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

Percentage Accurate: 90.3% → 93.5%

Time: 10.8s

Alternatives: 7

Speedup: 0.4×

• 49.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.3% 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: 93.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;x\_m \leq 2 \cdot 10^{+226}:\\ \;\;\;\;\mathsf{fma}\left(x\_m, x\_m, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot x\_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t)
 :precision binary64
 (if (<= x_m 2e+226) (fma x_m x_m (* (- (* z z) t) (* y -4.0))) (* x_m x_m)))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 2e+226) {
		tmp = fma(x_m, x_m, (((z * z) - t) * (y * -4.0)));
	} else {
		tmp = x_m * x_m;
	}
	return tmp;
}

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	tmp = 0.0
	if (x_m <= 2e+226)
		tmp = fma(x_m, x_m, Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0)));
	else
		tmp = Float64(x_m * x_m);
	end
	return tmp
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := If[LessEqual[x$95$m, 2e+226], N[(x$95$m * x$95$m + N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m * x$95$m), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.99999999999999992e226

   1. Initial program 91.7%

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

      1. fma-neg 95.5%

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

      2. distribute-lft-neg-in 95.5%

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

      3. *-commutative 95.5%

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

      4. distribute-rgt-neg-in 95.5%

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

      5. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

   if 1.99999999999999992e226 < x

   1. Initial program 70.0%

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

   3. Taylor expanded in y around 0 70.0%

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

   5. Simplified 95.0%

      \[\leadsto x \cdot x - \color{blue}{0} \]
   6. Step-by-step derivation

      1. --rgt-identity 95.0%

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

   7. Applied egg-rr 95.0%

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

Alternative 2: 92.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} t_1 := x\_m \cdot x\_m + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x\_m, x\_m, y \cdot \left(t \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t)
 :precision binary64
 (let* ((t_1 (+ (* x_m x_m) (* (* y 4.0) (- t (* z z))))))
   (if (<= t_1 INFINITY) t_1 (fma x_m x_m (* y (* t 4.0))))))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	double t_1 = (x_m * x_m) + ((y * 4.0) * (t - (z * z)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(x_m, x_m, (y * (t * 4.0)));
	}
	return tmp;
}

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	t_1 = Float64(Float64(x_m * x_m) + Float64(Float64(y * 4.0) * Float64(t - Float64(z * z))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(x_m, x_m, Float64(y * Float64(t * 4.0)));
	end
	return tmp
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m * x$95$m), $MachinePrecision] + N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x$95$m * x$95$m + N[(y * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) (-.f64 (*.f64 z z) t))) < +inf.0

   1. Initial program 96.8%

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

   if +inf.0 < (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) (-.f64 (*.f64 z z) t)))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 38.9%

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

      1. *-commutative 38.9%

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

      2. *-commutative 38.9%

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

      3. associate-*l* 38.9%

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

   5. Simplified 38.9%

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

      1. fma-neg 50.0%

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

      2. distribute-rgt-neg-in 50.0%

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

      3. *-commutative 50.0%

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

      4. distribute-lft-neg-in 50.0%

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

      5. metadata-eval 50.0%

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

   7. Applied egg-rr 50.0%

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

4. Final simplification 93.5%

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

Alternative 3: 92.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} t_1 := x\_m \cdot x\_m + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \left(y \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t)
 :precision binary64
 (let* ((t_1 (+ (* x_m x_m) (* (* y 4.0) (- t (* z z))))))
   (if (<= t_1 INFINITY) t_1 (* (* z z) (* y -4.0)))))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	double t_1 = (x_m * x_m) + ((y * 4.0) * (t - (z * z)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (z * z) * (y * -4.0);
	}
	return tmp;
}

Java

x_m = Math.abs(x);
public static double code(double x_m, double y, double z, double t) {
	double t_1 = (x_m * x_m) + ((y * 4.0) * (t - (z * z)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (z * z) * (y * -4.0);
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m, y, z, t):
	t_1 = (x_m * x_m) + ((y * 4.0) * (t - (z * z)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (z * z) * (y * -4.0)
	return tmp

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	t_1 = Float64(Float64(x_m * x_m) + Float64(Float64(y * 4.0) * Float64(t - Float64(z * z))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * z) * Float64(y * -4.0));
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m, y, z, t)
	t_1 = (x_m * x_m) + ((y * 4.0) * (t - (z * z)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (z * z) * (y * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m * x$95$m), $MachinePrecision] + N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(z * z), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) (-.f64 (*.f64 z z) t))) < +inf.0

   1. Initial program 96.8%

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

   if +inf.0 < (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) (-.f64 (*.f64 z z) t)))

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 0.0%

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

      4. swap-sqr 0.0%

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

      5. metadata-eval 0.0%

         \[\leadsto x \cdot x - \left(z \cdot z - t\right) \cdot \sqrt{\left(y \cdot y\right) \cdot \color{blue}{16}} \]

      6. metadata-eval 0.0%

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

      7. swap-sqr 0.0%

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

      8. sqrt-unprod 0.0%

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

      9. add-sqr-sqrt 44.4%

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

      10. add-cube-cbrt 44.4%

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

      11. pow3 44.4%

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

   4. Applied egg-rr 0.0%

      \[\leadsto x \cdot x - \color{blue}{{\left(\sqrt[3]{y \cdot \left(4 \cdot \left({z}^{2} - t\right)\right)}\right)}^{3}} \]

   5. Taylor expanded in z around inf 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left({z}^{2} \cdot {\left(\sqrt[3]{4}\right)}^{3}\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 44.6%

         \[\leadsto \color{blue}{-y \cdot \left({z}^{2} \cdot {\left(\sqrt[3]{4}\right)}^{3}\right)} \]

      2. rem-cube-cbrt 44.6%

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

      3. *-commutative 44.6%

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

      4. associate-*l* 44.6%

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

      5. *-commutative 44.6%

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

      6. distribute-rgt-neg-in 44.6%

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

      7. distribute-rgt-neg-in 44.6%

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

      8. metadata-eval 44.6%

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

   7. Simplified 44.6%

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

      1. unpow2 44.6%

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

   9. Applied egg-rr 44.6%

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

4. Final simplification 93.1%

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

Alternative 4: 80.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 1.52 \cdot 10^{+254}:\\ \;\;\;\;x\_m \cdot x\_m - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \left(y \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t)
 :precision binary64
 (if (<= (* z z) 1.52e+254)
   (- (* x_m x_m) (* y (* t -4.0)))
   (* (* z z) (* y -4.0))))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 1.52e+254) {
		tmp = (x_m * x_m) - (y * (t * -4.0));
	} else {
		tmp = (z * z) * (y * -4.0);
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m, y, z, t)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * z) <= 1.52d+254) then
        tmp = (x_m * x_m) - (y * (t * (-4.0d0)))
    else
        tmp = (z * z) * (y * (-4.0d0))
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 1.52e+254) {
		tmp = (x_m * x_m) - (y * (t * -4.0));
	} else {
		tmp = (z * z) * (y * -4.0);
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m, y, z, t):
	tmp = 0
	if (z * z) <= 1.52e+254:
		tmp = (x_m * x_m) - (y * (t * -4.0))
	else:
		tmp = (z * z) * (y * -4.0)
	return tmp

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 1.52e+254)
		tmp = Float64(Float64(x_m * x_m) - Float64(y * Float64(t * -4.0)));
	else
		tmp = Float64(Float64(z * z) * Float64(y * -4.0));
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m, y, z, t)
	tmp = 0.0;
	if ((z * z) <= 1.52e+254)
		tmp = (x_m * x_m) - (y * (t * -4.0));
	else
		tmp = (z * z) * (y * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 1.52e+254], N[(N[(x$95$m * x$95$m), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * z), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 1.51999999999999996e254

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0 83.7%

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

      1. *-commutative 83.7%

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

      2. *-commutative 83.7%

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

      3. associate-*l* 83.7%

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

   5. Simplified 83.7%

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

   if 1.51999999999999996e254 < (*.f64 z z)

   1. Initial program 74.8%

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

      1. *-commutative 74.8%

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

      2. add-sqr-sqrt 36.3%

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

      3. sqrt-unprod 36.0%

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

      4. swap-sqr 36.0%

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

      5. metadata-eval 36.0%

         \[\leadsto x \cdot x - \left(z \cdot z - t\right) \cdot \sqrt{\left(y \cdot y\right) \cdot \color{blue}{16}} \]

      6. metadata-eval 36.0%

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

      7. swap-sqr 36.0%

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

      8. sqrt-unprod 1.2%

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

      9. add-sqr-sqrt 8.7%

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

      10. add-cube-cbrt 8.7%

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

      11. pow3 8.7%

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

   4. Applied egg-rr 74.8%

      \[\leadsto x \cdot x - \color{blue}{{\left(\sqrt[3]{y \cdot \left(4 \cdot \left({z}^{2} - t\right)\right)}\right)}^{3}} \]

   5. Taylor expanded in z around inf 82.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left({z}^{2} \cdot {\left(\sqrt[3]{4}\right)}^{3}\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 82.3%

         \[\leadsto \color{blue}{-y \cdot \left({z}^{2} \cdot {\left(\sqrt[3]{4}\right)}^{3}\right)} \]

      2. rem-cube-cbrt 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*l* 82.3%

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

      5. *-commutative 82.3%

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

      6. distribute-rgt-neg-in 82.3%

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

      7. distribute-rgt-neg-in 82.3%

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

      8. metadata-eval 82.3%

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

   7. Simplified 82.3%

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

      1. unpow2 82.3%

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

   9. Applied egg-rr 82.3%

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

Alternative 5: 58.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 3.9 \cdot 10^{-41}:\\ \;\;\;\;x\_m \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \left(y \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t)
 :precision binary64
 (if (<= (* z z) 3.9e-41) (* x_m x_m) (* (* z z) (* y -4.0))))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 3.9e-41) {
		tmp = x_m * x_m;
	} else {
		tmp = (z * z) * (y * -4.0);
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m, y, z, t)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * z) <= 3.9d-41) then
        tmp = x_m * x_m
    else
        tmp = (z * z) * (y * (-4.0d0))
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 3.9e-41) {
		tmp = x_m * x_m;
	} else {
		tmp = (z * z) * (y * -4.0);
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m, y, z, t):
	tmp = 0
	if (z * z) <= 3.9e-41:
		tmp = x_m * x_m
	else:
		tmp = (z * z) * (y * -4.0)
	return tmp

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 3.9e-41)
		tmp = Float64(x_m * x_m);
	else
		tmp = Float64(Float64(z * z) * Float64(y * -4.0));
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m, y, z, t)
	tmp = 0.0;
	if ((z * z) <= 3.9e-41)
		tmp = x_m * x_m;
	else
		tmp = (z * z) * (y * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 3.9e-41], N[(x$95$m * x$95$m), $MachinePrecision], N[(N[(z * z), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 3.89999999999999991e-41

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 98.3%

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

   5. Simplified 59.3%

      \[\leadsto x \cdot x - \color{blue}{0} \]
   6. Step-by-step derivation

      1. --rgt-identity 59.3%

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

   7. Applied egg-rr 59.3%

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

   if 3.89999999999999991e-41 < (*.f64 z z)

   1. Initial program 83.1%

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

      1. *-commutative 83.1%

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

      2. add-sqr-sqrt 40.5%

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

      3. sqrt-unprod 41.3%

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

      4. swap-sqr 41.3%

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

      5. metadata-eval 41.3%

         \[\leadsto x \cdot x - \left(z \cdot z - t\right) \cdot \sqrt{\left(y \cdot y\right) \cdot \color{blue}{16}} \]

      6. metadata-eval 41.3%

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

      7. swap-sqr 41.3%

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

      8. sqrt-unprod 7.0%

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

      9. add-sqr-sqrt 20.1%

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

      10. add-cube-cbrt 20.1%

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

      11. pow3 20.1%

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

   4. Applied egg-rr 82.7%

      \[\leadsto x \cdot x - \color{blue}{{\left(\sqrt[3]{y \cdot \left(4 \cdot \left({z}^{2} - t\right)\right)}\right)}^{3}} \]

   5. Taylor expanded in z around inf 64.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left({z}^{2} \cdot {\left(\sqrt[3]{4}\right)}^{3}\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 64.8%

         \[\leadsto \color{blue}{-y \cdot \left({z}^{2} \cdot {\left(\sqrt[3]{4}\right)}^{3}\right)} \]

      2. rem-cube-cbrt 65.0%

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

      3. *-commutative 65.0%

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

      4. associate-*l* 65.0%

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

      5. *-commutative 65.0%

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

      6. distribute-rgt-neg-in 65.0%

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

      7. distribute-rgt-neg-in 65.0%

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

      8. metadata-eval 65.0%

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

   7. Simplified 65.0%

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

      1. unpow2 65.0%

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

   9. Applied egg-rr 65.0%

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

Alternative 6: 58.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;x\_m \leq 2.8 \cdot 10^{+24}:\\ \;\;\;\;4 \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot x\_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t)
 :precision binary64
 (if (<= x_m 2.8e+24) (* 4.0 (* t y)) (* x_m x_m)))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 2.8e+24) {
		tmp = 4.0 * (t * y);
	} else {
		tmp = x_m * x_m;
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m, y, z, t)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x_m <= 2.8d+24) then
        tmp = 4.0d0 * (t * y)
    else
        tmp = x_m * x_m
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 2.8e+24) {
		tmp = 4.0 * (t * y);
	} else {
		tmp = x_m * x_m;
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m, y, z, t):
	tmp = 0
	if x_m <= 2.8e+24:
		tmp = 4.0 * (t * y)
	else:
		tmp = x_m * x_m
	return tmp

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	tmp = 0.0
	if (x_m <= 2.8e+24)
		tmp = Float64(4.0 * Float64(t * y));
	else
		tmp = Float64(x_m * x_m);
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m, y, z, t)
	tmp = 0.0;
	if (x_m <= 2.8e+24)
		tmp = 4.0 * (t * y);
	else
		tmp = x_m * x_m;
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := If[LessEqual[x$95$m, 2.8e+24], N[(4.0 * N[(t * y), $MachinePrecision]), $MachinePrecision], N[(x$95$m * x$95$m), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.8000000000000002e24

   1. Initial program 92.8%

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

      1. fma-neg 95.0%

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

      2. distribute-lft-neg-in 95.0%

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

      3. *-commutative 95.0%

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

      4. distribute-rgt-neg-in 95.0%

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

      5. metadata-eval 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in t around inf 35.7%

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

      1. *-commutative 35.7%

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

   7. Simplified 35.7%

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

   if 2.8000000000000002e24 < x

   1. Initial program 82.1%

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

   3. Taylor expanded in y around 0 82.1%

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

   5. Simplified 70.5%

      \[\leadsto x \cdot x - \color{blue}{0} \]
   6. Step-by-step derivation

      1. --rgt-identity 70.5%

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

   7. Applied egg-rr 70.5%

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

4. Final simplification 44.8%

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

Alternative 7: 40.6% accurate, 4.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x\_m \cdot x\_m \end{array} \]

FPCore

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

C

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

Fortran

x_m = abs(x)
real(8) function code(x_m, y, z, t)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x_m * x_m
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := N[(x$95$m * x$95$m), $MachinePrecision]

Derivation

1. Initial program 90.0%

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

3. Taylor expanded in y around 0 90.0%

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

5. Simplified 41.8%

   \[\leadsto x \cdot x - \color{blue}{0} \]
6. Step-by-step derivation

   1. --rgt-identity 41.8%

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

7. Applied egg-rr 41.8%

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

Developer Target 1: 90.3% 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 2024144 
(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))))