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

Percentage Accurate: 90.8% → 94.7%

Time: 8.5s

Alternatives: 6

Speedup: 0.6×

• 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: 90.8% 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: 94.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot 4 \leq -2 \cdot 10^{-298} \lor \neg \left(y \cdot 4 \leq 4 \cdot 10^{-73}\right):\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(-4 \cdot \left(y \cdot t\right) + 4 \cdot {\left(z \cdot \sqrt{y}\right)}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y 4.0) -2e-298) (not (<= (* y 4.0) 4e-73)))
   (fma x x (* (- (* z z) t) (* y -4.0)))
   (- (* x x) (+ (* -4.0 (* y t)) (* 4.0 (pow (* z (sqrt y)) 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * 4.0) <= -2e-298) || !((y * 4.0) <= 4e-73)) {
		tmp = fma(x, x, (((z * z) - t) * (y * -4.0)));
	} else {
		tmp = (x * x) - ((-4.0 * (y * t)) + (4.0 * pow((z * sqrt(y)), 2.0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y * 4.0) <= -2e-298) || !(Float64(y * 4.0) <= 4e-73))
		tmp = fma(x, x, Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0)));
	else
		tmp = Float64(Float64(x * x) - Float64(Float64(-4.0 * Float64(y * t)) + Float64(4.0 * (Float64(z * sqrt(y)) ^ 2.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y * 4.0), $MachinePrecision], -2e-298], N[Not[LessEqual[N[(y * 4.0), $MachinePrecision], 4e-73]], $MachinePrecision]], N[(x * x + N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] - N[(N[(-4.0 * N[(y * t), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[Power[N[(z * N[Sqrt[y], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y 4) < -1.99999999999999982e-298 or 3.99999999999999999e-73 < (*.f64 y 4)

   1. Initial program 90.1%

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

      1. fma-neg 93.2%

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

      2. distribute-lft-neg-in 93.2%

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

      3. *-commutative 93.2%

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

      4. distribute-rgt-neg-in 93.2%

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

      5. metadata-eval 93.2%

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

   3. Simplified 93.2%

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

   if -1.99999999999999982e-298 < (*.f64 y 4) < 3.99999999999999999e-73

   1. Initial program 82.6%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 82.6%

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

      1. add-sqr-sqrt 82.6%

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

      2. pow2 82.6%

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

      3. *-commutative 82.6%

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

      4. sqrt-prod 82.6%

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

      5. unpow2 82.6%

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

      6. sqrt-prod 44.9%

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

      7. add-sqr-sqrt 98.1%

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

   5. Applied egg-rr 98.1%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 4 \leq -2 \cdot 10^{-298} \lor \neg \left(y \cdot 4 \leq 4 \cdot 10^{-73}\right):\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - \left(-4 \cdot \left(y \cdot t\right) + 4 \cdot {\left(z \cdot \sqrt{y}\right)}^{2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 88.4%

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

   1. fma-neg 90.7%

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

   2. distribute-lft-neg-in 90.7%

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

   3. *-commutative 90.7%

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

   4. distribute-rgt-neg-in 90.7%

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

   5. metadata-eval 90.7%

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

3. Simplified 90.7%

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

5. Final simplification 90.7%

   \[\leadsto \mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right) \]
6. Add Preprocessing

Alternative 3: 92.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 4 \cdot 10^{+268}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;{x}^{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x x) 4e+268) (+ (* x x) (* (* y 4.0) (- t (* z z)))) (pow x 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 4e+268) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = pow(x, 2.0);
	}
	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) <= 4d+268) then
        tmp = (x * x) + ((y * 4.0d0) * (t - (z * z)))
    else
        tmp = x ** 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 4e+268) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = Math.pow(x, 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x * x) <= 4e+268:
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)))
	else:
		tmp = math.pow(x, 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * x) <= 4e+268)
		tmp = Float64(Float64(x * x) + Float64(Float64(y * 4.0) * Float64(t - Float64(z * z))));
	else
		tmp = x ^ 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * x) <= 4e+268)
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	else
		tmp = x ^ 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 4e+268], N[(N[(x * x), $MachinePrecision] + N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[x, 2.0], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 3.9999999999999999e268

   1. Initial program 91.7%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]
   2. Add Preprocessing

   if 3.9999999999999999e268 < (*.f64 x x)

   1. Initial program 78.8%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 89.6%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 4 \cdot 10^{+268}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;{x}^{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 5 \cdot 10^{+306}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x x) 5e+306)
   (+ (* x x) (* (* y 4.0) (- t (* z z))))
   (- (* x x) (* y (* t -4.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 5e+306) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = (x * x) - (y * (t * -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) <= 5d+306) then
        tmp = (x * x) + ((y * 4.0d0) * (t - (z * z)))
    else
        tmp = (x * x) - (y * (t * (-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) <= 5e+306) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = (x * x) - (y * (t * -4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x * x) <= 5e+306:
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)))
	else:
		tmp = (x * x) - (y * (t * -4.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * x) <= 5e+306)
		tmp = Float64(Float64(x * x) + Float64(Float64(y * 4.0) * Float64(t - Float64(z * z))));
	else
		tmp = Float64(Float64(x * x) - Float64(y * Float64(t * -4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * x) <= 5e+306)
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	else
		tmp = (x * x) - (y * (t * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 5e+306], N[(N[(x * x), $MachinePrecision] + N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 4.99999999999999993e306

   1. Initial program 91.6%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]
   2. Add Preprocessing

   if 4.99999999999999993e306 < (*.f64 x x)

   1. Initial program 77.2%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 86.0%

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

      1. *-commutative 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-*l* 86.0%

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

   5. Simplified 86.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 5 \cdot 10^{+306}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.2% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

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 * (t * (-4.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.4%

   \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0 61.4%

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

   1. *-commutative 61.4%

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

   2. *-commutative 61.4%

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

   3. associate-*l* 61.4%

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

5. Simplified 61.4%

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

6. Final simplification 61.4%

   \[\leadsto x \cdot x - y \cdot \left(t \cdot -4\right) \]
7. Add Preprocessing

Alternative 6: 32.0% accurate, 2.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 4.0 * (y * 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 = 4.0d0 * (y * t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.4%

   \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]
2. Add Preprocessing

3. Taylor expanded in t around inf 33.4%

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

   1. *-commutative 33.4%

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

5. Simplified 33.4%

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

6. Final simplification 33.4%

   \[\leadsto 4 \cdot \left(y \cdot t\right) \]
7. Add Preprocessing

Developer target: 90.8% 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 2024020 
(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))))