

      20. add-sqr-sqrt 36.9%

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

      21. add-sqr-sqrt 17.7%

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

      22. sqrt-unprod 43.1%

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

      23. sqr-neg 43.1%

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

   9. Applied egg-rr 67.7%

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

       1. associate-/l* 81.4%

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

       2. +-commutative 81.4%

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

       3. unsub-neg 81.4%

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

   11. Simplified 81.4%

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

       1. clear-num 80.6%

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

       2. associate-/r/ 81.4%

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

       3. clear-num 81.8%

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

   13. Applied egg-rr 81.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+24} \lor \neg \left(y \leq 3.2 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.06e+83) x (if (<= z 1.95e+144) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.06e+83) {
		tmp = x;
	} else if (z <= 1.95e+144) {
		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 <= (-1.06d+83)) then
        tmp = x
    else if (z <= 1.95d+144) 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 <= -1.06e+83) {
		tmp = x;
	} else if (z <= 1.95e+144) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.06e+83:
		tmp = x
	elif z <= 1.95e+144:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.06e+83)
		tmp = x;
	elseif (z <= 1.95e+144)
		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 <= -1.06e+83)
		tmp = x;
	elseif (z <= 1.95e+144)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.06e+83], x, If[LessEqual[z, 1.95e+144], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05999999999999995e83 or 1.95000000000000009e144 < z

   1. Initial program 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 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. Add Preprocessing

   5. Taylor expanded in z around inf 71.3%

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

   if -1.05999999999999995e83 < z < 1.95000000000000009e144

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*l/ 96.0%

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

      3. *-commutative 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. Add Preprocessing

   5. Taylor expanded in y around inf 75.5%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.22e+26)
   (* x (/ y (- t z)))
   (if (<= y 1.8e-52) (* x (/ z (- z t))) (/ x (/ (- t z) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.22e+26) {
		tmp = x * (y / (t - z));
	} else if (y <= 1.8e-52) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x / ((t - z) / y);
	}
	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 <= (-1.22d+26)) then
        tmp = x * (y / (t - z))
    else if (y <= 1.8d-52) then
        tmp = x * (z / (z - t))
    else
        tmp = x / ((t - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.22e+26) {
		tmp = x * (y / (t - z));
	} else if (y <= 1.8e-52) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x / ((t - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.22e+26:
		tmp = x * (y / (t - z))
	elif y <= 1.8e-52:
		tmp = x * (z / (z - t))
	else:
		tmp = x / ((t - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.22e+26)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (y <= 1.8e-52)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = Float64(x / Float64(Float64(t - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.22e+26)
		tmp = x * (y / (t - z));
	elseif (y <= 1.8e-52)
		tmp = x * (z / (z - t));
	else
		tmp = x / ((t - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.22e+26], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-52], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2200000000000001e26

   1. Initial program 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-*l/ 98.2%

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

      3. *-commutative 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. Add Preprocessing

   5. Taylor expanded in y around inf 77.7%

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

   if -1.2200000000000001e26 < y < 1.79999999999999994e-52

   1. Initial program 82.9%

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

      1. *-commutative 82.9%

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

      2. associate-*l/ 96.2%

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

      3. *-commutative 96.2%

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

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.7%

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

      1. associate-*r/ 67.7%

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

      2. mul-1-neg 67.7%

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

      3. distribute-rgt-neg-out 67.7%

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

      4. associate-*l/ 79.2%

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

   7. Simplified 79.2%

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

      1. associate-*l/ 67.7%

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

      2. frac-2neg 67.7%

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

      3. add-sqr-sqrt 35.4%

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

      4. sqrt-unprod 35.2%

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

      5. sqr-neg 35.2%

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

      6. sqrt-unprod 10.3%

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

      7. add-sqr-sqrt 17.4%

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

      8. distribute-rgt-neg-out 17.4%

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

      9. add-sqr-sqrt 7.1%

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

      10. sqrt-unprod 33.2%

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

      11. sqr-neg 33.2%

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

      12. sqrt-unprod 32.0%

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

      13. add-sqr-sqrt 67.7%

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

      14. sub-neg 67.7%

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

      15. distribute-neg-in 67.7%

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

      16. add-sqr-sqrt 35.5%

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

      17. sqrt-unprod 43.9%

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

      18. sqr-neg 43.9%

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

      19. sqrt-unprod 19.2%

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

      20. add-sqr-sqrt 36.9%

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

      21. add-sqr-sqrt 17.7%

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

      22. sqrt-unprod 43.1%

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

      23. sqr-neg 43.1%

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

   9. Applied egg-rr 67.7%

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

       1. associate-/l* 81.4%

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

       2. +-commutative 81.4%

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

       3. unsub-neg 81.4%

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

   11. Simplified 81.4%

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

       1. clear-num 80.6%

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

       2. associate-/r/ 81.4%

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

       3. clear-num 81.8%

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

   13. Applied egg-rr 81.8%

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

   if 1.79999999999999994e-52 < y

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-*l/ 98.5%

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

      3. *-commutative 98.5%

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

   3. Simplified 98.5%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.3%

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

      1. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0295:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.0295) x (if (<= z 2.1e+118) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.0295) {
		tmp = x;
	} else if (z <= 2.1e+118) {
		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 <= (-0.0295d0)) then
        tmp = x
    else if (z <= 2.1d+118) 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 <= -0.0295) {
		tmp = x;
	} else if (z <= 2.1e+118) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.0295:
		tmp = x
	elif z <= 2.1e+118:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.0295)
		tmp = x;
	elseif (z <= 2.1e+118)
		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 <= -0.0295)
		tmp = x;
	elseif (z <= 2.1e+118)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.0295], x, If[LessEqual[z, 2.1e+118], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -0.029499999999999998 or 2.1e118 < z

   1. Initial program 72.0%

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

      1. *-commutative 72.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 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. Add Preprocessing

   5. Taylor expanded in z around inf 62.1%

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

   if -0.029499999999999998 < z < 2.1e118

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*l/ 95.5%

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

      3. *-commutative 95.5%

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

   3. Simplified 95.5%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 68.4%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0295:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.000102:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.000102) x (if (<= z 3.6e+118) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.000102) {
		tmp = x;
	} else if (z <= 3.6e+118) {
		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 <= (-0.000102d0)) then
        tmp = x
    else if (z <= 3.6d+118) 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 <= -0.000102) {
		tmp = x;
	} else if (z <= 3.6e+118) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.000102:
		tmp = x
	elif z <= 3.6e+118:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.000102)
		tmp = x;
	elseif (z <= 3.6e+118)
		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 <= -0.000102)
		tmp = x;
	elseif (z <= 3.6e+118)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.000102], x, If[LessEqual[z, 3.6e+118], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.01999999999999999e-4 or 3.6e118 < z

   1. Initial program 72.0%

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

      1. *-commutative 72.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 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. Add Preprocessing

   5. Taylor expanded in z around inf 62.1%

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

   if -1.01999999999999999e-4 < z < 3.6e118

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*l/ 95.5%

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

      3. *-commutative 95.5%

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

   3. Simplified 95.5%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 67.0%

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

      1. associate-/l* 68.9%

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

   7. Simplified 68.9%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.000102:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.9% 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 84.9%

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

   1. *-commutative 84.9%

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

   2. associate-*l/ 97.4%

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

   3. *-commutative 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. Add Preprocessing

5. Taylor expanded in z around inf 32.9%

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

6. Final simplification 32.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.8% 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 2024020 
(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)))