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

Percentage Accurate: 91.5% → 96.6%

Time: 9.5s

Alternatives: 10

Speedup: 0.9×

• 48.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.5% 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: 96.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;z\_m \leq 6.7 \cdot 10^{+156}:\\ \;\;\;\;\mathsf{fma}\left(x, x, y \cdot \left(\mathsf{fma}\left(z\_m, z\_m, -t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z\_m \cdot \left(y \cdot \left(z\_m \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= z_m 6.7e+156)
   (fma x x (* y (* (fma z_m z_m (- t)) -4.0)))
   (- (* x x) (* z_m (* y (* z_m 4.0))))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (z_m <= 6.7e+156) {
		tmp = fma(x, x, (y * (fma(z_m, z_m, -t) * -4.0)));
	} else {
		tmp = (x * x) - (z_m * (y * (z_m * 4.0)));
	}
	return tmp;
}

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (z_m <= 6.7e+156)
		tmp = fma(x, x, Float64(y * Float64(fma(z_m, z_m, Float64(-t)) * -4.0)));
	else
		tmp = Float64(Float64(x * x) - Float64(z_m * Float64(y * Float64(z_m * 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, 6.7e+156], N[(x * x + N[(y * N[(N[(z$95$m * z$95$m + (-t)), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] - N[(z$95$m * N[(y * N[(z$95$m * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.7e156

   1. Initial program 94.3%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. distribute-rgt-neg-in N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-neg N/A

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

      15. lift-*.f64 N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-neg.f64 N/A

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

      18. metadata-eval 96.1

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

   4. Applied rewrites 96.1%

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

   if 6.7e156 < z

   1. Initial program 80.3%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 96.5

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

   5. Applied rewrites 96.5%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6.7 \cdot 10^{+156}:\\ \;\;\;\;\mathsf{fma}\left(x, x, y \cdot \left(\mathsf{fma}\left(z, z, -t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(y \cdot \left(z \cdot 4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 50.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} t_1 := \left(z\_m \cdot -4\right) \cdot \left(z\_m \cdot y\right)\\ \mathbf{if}\;x \leq 2.55 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(t \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (let* ((t_1 (* (* z_m -4.0) (* z_m y))))
   (if (<= x 2.55e-172)
     t_1
     (if (<= x 2.8e-24) (* y (* t 4.0)) (if (<= x 1.1e+43) t_1 (* x x))))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double t_1 = (z_m * -4.0) * (z_m * y);
	double tmp;
	if (x <= 2.55e-172) {
		tmp = t_1;
	} else if (x <= 2.8e-24) {
		tmp = y * (t * 4.0);
	} else if (x <= 1.1e+43) {
		tmp = t_1;
	} else {
		tmp = x * x;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (z_m * (-4.0d0)) * (z_m * y)
    if (x <= 2.55d-172) then
        tmp = t_1
    else if (x <= 2.8d-24) then
        tmp = y * (t * 4.0d0)
    else if (x <= 1.1d+43) then
        tmp = t_1
    else
        tmp = x * x
    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 t_1 = (z_m * -4.0) * (z_m * y);
	double tmp;
	if (x <= 2.55e-172) {
		tmp = t_1;
	} else if (x <= 2.8e-24) {
		tmp = y * (t * 4.0);
	} else if (x <= 1.1e+43) {
		tmp = t_1;
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

z_m = math.fabs(z)
def code(x, y, z_m, t):
	t_1 = (z_m * -4.0) * (z_m * y)
	tmp = 0
	if x <= 2.55e-172:
		tmp = t_1
	elif x <= 2.8e-24:
		tmp = y * (t * 4.0)
	elif x <= 1.1e+43:
		tmp = t_1
	else:
		tmp = x * x
	return tmp

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	t_1 = Float64(Float64(z_m * -4.0) * Float64(z_m * y))
	tmp = 0.0
	if (x <= 2.55e-172)
		tmp = t_1;
	elseif (x <= 2.8e-24)
		tmp = Float64(y * Float64(t * 4.0));
	elseif (x <= 1.1e+43)
		tmp = t_1;
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

z_m = abs(z);
function tmp_2 = code(x, y, z_m, t)
	t_1 = (z_m * -4.0) * (z_m * y);
	tmp = 0.0;
	if (x <= 2.55e-172)
		tmp = t_1;
	elseif (x <= 2.8e-24)
		tmp = y * (t * 4.0);
	elseif (x <= 1.1e+43)
		tmp = t_1;
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := Block[{t$95$1 = N[(N[(z$95$m * -4.0), $MachinePrecision] * N[(z$95$m * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 2.55e-172], t$95$1, If[LessEqual[x, 2.8e-24], N[(y * N[(t * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+43], t$95$1, N[(x * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 2.5499999999999999e-172 or 2.8000000000000002e-24 < x < 1.1e43

   1. Initial program 93.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 42.3

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

   5. Applied rewrites 42.3%

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

   7. Applied rewrites 44.6%

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

   if 2.5499999999999999e-172 < x < 2.8000000000000002e-24

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 60.7

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

   5. Applied rewrites 60.7%

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

   if 1.1e43 < x

   1. Initial program 87.9%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 71.4

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

   5. Applied rewrites 71.4%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.55 \cdot 10^{-172}:\\ \;\;\;\;\left(z \cdot -4\right) \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(t \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+43}:\\ \;\;\;\;\left(z \cdot -4\right) \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} t_1 := -4 \cdot \left(y \cdot \left(z\_m \cdot z\_m\right)\right)\\ \mathbf{if}\;x \leq 2.55 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \left(t \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (let* ((t_1 (* -4.0 (* y (* z_m z_m)))))
   (if (<= x 2.55e-172)
     t_1
     (if (<= x 1.65e-38) (* y (* t 4.0)) (if (<= x 1.1e+43) t_1 (* x x))))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double t_1 = -4.0 * (y * (z_m * z_m));
	double tmp;
	if (x <= 2.55e-172) {
		tmp = t_1;
	} else if (x <= 1.65e-38) {
		tmp = y * (t * 4.0);
	} else if (x <= 1.1e+43) {
		tmp = t_1;
	} else {
		tmp = x * x;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (y * (z_m * z_m))
    if (x <= 2.55d-172) then
        tmp = t_1
    else if (x <= 1.65d-38) then
        tmp = y * (t * 4.0d0)
    else if (x <= 1.1d+43) then
        tmp = t_1
    else
        tmp = x * x
    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 t_1 = -4.0 * (y * (z_m * z_m));
	double tmp;
	if (x <= 2.55e-172) {
		tmp = t_1;
	} else if (x <= 1.65e-38) {
		tmp = y * (t * 4.0);
	} else if (x <= 1.1e+43) {
		tmp = t_1;
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

z_m = math.fabs(z)
def code(x, y, z_m, t):
	t_1 = -4.0 * (y * (z_m * z_m))
	tmp = 0
	if x <= 2.55e-172:
		tmp = t_1
	elif x <= 1.65e-38:
		tmp = y * (t * 4.0)
	elif x <= 1.1e+43:
		tmp = t_1
	else:
		tmp = x * x
	return tmp

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	t_1 = Float64(-4.0 * Float64(y * Float64(z_m * z_m)))
	tmp = 0.0
	if (x <= 2.55e-172)
		tmp = t_1;
	elseif (x <= 1.65e-38)
		tmp = Float64(y * Float64(t * 4.0));
	elseif (x <= 1.1e+43)
		tmp = t_1;
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

z_m = abs(z);
function tmp_2 = code(x, y, z_m, t)
	t_1 = -4.0 * (y * (z_m * z_m));
	tmp = 0.0;
	if (x <= 2.55e-172)
		tmp = t_1;
	elseif (x <= 1.65e-38)
		tmp = y * (t * 4.0);
	elseif (x <= 1.1e+43)
		tmp = t_1;
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := Block[{t$95$1 = N[(-4.0 * N[(y * N[(z$95$m * z$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 2.55e-172], t$95$1, If[LessEqual[x, 1.65e-38], N[(y * N[(t * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+43], t$95$1, N[(x * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 2.5499999999999999e-172 or 1.6500000000000001e-38 < x < 1.1e43

   1. Initial program 93.4%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 42.4

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

   5. Applied rewrites 42.4%

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

   if 2.5499999999999999e-172 < x < 1.6500000000000001e-38

   1. Initial program 97.4%

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

   3. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 61.1

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

   5. Applied rewrites 61.1%

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

   if 1.1e43 < x

   1. Initial program 87.9%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 71.4

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

   5. Applied rewrites 71.4%

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

Alternative 4: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(z\_m, z\_m \cdot -4, t \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, t \cdot 4, x \cdot x\right)\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= (* x x) 2e+82)
   (* y (fma z_m (* z_m -4.0) (* t 4.0)))
   (fma y (* t 4.0) (* x x))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if ((x * x) <= 2e+82) {
		tmp = y * fma(z_m, (z_m * -4.0), (t * 4.0));
	} else {
		tmp = fma(y, (t * 4.0), (x * x));
	}
	return tmp;
}

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (Float64(x * x) <= 2e+82)
		tmp = Float64(y * fma(z_m, Float64(z_m * -4.0), Float64(t * 4.0)));
	else
		tmp = fma(y, Float64(t * 4.0), Float64(x * x));
	end
	return tmp
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 2e+82], N[(y * N[(z$95$m * N[(z$95$m * -4.0), $MachinePrecision] + N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(t * 4.0), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 1.9999999999999999e82

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 83.5

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

   5. Applied rewrites 83.5%

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

   7. Applied rewrites 83.5%

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

   9. Applied rewrites 84.2%

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

   if 1.9999999999999999e82 < (*.f64 x x)

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 4 \cdot t, {x}^{2}\right)} \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{t \cdot 4}, {x}^{2}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{t \cdot 4}, {x}^{2}\right) \]

      9. unpow2 N/A

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

      10. lower-*.f64 86.7

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

   5. Applied rewrites 86.7%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(z, z \cdot -4, t \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, t \cdot 4, x \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;z\_m \leq 8.2 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(x, x, y \cdot \left(t \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z\_m \cdot \left(y \cdot \left(z\_m \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= z_m 8.2e-16)
   (fma x x (* y (* t 4.0)))
   (- (* x x) (* z_m (* y (* z_m 4.0))))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (z_m <= 8.2e-16) {
		tmp = fma(x, x, (y * (t * 4.0)));
	} else {
		tmp = (x * x) - (z_m * (y * (z_m * 4.0)));
	}
	return tmp;
}

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (z_m <= 8.2e-16)
		tmp = fma(x, x, Float64(y * Float64(t * 4.0)));
	else
		tmp = Float64(Float64(x * x) - Float64(z_m * Float64(y * Float64(z_m * 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, 8.2e-16], N[(x * x + N[(y * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] - N[(z$95$m * N[(y * N[(z$95$m * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.20000000000000012e-16

   1. Initial program 93.3%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. distribute-rgt-neg-in N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-neg N/A

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

      15. lift-*.f64 N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-neg.f64 N/A

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

      18. metadata-eval 95.3

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

   4. Applied rewrites 95.3%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 77.8

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

   7. Applied rewrites 77.8%

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

   if 8.20000000000000012e-16 < z

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 89.4

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

   5. Applied rewrites 89.4%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.2 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(x, x, y \cdot \left(t \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(y \cdot \left(z \cdot 4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2 \cdot 10^{+82}:\\ \;\;\;\;\left(z\_m \cdot z\_m - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, t \cdot 4, x \cdot x\right)\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= (* x x) 2e+82)
   (* (- (* z_m z_m) t) (* y -4.0))
   (fma y (* t 4.0) (* x x))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if ((x * x) <= 2e+82) {
		tmp = ((z_m * z_m) - t) * (y * -4.0);
	} else {
		tmp = fma(y, (t * 4.0), (x * x));
	}
	return tmp;
}

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (Float64(x * x) <= 2e+82)
		tmp = Float64(Float64(Float64(z_m * z_m) - t) * Float64(y * -4.0));
	else
		tmp = fma(y, Float64(t * 4.0), Float64(x * x));
	end
	return tmp
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 2e+82], N[(N[(N[(z$95$m * z$95$m), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(t * 4.0), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 1.9999999999999999e82

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 83.5

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

   5. Applied rewrites 83.5%

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

   if 1.9999999999999999e82 < (*.f64 x x)

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 4 \cdot t, {x}^{2}\right)} \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{t \cdot 4}, {x}^{2}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{t \cdot 4}, {x}^{2}\right) \]

      9. unpow2 N/A

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

      10. lower-*.f64 86.7

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

   5. Applied rewrites 86.7%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2 \cdot 10^{+82}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, t \cdot 4, x \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;z\_m \cdot z\_m \leq 4 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(x, x, y \cdot \left(t \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z\_m \cdot -4\right) \cdot \left(z\_m \cdot y\right)\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= (* z_m z_m) 4e+99)
   (fma x x (* y (* t 4.0)))
   (* (* z_m -4.0) (* z_m y))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if ((z_m * z_m) <= 4e+99) {
		tmp = fma(x, x, (y * (t * 4.0)));
	} else {
		tmp = (z_m * -4.0) * (z_m * y);
	}
	return tmp;
}

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (Float64(z_m * z_m) <= 4e+99)
		tmp = fma(x, x, Float64(y * Float64(t * 4.0)));
	else
		tmp = Float64(Float64(z_m * -4.0) * Float64(z_m * y));
	end
	return tmp
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := If[LessEqual[N[(z$95$m * z$95$m), $MachinePrecision], 4e+99], N[(x * x + N[(y * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z$95$m * -4.0), $MachinePrecision] * N[(z$95$m * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 3.9999999999999999e99

   1. Initial program 98.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. distribute-rgt-neg-in N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-neg N/A

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

      15. lift-*.f64 N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-neg.f64 N/A

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

      18. metadata-eval 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 88.8

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

   7. Applied rewrites 88.8%

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

   if 3.9999999999999999e99 < (*.f64 z z)

   1. Initial program 84.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 71.2

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

   5. Applied rewrites 71.2%

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

   7. Applied rewrites 75.7%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(x, x, y \cdot \left(t \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -4\right) \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;z\_m \cdot z\_m \leq 4 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(y, t \cdot 4, x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z\_m \cdot -4\right) \cdot \left(z\_m \cdot y\right)\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= (* z_m z_m) 4e+99)
   (fma y (* t 4.0) (* x x))
   (* (* z_m -4.0) (* z_m y))))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if ((z_m * z_m) <= 4e+99) {
		tmp = fma(y, (t * 4.0), (x * x));
	} else {
		tmp = (z_m * -4.0) * (z_m * y);
	}
	return tmp;
}

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (Float64(z_m * z_m) <= 4e+99)
		tmp = fma(y, Float64(t * 4.0), Float64(x * x));
	else
		tmp = Float64(Float64(z_m * -4.0) * Float64(z_m * y));
	end
	return tmp
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := If[LessEqual[N[(z$95$m * z$95$m), $MachinePrecision], 4e+99], N[(y * N[(t * 4.0), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision], N[(N[(z$95$m * -4.0), $MachinePrecision] * N[(z$95$m * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 3.9999999999999999e99

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 4 \cdot t, {x}^{2}\right)} \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{t \cdot 4}, {x}^{2}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{t \cdot 4}, {x}^{2}\right) \]

      9. unpow2 N/A

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

      10. lower-*.f64 87.5

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

   5. Applied rewrites 87.5%

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

   if 3.9999999999999999e99 < (*.f64 z z)

   1. Initial program 84.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 71.2

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

   5. Applied rewrites 71.2%

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

   7. Applied rewrites 75.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(y, t \cdot 4, x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -4\right) \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 1.9 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \left(t \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
(FPCore (x y z_m t)
 :precision binary64
 (if (<= (* x x) 1.9e-47) (* y (* t 4.0)) (* x x)))

C

z_m = fabs(z);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if ((x * x) <= 1.9e-47) {
		tmp = y * (t * 4.0);
	} else {
		tmp = x * x;
	}
	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 ((x * x) <= 1.9d-47) then
        tmp = y * (t * 4.0d0)
    else
        tmp = x * x
    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 ((x * x) <= 1.9e-47) {
		tmp = y * (t * 4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

z_m = math.fabs(z)
def code(x, y, z_m, t):
	tmp = 0
	if (x * x) <= 1.9e-47:
		tmp = y * (t * 4.0)
	else:
		tmp = x * x
	return tmp

Julia

z_m = abs(z)
function code(x, y, z_m, t)
	tmp = 0.0
	if (Float64(x * x) <= 1.9e-47)
		tmp = Float64(y * Float64(t * 4.0));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

z_m = abs(z);
function tmp_2 = code(x, y, z_m, t)
	tmp = 0.0;
	if ((x * x) <= 1.9e-47)
		tmp = y * (t * 4.0);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
code[x_, y_, z$95$m_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 1.9e-47], N[(y * N[(t * 4.0), $MachinePrecision]), $MachinePrecision], N[(x * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 1.90000000000000007e-47

   1. Initial program 94.1%

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

   3. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 50.0

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

   5. Applied rewrites 50.0%

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

   if 1.90000000000000007e-47 < (*.f64 x x)

   1. Initial program 91.6%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

Alternative 10: 41.2% accurate, 4.5× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.7%

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

3. Taylor expanded in x around inf

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

   1. unpow2 N/A

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

   2. lower-*.f64 44.7

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

5. Applied rewrites 44.7%

   \[\leadsto \color{blue}{x \cdot x} \]
6. Add Preprocessing

Developer Target 1: 91.6% 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 2024233 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* x x) (* 4 (* y (- (* z z) t)))))

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