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

Percentage Accurate: 90.0% → 95.1%

Time: 11.6s

Alternatives: 7

Speedup: 0.9×

• 48.9% 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: 90.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{\frac{1}{y}}{z \cdot -4}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 5e+267)
   (fma x x (* (- (* z z) t) (* y -4.0)))
   (/ z (/ (/ 1.0 y) (* z -4.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 5e+267) {
		tmp = fma(x, x, (((z * z) - t) * (y * -4.0)));
	} else {
		tmp = z / ((1.0 / y) / (z * -4.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 5e+267)
		tmp = fma(x, x, Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0)));
	else
		tmp = Float64(z / Float64(Float64(1.0 / y) / Float64(z * -4.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 5e+267], N[(x * x + N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / N[(N[(1.0 / y), $MachinePrecision] / N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 4.9999999999999999e267

   1. Initial program 98.8%

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

      1. associate-*l* 98.8%

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

      2. sqr-neg 98.8%

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

      3. associate-*l* 98.8%

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

      4. fma-neg 99.4%

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

      5. *-commutative 99.4%

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

      6. sqr-neg 99.4%

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

      7. distribute-rgt-neg-in 99.4%

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

      8. distribute-rgt-neg-in 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   if 4.9999999999999999e267 < (*.f64 z z)

   1. Initial program 69.5%

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

   2. Taylor expanded in z around inf 72.1%

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

      1. associate-*r* 72.1%

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

      2. *-commutative 72.1%

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

      3. unpow2 72.1%

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

      4. associate-*r* 72.1%

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

      5. associate-*r* 72.1%

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

      6. *-commutative 72.1%

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

      7. *-commutative 72.1%

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

   4. Simplified 72.1%

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

      1. /-rgt-identity 72.1%

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

      2. associate-*r* 72.1%

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

      3. *-commutative 72.1%

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

      4. remove-double-div 72.1%

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

      5. un-div-inv 72.1%

         \[\leadsto \frac{y}{1} \cdot \color{blue}{\frac{-4}{\frac{1}{z \cdot z}}} \]

      6. times-frac 72.1%

         \[\leadsto \color{blue}{\frac{y \cdot -4}{1 \cdot \frac{1}{z \cdot z}}} \]

      7. metadata-eval 72.1%

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

      8. distribute-rgt-neg-in 72.1%

         \[\leadsto \frac{\color{blue}{-y \cdot 4}}{1 \cdot \frac{1}{z \cdot z}} \]

      9. div-inv 72.1%

         \[\leadsto \frac{-y \cdot 4}{\color{blue}{\frac{1}{z \cdot z}}} \]

      10. distribute-neg-frac 72.1%

          \[\leadsto \color{blue}{-\frac{y \cdot 4}{\frac{1}{z \cdot z}}} \]

      11. neg-sub0 72.1%

          \[\leadsto \color{blue}{0 - \frac{y \cdot 4}{\frac{1}{z \cdot z}}} \]

      12. associate-/r* 73.7%

          \[\leadsto 0 - \frac{y \cdot 4}{\color{blue}{\frac{\frac{1}{z}}{z}}} \]

      13. associate-/r/ 88.6%

          \[\leadsto 0 - \color{blue}{\frac{y \cdot 4}{\frac{1}{z}} \cdot z} \]

      14. cancel-sign-sub-inv 88.6%

          \[\leadsto \color{blue}{0 + \left(-\frac{y \cdot 4}{\frac{1}{z}}\right) \cdot z} \]

      15. div-inv 88.6%

          \[\leadsto 0 + \left(-\color{blue}{\left(y \cdot 4\right) \cdot \frac{1}{\frac{1}{z}}}\right) \cdot z \]

      16. remove-double-div 88.6%

          \[\leadsto 0 + \left(-\left(y \cdot 4\right) \cdot \color{blue}{z}\right) \cdot z \]

   6. Applied egg-rr 88.6%

      \[\leadsto \color{blue}{0 + \left(-\left(y \cdot 4\right) \cdot z\right) \cdot z} \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 88.6%

         \[\leadsto 0 + \color{blue}{\left(\left(-y \cdot 4\right) \cdot z\right)} \cdot z \]

      2. associate-*l* 72.1%

         \[\leadsto 0 + \color{blue}{\left(-y \cdot 4\right) \cdot \left(z \cdot z\right)} \]

      3. distribute-rgt-neg-in 72.1%

         \[\leadsto 0 + \color{blue}{\left(y \cdot \left(-4\right)\right)} \cdot \left(z \cdot z\right) \]

      4. metadata-eval 72.1%

         \[\leadsto 0 + \left(y \cdot \color{blue}{-4}\right) \cdot \left(z \cdot z\right) \]

      5. associate-*l* 72.1%

         \[\leadsto 0 + \color{blue}{y \cdot \left(-4 \cdot \left(z \cdot z\right)\right)} \]

      6. *-commutative 72.1%

         \[\leadsto 0 + \color{blue}{\left(-4 \cdot \left(z \cdot z\right)\right) \cdot y} \]

      7. remove-double-div 72.1%

         \[\leadsto 0 + \left(-4 \cdot \left(z \cdot z\right)\right) \cdot \color{blue}{\frac{1}{\frac{1}{y}}} \]

      8. div-inv 72.1%

         \[\leadsto 0 + \color{blue}{\frac{-4 \cdot \left(z \cdot z\right)}{\frac{1}{y}}} \]

      9. associate-*r* 72.1%

         \[\leadsto 0 + \frac{\color{blue}{\left(-4 \cdot z\right) \cdot z}}{\frac{1}{y}} \]

      10. *-commutative 72.1%

          \[\leadsto 0 + \frac{\color{blue}{z \cdot \left(-4 \cdot z\right)}}{\frac{1}{y}} \]

      11. associate-/l* 88.7%

          \[\leadsto 0 + \color{blue}{\frac{z}{\frac{\frac{1}{y}}{-4 \cdot z}}} \]

      12. *-commutative 88.7%

          \[\leadsto 0 + \frac{z}{\frac{\frac{1}{y}}{\color{blue}{z \cdot -4}}} \]

   8. Applied egg-rr 88.7%

      \[\leadsto 0 + \color{blue}{\frac{z}{\frac{\frac{1}{y}}{z \cdot -4}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{\frac{1}{y}}{z \cdot -4}}\\ \end{array} \]

Alternative 2: 58.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{-308}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \cdot z \leq 10^{-55}:\\ \;\;\;\;4 \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;z \cdot z \leq 10^{+56}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 1e-308)
   (* x x)
   (if (<= (* z z) 1e-55)
     (* 4.0 (* t y))
     (if (<= (* z z) 1e+56) (* x x) (* y (* z (* z -4.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 1e-308) {
		tmp = x * x;
	} else if ((z * z) <= 1e-55) {
		tmp = 4.0 * (t * y);
	} else if ((z * z) <= 1e+56) {
		tmp = x * x;
	} else {
		tmp = y * (z * (z * -4.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * z) <= 1d-308) then
        tmp = x * x
    else if ((z * z) <= 1d-55) then
        tmp = 4.0d0 * (t * y)
    else if ((z * z) <= 1d+56) then
        tmp = x * x
    else
        tmp = y * (z * (z * (-4.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 1e-308) {
		tmp = x * x;
	} else if ((z * z) <= 1e-55) {
		tmp = 4.0 * (t * y);
	} else if ((z * z) <= 1e+56) {
		tmp = x * x;
	} else {
		tmp = y * (z * (z * -4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * z) <= 1e-308:
		tmp = x * x
	elif (z * z) <= 1e-55:
		tmp = 4.0 * (t * y)
	elif (z * z) <= 1e+56:
		tmp = x * x
	else:
		tmp = y * (z * (z * -4.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 1e-308)
		tmp = Float64(x * x);
	elseif (Float64(z * z) <= 1e-55)
		tmp = Float64(4.0 * Float64(t * y));
	elseif (Float64(z * z) <= 1e+56)
		tmp = Float64(x * x);
	else
		tmp = Float64(y * Float64(z * Float64(z * -4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * z) <= 1e-308)
		tmp = x * x;
	elseif ((z * z) <= 1e-55)
		tmp = 4.0 * (t * y);
	elseif ((z * z) <= 1e+56)
		tmp = x * x;
	else
		tmp = y * (z * (z * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 1e-308], N[(x * x), $MachinePrecision], If[LessEqual[N[(z * z), $MachinePrecision], 1e-55], N[(4.0 * N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * z), $MachinePrecision], 1e+56], N[(x * x), $MachinePrecision], N[(y * N[(z * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z z) < 9.9999999999999991e-309 or 9.99999999999999995e-56 < (*.f64 z z) < 1.00000000000000009e56

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 64.2%

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

      1. unpow2 64.2%

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

   4. Simplified 64.2%

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

   if 9.9999999999999991e-309 < (*.f64 z z) < 9.99999999999999995e-56

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 60.2%

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

      1. *-commutative 60.2%

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

   4. Simplified 60.2%

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

   if 1.00000000000000009e56 < (*.f64 z z)

   1. Initial program 79.7%

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

   2. Taylor expanded in z around inf 70.1%

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

      1. associate-*r* 70.1%

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

      2. *-commutative 70.1%

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

      3. unpow2 70.1%

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

      4. associate-*r* 70.1%

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

      5. associate-*r* 70.1%

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

      6. *-commutative 70.1%

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

      7. *-commutative 70.1%

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

   4. Simplified 70.1%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{-308}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \cdot z \leq 10^{-55}:\\ \;\;\;\;4 \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;z \cdot z \leq 10^{+56}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\\ \end{array} \]

Alternative 3: 92.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{+139}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{\frac{1}{y}}{z \cdot -4}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 3.7e+139)
   (+ (* x x) (* (* y 4.0) (- t (* z z))))
   (/ z (/ (/ 1.0 y) (* z -4.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3.7e+139) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = z / ((1.0 / y) / (z * -4.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 3.7d+139) then
        tmp = (x * x) + ((y * 4.0d0) * (t - (z * z)))
    else
        tmp = z / ((1.0d0 / y) / (z * (-4.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3.7e+139) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = z / ((1.0 / y) / (z * -4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 3.7e+139:
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)))
	else:
		tmp = z / ((1.0 / y) / (z * -4.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 3.7e+139)
		tmp = Float64(Float64(x * x) + Float64(Float64(y * 4.0) * Float64(t - Float64(z * z))));
	else
		tmp = Float64(z / Float64(Float64(1.0 / y) / Float64(z * -4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 3.7e+139)
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	else
		tmp = z / ((1.0 / y) / (z * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 3.7e+139], N[(N[(x * x), $MachinePrecision] + N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / N[(N[(1.0 / y), $MachinePrecision] / N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.69999999999999992e139

   1. Initial program 94.1%

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

   if 3.69999999999999992e139 < z

   1. Initial program 69.1%

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

   2. Taylor expanded in z around inf 69.1%

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

      1. associate-*r* 69.1%

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

      2. *-commutative 69.1%

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

      3. unpow2 69.1%

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

      4. associate-*r* 69.1%

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

      5. associate-*r* 69.1%

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

      6. *-commutative 69.1%

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

      7. *-commutative 69.1%

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

   4. Simplified 69.1%

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

      1. /-rgt-identity 69.1%

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

      2. associate-*r* 69.1%

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

      3. *-commutative 69.1%

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

      4. remove-double-div 69.1%

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

      5. un-div-inv 69.1%

         \[\leadsto \frac{y}{1} \cdot \color{blue}{\frac{-4}{\frac{1}{z \cdot z}}} \]

      6. times-frac 69.1%

         \[\leadsto \color{blue}{\frac{y \cdot -4}{1 \cdot \frac{1}{z \cdot z}}} \]

      7. metadata-eval 69.1%

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

      8. distribute-rgt-neg-in 69.1%

         \[\leadsto \frac{\color{blue}{-y \cdot 4}}{1 \cdot \frac{1}{z \cdot z}} \]

      9. div-inv 69.1%

         \[\leadsto \frac{-y \cdot 4}{\color{blue}{\frac{1}{z \cdot z}}} \]

      10. distribute-neg-frac 69.1%

          \[\leadsto \color{blue}{-\frac{y \cdot 4}{\frac{1}{z \cdot z}}} \]

      11. neg-sub0 69.1%

          \[\leadsto \color{blue}{0 - \frac{y \cdot 4}{\frac{1}{z \cdot z}}} \]

      12. associate-/r* 70.2%

          \[\leadsto 0 - \frac{y \cdot 4}{\color{blue}{\frac{\frac{1}{z}}{z}}} \]

      13. associate-/r/ 81.8%

          \[\leadsto 0 - \color{blue}{\frac{y \cdot 4}{\frac{1}{z}} \cdot z} \]

      14. cancel-sign-sub-inv 81.8%

          \[\leadsto \color{blue}{0 + \left(-\frac{y \cdot 4}{\frac{1}{z}}\right) \cdot z} \]

      15. div-inv 81.9%

          \[\leadsto 0 + \left(-\color{blue}{\left(y \cdot 4\right) \cdot \frac{1}{\frac{1}{z}}}\right) \cdot z \]

      16. remove-double-div 81.9%

          \[\leadsto 0 + \left(-\left(y \cdot 4\right) \cdot \color{blue}{z}\right) \cdot z \]

   6. Applied egg-rr 81.9%

      \[\leadsto \color{blue}{0 + \left(-\left(y \cdot 4\right) \cdot z\right) \cdot z} \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 81.9%

         \[\leadsto 0 + \color{blue}{\left(\left(-y \cdot 4\right) \cdot z\right)} \cdot z \]

      2. associate-*l* 69.1%

         \[\leadsto 0 + \color{blue}{\left(-y \cdot 4\right) \cdot \left(z \cdot z\right)} \]

      3. distribute-rgt-neg-in 69.1%

         \[\leadsto 0 + \color{blue}{\left(y \cdot \left(-4\right)\right)} \cdot \left(z \cdot z\right) \]

      4. metadata-eval 69.1%

         \[\leadsto 0 + \left(y \cdot \color{blue}{-4}\right) \cdot \left(z \cdot z\right) \]

      5. associate-*l* 69.1%

         \[\leadsto 0 + \color{blue}{y \cdot \left(-4 \cdot \left(z \cdot z\right)\right)} \]

      6. *-commutative 69.1%

         \[\leadsto 0 + \color{blue}{\left(-4 \cdot \left(z \cdot z\right)\right) \cdot y} \]

      7. remove-double-div 69.1%

         \[\leadsto 0 + \left(-4 \cdot \left(z \cdot z\right)\right) \cdot \color{blue}{\frac{1}{\frac{1}{y}}} \]

      8. div-inv 69.1%

         \[\leadsto 0 + \color{blue}{\frac{-4 \cdot \left(z \cdot z\right)}{\frac{1}{y}}} \]

      9. associate-*r* 69.1%

         \[\leadsto 0 + \frac{\color{blue}{\left(-4 \cdot z\right) \cdot z}}{\frac{1}{y}} \]

      10. *-commutative 69.1%

          \[\leadsto 0 + \frac{\color{blue}{z \cdot \left(-4 \cdot z\right)}}{\frac{1}{y}} \]

      11. associate-/l* 81.9%

          \[\leadsto 0 + \color{blue}{\frac{z}{\frac{\frac{1}{y}}{-4 \cdot z}}} \]

      12. *-commutative 81.9%

          \[\leadsto 0 + \frac{z}{\frac{\frac{1}{y}}{\color{blue}{z \cdot -4}}} \]

   8. Applied egg-rr 81.9%

      \[\leadsto 0 + \color{blue}{\frac{z}{\frac{\frac{1}{y}}{z \cdot -4}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{+139}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{\frac{1}{y}}{z \cdot -4}}\\ \end{array} \]

Alternative 4: 81.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+74}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 5e+74) (- (* x x) (* y (* t -4.0))) (* y (* z (* z -4.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 5e+74) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = y * (z * (z * -4.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * z) <= 5d+74) then
        tmp = (x * x) - (y * (t * (-4.0d0)))
    else
        tmp = y * (z * (z * (-4.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 5e+74) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = y * (z * (z * -4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * z) <= 5e+74:
		tmp = (x * x) - (y * (t * -4.0))
	else:
		tmp = y * (z * (z * -4.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 5e+74)
		tmp = Float64(Float64(x * x) - Float64(y * Float64(t * -4.0)));
	else
		tmp = Float64(y * Float64(z * Float64(z * -4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * z) <= 5e+74)
		tmp = (x * x) - (y * (t * -4.0));
	else
		tmp = y * (z * (z * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 5e+74], N[(N[(x * x), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 4.99999999999999963e74

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 93.6%

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

      1. associate-*r* 93.6%

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

      2. *-commutative 93.6%

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

      3. *-commutative 93.6%

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

   4. Simplified 93.6%

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

   if 4.99999999999999963e74 < (*.f64 z z)

   1. Initial program 78.5%

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

   2. Taylor expanded in z around inf 71.5%

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

      1. associate-*r* 71.5%

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

      2. *-commutative 71.5%

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

      3. unpow2 71.5%

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

      4. associate-*r* 71.5%

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

      5. associate-*r* 71.5%

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

      6. *-commutative 71.5%

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

      7. *-commutative 71.5%

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

   4. Simplified 71.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+74}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\\ \end{array} \]

Alternative 5: 75.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.05 \cdot 10^{+38}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot \left(4 \cdot \left(-y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.05e+38) (- (* x x) (* y (* t -4.0))) (* z (* z (* 4.0 (- y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.05e+38) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = z * (z * (4.0 * -y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 1.05d+38) then
        tmp = (x * x) - (y * (t * (-4.0d0)))
    else
        tmp = z * (z * (4.0d0 * -y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.05e+38) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = z * (z * (4.0 * -y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 1.05e+38:
		tmp = (x * x) - (y * (t * -4.0))
	else:
		tmp = z * (z * (4.0 * -y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.05e+38)
		tmp = Float64(Float64(x * x) - Float64(y * Float64(t * -4.0)));
	else
		tmp = Float64(z * Float64(z * Float64(4.0 * Float64(-y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 1.05e+38)
		tmp = (x * x) - (y * (t * -4.0));
	else
		tmp = z * (z * (4.0 * -y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 1.05e+38], N[(N[(x * x), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(z * N[(4.0 * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.05e38

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 73.1%

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

      1. associate-*r* 73.1%

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

      2. *-commutative 73.1%

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

      3. *-commutative 73.1%

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

   4. Simplified 73.1%

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

   if 1.05e38 < z

   1. Initial program 77.7%

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

   2. Taylor expanded in z around inf 67.2%

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

      1. associate-*r* 67.2%

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

      2. *-commutative 67.2%

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

      3. unpow2 67.2%

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

      4. associate-*r* 67.2%

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

      5. associate-*r* 67.2%

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

      6. *-commutative 67.2%

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

      7. *-commutative 67.2%

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

   4. Simplified 67.2%

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

      1. /-rgt-identity 67.2%

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

      2. associate-*r* 67.2%

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

      3. *-commutative 67.2%

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

      4. remove-double-div 67.2%

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

      5. un-div-inv 67.2%

         \[\leadsto \frac{y}{1} \cdot \color{blue}{\frac{-4}{\frac{1}{z \cdot z}}} \]

      6. times-frac 67.2%

         \[\leadsto \color{blue}{\frac{y \cdot -4}{1 \cdot \frac{1}{z \cdot z}}} \]

      7. metadata-eval 67.2%

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

      8. distribute-rgt-neg-in 67.2%

         \[\leadsto \frac{\color{blue}{-y \cdot 4}}{1 \cdot \frac{1}{z \cdot z}} \]

      9. div-inv 67.2%

         \[\leadsto \frac{-y \cdot 4}{\color{blue}{\frac{1}{z \cdot z}}} \]

      10. distribute-neg-frac 67.2%

          \[\leadsto \color{blue}{-\frac{y \cdot 4}{\frac{1}{z \cdot z}}} \]

      11. neg-sub0 67.2%

          \[\leadsto \color{blue}{0 - \frac{y \cdot 4}{\frac{1}{z \cdot z}}} \]

      12. associate-/r* 67.8%

          \[\leadsto 0 - \frac{y \cdot 4}{\color{blue}{\frac{\frac{1}{z}}{z}}} \]

      13. associate-/r/ 75.6%

          \[\leadsto 0 - \color{blue}{\frac{y \cdot 4}{\frac{1}{z}} \cdot z} \]

      14. cancel-sign-sub-inv 75.6%

          \[\leadsto \color{blue}{0 + \left(-\frac{y \cdot 4}{\frac{1}{z}}\right) \cdot z} \]

      15. div-inv 75.7%

          \[\leadsto 0 + \left(-\color{blue}{\left(y \cdot 4\right) \cdot \frac{1}{\frac{1}{z}}}\right) \cdot z \]

      16. remove-double-div 75.7%

          \[\leadsto 0 + \left(-\left(y \cdot 4\right) \cdot \color{blue}{z}\right) \cdot z \]

   6. Applied egg-rr 75.7%

      \[\leadsto \color{blue}{0 + \left(-\left(y \cdot 4\right) \cdot z\right) \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.05 \cdot 10^{+38}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot \left(4 \cdot \left(-y\right)\right)\right)\\ \end{array} \]

Alternative 6: 44.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.35 \cdot 10^{+36}:\\ \;\;\;\;4 \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 1.35e+36) (* 4.0 (* t y)) (* x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.35e+36) {
		tmp = 4.0 * (t * y);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= 1.35d+36) then
        tmp = 4.0d0 * (t * y)
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.35e+36) {
		tmp = 4.0 * (t * y);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 1.35e+36:
		tmp = 4.0 * (t * y)
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 1.35e+36)
		tmp = Float64(4.0 * Float64(t * y));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 1.35e+36)
		tmp = 4.0 * (t * y);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 1.35e+36], N[(4.0 * N[(t * y), $MachinePrecision]), $MachinePrecision], N[(x * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.35e36

   1. Initial program 90.4%

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

   2. Taylor expanded in t around inf 34.1%

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

      1. *-commutative 34.1%

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

   4. Simplified 34.1%

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

   if 1.35e36 < x

   1. Initial program 88.2%

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

   2. Taylor expanded in x around inf 74.5%

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

      1. unpow2 74.5%

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

   4. Simplified 74.5%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.35 \cdot 10^{+36}:\\ \;\;\;\;4 \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 7: 41.0% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.9%

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

2. Taylor expanded in x around inf 39.5%

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

   1. unpow2 39.5%

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

4. Simplified 39.5%

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

5. Final simplification 39.5%

   \[\leadsto x \cdot x \]

Developer target: 90.1% 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 2023297 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"
  :precision binary64

  :herbie-target
  (- (* x x) (* 4.0 (* y (- (* z z) t))))

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