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

Percentage Accurate: 91.0% → 95.3%

Time: 9.0s

Alternatives: 10

Speedup: 0.8×

• 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: 91.0% 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: 95.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+292}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + \left(4 \cdot \left(t \cdot y\right) - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 1e+292)
   (fma x x (* (- (* z z) t) (* y -4.0)))
   (+ (* x x) (- (* 4.0 (* t y)) (* z (* z (* y 4.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 1e+292) {
		tmp = fma(x, x, (((z * z) - t) * (y * -4.0)));
	} else {
		tmp = (x * x) + ((4.0 * (t * y)) - (z * (z * (y * 4.0))));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 1e+292)
		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(t * y)) - Float64(z * Float64(z * Float64(y * 4.0)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 1e+292], 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[(t * y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(z * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 1e292

   1. Initial program 97.9%

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

      1. fma-neg 98.9%

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

      2. *-commutative 98.9%

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

      3. distribute-rgt-neg-in 98.9%

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

      4. distribute-rgt-neg-in 98.9%

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

      5. metadata-eval 98.9%

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

   3. Simplified 98.9%

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

   if 1e292 < (*.f64 z z)

   1. Initial program 75.6%

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

      1. add-cube-cbrt 75.5%

         \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot z - t} \cdot \sqrt[3]{z \cdot z - t}\right) \cdot \sqrt[3]{z \cdot z - t}\right)} \]

      2. pow3 75.5%

         \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{{\left(\sqrt[3]{z \cdot z - t}\right)}^{3}} \]

   3. Applied egg-rr 75.5%

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

      1. unpow3 75.5%

         \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot z - t} \cdot \sqrt[3]{z \cdot z - t}\right) \cdot \sqrt[3]{z \cdot z - t}\right)} \]

      2. add-cube-cbrt 75.6%

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

      3. sub-neg 75.6%

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

      4. distribute-lft-in 74.0%

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

      5. *-commutative 74.0%

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

   5. Applied egg-rr 74.0%

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

      1. fma-def 74.0%

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

      2. distribute-rgt-neg-out 74.0%

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

      3. add-sqr-sqrt 37.8%

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

      4. sqrt-prod 62.0%

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

      5. sqr-neg 62.0%

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

      6. sqrt-prod 36.2%

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

      7. add-sqr-sqrt 75.6%

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

      8. *-commutative 75.6%

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

      9. *-commutative 75.6%

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

      10. fma-neg 75.6%

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

      11. associate-*l* 95.1%

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

      12. add-sqr-sqrt 49.9%

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

      13. add-sqr-sqrt 95.1%

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

      14. add-sqr-sqrt 46.7%

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

      15. sqrt-prod 72.7%

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

      16. sqr-neg 72.7%

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

      17. sqrt-prod 46.8%

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

      18. add-sqr-sqrt 93.5%

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

   7. Applied egg-rr 93.5%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+292}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + \left(4 \cdot \left(t \cdot y\right) - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right)\\ \end{array} \]

Alternative 2: 87.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot x - \left(z \cdot z\right) \cdot \left(y \cdot 4\right)\\ t_2 := x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{if}\;z \cdot z \leq 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot z \leq 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot z \leq 4 \cdot 10^{+258}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x x) (* (* z z) (* y 4.0))))
        (t_2 (- (* x x) (* t (* y -4.0)))))
   (if (<= (* z z) 1e-57)
     t_2
     (if (<= (* z z) 1e+37)
       t_1
       (if (<= (* z z) 1e+105)
         t_2
         (if (<= (* z z) 4e+258) t_1 (* -4.0 (* z (* z y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) - ((z * z) * (y * 4.0));
	double t_2 = (x * x) - (t * (y * -4.0));
	double tmp;
	if ((z * z) <= 1e-57) {
		tmp = t_2;
	} else if ((z * z) <= 1e+37) {
		tmp = t_1;
	} else if ((z * z) <= 1e+105) {
		tmp = t_2;
	} else if ((z * z) <= 4e+258) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * x) - ((z * z) * (y * 4.0d0))
    t_2 = (x * x) - (t * (y * (-4.0d0)))
    if ((z * z) <= 1d-57) then
        tmp = t_2
    else if ((z * z) <= 1d+37) then
        tmp = t_1
    else if ((z * z) <= 1d+105) then
        tmp = t_2
    else if ((z * z) <= 4d+258) then
        tmp = t_1
    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 t_1 = (x * x) - ((z * z) * (y * 4.0));
	double t_2 = (x * x) - (t * (y * -4.0));
	double tmp;
	if ((z * z) <= 1e-57) {
		tmp = t_2;
	} else if ((z * z) <= 1e+37) {
		tmp = t_1;
	} else if ((z * z) <= 1e+105) {
		tmp = t_2;
	} else if ((z * z) <= 4e+258) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) - ((z * z) * (y * 4.0))
	t_2 = (x * x) - (t * (y * -4.0))
	tmp = 0
	if (z * z) <= 1e-57:
		tmp = t_2
	elif (z * z) <= 1e+37:
		tmp = t_1
	elif (z * z) <= 1e+105:
		tmp = t_2
	elif (z * z) <= 4e+258:
		tmp = t_1
	else:
		tmp = -4.0 * (z * (z * y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) - Float64(Float64(z * z) * Float64(y * 4.0)))
	t_2 = Float64(Float64(x * x) - Float64(t * Float64(y * -4.0)))
	tmp = 0.0
	if (Float64(z * z) <= 1e-57)
		tmp = t_2;
	elseif (Float64(z * z) <= 1e+37)
		tmp = t_1;
	elseif (Float64(z * z) <= 1e+105)
		tmp = t_2;
	elseif (Float64(z * z) <= 4e+258)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(z * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) - ((z * z) * (y * 4.0));
	t_2 = (x * x) - (t * (y * -4.0));
	tmp = 0.0;
	if ((z * z) <= 1e-57)
		tmp = t_2;
	elseif ((z * z) <= 1e+37)
		tmp = t_1;
	elseif ((z * z) <= 1e+105)
		tmp = t_2;
	elseif ((z * z) <= 4e+258)
		tmp = t_1;
	else
		tmp = -4.0 * (z * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] - N[(N[(z * z), $MachinePrecision] * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * x), $MachinePrecision] - N[(t * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * z), $MachinePrecision], 1e-57], t$95$2, If[LessEqual[N[(z * z), $MachinePrecision], 1e+37], t$95$1, If[LessEqual[N[(z * z), $MachinePrecision], 1e+105], t$95$2, If[LessEqual[N[(z * z), $MachinePrecision], 4e+258], t$95$1, N[(-4.0 * N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z z) < 9.99999999999999955e-58 or 9.99999999999999954e36 < (*.f64 z z) < 9.9999999999999994e104

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0 95.2%

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

      1. associate-*r* 95.2%

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

   4. Simplified 95.2%

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

   if 9.99999999999999955e-58 < (*.f64 z z) < 9.99999999999999954e36 or 9.9999999999999994e104 < (*.f64 z z) < 4.00000000000000023e258

   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 97.7%

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

      1. unpow2 97.7%

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

   4. Simplified 97.7%

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

   if 4.00000000000000023e258 < (*.f64 z z)

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 80.0%

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

      1. unpow2 80.0%

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

      2. *-commutative 80.0%

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

      3. associate-*l* 89.0%

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

   4. Simplified 89.0%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{-57}:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 10^{+37}:\\ \;\;\;\;x \cdot x - \left(z \cdot z\right) \cdot \left(y \cdot 4\right)\\ \mathbf{elif}\;z \cdot z \leq 10^{+105}:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 4 \cdot 10^{+258}:\\ \;\;\;\;x \cdot x - \left(z \cdot z\right) \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 3: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2.7 \cdot 10^{+66} \lor \neg \left(x \cdot x \leq 1.7 \cdot 10^{+187}\right) \land x \cdot x \leq 1.1 \cdot 10^{+217}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* x x) 2.7e+66)
         (and (not (<= (* x x) 1.7e+187)) (<= (* x x) 1.1e+217)))
   (* (- (* z z) t) (* y -4.0))
   (* x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) <= 2.7e+66) || (!((x * x) <= 1.7e+187) && ((x * x) <= 1.1e+217))) {
		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) <= 2.7d+66) .or. (.not. ((x * x) <= 1.7d+187)) .and. ((x * x) <= 1.1d+217)) 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) <= 2.7e+66) || (!((x * x) <= 1.7e+187) && ((x * x) <= 1.1e+217))) {
		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) <= 2.7e+66) or (not ((x * x) <= 1.7e+187) and ((x * x) <= 1.1e+217)):
		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) <= 2.7e+66) || (!(Float64(x * x) <= 1.7e+187) && (Float64(x * x) <= 1.1e+217)))
		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) <= 2.7e+66) || (~(((x * x) <= 1.7e+187)) && ((x * x) <= 1.1e+217)))
		tmp = ((z * z) - t) * (y * -4.0);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x * x), $MachinePrecision], 2.7e+66], And[N[Not[LessEqual[N[(x * x), $MachinePrecision], 1.7e+187]], $MachinePrecision], LessEqual[N[(x * x), $MachinePrecision], 1.1e+217]]], 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) < 2.7e66 or 1.7e187 < (*.f64 x x) < 1.1e217

   1. Initial program 92.9%

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

   2. Taylor expanded in x around 0 83.0%

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

      1. *-commutative 83.0%

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

      2. *-commutative 83.0%

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

      3. unpow2 83.0%

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

      4. *-commutative 83.0%

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

      5. associate-*l* 83.0%

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

   4. Simplified 83.0%

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

   if 2.7e66 < (*.f64 x x) < 1.7e187 or 1.1e217 < (*.f64 x x)

   1. Initial program 92.0%

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

   2. Taylor expanded in x around inf 82.6%

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

      1. unpow2 82.6%

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

   4. Simplified 82.6%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2.7 \cdot 10^{+66} \lor \neg \left(x \cdot x \leq 1.7 \cdot 10^{+187}\right) \land x \cdot x \leq 1.1 \cdot 10^{+217}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 4: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 10^{+187}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 10^{+252}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x x) (* t (* y -4.0)))))
   (if (<= (* z z) 2e+149)
     t_1
     (if (<= (* z z) 1e+187)
       (* (- (* z z) t) (* y -4.0))
       (if (<= (* z z) 1e+252) t_1 (* -4.0 (* z (* z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) - (t * (y * -4.0));
	double tmp;
	if ((z * z) <= 2e+149) {
		tmp = t_1;
	} else if ((z * z) <= 1e+187) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else if ((z * z) <= 1e+252) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x * x) - (t * (y * (-4.0d0)))
    if ((z * z) <= 2d+149) then
        tmp = t_1
    else if ((z * z) <= 1d+187) then
        tmp = ((z * z) - t) * (y * (-4.0d0))
    else if ((z * z) <= 1d+252) then
        tmp = t_1
    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 t_1 = (x * x) - (t * (y * -4.0));
	double tmp;
	if ((z * z) <= 2e+149) {
		tmp = t_1;
	} else if ((z * z) <= 1e+187) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else if ((z * z) <= 1e+252) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) - (t * (y * -4.0))
	tmp = 0
	if (z * z) <= 2e+149:
		tmp = t_1
	elif (z * z) <= 1e+187:
		tmp = ((z * z) - t) * (y * -4.0)
	elif (z * z) <= 1e+252:
		tmp = t_1
	else:
		tmp = -4.0 * (z * (z * y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) - Float64(t * Float64(y * -4.0)))
	tmp = 0.0
	if (Float64(z * z) <= 2e+149)
		tmp = t_1;
	elseif (Float64(z * z) <= 1e+187)
		tmp = Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0));
	elseif (Float64(z * z) <= 1e+252)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(z * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) - (t * (y * -4.0));
	tmp = 0.0;
	if ((z * z) <= 2e+149)
		tmp = t_1;
	elseif ((z * z) <= 1e+187)
		tmp = ((z * z) - t) * (y * -4.0);
	elseif ((z * z) <= 1e+252)
		tmp = t_1;
	else
		tmp = -4.0 * (z * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

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[N[(z * z), $MachinePrecision], 2e+149], t$95$1, If[LessEqual[N[(z * z), $MachinePrecision], 1e+187], N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * z), $MachinePrecision], 1e+252], t$95$1, N[(-4.0 * N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z z) < 2.0000000000000001e149 or 9.99999999999999907e186 < (*.f64 z z) < 1.0000000000000001e252

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 90.0%

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

      1. associate-*r* 90.0%

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

   4. Simplified 90.0%

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

   if 2.0000000000000001e149 < (*.f64 z z) < 9.99999999999999907e186

   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 0 79.0%

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

      1. *-commutative 79.0%

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

      2. *-commutative 79.0%

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

      3. unpow2 79.0%

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

      4. *-commutative 79.0%

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

      5. associate-*l* 79.0%

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

   4. Simplified 79.0%

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

   if 1.0000000000000001e252 < (*.f64 z z)

   1. Initial program 76.1%

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

   2. Taylor expanded in z around inf 80.3%

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

      1. unpow2 80.3%

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

      2. *-commutative 80.3%

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

      3. associate-*l* 89.2%

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

   4. Simplified 89.2%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+149}:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 10^{+187}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 10^{+252}:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 5: 58.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \mathbf{if}\;x \cdot x \leq 6.5 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 1.9 \cdot 10^{-151}:\\ \;\;\;\;4 \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;x \cdot x \leq 7 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -4.0 (* (* z z) y))))
   (if (<= (* x x) 6.5e-217)
     t_1
     (if (<= (* x x) 1.9e-151)
       (* 4.0 (* t y))
       (if (<= (* x x) 7e+20) 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) <= 6.5e-217) {
		tmp = t_1;
	} else if ((x * x) <= 1.9e-151) {
		tmp = 4.0 * (t * y);
	} else if ((x * x) <= 7e+20) {
		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) <= 6.5d-217) then
        tmp = t_1
    else if ((x * x) <= 1.9d-151) then
        tmp = 4.0d0 * (t * y)
    else if ((x * x) <= 7d+20) 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) <= 6.5e-217) {
		tmp = t_1;
	} else if ((x * x) <= 1.9e-151) {
		tmp = 4.0 * (t * y);
	} else if ((x * x) <= 7e+20) {
		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) <= 6.5e-217:
		tmp = t_1
	elif (x * x) <= 1.9e-151:
		tmp = 4.0 * (t * y)
	elif (x * x) <= 7e+20:
		tmp = t_1
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-4.0 * Float64(Float64(z * z) * y))
	tmp = 0.0
	if (Float64(x * x) <= 6.5e-217)
		tmp = t_1;
	elseif (Float64(x * x) <= 1.9e-151)
		tmp = Float64(4.0 * Float64(t * y));
	elseif (Float64(x * x) <= 7e+20)
		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) <= 6.5e-217)
		tmp = t_1;
	elseif ((x * x) <= 1.9e-151)
		tmp = 4.0 * (t * y);
	elseif ((x * x) <= 7e+20)
		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[(N[(z * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * x), $MachinePrecision], 6.5e-217], t$95$1, If[LessEqual[N[(x * x), $MachinePrecision], 1.9e-151], N[(4.0 * N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * x), $MachinePrecision], 7e+20], t$95$1, N[(x * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x x) < 6.4999999999999996e-217 or 1.89999999999999985e-151 < (*.f64 x x) < 7e20

   1. Initial program 92.7%

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

   2. Taylor expanded in z around inf 54.6%

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

      1. unpow2 54.6%

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

   4. Simplified 54.6%

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

   if 6.4999999999999996e-217 < (*.f64 x x) < 1.89999999999999985e-151

   1. Initial program 93.2%

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

   2. Taylor expanded in t around inf 60.7%

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

   if 7e20 < (*.f64 x x)

   1. Initial program 92.2%

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

   2. Taylor expanded in x around inf 76.2%

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

      1. unpow2 76.2%

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

   4. Simplified 76.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 6.5 \cdot 10^{-217}:\\ \;\;\;\;-4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \mathbf{elif}\;x \cdot x \leq 1.9 \cdot 10^{-151}:\\ \;\;\;\;4 \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;x \cdot x \leq 7 \cdot 10^{+20}:\\ \;\;\;\;-4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 6: 61.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;x \cdot x \leq 8 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 1.65 \cdot 10^{-152}:\\ \;\;\;\;4 \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;x \cdot x \leq 6 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -4.0 (* z (* z y)))))
   (if (<= (* x x) 8e-219)
     t_1
     (if (<= (* x x) 1.65e-152)
       (* 4.0 (* t y))
       (if (<= (* x x) 6e+63) 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-219) {
		tmp = t_1;
	} else if ((x * x) <= 1.65e-152) {
		tmp = 4.0 * (t * y);
	} else if ((x * x) <= 6e+63) {
		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-219) then
        tmp = t_1
    else if ((x * x) <= 1.65d-152) then
        tmp = 4.0d0 * (t * y)
    else if ((x * x) <= 6d+63) 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-219) {
		tmp = t_1;
	} else if ((x * x) <= 1.65e-152) {
		tmp = 4.0 * (t * y);
	} else if ((x * x) <= 6e+63) {
		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-219:
		tmp = t_1
	elif (x * x) <= 1.65e-152:
		tmp = 4.0 * (t * y)
	elif (x * x) <= 6e+63:
		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-219)
		tmp = t_1;
	elseif (Float64(x * x) <= 1.65e-152)
		tmp = Float64(4.0 * Float64(t * y));
	elseif (Float64(x * x) <= 6e+63)
		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-219)
		tmp = t_1;
	elseif ((x * x) <= 1.65e-152)
		tmp = 4.0 * (t * y);
	elseif ((x * x) <= 6e+63)
		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-219], t$95$1, If[LessEqual[N[(x * x), $MachinePrecision], 1.65e-152], N[(4.0 * N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * x), $MachinePrecision], 6e+63], t$95$1, N[(x * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x x) < 8.0000000000000003e-219 or 1.64999999999999999e-152 < (*.f64 x x) < 5.99999999999999998e63

   1. Initial program 92.5%

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

   2. Taylor expanded in z around inf 52.8%

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

      1. unpow2 52.8%

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

      2. *-commutative 52.8%

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

      3. associate-*l* 60.1%

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

   4. Simplified 60.1%

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

   if 8.0000000000000003e-219 < (*.f64 x x) < 1.64999999999999999e-152

   1. Initial program 93.2%

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

   2. Taylor expanded in t around inf 60.7%

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

   if 5.99999999999999998e63 < (*.f64 x x)

   1. Initial program 92.3%

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

   2. Taylor expanded in x around inf 79.2%

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

      1. unpow2 79.2%

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

   4. Simplified 79.2%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 8 \cdot 10^{-219}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \cdot x \leq 1.65 \cdot 10^{-152}:\\ \;\;\;\;4 \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;x \cdot x \leq 6 \cdot 10^{+63}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 7: 94.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+132}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + \left(4 \cdot \left(t \cdot y\right) - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.8e+132)
   (* x x)
   (+ (* x x) (- (* 4.0 (* t y)) (* z (* z (* y 4.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.8e+132) {
		tmp = x * x;
	} else {
		tmp = (x * x) + ((4.0 * (t * y)) - (z * (z * (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 <= (-2.8d+132)) then
        tmp = x * x
    else
        tmp = (x * x) + ((4.0d0 * (t * y)) - (z * (z * (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 <= -2.8e+132) {
		tmp = x * x;
	} else {
		tmp = (x * x) + ((4.0 * (t * y)) - (z * (z * (y * 4.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.8e+132:
		tmp = x * x
	else:
		tmp = (x * x) + ((4.0 * (t * y)) - (z * (z * (y * 4.0))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.8e+132)
		tmp = Float64(x * x);
	else
		tmp = Float64(Float64(x * x) + Float64(Float64(4.0 * Float64(t * y)) - Float64(z * Float64(z * Float64(y * 4.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.8e+132)
		tmp = x * x;
	else
		tmp = (x * x) + ((4.0 * (t * y)) - (z * (z * (y * 4.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.8e+132], N[(x * x), $MachinePrecision], N[(N[(x * x), $MachinePrecision] + N[(N[(4.0 * N[(t * y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(z * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7999999999999999e132

   1. Initial program 84.6%

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

   2. Taylor expanded in x around inf 92.5%

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

      1. unpow2 92.5%

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

   4. Simplified 92.5%

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

   if -2.7999999999999999e132 < x

   1. Initial program 93.9%

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

      1. add-cube-cbrt 93.4%

         \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot z - t} \cdot \sqrt[3]{z \cdot z - t}\right) \cdot \sqrt[3]{z \cdot z - t}\right)} \]

      2. pow3 93.4%

         \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{{\left(\sqrt[3]{z \cdot z - t}\right)}^{3}} \]

   3. Applied egg-rr 93.4%

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

      1. unpow3 93.4%

         \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot z - t} \cdot \sqrt[3]{z \cdot z - t}\right) \cdot \sqrt[3]{z \cdot z - t}\right)} \]

      2. add-cube-cbrt 93.9%

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

      3. sub-neg 93.9%

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

      4. distribute-lft-in 92.0%

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

      5. *-commutative 92.0%

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

   5. Applied egg-rr 92.0%

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

      1. fma-def 92.5%

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

      2. distribute-rgt-neg-out 92.5%

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

      3. add-sqr-sqrt 48.5%

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

      4. sqrt-prod 71.3%

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

      5. sqr-neg 71.3%

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

      6. sqrt-prod 31.0%

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

      7. add-sqr-sqrt 65.0%

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

      8. *-commutative 65.0%

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

      9. *-commutative 65.0%

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

      10. fma-neg 65.0%

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

      11. associate-*l* 70.5%

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

      12. add-sqr-sqrt 43.8%

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

      13. add-sqr-sqrt 70.5%

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

      14. add-sqr-sqrt 34.0%

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

      15. sqrt-prod 73.8%

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

      16. sqr-neg 73.8%

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

      17. sqrt-prod 50.6%

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

      18. add-sqr-sqrt 97.6%

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

   7. Applied egg-rr 97.6%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+132}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + \left(4 \cdot \left(t \cdot y\right) - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\right)\\ \end{array} \]

Alternative 8: 95.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+258}:\\ \;\;\;\;x \cdot x - \left(z \cdot z - t\right) \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 4e+258)
   (- (* 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) <= 4e+258) {
		tmp = (x * x) - (((z * z) - t) * (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+258) then
        tmp = (x * x) - (((z * z) - t) * (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+258) {
		tmp = (x * x) - (((z * z) - t) * (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+258:
		tmp = (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) <= 4e+258)
		tmp = Float64(Float64(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

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * z) <= 4e+258)
		tmp = (x * x) - (((z * z) - t) * (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+258], N[(N[(x * x), $MachinePrecision] - 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) < 4.00000000000000023e258

   1. Initial program 98.9%

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

   if 4.00000000000000023e258 < (*.f64 z z)

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 80.0%

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

      1. unpow2 80.0%

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

      2. *-commutative 80.0%

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

      3. associate-*l* 89.0%

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

   4. Simplified 89.0%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+258}:\\ \;\;\;\;x \cdot x - \left(z \cdot z - t\right) \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 9: 60.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 1.16 \cdot 10^{+17}:\\ \;\;\;\;4 \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x x) 1.16e+17) (* 4.0 (* t y)) (* x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 1.16e+17) {
		tmp = 4.0 * (t * y);
	} 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) <= 1.16d+17) then
        tmp = 4.0d0 * (t * y)
    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) <= 1.16e+17) {
		tmp = 4.0 * (t * y);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x * x) <= 1.16e+17:
		tmp = 4.0 * (t * y)
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * x) <= 1.16e+17)
		tmp = Float64(4.0 * Float64(t * y));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * x) <= 1.16e+17)
		tmp = 4.0 * (t * y);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 1.16e+17], N[(4.0 * N[(t * y), $MachinePrecision]), $MachinePrecision], N[(x * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 1.16e17

   1. Initial program 92.7%

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

   2. Taylor expanded in t around inf 43.2%

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

   if 1.16e17 < (*.f64 x x)

   1. Initial program 92.2%

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

   2. Taylor expanded in x around inf 76.2%

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

      1. unpow2 76.2%

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

   4. Simplified 76.2%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 1.16 \cdot 10^{+17}:\\ \;\;\;\;4 \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 10: 41.5% 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 92.5%

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

2. Taylor expanded in x around inf 44.2%

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

   1. unpow2 44.2%

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

4. Simplified 44.2%

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

5. Final simplification 44.2%

   \[\leadsto x \cdot x \]

Developer target: 91.0% 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 2023195 
(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))))