Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B

Percentage Accurate: 90.4% → 95.9%

Time: 7.7s

Alternatives: 9

Speedup: 0.8×

• 49.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* x x) (* (* y 4.0) (- (* z z) t))))

C

double code(double x, double y, double z, double t) {
	return (x * x) - ((y * 4.0) * ((z * z) - t));
}

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 * x) - ((y * 4.0d0) * ((z * z) - t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * x) - ((y * 4.0) * ((z * z) - t));
}

Python

def code(x, y, z, t):
	return (x * x) - ((y * 4.0) * ((z * z) - t))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * x) - Float64(Float64(y * 4.0) * Float64(Float64(z * z) - t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * x) - ((y * 4.0) * ((z * z) - t));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * x), $MachinePrecision] - N[(N[(y * 4.0), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* x x) (* (* y 4.0) (- (* z z) t))))

C

double code(double x, double y, double z, double t) {
	return (x * x) - ((y * 4.0) * ((z * z) - t));
}

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 * x) - ((y * 4.0d0) * ((z * z) - t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * x) - ((y * 4.0) * ((z * z) - t));
}

Python

def code(x, y, z, t):
	return (x * x) - ((y * 4.0) * ((z * z) - t))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * x) - Float64(Float64(y * 4.0) * Float64(Float64(z * z) - t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * x) - ((y * 4.0) * ((z * z) - t));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * x), $MachinePrecision] - N[(N[(y * 4.0), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+302}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 1e+302)
   (fma x x (* (- (* z z) t) (* y -4.0)))
   (* -4.0 (* z (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 1e+302) {
		tmp = fma(x, x, (((z * z) - t) * (y * -4.0)));
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 1e+302)
		tmp = fma(x, x, Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0)));
	else
		tmp = Float64(-4.0 * Float64(z * Float64(z * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 1e+302], N[(x * x + N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 1.0000000000000001e302

   1. Initial program 98.3%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]
   2. Step-by-step derivation

      1. fma-neg 98.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, -\left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\right)} \]

      2. *-commutative 98.8%

         \[\leadsto \mathsf{fma}\left(x, x, -\color{blue}{\left(z \cdot z - t\right) \cdot \left(y \cdot 4\right)}\right) \]

      3. distribute-rgt-neg-in 98.8%

         \[\leadsto \mathsf{fma}\left(x, x, \color{blue}{\left(z \cdot z - t\right) \cdot \left(-y \cdot 4\right)}\right) \]

      4. distribute-rgt-neg-in 98.8%

         \[\leadsto \mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \color{blue}{\left(y \cdot \left(-4\right)\right)}\right) \]

      5. metadata-eval 98.8%

         \[\leadsto \mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot \color{blue}{-4}\right)\right) \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)} \]

   if 1.0000000000000001e302 < (*.f64 z z)

   1. Initial program 62.4%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around inf 65.2%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot {z}^{2}\right)} \]
   3. Step-by-step derivation

      1. unpow2 65.2%

         \[\leadsto -4 \cdot \left(y \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

      2. *-commutative 65.2%

         \[\leadsto -4 \cdot \color{blue}{\left(\left(z \cdot z\right) \cdot y\right)} \]

      3. associate-*l* 82.2%

         \[\leadsto -4 \cdot \color{blue}{\left(z \cdot \left(z \cdot y\right)\right)} \]

   4. Simplified 82.2%

      \[\leadsto \color{blue}{-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+302}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 2: 61.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;x \cdot x \leq 8 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 4.9 \cdot 10^{-167}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{elif}\;x \cdot x \leq 5.2 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -4.0 (* z (* z y)))))
   (if (<= (* x x) 8e-293)
     t_1
     (if (<= (* x x) 4.9e-167)
       (* t (* y 4.0))
       (if (<= (* x x) 5.2e+118) t_1 (* x x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -4.0 * (z * (z * y));
	double tmp;
	if ((x * x) <= 8e-293) {
		tmp = t_1;
	} else if ((x * x) <= 4.9e-167) {
		tmp = t * (y * 4.0);
	} else if ((x * x) <= 5.2e+118) {
		tmp = t_1;
	} else {
		tmp = x * 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 = (-4.0d0) * (z * (z * y))
    if ((x * x) <= 8d-293) then
        tmp = t_1
    else if ((x * x) <= 4.9d-167) then
        tmp = t * (y * 4.0d0)
    else if ((x * x) <= 5.2d+118) then
        tmp = t_1
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -4.0 * (z * (z * y));
	double tmp;
	if ((x * x) <= 8e-293) {
		tmp = t_1;
	} else if ((x * x) <= 4.9e-167) {
		tmp = t * (y * 4.0);
	} else if ((x * x) <= 5.2e+118) {
		tmp = t_1;
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -4.0 * (z * (z * y))
	tmp = 0
	if (x * x) <= 8e-293:
		tmp = t_1
	elif (x * x) <= 4.9e-167:
		tmp = t * (y * 4.0)
	elif (x * x) <= 5.2e+118:
		tmp = t_1
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-4.0 * Float64(z * Float64(z * y)))
	tmp = 0.0
	if (Float64(x * x) <= 8e-293)
		tmp = t_1;
	elseif (Float64(x * x) <= 4.9e-167)
		tmp = Float64(t * Float64(y * 4.0));
	elseif (Float64(x * x) <= 5.2e+118)
		tmp = t_1;
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -4.0 * (z * (z * y));
	tmp = 0.0;
	if ((x * x) <= 8e-293)
		tmp = t_1;
	elseif ((x * x) <= 4.9e-167)
		tmp = t * (y * 4.0);
	elseif ((x * x) <= 5.2e+118)
		tmp = t_1;
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-4.0 * N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * x), $MachinePrecision], 8e-293], t$95$1, If[LessEqual[N[(x * x), $MachinePrecision], 4.9e-167], N[(t * N[(y * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * x), $MachinePrecision], 5.2e+118], t$95$1, N[(x * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x x) < 8.0000000000000004e-293 or 4.90000000000000003e-167 < (*.f64 x x) < 5.20000000000000032e118

   1. Initial program 86.4%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around inf 42.8%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot {z}^{2}\right)} \]
   3. Step-by-step derivation

      1. unpow2 42.8%

         \[\leadsto -4 \cdot \left(y \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

      2. *-commutative 42.8%

         \[\leadsto -4 \cdot \color{blue}{\left(\left(z \cdot z\right) \cdot y\right)} \]

      3. associate-*l* 56.3%

         \[\leadsto -4 \cdot \color{blue}{\left(z \cdot \left(z \cdot y\right)\right)} \]

   4. Simplified 56.3%

      \[\leadsto \color{blue}{-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)} \]

   if 8.0000000000000004e-293 < (*.f64 x x) < 4.90000000000000003e-167

   1. Initial program 96.7%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in t around inf 61.7%

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

      1. associate-*r* 61.7%

         \[\leadsto \color{blue}{\left(4 \cdot y\right) \cdot t} \]

   4. Simplified 61.7%

      \[\leadsto \color{blue}{\left(4 \cdot y\right) \cdot t} \]

   if 5.20000000000000032e118 < (*.f64 x x)

   1. Initial program 88.2%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in x around inf 88.0%

      \[\leadsto \color{blue}{{x}^{2}} \]
   3. Step-by-step derivation

      1. unpow2 88.0%

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

   4. Simplified 88.0%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 8 \cdot 10^{-293}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \cdot x \leq 4.9 \cdot 10^{-167}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{elif}\;x \cdot x \leq 5.2 \cdot 10^{+118}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 3: 89.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{-6}:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 10^{+302}:\\ \;\;\;\;x \cdot x - \left(z \cdot z\right) \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 4e-6)
   (- (* x x) (* t (* y -4.0)))
   (if (<= (* z z) 1e+302)
     (- (* x x) (* (* z z) (* y 4.0)))
     (* -4.0 (* z (* z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 4e-6) {
		tmp = (x * x) - (t * (y * -4.0));
	} else if ((z * z) <= 1e+302) {
		tmp = (x * x) - ((z * z) * (y * 4.0));
	} else {
		tmp = -4.0 * (z * (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 ((z * z) <= 4d-6) then
        tmp = (x * x) - (t * (y * (-4.0d0)))
    else if ((z * z) <= 1d+302) then
        tmp = (x * x) - ((z * z) * (y * 4.0d0))
    else
        tmp = (-4.0d0) * (z * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 4e-6) {
		tmp = (x * x) - (t * (y * -4.0));
	} else if ((z * z) <= 1e+302) {
		tmp = (x * x) - ((z * z) * (y * 4.0));
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * z) <= 4e-6:
		tmp = (x * x) - (t * (y * -4.0))
	elif (z * z) <= 1e+302:
		tmp = (x * x) - ((z * z) * (y * 4.0))
	else:
		tmp = -4.0 * (z * (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 4e-6)
		tmp = Float64(Float64(x * x) - Float64(t * Float64(y * -4.0)));
	elseif (Float64(z * z) <= 1e+302)
		tmp = Float64(Float64(x * x) - Float64(Float64(z * z) * Float64(y * 4.0)));
	else
		tmp = Float64(-4.0 * Float64(z * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * z) <= 4e-6)
		tmp = (x * x) - (t * (y * -4.0));
	elseif ((z * z) <= 1e+302)
		tmp = (x * x) - ((z * z) * (y * 4.0));
	else
		tmp = -4.0 * (z * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 4e-6], N[(N[(x * x), $MachinePrecision] - N[(t * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * z), $MachinePrecision], 1e+302], N[(N[(x * x), $MachinePrecision] - N[(N[(z * z), $MachinePrecision] * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z z) < 3.99999999999999982e-6

   1. Initial program 98.3%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around 0 92.9%

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

      1. associate-*r* 92.9%

         \[\leadsto x \cdot x - \color{blue}{\left(-4 \cdot y\right) \cdot t} \]

   4. Simplified 92.9%

      \[\leadsto x \cdot x - \color{blue}{\left(-4 \cdot y\right) \cdot t} \]

   if 3.99999999999999982e-6 < (*.f64 z z) < 1.0000000000000001e302

   1. Initial program 98.3%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around inf 87.5%

      \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{{z}^{2}} \]
   3. Step-by-step derivation

      1. unpow2 87.5%

         \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(z \cdot z\right)} \]

   4. Simplified 87.5%

      \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(z \cdot z\right)} \]

   if 1.0000000000000001e302 < (*.f64 z z)

   1. Initial program 62.4%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around inf 65.2%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot {z}^{2}\right)} \]
   3. Step-by-step derivation

      1. unpow2 65.2%

         \[\leadsto -4 \cdot \left(y \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

      2. *-commutative 65.2%

         \[\leadsto -4 \cdot \color{blue}{\left(\left(z \cdot z\right) \cdot y\right)} \]

      3. associate-*l* 82.2%

         \[\leadsto -4 \cdot \color{blue}{\left(z \cdot \left(z \cdot y\right)\right)} \]

   4. Simplified 82.2%

      \[\leadsto \color{blue}{-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{-6}:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 10^{+302}:\\ \;\;\;\;x \cdot x - \left(z \cdot z\right) \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 4: 59.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot 4\right)\\ \mathbf{if}\;x \cdot x \leq 1.65 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 7.2 \cdot 10^{-47}:\\ \;\;\;\;-4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \mathbf{elif}\;x \cdot x \leq 2.35 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (* y 4.0))))
   (if (<= (* x x) 1.65e-81)
     t_1
     (if (<= (* x x) 7.2e-47)
       (* -4.0 (* (* z z) y))
       (if (<= (* x x) 2.35e+98) t_1 (* x x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y * 4.0);
	double tmp;
	if ((x * x) <= 1.65e-81) {
		tmp = t_1;
	} else if ((x * x) <= 7.2e-47) {
		tmp = -4.0 * ((z * z) * y);
	} else if ((x * x) <= 2.35e+98) {
		tmp = t_1;
	} else {
		tmp = x * 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 = t * (y * 4.0d0)
    if ((x * x) <= 1.65d-81) then
        tmp = t_1
    else if ((x * x) <= 7.2d-47) then
        tmp = (-4.0d0) * ((z * z) * y)
    else if ((x * x) <= 2.35d+98) then
        tmp = t_1
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y * 4.0);
	double tmp;
	if ((x * x) <= 1.65e-81) {
		tmp = t_1;
	} else if ((x * x) <= 7.2e-47) {
		tmp = -4.0 * ((z * z) * y);
	} else if ((x * x) <= 2.35e+98) {
		tmp = t_1;
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y * 4.0)
	tmp = 0
	if (x * x) <= 1.65e-81:
		tmp = t_1
	elif (x * x) <= 7.2e-47:
		tmp = -4.0 * ((z * z) * y)
	elif (x * x) <= 2.35e+98:
		tmp = t_1
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y * 4.0))
	tmp = 0.0
	if (Float64(x * x) <= 1.65e-81)
		tmp = t_1;
	elseif (Float64(x * x) <= 7.2e-47)
		tmp = Float64(-4.0 * Float64(Float64(z * z) * y));
	elseif (Float64(x * x) <= 2.35e+98)
		tmp = t_1;
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y * 4.0);
	tmp = 0.0;
	if ((x * x) <= 1.65e-81)
		tmp = t_1;
	elseif ((x * x) <= 7.2e-47)
		tmp = -4.0 * ((z * z) * y);
	elseif ((x * x) <= 2.35e+98)
		tmp = t_1;
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * x), $MachinePrecision], 1.65e-81], t$95$1, If[LessEqual[N[(x * x), $MachinePrecision], 7.2e-47], N[(-4.0 * N[(N[(z * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * x), $MachinePrecision], 2.35e+98], t$95$1, N[(x * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x x) < 1.64999999999999994e-81 or 7.19999999999999982e-47 < (*.f64 x x) < 2.34999999999999985e98

   1. Initial program 88.3%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in t around inf 50.3%

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

      1. associate-*r* 50.3%

         \[\leadsto \color{blue}{\left(4 \cdot y\right) \cdot t} \]

   4. Simplified 50.3%

      \[\leadsto \color{blue}{\left(4 \cdot y\right) \cdot t} \]

   if 1.64999999999999994e-81 < (*.f64 x x) < 7.19999999999999982e-47

   1. Initial program 99.8%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around inf 75.5%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot {z}^{2}\right)} \]
   3. Step-by-step derivation

      1. unpow2 75.5%

         \[\leadsto -4 \cdot \left(y \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

   4. Simplified 75.5%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot \left(z \cdot z\right)\right)} \]

   if 2.34999999999999985e98 < (*.f64 x x)

   1. Initial program 87.4%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in x around inf 87.2%

      \[\leadsto \color{blue}{{x}^{2}} \]
   3. Step-by-step derivation

      1. unpow2 87.2%

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

   4. Simplified 87.2%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 1.65 \cdot 10^{-81}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{elif}\;x \cdot x \leq 7.2 \cdot 10^{-47}:\\ \;\;\;\;-4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \mathbf{elif}\;x \cdot x \leq 2.35 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 5: 95.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+302}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 1e+302)
   (+ (* x x) (* (* y 4.0) (- t (* z z))))
   (* -4.0 (* z (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 1e+302) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = -4.0 * (z * (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 ((z * z) <= 1d+302) then
        tmp = (x * x) + ((y * 4.0d0) * (t - (z * z)))
    else
        tmp = (-4.0d0) * (z * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 1e+302) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * z) <= 1e+302:
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)))
	else:
		tmp = -4.0 * (z * (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 1e+302)
		tmp = Float64(Float64(x * x) + Float64(Float64(y * 4.0) * Float64(t - Float64(z * z))));
	else
		tmp = Float64(-4.0 * Float64(z * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * z) <= 1e+302)
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	else
		tmp = -4.0 * (z * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 1e+302], N[(N[(x * x), $MachinePrecision] + N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 1.0000000000000001e302

   1. Initial program 98.3%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   if 1.0000000000000001e302 < (*.f64 z z)

   1. Initial program 62.4%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around inf 65.2%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot {z}^{2}\right)} \]
   3. Step-by-step derivation

      1. unpow2 65.2%

         \[\leadsto -4 \cdot \left(y \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

      2. *-commutative 65.2%

         \[\leadsto -4 \cdot \color{blue}{\left(\left(z \cdot z\right) \cdot y\right)} \]

      3. associate-*l* 82.2%

         \[\leadsto -4 \cdot \color{blue}{\left(z \cdot \left(z \cdot y\right)\right)} \]

   4. Simplified 82.2%

      \[\leadsto \color{blue}{-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+302}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 6: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2.75 \cdot 10^{+109}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x x) 2.75e+109) (* (- (* z z) t) (* y -4.0)) (* x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 2.75e+109) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else {
		tmp = x * 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 ((x * x) <= 2.75d+109) then
        tmp = ((z * z) - t) * (y * (-4.0d0))
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 2.75e+109) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x * x) <= 2.75e+109:
		tmp = ((z * z) - t) * (y * -4.0)
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * x) <= 2.75e+109)
		tmp = Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * x) <= 2.75e+109)
		tmp = ((z * z) - t) * (y * -4.0);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 2.75e+109], N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision], N[(x * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 2.7499999999999999e109

   1. Initial program 88.4%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in x around 0 79.6%

      \[\leadsto \color{blue}{-4 \cdot \left(\left({z}^{2} - t\right) \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative 79.6%

         \[\leadsto \color{blue}{\left(\left({z}^{2} - t\right) \cdot y\right) \cdot -4} \]

      2. *-commutative 79.6%

         \[\leadsto \color{blue}{\left(y \cdot \left({z}^{2} - t\right)\right)} \cdot -4 \]

      3. unpow2 79.6%

         \[\leadsto \left(y \cdot \left(\color{blue}{z \cdot z} - t\right)\right) \cdot -4 \]

      4. *-commutative 79.6%

         \[\leadsto \color{blue}{\left(\left(z \cdot z - t\right) \cdot y\right)} \cdot -4 \]

      5. associate-*l* 79.6%

         \[\leadsto \color{blue}{\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)} \]

   4. Simplified 79.6%

      \[\leadsto \color{blue}{\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)} \]

   if 2.7499999999999999e109 < (*.f64 x x)

   1. Initial program 88.2%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in x around inf 88.0%

      \[\leadsto \color{blue}{{x}^{2}} \]
   3. Step-by-step derivation

      1. unpow2 88.0%

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

   4. Simplified 88.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2.75 \cdot 10^{+109}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 7: 82.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 8 \cdot 10^{+87}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x x) 8e+87)
   (* (- (* z z) t) (* y -4.0))
   (- (* x x) (* t (* y -4.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 8e+87) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else {
		tmp = (x * x) - (t * (y * -4.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x * x) <= 8d+87) then
        tmp = ((z * z) - t) * (y * (-4.0d0))
    else
        tmp = (x * x) - (t * (y * (-4.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 8e+87) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else {
		tmp = (x * x) - (t * (y * -4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x * x) <= 8e+87:
		tmp = ((z * z) - t) * (y * -4.0)
	else:
		tmp = (x * x) - (t * (y * -4.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * x) <= 8e+87)
		tmp = Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0));
	else
		tmp = Float64(Float64(x * x) - Float64(t * Float64(y * -4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * x) <= 8e+87)
		tmp = ((z * z) - t) * (y * -4.0);
	else
		tmp = (x * x) - (t * (y * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 8e+87], N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] - N[(t * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 7.9999999999999997e87

   1. Initial program 89.3%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in x around 0 80.1%

      \[\leadsto \color{blue}{-4 \cdot \left(\left({z}^{2} - t\right) \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative 80.1%

         \[\leadsto \color{blue}{\left(\left({z}^{2} - t\right) \cdot y\right) \cdot -4} \]

      2. *-commutative 80.1%

         \[\leadsto \color{blue}{\left(y \cdot \left({z}^{2} - t\right)\right)} \cdot -4 \]

      3. unpow2 80.1%

         \[\leadsto \left(y \cdot \left(\color{blue}{z \cdot z} - t\right)\right) \cdot -4 \]

      4. *-commutative 80.1%

         \[\leadsto \color{blue}{\left(\left(z \cdot z - t\right) \cdot y\right)} \cdot -4 \]

      5. associate-*l* 80.1%

         \[\leadsto \color{blue}{\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)} \]

   4. Simplified 80.1%

      \[\leadsto \color{blue}{\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)} \]

   if 7.9999999999999997e87 < (*.f64 x x)

   1. Initial program 87.0%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around 0 90.4%

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

      1. associate-*r* 90.4%

         \[\leadsto x \cdot x - \color{blue}{\left(-4 \cdot y\right) \cdot t} \]

   4. Simplified 90.4%

      \[\leadsto x \cdot x - \color{blue}{\left(-4 \cdot y\right) \cdot t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 8 \cdot 10^{+87}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \end{array} \]

Alternative 8: 59.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 6.1 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x x) 6.1e+97) (* t (* y 4.0)) (* x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 6.1e+97) {
		tmp = t * (y * 4.0);
	} else {
		tmp = x * 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 ((x * x) <= 6.1d+97) then
        tmp = t * (y * 4.0d0)
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 6.1e+97) {
		tmp = t * (y * 4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x * x) <= 6.1e+97:
		tmp = t * (y * 4.0)
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * x) <= 6.1e+97)
		tmp = Float64(t * Float64(y * 4.0));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * x) <= 6.1e+97)
		tmp = t * (y * 4.0);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 6.1e+97], N[(t * N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(x * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 6.1e97

   1. Initial program 88.9%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in t around inf 48.4%

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

      1. associate-*r* 48.4%

         \[\leadsto \color{blue}{\left(4 \cdot y\right) \cdot t} \]

   4. Simplified 48.4%

      \[\leadsto \color{blue}{\left(4 \cdot y\right) \cdot t} \]

   if 6.1e97 < (*.f64 x x)

   1. Initial program 87.4%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in x around inf 87.2%

      \[\leadsto \color{blue}{{x}^{2}} \]
   3. Step-by-step derivation

      1. unpow2 87.2%

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

   4. Simplified 87.2%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 6.1 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 9: 41.0% accurate, 4.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * 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 * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x * x), $MachinePrecision]

Derivation

1. Initial program 88.3%

   \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

2. Taylor expanded in x around inf 42.3%

   \[\leadsto \color{blue}{{x}^{2}} \]
3. Step-by-step derivation

   1. unpow2 42.3%

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

4. Simplified 42.3%

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

5. Final simplification 42.3%

   \[\leadsto x \cdot x \]

Developer target: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* x x) (* 4.0 (* y (- (* z z) t)))))

C

double code(double x, double y, double z, double t) {
	return (x * x) - (4.0 * (y * ((z * z) - t)));
}

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 * x) - (4.0d0 * (y * ((z * z) - t)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * x) - (4.0 * (y * ((z * z) - t)));
}

Python

def code(x, y, z, t):
	return (x * x) - (4.0 * (y * ((z * z) - t)))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * x) - Float64(4.0 * Float64(y * Float64(Float64(z * z) - t))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * x) - (4.0 * (y * ((z * z) - t)));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * x), $MachinePrecision] - N[(4.0 * N[(y * N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023244 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"
  :precision binary64

  :herbie-target
  (- (* x x) (* 4.0 (* y (- (* z z) t))))

  (- (* x x) (* (* y 4.0) (- (* z z) t))))