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

Percentage Accurate: 90.4% → 93.7%

Time: 12.5s

Alternatives: 8

Speedup: 0.6×

• 49.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.4% 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: 93.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+280}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 4, \mathsf{fma}\left(z, -z, t\right), x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{z}{\frac{t}{z}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 2e+280)
   (fma (* y 4.0) (fma z (- z) t) (* x x))
   (* (* t -4.0) (* y (+ -1.0 (/ z (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 2e+280) {
		tmp = fma((y * 4.0), fma(z, -z, t), (x * x));
	} else {
		tmp = (t * -4.0) * (y * (-1.0 + (z / (t / z))));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 2e+280)
		tmp = fma(Float64(y * 4.0), fma(z, Float64(-z), t), Float64(x * x));
	else
		tmp = Float64(Float64(t * -4.0) * Float64(y * Float64(-1.0 + Float64(z / Float64(t / z)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 2e+280], N[(N[(y * 4.0), $MachinePrecision] * N[(z * (-z) + t), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] * N[(y * N[(-1.0 + N[(z / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 2.0000000000000001e280

   1. Initial program 99.4%

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

      1. cancel-sign-sub-inv 99.4%

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

      2. distribute-lft-neg-out 99.4%

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

      3. +-commutative 99.4%

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

      4. associate-*l* 99.4%

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

      5. distribute-lft-neg-in 99.4%

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

      6. associate-*l* 99.4%

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

      7. distribute-rgt-neg-in 99.4%

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

      8. fma-define 99.9%

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

      9. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(y \cdot 4, \color{blue}{0 - \left(z \cdot z - t\right)}, x \cdot x\right) \]

      10. associate-+l- 99.9%

          \[\leadsto \mathsf{fma}\left(y \cdot 4, \color{blue}{\left(0 - z \cdot z\right) + t}, x \cdot x\right) \]

      11. neg-sub0 99.9%

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

      12. distribute-rgt-neg-out 99.9%

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

      13. fma-define 99.9%

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

   3. Simplified 99.9%

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

   if 2.0000000000000001e280 < (*.f64 z z)

   1. Initial program 68.3%

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

   3. Taylor expanded in t around inf 68.3%

      \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(t \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right)} \]

   4. Taylor expanded in x around 0 75.2%

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

      1. associate-*r* 75.2%

         \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right)} \]

      2. *-commutative 75.2%

         \[\leadsto \color{blue}{\left(t \cdot -4\right)} \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right) \]

      3. sub-neg 75.2%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \color{blue}{\left(\frac{{z}^{2}}{t} + \left(-1\right)\right)}\right) \]

      4. metadata-eval 75.2%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} + \color{blue}{-1}\right)\right) \]

      5. +-commutative 75.2%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \color{blue}{\left(-1 + \frac{{z}^{2}}{t}\right)}\right) \]

   6. Simplified 75.2%

      \[\leadsto \color{blue}{\left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{{z}^{2}}{t}\right)\right)} \]
   7. Step-by-step derivation

      1. unpow2 75.2%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{\color{blue}{z \cdot z}}{t}\right)\right) \]

      2. associate-/l* 80.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{z \cdot \frac{z}{t}}\right)\right) \]

   8. Applied egg-rr 80.3%

      \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{z \cdot \frac{z}{t}}\right)\right) \]
   9. Step-by-step derivation

      1. clear-num 80.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + z \cdot \color{blue}{\frac{1}{\frac{t}{z}}}\right)\right) \]

      2. un-div-inv 80.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{\frac{z}{\frac{t}{z}}}\right)\right) \]

   10. Applied egg-rr 80.3%

       \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{\frac{z}{\frac{t}{z}}}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 93.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+280}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 4, t - z \cdot z, x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{z}{\frac{t}{z}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 2e+280)
   (fma (* y 4.0) (- t (* z z)) (* x x))
   (* (* t -4.0) (* y (+ -1.0 (/ z (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 2e+280) {
		tmp = fma((y * 4.0), (t - (z * z)), (x * x));
	} else {
		tmp = (t * -4.0) * (y * (-1.0 + (z / (t / z))));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 2e+280)
		tmp = fma(Float64(y * 4.0), Float64(t - Float64(z * z)), Float64(x * x));
	else
		tmp = Float64(Float64(t * -4.0) * Float64(y * Float64(-1.0 + Float64(z / Float64(t / z)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 2e+280], N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] * N[(y * N[(-1.0 + N[(z / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 2.0000000000000001e280

   1. Initial program 99.4%

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

      1. cancel-sign-sub-inv 99.4%

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

      2. distribute-lft-neg-out 99.4%

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

      3. +-commutative 99.4%

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

      4. associate-*l* 99.4%

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

      5. distribute-lft-neg-in 99.4%

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

      6. associate-*l* 99.4%

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

      7. distribute-rgt-neg-in 99.4%

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

      8. fma-define 99.9%

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

      9. sub-neg 99.9%

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

      10. +-commutative 99.9%

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

      11. distribute-neg-in 99.9%

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

      12. remove-double-neg 99.9%

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

      13. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   if 2.0000000000000001e280 < (*.f64 z z)

   1. Initial program 68.3%

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

   3. Taylor expanded in t around inf 68.3%

      \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(t \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right)} \]

   4. Taylor expanded in x around 0 75.2%

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

      1. associate-*r* 75.2%

         \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right)} \]

      2. *-commutative 75.2%

         \[\leadsto \color{blue}{\left(t \cdot -4\right)} \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right) \]

      3. sub-neg 75.2%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \color{blue}{\left(\frac{{z}^{2}}{t} + \left(-1\right)\right)}\right) \]

      4. metadata-eval 75.2%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} + \color{blue}{-1}\right)\right) \]

      5. +-commutative 75.2%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \color{blue}{\left(-1 + \frac{{z}^{2}}{t}\right)}\right) \]

   6. Simplified 75.2%

      \[\leadsto \color{blue}{\left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{{z}^{2}}{t}\right)\right)} \]
   7. Step-by-step derivation

      1. unpow2 75.2%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{\color{blue}{z \cdot z}}{t}\right)\right) \]

      2. associate-/l* 80.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{z \cdot \frac{z}{t}}\right)\right) \]

   8. Applied egg-rr 80.3%

      \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{z \cdot \frac{z}{t}}\right)\right) \]
   9. Step-by-step derivation

      1. clear-num 80.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + z \cdot \color{blue}{\frac{1}{\frac{t}{z}}}\right)\right) \]

      2. un-div-inv 80.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{\frac{z}{\frac{t}{z}}}\right)\right) \]

   10. Applied egg-rr 80.3%

       \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{\frac{z}{\frac{t}{z}}}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 92.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 90.5%

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

   1. fma-neg 92.5%

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

   2. distribute-lft-neg-in 92.5%

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

   3. *-commutative 92.5%

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

   4. distribute-rgt-neg-in 92.5%

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

   5. metadata-eval 92.5%

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

3. Simplified 92.5%

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

Alternative 4: 92.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+280}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{z}{\frac{t}{z}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 2e+280)
   (+ (* x x) (* (* y 4.0) (- t (* z z))))
   (* (* t -4.0) (* y (+ -1.0 (/ z (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 2e+280) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = (t * -4.0) * (y * (-1.0 + (z / (t / z))));
	}
	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) <= 2d+280) then
        tmp = (x * x) + ((y * 4.0d0) * (t - (z * z)))
    else
        tmp = (t * (-4.0d0)) * (y * ((-1.0d0) + (z / (t / z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 2e+280) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = (t * -4.0) * (y * (-1.0 + (z / (t / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * z) <= 2e+280:
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)))
	else:
		tmp = (t * -4.0) * (y * (-1.0 + (z / (t / z))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 2e+280)
		tmp = Float64(Float64(x * x) + Float64(Float64(y * 4.0) * Float64(t - Float64(z * z))));
	else
		tmp = Float64(Float64(t * -4.0) * Float64(y * Float64(-1.0 + Float64(z / Float64(t / z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * z) <= 2e+280)
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	else
		tmp = (t * -4.0) * (y * (-1.0 + (z / (t / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 2e+280], N[(N[(x * x), $MachinePrecision] + N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] * N[(y * N[(-1.0 + N[(z / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 2.0000000000000001e280

   1. Initial program 99.4%

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

   if 2.0000000000000001e280 < (*.f64 z z)

   1. Initial program 68.3%

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

   3. Taylor expanded in t around inf 68.3%

      \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(t \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right)} \]

   4. Taylor expanded in x around 0 75.2%

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

      1. associate-*r* 75.2%

         \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right)} \]

      2. *-commutative 75.2%

         \[\leadsto \color{blue}{\left(t \cdot -4\right)} \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right) \]

      3. sub-neg 75.2%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \color{blue}{\left(\frac{{z}^{2}}{t} + \left(-1\right)\right)}\right) \]

      4. metadata-eval 75.2%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} + \color{blue}{-1}\right)\right) \]

      5. +-commutative 75.2%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \color{blue}{\left(-1 + \frac{{z}^{2}}{t}\right)}\right) \]

   6. Simplified 75.2%

      \[\leadsto \color{blue}{\left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{{z}^{2}}{t}\right)\right)} \]
   7. Step-by-step derivation

      1. unpow2 75.2%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{\color{blue}{z \cdot z}}{t}\right)\right) \]

      2. associate-/l* 80.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{z \cdot \frac{z}{t}}\right)\right) \]

   8. Applied egg-rr 80.3%

      \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{z \cdot \frac{z}{t}}\right)\right) \]
   9. Step-by-step derivation

      1. clear-num 80.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + z \cdot \color{blue}{\frac{1}{\frac{t}{z}}}\right)\right) \]

      2. un-div-inv 80.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{\frac{z}{\frac{t}{z}}}\right)\right) \]

   10. Applied egg-rr 80.3%

       \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{\frac{z}{\frac{t}{z}}}\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+280}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{z}{\frac{t}{z}}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{z}{\frac{t}{z}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 5.2e+40)
   (- (* x x) (* y (* t -4.0)))
   (* (* t -4.0) (* y (+ -1.0 (/ z (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.2e+40) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = (t * -4.0) * (y * (-1.0 + (z / (t / z))));
	}
	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 <= 5.2d+40) then
        tmp = (x * x) - (y * (t * (-4.0d0)))
    else
        tmp = (t * (-4.0d0)) * (y * ((-1.0d0) + (z / (t / z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.2e+40) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = (t * -4.0) * (y * (-1.0 + (z / (t / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 5.2e+40:
		tmp = (x * x) - (y * (t * -4.0))
	else:
		tmp = (t * -4.0) * (y * (-1.0 + (z / (t / z))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 5.2e+40)
		tmp = Float64(Float64(x * x) - Float64(y * Float64(t * -4.0)));
	else
		tmp = Float64(Float64(t * -4.0) * Float64(y * Float64(-1.0 + Float64(z / Float64(t / z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 5.2e+40)
		tmp = (x * x) - (y * (t * -4.0));
	else
		tmp = (t * -4.0) * (y * (-1.0 + (z / (t / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 5.2e+40], N[(N[(x * x), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] * N[(y * N[(-1.0 + N[(z / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.2000000000000001e40

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 75.1%

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

      1. *-commutative 75.1%

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

      2. *-commutative 75.1%

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

      3. associate-*l* 75.1%

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

   5. Simplified 75.1%

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

   if 5.2000000000000001e40 < z

   1. Initial program 81.3%

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

   3. Taylor expanded in t around inf 72.0%

      \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(t \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right)} \]

   4. Taylor expanded in x around 0 74.3%

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

      1. associate-*r* 74.3%

         \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right)} \]

      2. *-commutative 74.3%

         \[\leadsto \color{blue}{\left(t \cdot -4\right)} \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right) \]

      3. sub-neg 74.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \color{blue}{\left(\frac{{z}^{2}}{t} + \left(-1\right)\right)}\right) \]

      4. metadata-eval 74.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} + \color{blue}{-1}\right)\right) \]

      5. +-commutative 74.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \color{blue}{\left(-1 + \frac{{z}^{2}}{t}\right)}\right) \]

   6. Simplified 74.3%

      \[\leadsto \color{blue}{\left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{{z}^{2}}{t}\right)\right)} \]
   7. Step-by-step derivation

      1. unpow2 74.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{\color{blue}{z \cdot z}}{t}\right)\right) \]

      2. associate-/l* 77.9%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{z \cdot \frac{z}{t}}\right)\right) \]

   8. Applied egg-rr 77.9%

      \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{z \cdot \frac{z}{t}}\right)\right) \]
   9. Step-by-step derivation

      1. clear-num 77.9%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + z \cdot \color{blue}{\frac{1}{\frac{t}{z}}}\right)\right) \]

      2. un-div-inv 77.9%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{\frac{z}{\frac{t}{z}}}\right)\right) \]

   10. Applied egg-rr 77.9%

       \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{\frac{z}{\frac{t}{z}}}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.8 \cdot 10^{+40}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + z \cdot \frac{z}{t}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 5.8e+40)
   (- (* x x) (* y (* t -4.0)))
   (* (* t -4.0) (* y (+ -1.0 (* z (/ z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.8e+40) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = (t * -4.0) * (y * (-1.0 + (z * (z / t))));
	}
	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 <= 5.8d+40) then
        tmp = (x * x) - (y * (t * (-4.0d0)))
    else
        tmp = (t * (-4.0d0)) * (y * ((-1.0d0) + (z * (z / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.8e+40) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = (t * -4.0) * (y * (-1.0 + (z * (z / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 5.8e+40:
		tmp = (x * x) - (y * (t * -4.0))
	else:
		tmp = (t * -4.0) * (y * (-1.0 + (z * (z / t))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 5.8e+40)
		tmp = Float64(Float64(x * x) - Float64(y * Float64(t * -4.0)));
	else
		tmp = Float64(Float64(t * -4.0) * Float64(y * Float64(-1.0 + Float64(z * Float64(z / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 5.8e+40)
		tmp = (x * x) - (y * (t * -4.0));
	else
		tmp = (t * -4.0) * (y * (-1.0 + (z * (z / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 5.8e+40], N[(N[(x * x), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] * N[(y * N[(-1.0 + N[(z * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.80000000000000035e40

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 75.1%

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

      1. *-commutative 75.1%

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

      2. *-commutative 75.1%

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

      3. associate-*l* 75.1%

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

   5. Simplified 75.1%

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

   if 5.80000000000000035e40 < z

   1. Initial program 81.3%

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

   3. Taylor expanded in t around inf 72.0%

      \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot \color{blue}{\left(t \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right)} \]

   4. Taylor expanded in x around 0 74.3%

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

      1. associate-*r* 74.3%

         \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right)} \]

      2. *-commutative 74.3%

         \[\leadsto \color{blue}{\left(t \cdot -4\right)} \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} - 1\right)\right) \]

      3. sub-neg 74.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \color{blue}{\left(\frac{{z}^{2}}{t} + \left(-1\right)\right)}\right) \]

      4. metadata-eval 74.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(\frac{{z}^{2}}{t} + \color{blue}{-1}\right)\right) \]

      5. +-commutative 74.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \color{blue}{\left(-1 + \frac{{z}^{2}}{t}\right)}\right) \]

   6. Simplified 74.3%

      \[\leadsto \color{blue}{\left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{{z}^{2}}{t}\right)\right)} \]
   7. Step-by-step derivation

      1. unpow2 74.3%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \frac{\color{blue}{z \cdot z}}{t}\right)\right) \]

      2. associate-/l* 77.9%

         \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{z \cdot \frac{z}{t}}\right)\right) \]

   8. Applied egg-rr 77.9%

      \[\leadsto \left(t \cdot -4\right) \cdot \left(y \cdot \left(-1 + \color{blue}{z \cdot \frac{z}{t}}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 65.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.5%

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

3. Taylor expanded in z around 0 64.3%

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

   1. *-commutative 64.3%

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

   2. *-commutative 64.3%

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

   3. associate-*l* 64.3%

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

5. Simplified 64.3%

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

Alternative 8: 31.7% accurate, 2.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.5%

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

3. Taylor expanded in t around inf 31.9%

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

   1. *-commutative 31.9%

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

5. Simplified 31.9%

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

Developer target: 90.5% 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 2024085 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"
  :precision binary64

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

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