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

Percentage Accurate: 91.2% → 96.5%

Time: 9.1s

Alternatives: 8

Speedup: 0.7×

• 49.2% 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: 91.2% 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: 96.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;z_m \leq 2 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 4, \mathsf{fma}\left(z_m, -z_m, t\right), x \cdot x\right)\\ \mathbf{elif}\;z_m \leq 7.2 \cdot 10^{+251}:\\ \;\;\;\;x \cdot x - z_m \cdot \left(z_m \cdot \left(y \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z_m \cdot z_m - t\right) \cdot \left(y \cdot -4\right)\right)\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= z_m 2e+109)
   (fma (* y 4.0) (fma z_m (- z_m) t) (* x x))
   (if (<= z_m 7.2e+251)
     (- (* x x) (* z_m (* z_m (* y 4.0))))
     (fma x x (* (- (* z_m z_m) t) (* y -4.0))))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (z_m <= 2e+109) {
		tmp = fma((y * 4.0), fma(z_m, -z_m, t), (x * x));
	} else if (z_m <= 7.2e+251) {
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)));
	} else {
		tmp = fma(x, x, (((z_m * z_m) - t) * (y * -4.0)));
	}
	return tmp;
}

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (z_m <= 2e+109)
		tmp = fma(Float64(y * 4.0), fma(z_m, Float64(-z_m), t), Float64(x * x));
	elseif (z_m <= 7.2e+251)
		tmp = Float64(Float64(x * x) - Float64(z_m * Float64(z_m * Float64(y * 4.0))));
	else
		tmp = fma(x, x, Float64(Float64(Float64(z_m * z_m) - t) * Float64(y * -4.0)));
	end
	return tmp
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := If[LessEqual[z$95$m, 2e+109], N[(N[(y * 4.0), $MachinePrecision] * N[(z$95$m * (-z$95$m) + t), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z$95$m, 7.2e+251], N[(N[(x * x), $MachinePrecision] - N[(z$95$m * N[(z$95$m * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * x + N[(N[(N[(z$95$m * z$95$m), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 2: 96.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;z_m \leq 1.75 \cdot 10^{+109} \lor \neg \left(z_m \leq 4.4 \cdot 10^{+251}\right):\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z_m \cdot z_m - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z_m \cdot \left(z_m \cdot \left(y \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (or (<= z_m 1.75e+109) (not (<= z_m 4.4e+251)))
   (fma x x (* (- (* z_m z_m) t) (* y -4.0)))
   (- (* x x) (* z_m (* z_m (* y 4.0))))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if ((z_m <= 1.75e+109) || !(z_m <= 4.4e+251)) {
		tmp = fma(x, x, (((z_m * z_m) - t) * (y * -4.0)));
	} else {
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)));
	}
	return tmp;
}

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if ((z_m <= 1.75e+109) || !(z_m <= 4.4e+251))
		tmp = fma(x, x, Float64(Float64(Float64(z_m * z_m) - t) * Float64(y * -4.0)));
	else
		tmp = Float64(Float64(x * x) - Float64(z_m * Float64(z_m * Float64(y * 4.0))));
	end
	return tmp
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := If[Or[LessEqual[z$95$m, 1.75e+109], N[Not[LessEqual[z$95$m, 4.4e+251]], $MachinePrecision]], N[(x * x + N[(N[(N[(z$95$m * z$95$m), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] - N[(z$95$m * N[(z$95$m * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 95.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;z_m \leq 10^{+107}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z_m \cdot z_m\right)\\ \mathbf{elif}\;z_m \leq 1.12 \cdot 10^{+252}:\\ \;\;\;\;x \cdot x - z_m \cdot \left(z_m \cdot \left(y \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -4\right) \cdot {z_m}^{2}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= z_m 1e+107)
   (+ (* x x) (* (* y 4.0) (- t (* z_m z_m))))
   (if (<= z_m 1.12e+252)
     (- (* x x) (* z_m (* z_m (* y 4.0))))
     (* (* y -4.0) (pow z_m 2.0)))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (z_m <= 1e+107) {
		tmp = (x * x) + ((y * 4.0) * (t - (z_m * z_m)));
	} else if (z_m <= 1.12e+252) {
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)));
	} else {
		tmp = (y * -4.0) * pow(z_m, 2.0);
	}
	return tmp;
}

Fortran

z_m = abs(z)
real(8) function code(x, y, z_m, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z_m <= 1d+107) then
        tmp = (x * x) + ((y * 4.0d0) * (t - (z_m * z_m)))
    else if (z_m <= 1.12d+252) then
        tmp = (x * x) - (z_m * (z_m * (y * 4.0d0)))
    else
        tmp = (y * (-4.0d0)) * (z_m ** 2.0d0)
    end if
    code = tmp
end function

Java

z_m = Math.abs(z);
public static double code(double x, double y, double z_m, double t) {
	double tmp;
	if (z_m <= 1e+107) {
		tmp = (x * x) + ((y * 4.0) * (t - (z_m * z_m)));
	} else if (z_m <= 1.12e+252) {
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)));
	} else {
		tmp = (y * -4.0) * Math.pow(z_m, 2.0);
	}
	return tmp;
}

Python

z_m = math.fabs(z)
def code(x, y, z_m, t):
	tmp = 0
	if z_m <= 1e+107:
		tmp = (x * x) + ((y * 4.0) * (t - (z_m * z_m)))
	elif z_m <= 1.12e+252:
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)))
	else:
		tmp = (y * -4.0) * math.pow(z_m, 2.0)
	return tmp

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (z_m <= 1e+107)
		tmp = Float64(Float64(x * x) + Float64(Float64(y * 4.0) * Float64(t - Float64(z_m * z_m))));
	elseif (z_m <= 1.12e+252)
		tmp = Float64(Float64(x * x) - Float64(z_m * Float64(z_m * Float64(y * 4.0))));
	else
		tmp = Float64(Float64(y * -4.0) * (z_m ^ 2.0));
	end
	return tmp
end

MATLAB

z_m = abs(z);
function tmp_2 = code(x, y, z_m, t)
	tmp = 0.0;
	if (z_m <= 1e+107)
		tmp = (x * x) + ((y * 4.0) * (t - (z_m * z_m)));
	elseif (z_m <= 1.12e+252)
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)));
	else
		tmp = (y * -4.0) * (z_m ^ 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := If[LessEqual[z$95$m, 1e+107], N[(N[(x * x), $MachinePrecision] + N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z$95$m * z$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z$95$m, 1.12e+252], N[(N[(x * x), $MachinePrecision] - N[(z$95$m * N[(z$95$m * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * -4.0), $MachinePrecision] * N[Power[z$95$m, 2.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 95.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;z_m \cdot z_m - t \leq 5 \cdot 10^{+280}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z_m \cdot z_m\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z_m \cdot \left(z_m \cdot \left(y \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= (- (* z_m z_m) t) 5e+280)
   (+ (* x x) (* (* y 4.0) (- t (* z_m z_m))))
   (- (* x x) (* z_m (* z_m (* y 4.0))))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (((z_m * z_m) - t) <= 5e+280) {
		tmp = (x * x) + ((y * 4.0) * (t - (z_m * z_m)));
	} else {
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)));
	}
	return tmp;
}

Fortran

z_m = abs(z)
real(8) function code(x, y, z_m, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z_m * z_m) - t) <= 5d+280) then
        tmp = (x * x) + ((y * 4.0d0) * (t - (z_m * z_m)))
    else
        tmp = (x * x) - (z_m * (z_m * (y * 4.0d0)))
    end if
    code = tmp
end function

Java

z_m = Math.abs(z);
public static double code(double x, double y, double z_m, double t) {
	double tmp;
	if (((z_m * z_m) - t) <= 5e+280) {
		tmp = (x * x) + ((y * 4.0) * (t - (z_m * z_m)));
	} else {
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)));
	}
	return tmp;
}

Python

z_m = math.fabs(z)
def code(x, y, z_m, t):
	tmp = 0
	if ((z_m * z_m) - t) <= 5e+280:
		tmp = (x * x) + ((y * 4.0) * (t - (z_m * z_m)))
	else:
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)))
	return tmp

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (Float64(Float64(z_m * z_m) - t) <= 5e+280)
		tmp = Float64(Float64(x * x) + Float64(Float64(y * 4.0) * Float64(t - Float64(z_m * z_m))));
	else
		tmp = Float64(Float64(x * x) - Float64(z_m * Float64(z_m * Float64(y * 4.0))));
	end
	return tmp
end

MATLAB

z_m = abs(z);
function tmp_2 = code(x, y, z_m, t)
	tmp = 0.0;
	if (((z_m * z_m) - t) <= 5e+280)
		tmp = (x * x) + ((y * 4.0) * (t - (z_m * z_m)));
	else
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := If[LessEqual[N[(N[(z$95$m * z$95$m), $MachinePrecision] - t), $MachinePrecision], 5e+280], N[(N[(x * x), $MachinePrecision] + N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z$95$m * z$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] - N[(z$95$m * N[(z$95$m * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 5: 90.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;z_m \leq 1550:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z_m \cdot \left(z_m \cdot \left(y \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= z_m 1550.0)
   (- (* x x) (* y (* t -4.0)))
   (- (* x x) (* z_m (* z_m (* y 4.0))))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (z_m <= 1550.0) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)));
	}
	return tmp;
}

Fortran

z_m = abs(z)
real(8) function code(x, y, z_m, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z_m <= 1550.0d0) then
        tmp = (x * x) - (y * (t * (-4.0d0)))
    else
        tmp = (x * x) - (z_m * (z_m * (y * 4.0d0)))
    end if
    code = tmp
end function

Java

z_m = Math.abs(z);
public static double code(double x, double y, double z_m, double t) {
	double tmp;
	if (z_m <= 1550.0) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)));
	}
	return tmp;
}

Python

z_m = math.fabs(z)
def code(x, y, z_m, t):
	tmp = 0
	if z_m <= 1550.0:
		tmp = (x * x) - (y * (t * -4.0))
	else:
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)))
	return tmp

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (z_m <= 1550.0)
		tmp = Float64(Float64(x * x) - Float64(y * Float64(t * -4.0)));
	else
		tmp = Float64(Float64(x * x) - Float64(z_m * Float64(z_m * Float64(y * 4.0))));
	end
	return tmp
end

MATLAB

z_m = abs(z);
function tmp_2 = code(x, y, z_m, t)
	tmp = 0.0;
	if (z_m <= 1550.0)
		tmp = (x * x) - (y * (t * -4.0));
	else
		tmp = (x * x) - (z_m * (z_m * (y * 4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := If[LessEqual[z$95$m, 1550.0], N[(N[(x * x), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] - N[(z$95$m * N[(z$95$m * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 6: 67.9% accurate, 1.4× speedup

Math

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

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t) :precision binary64 (- (* x x) (* y (* t -4.0))))

C

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

Fortran

z_m = abs(z)
real(8) function code(x, y, z_m, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    code = (x * x) - (y * (t * (-4.0d0)))
end function

Java

z_m = Math.abs(z);
public static double code(double x, double y, double z_m, double t) {
	return (x * x) - (y * (t * -4.0));
}

Python

z_m = math.fabs(z)
def code(x, y, z_m, t):
	return (x * x) - (y * (t * -4.0))

Julia

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

MATLAB

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

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := N[(N[(x * x), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 7: 32.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;z_m \leq 7.5 \cdot 10^{+112}:\\ \;\;\;\;4 \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= z_m 7.5e+112) (* 4.0 (* y t)) (* -4.0 (* y t))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (z_m <= 7.5e+112) {
		tmp = 4.0 * (y * t);
	} else {
		tmp = -4.0 * (y * t);
	}
	return tmp;
}

Fortran

z_m = abs(z)
real(8) function code(x, y, z_m, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z_m <= 7.5d+112) then
        tmp = 4.0d0 * (y * t)
    else
        tmp = (-4.0d0) * (y * t)
    end if
    code = tmp
end function

Java

z_m = Math.abs(z);
public static double code(double x, double y, double z_m, double t) {
	double tmp;
	if (z_m <= 7.5e+112) {
		tmp = 4.0 * (y * t);
	} else {
		tmp = -4.0 * (y * t);
	}
	return tmp;
}

Python

z_m = math.fabs(z)
def code(x, y, z_m, t):
	tmp = 0
	if z_m <= 7.5e+112:
		tmp = 4.0 * (y * t)
	else:
		tmp = -4.0 * (y * t)
	return tmp

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (z_m <= 7.5e+112)
		tmp = Float64(4.0 * Float64(y * t));
	else
		tmp = Float64(-4.0 * Float64(y * t));
	end
	return tmp
end

MATLAB

z_m = abs(z);
function tmp_2 = code(x, y, z_m, t)
	tmp = 0.0;
	if (z_m <= 7.5e+112)
		tmp = 4.0 * (y * t);
	else
		tmp = -4.0 * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := If[LessEqual[z$95$m, 7.5e+112], N[(4.0 * N[(y * t), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 5.9% accurate, 2.6× speedup

Math

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

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t) :precision binary64 (* -4.0 (* y t)))

C

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

Fortran

z_m = abs(z)
real(8) function code(x, y, z_m, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    code = (-4.0d0) * (y * t)
end function

Java

z_m = Math.abs(z);
public static double code(double x, double y, double z_m, double t) {
	return -4.0 * (y * t);
}

Python

z_m = math.fabs(z)
def code(x, y, z_m, t):
	return -4.0 * (y * t)

Julia

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

MATLAB

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

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := N[(-4.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 91.2% 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 2023342 
(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))))