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

Percentage Accurate: 90.9% → 95.6%

Time: 6.5s

Alternatives: 8

Speedup: 0.9×

• 49.8% 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: 90.9% 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: 95.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} z = |z|\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{+173}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= z 3.8e+173)
   (fma x x (* (- (* z z) t) (* y -4.0)))
   (* -4.0 (* z (* z y)))))

C

z = abs(z);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3.8e+173) {
		tmp = fma(x, x, (((z * z) - t) * (y * -4.0)));
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Julia

z = abs(z)
function code(x, y, z, t)
	tmp = 0.0
	if (z <= 3.8e+173)
		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

NOTE: z should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[z, 3.8e+173], 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 z < 3.80000000000000011e173

   1. Initial program 97.0%

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

      1. fma-neg 97.0%

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

      2. *-commutative 97.0%

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

      3. distribute-rgt-neg-in 97.0%

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

      4. distribute-rgt-neg-in 97.0%

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

      5. metadata-eval 97.0%

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

   3. Simplified 97.0%

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

   if 3.80000000000000011e173 < z

   1. Initial program 78.1%

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

   2. Taylor expanded in z around inf 81.5%

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

      1. unpow2 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-*l* 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{+173}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 2: 56.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} z = |z|\\ \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot 4\right)\\ \mathbf{if}\;z \leq 6 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-88}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \leq 0.00031:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+76} \lor \neg \left(z \leq 1.4 \cdot 10^{+95}\right):\\ \;\;\;\;-4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (* y 4.0))))
   (if (<= z 6e-188)
     t_1
     (if (<= z 7.8e-88)
       (* x x)
       (if (<= z 0.00031)
         t_1
         (if (or (<= z 8.6e+76) (not (<= z 1.4e+95)))
           (* -4.0 (* (* z z) y))
           (* x x)))))))

C

z = abs(z);
double code(double x, double y, double z, double t) {
	double t_1 = t * (y * 4.0);
	double tmp;
	if (z <= 6e-188) {
		tmp = t_1;
	} else if (z <= 7.8e-88) {
		tmp = x * x;
	} else if (z <= 0.00031) {
		tmp = t_1;
	} else if ((z <= 8.6e+76) || !(z <= 1.4e+95)) {
		tmp = -4.0 * ((z * z) * y);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Fortran

NOTE: z should be positive before calling this function
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 (z <= 6d-188) then
        tmp = t_1
    else if (z <= 7.8d-88) then
        tmp = x * x
    else if (z <= 0.00031d0) then
        tmp = t_1
    else if ((z <= 8.6d+76) .or. (.not. (z <= 1.4d+95))) then
        tmp = (-4.0d0) * ((z * z) * y)
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

z = Math.abs(z);
public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y * 4.0);
	double tmp;
	if (z <= 6e-188) {
		tmp = t_1;
	} else if (z <= 7.8e-88) {
		tmp = x * x;
	} else if (z <= 0.00031) {
		tmp = t_1;
	} else if ((z <= 8.6e+76) || !(z <= 1.4e+95)) {
		tmp = -4.0 * ((z * z) * y);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

z = abs(z)
def code(x, y, z, t):
	t_1 = t * (y * 4.0)
	tmp = 0
	if z <= 6e-188:
		tmp = t_1
	elif z <= 7.8e-88:
		tmp = x * x
	elif z <= 0.00031:
		tmp = t_1
	elif (z <= 8.6e+76) or not (z <= 1.4e+95):
		tmp = -4.0 * ((z * z) * y)
	else:
		tmp = x * x
	return tmp

Julia

z = abs(z)
function code(x, y, z, t)
	t_1 = Float64(t * Float64(y * 4.0))
	tmp = 0.0
	if (z <= 6e-188)
		tmp = t_1;
	elseif (z <= 7.8e-88)
		tmp = Float64(x * x);
	elseif (z <= 0.00031)
		tmp = t_1;
	elseif ((z <= 8.6e+76) || !(z <= 1.4e+95))
		tmp = Float64(-4.0 * Float64(Float64(z * z) * y));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

z = abs(z)
function tmp_2 = code(x, y, z, t)
	t_1 = t * (y * 4.0);
	tmp = 0.0;
	if (z <= 6e-188)
		tmp = t_1;
	elseif (z <= 7.8e-88)
		tmp = x * x;
	elseif (z <= 0.00031)
		tmp = t_1;
	elseif ((z <= 8.6e+76) || ~((z <= 1.4e+95)))
		tmp = -4.0 * ((z * z) * y);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z should be positive before calling this function
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 6e-188], t$95$1, If[LessEqual[z, 7.8e-88], N[(x * x), $MachinePrecision], If[LessEqual[z, 0.00031], t$95$1, If[Or[LessEqual[z, 8.6e+76], N[Not[LessEqual[z, 1.4e+95]], $MachinePrecision]], N[(-4.0 * N[(N[(z * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < 6.00000000000000033e-188 or 7.79999999999999985e-88 < z < 3.1e-4

   1. Initial program 97.0%

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

   2. Taylor expanded in t around inf 42.0%

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

      1. associate-*r* 42.0%

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

   4. Simplified 42.0%

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

   if 6.00000000000000033e-188 < z < 7.79999999999999985e-88 or 8.59999999999999957e76 < z < 1.3999999999999999e95

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 74.5%

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

      1. unpow2 74.5%

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

   4. Simplified 74.5%

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

   if 3.1e-4 < z < 8.59999999999999957e76 or 1.3999999999999999e95 < z

   1. Initial program 87.9%

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

   2. Taylor expanded in z around inf 68.6%

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

      1. unpow2 68.6%

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

   4. Simplified 68.6%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6 \cdot 10^{-188}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-88}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \leq 0.00031:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+76} \lor \neg \left(z \leq 1.4 \cdot 10^{+95}\right):\\ \;\;\;\;-4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 3: 59.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} z = |z|\\ \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot 4\right)\\ \mathbf{if}\;z \leq 3 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-88}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \leq 0.00088:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;-4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+95}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (* y 4.0))))
   (if (<= z 3e-186)
     t_1
     (if (<= z 1.45e-88)
       (* x x)
       (if (<= z 0.00088)
         t_1
         (if (<= z 8.5e+74)
           (* -4.0 (* (* z z) y))
           (if (<= z 1.4e+95) (* x x) (* -4.0 (* z (* z y))))))))))

C

z = abs(z);
double code(double x, double y, double z, double t) {
	double t_1 = t * (y * 4.0);
	double tmp;
	if (z <= 3e-186) {
		tmp = t_1;
	} else if (z <= 1.45e-88) {
		tmp = x * x;
	} else if (z <= 0.00088) {
		tmp = t_1;
	} else if (z <= 8.5e+74) {
		tmp = -4.0 * ((z * z) * y);
	} else if (z <= 1.4e+95) {
		tmp = x * x;
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Fortran

NOTE: z should be positive before calling this function
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 (z <= 3d-186) then
        tmp = t_1
    else if (z <= 1.45d-88) then
        tmp = x * x
    else if (z <= 0.00088d0) then
        tmp = t_1
    else if (z <= 8.5d+74) then
        tmp = (-4.0d0) * ((z * z) * y)
    else if (z <= 1.4d+95) then
        tmp = x * x
    else
        tmp = (-4.0d0) * (z * (z * y))
    end if
    code = tmp
end function

Java

z = Math.abs(z);
public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y * 4.0);
	double tmp;
	if (z <= 3e-186) {
		tmp = t_1;
	} else if (z <= 1.45e-88) {
		tmp = x * x;
	} else if (z <= 0.00088) {
		tmp = t_1;
	} else if (z <= 8.5e+74) {
		tmp = -4.0 * ((z * z) * y);
	} else if (z <= 1.4e+95) {
		tmp = x * x;
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Python

z = abs(z)
def code(x, y, z, t):
	t_1 = t * (y * 4.0)
	tmp = 0
	if z <= 3e-186:
		tmp = t_1
	elif z <= 1.45e-88:
		tmp = x * x
	elif z <= 0.00088:
		tmp = t_1
	elif z <= 8.5e+74:
		tmp = -4.0 * ((z * z) * y)
	elif z <= 1.4e+95:
		tmp = x * x
	else:
		tmp = -4.0 * (z * (z * y))
	return tmp

Julia

z = abs(z)
function code(x, y, z, t)
	t_1 = Float64(t * Float64(y * 4.0))
	tmp = 0.0
	if (z <= 3e-186)
		tmp = t_1;
	elseif (z <= 1.45e-88)
		tmp = Float64(x * x);
	elseif (z <= 0.00088)
		tmp = t_1;
	elseif (z <= 8.5e+74)
		tmp = Float64(-4.0 * Float64(Float64(z * z) * y));
	elseif (z <= 1.4e+95)
		tmp = Float64(x * x);
	else
		tmp = Float64(-4.0 * Float64(z * Float64(z * y)));
	end
	return tmp
end

MATLAB

z = abs(z)
function tmp_2 = code(x, y, z, t)
	t_1 = t * (y * 4.0);
	tmp = 0.0;
	if (z <= 3e-186)
		tmp = t_1;
	elseif (z <= 1.45e-88)
		tmp = x * x;
	elseif (z <= 0.00088)
		tmp = t_1;
	elseif (z <= 8.5e+74)
		tmp = -4.0 * ((z * z) * y);
	elseif (z <= 1.4e+95)
		tmp = x * x;
	else
		tmp = -4.0 * (z * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z should be positive before calling this function
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 3e-186], t$95$1, If[LessEqual[z, 1.45e-88], N[(x * x), $MachinePrecision], If[LessEqual[z, 0.00088], t$95$1, If[LessEqual[z, 8.5e+74], N[(-4.0 * N[(N[(z * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+95], N[(x * x), $MachinePrecision], N[(-4.0 * N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < 3.0000000000000001e-186 or 1.4500000000000001e-88 < z < 8.80000000000000031e-4

   1. Initial program 97.0%

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

   2. Taylor expanded in t around inf 42.0%

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

      1. associate-*r* 42.0%

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

   4. Simplified 42.0%

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

   if 3.0000000000000001e-186 < z < 1.4500000000000001e-88 or 8.50000000000000028e74 < z < 1.3999999999999999e95

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 74.5%

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

      1. unpow2 74.5%

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

   4. Simplified 74.5%

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

   if 8.80000000000000031e-4 < z < 8.50000000000000028e74

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 49.3%

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

      1. unpow2 49.3%

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

   4. Simplified 49.3%

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

   if 1.3999999999999999e95 < z

   1. Initial program 82.0%

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

   2. Taylor expanded in z around inf 78.0%

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

      1. unpow2 78.0%

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

      2. *-commutative 78.0%

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

      3. associate-*l* 91.6%

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

   4. Simplified 91.6%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3 \cdot 10^{-186}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-88}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \leq 0.00088:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;-4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+95}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 4: 85.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} z = |z|\\ \\ \begin{array}{l} t_1 := x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{if}\;z \leq 440000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+72}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x x) (* t (* y -4.0)))))
   (if (<= z 440000.0)
     t_1
     (if (<= z 8.5e+72)
       (* (- (* z z) t) (* y -4.0))
       (if (<= z 4.9e+95) t_1 (* -4.0 (* z (* z y))))))))

C

z = abs(z);
double code(double x, double y, double z, double t) {
	double t_1 = (x * x) - (t * (y * -4.0));
	double tmp;
	if (z <= 440000.0) {
		tmp = t_1;
	} else if (z <= 8.5e+72) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else if (z <= 4.9e+95) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Fortran

NOTE: z should be positive before calling this function
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 * x) - (t * (y * (-4.0d0)))
    if (z <= 440000.0d0) then
        tmp = t_1
    else if (z <= 8.5d+72) then
        tmp = ((z * z) - t) * (y * (-4.0d0))
    else if (z <= 4.9d+95) then
        tmp = t_1
    else
        tmp = (-4.0d0) * (z * (z * y))
    end if
    code = tmp
end function

Java

z = Math.abs(z);
public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) - (t * (y * -4.0));
	double tmp;
	if (z <= 440000.0) {
		tmp = t_1;
	} else if (z <= 8.5e+72) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else if (z <= 4.9e+95) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Python

z = abs(z)
def code(x, y, z, t):
	t_1 = (x * x) - (t * (y * -4.0))
	tmp = 0
	if z <= 440000.0:
		tmp = t_1
	elif z <= 8.5e+72:
		tmp = ((z * z) - t) * (y * -4.0)
	elif z <= 4.9e+95:
		tmp = t_1
	else:
		tmp = -4.0 * (z * (z * y))
	return tmp

Julia

z = abs(z)
function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) - Float64(t * Float64(y * -4.0)))
	tmp = 0.0
	if (z <= 440000.0)
		tmp = t_1;
	elseif (z <= 8.5e+72)
		tmp = Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0));
	elseif (z <= 4.9e+95)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(z * Float64(z * y)));
	end
	return tmp
end

MATLAB

z = abs(z)
function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) - (t * (y * -4.0));
	tmp = 0.0;
	if (z <= 440000.0)
		tmp = t_1;
	elseif (z <= 8.5e+72)
		tmp = ((z * z) - t) * (y * -4.0);
	elseif (z <= 4.9e+95)
		tmp = t_1;
	else
		tmp = -4.0 * (z * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z should be positive before calling this function
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] - N[(t * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 440000.0], t$95$1, If[LessEqual[z, 8.5e+72], N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+95], t$95$1, N[(-4.0 * N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < 4.4e5 or 8.5000000000000004e72 < z < 4.8999999999999999e95

   1. Initial program 97.4%

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

   2. Taylor expanded in z around 0 81.6%

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

      1. associate-*r* 81.6%

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

   4. Simplified 81.6%

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

   if 4.4e5 < z < 8.5000000000000004e72

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 69.8%

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

      1. *-commutative 69.8%

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

      2. *-commutative 69.8%

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

      3. unpow2 69.8%

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

      4. *-commutative 69.8%

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

      5. associate-*l* 69.8%

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

   4. Simplified 69.8%

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

   if 4.8999999999999999e95 < z

   1. Initial program 82.0%

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

   2. Taylor expanded in z around inf 78.0%

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

      1. unpow2 78.0%

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

      2. *-commutative 78.0%

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

      3. associate-*l* 91.6%

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

   4. Simplified 91.6%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 440000:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+72}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+95}:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 5: 95.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} z = |z|\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{+173}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= z 4.5e+173)
   (+ (* x x) (* (* y 4.0) (- t (* z z))))
   (* -4.0 (* z (* z y)))))

C

z = abs(z);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 4.5e+173) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Fortran

NOTE: z should be positive before calling this function
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 <= 4.5d+173) then
        tmp = (x * x) + ((y * 4.0d0) * (t - (z * z)))
    else
        tmp = (-4.0d0) * (z * (z * y))
    end if
    code = tmp
end function

Java

z = Math.abs(z);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 4.5e+173) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Python

z = abs(z)
def code(x, y, z, t):
	tmp = 0
	if z <= 4.5e+173:
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)))
	else:
		tmp = -4.0 * (z * (z * y))
	return tmp

Julia

z = abs(z)
function code(x, y, z, t)
	tmp = 0.0
	if (z <= 4.5e+173)
		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

z = abs(z)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 4.5e+173)
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	else
		tmp = -4.0 * (z * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[z, 4.5e+173], 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 z < 4.5000000000000002e173

   1. Initial program 97.0%

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

   if 4.5000000000000002e173 < z

   1. Initial program 78.1%

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

   2. Taylor expanded in z around inf 81.5%

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

      1. unpow2 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-*l* 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{+173}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 6: 80.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} z = |z|\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2.9 \cdot 10^{+142}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= (* x x) 2.9e+142) (* (- (* z z) t) (* y -4.0)) (* x x)))

C

z = abs(z);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 2.9e+142) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Fortran

NOTE: z should be positive before calling this function
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) <= 2.9d+142) then
        tmp = ((z * z) - t) * (y * (-4.0d0))
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

z = Math.abs(z);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 2.9e+142) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

z = abs(z)
def code(x, y, z, t):
	tmp = 0
	if (x * x) <= 2.9e+142:
		tmp = ((z * z) - t) * (y * -4.0)
	else:
		tmp = x * x
	return tmp

Julia

z = abs(z)
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * x) <= 2.9e+142)
		tmp = Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

z = abs(z)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * x) <= 2.9e+142)
		tmp = ((z * z) - t) * (y * -4.0);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 2.9e+142], 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) < 2.90000000000000013e142

   1. Initial program 93.8%

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

   2. Taylor expanded in x around 0 80.4%

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

      1. *-commutative 80.4%

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

      2. *-commutative 80.4%

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

      3. unpow2 80.4%

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

      4. *-commutative 80.4%

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

      5. associate-*l* 80.4%

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

   4. Simplified 80.4%

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

   if 2.90000000000000013e142 < (*.f64 x x)

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf 83.9%

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

      1. unpow2 83.9%

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

   4. Simplified 83.9%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2.9 \cdot 10^{+142}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 7: 59.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} z = |z|\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 8 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z t)
 :precision binary64
 (if (<= (* x x) 8e-74) (* t (* y 4.0)) (* x x)))

C

z = abs(z);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 8e-74) {
		tmp = t * (y * 4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Fortran

NOTE: z should be positive before calling this function
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-74) then
        tmp = t * (y * 4.0d0)
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

z = Math.abs(z);
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 8e-74) {
		tmp = t * (y * 4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

z = abs(z)
def code(x, y, z, t):
	tmp = 0
	if (x * x) <= 8e-74:
		tmp = t * (y * 4.0)
	else:
		tmp = x * x
	return tmp

Julia

z = abs(z)
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * x) <= 8e-74)
		tmp = Float64(t * Float64(y * 4.0));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

z = abs(z)
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * x) <= 8e-74)
		tmp = t * (y * 4.0);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z should be positive before calling this function
code[x_, y_, z_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 8e-74], N[(t * N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(x * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 7.99999999999999966e-74

   1. Initial program 91.9%

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

   2. Taylor expanded in t around inf 54.4%

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

      1. associate-*r* 54.4%

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

   4. Simplified 54.4%

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

   if 7.99999999999999966e-74 < (*.f64 x x)

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf 66.8%

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

      1. unpow2 66.8%

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

   4. Simplified 66.8%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 8 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 8: 41.2% accurate, 4.3× speedup

Math

\[\begin{array}{l} z = |z|\\ \\ x \cdot x \end{array} \]

FPCore

NOTE: z should be positive before calling this function
(FPCore (x y z t) :precision binary64 (* x x))

C

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

Fortran

NOTE: z should be positive before calling this function
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

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: z should be positive before calling this function
code[x_, y_, z_, t_] := N[(x * x), $MachinePrecision]

Derivation

1. Initial program 94.8%

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

2. Taylor expanded in x around inf 40.4%

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

   1. unpow2 40.4%

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

4. Simplified 40.4%

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

5. Final simplification 40.4%

   \[\leadsto x \cdot x \]

Developer target: 90.9% 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 2023224 
(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))))