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

Percentage Accurate: 91.3% → 96.4%

Time: 9.5s

Alternatives: 10

Speedup: 0.8×

• 50.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.3% 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: 96.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(z \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 5e+307)
   (fma x x (* (- (* z z) t) (* y -4.0)))
   (* (* z y) (* z -4.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 5e+307) {
		tmp = fma(x, x, (((z * z) - t) * (y * -4.0)));
	} else {
		tmp = (z * y) * (z * -4.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 5e+307)
		tmp = fma(x, x, Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0)));
	else
		tmp = Float64(Float64(z * y) * Float64(z * -4.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 5e+307], N[(x * x + N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 5e307

   1. Initial program 96.2%

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

      1. fma-neg 97.8%

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

      2. *-commutative 97.8%

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

      3. distribute-rgt-neg-in 97.8%

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

      4. distribute-rgt-neg-in 97.8%

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

      5. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

   if 5e307 < (*.f64 z z)

   1. Initial program 68.2%

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

   2. Taylor expanded in z around inf 78.2%

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

      1. *-commutative 78.2%

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

      2. unpow2 78.2%

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

      3. associate-*l* 78.2%

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

   4. Simplified 78.2%

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

      1. expm1-log1p-u 30.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\right)\right)} \]

      2. expm1-udef 30.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\right)} - 1} \]

      3. associate-*l* 30.4%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\left(z \cdot \left(z \cdot -4\right)\right)}\right)} - 1 \]

   6. Applied egg-rr 30.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 30.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\right)\right)} \]

      2. expm1-log1p 78.2%

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

      3. associate-*r* 92.9%

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

   8. Simplified 92.9%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(z \cdot -4\right)\\ \end{array} \]

Alternative 2: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 2 \cdot 10^{+132}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 5 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(z \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x x) (* y (* t -4.0)))))
   (if (<= (* z z) 4e+34)
     t_1
     (if (<= (* z z) 2e+132)
       (* (- (* z z) t) (* y -4.0))
       (if (<= (* z z) 5e+206) t_1 (* (* z y) (* z -4.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * x) - (y * (t * -4.0));
	double tmp;
	if ((z * z) <= 4e+34) {
		tmp = t_1;
	} else if ((z * z) <= 2e+132) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else if ((z * z) <= 5e+206) {
		tmp = t_1;
	} else {
		tmp = (z * 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) :: t_1
    real(8) :: tmp
    t_1 = (x * x) - (y * (t * (-4.0d0)))
    if ((z * z) <= 4d+34) then
        tmp = t_1
    else if ((z * z) <= 2d+132) then
        tmp = ((z * z) - t) * (y * (-4.0d0))
    else if ((z * z) <= 5d+206) then
        tmp = t_1
    else
        tmp = (z * y) * (z * (-4.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * x) - (y * (t * -4.0));
	double tmp;
	if ((z * z) <= 4e+34) {
		tmp = t_1;
	} else if ((z * z) <= 2e+132) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else if ((z * z) <= 5e+206) {
		tmp = t_1;
	} else {
		tmp = (z * y) * (z * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * x) - (y * (t * -4.0))
	tmp = 0
	if (z * z) <= 4e+34:
		tmp = t_1
	elif (z * z) <= 2e+132:
		tmp = ((z * z) - t) * (y * -4.0)
	elif (z * z) <= 5e+206:
		tmp = t_1
	else:
		tmp = (z * y) * (z * -4.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * x) - Float64(y * Float64(t * -4.0)))
	tmp = 0.0
	if (Float64(z * z) <= 4e+34)
		tmp = t_1;
	elseif (Float64(z * z) <= 2e+132)
		tmp = Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0));
	elseif (Float64(z * z) <= 5e+206)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * y) * Float64(z * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * x) - (y * (t * -4.0));
	tmp = 0.0;
	if ((z * z) <= 4e+34)
		tmp = t_1;
	elseif ((z * z) <= 2e+132)
		tmp = ((z * z) - t) * (y * -4.0);
	elseif ((z * z) <= 5e+206)
		tmp = t_1;
	else
		tmp = (z * y) * (z * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * z), $MachinePrecision], 4e+34], t$95$1, If[LessEqual[N[(z * z), $MachinePrecision], 2e+132], N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * z), $MachinePrecision], 5e+206], t$95$1, N[(N[(z * y), $MachinePrecision] * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z z) < 3.99999999999999978e34 or 1.99999999999999998e132 < (*.f64 z z) < 5.0000000000000002e206

   1. Initial program 97.3%

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

   2. Taylor expanded in z around 0 90.3%

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

      1. associate-*l* 90.3%

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

   4. Simplified 90.3%

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

   if 3.99999999999999978e34 < (*.f64 z z) < 1.99999999999999998e132

   1. Initial program 95.0%

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

   2. Taylor expanded in x around 0 78.4%

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

      1. associate-*r* 78.4%

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

      2. unpow2 78.4%

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

      3. *-commutative 78.4%

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

      4. *-commutative 78.4%

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

   4. Simplified 78.4%

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

   if 5.0000000000000002e206 < (*.f64 z z)

   1. Initial program 71.8%

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

   2. Taylor expanded in z around inf 77.7%

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

      1. *-commutative 77.7%

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

      2. unpow2 77.7%

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

      3. associate-*l* 77.7%

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

   4. Simplified 77.7%

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

      1. expm1-log1p-u 36.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\right)\right)} \]

      2. expm1-udef 33.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\right)} - 1} \]

      3. associate-*l* 33.5%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\left(z \cdot \left(z \cdot -4\right)\right)}\right)} - 1 \]

   6. Applied egg-rr 33.5%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 36.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\right)\right)} \]

      2. expm1-log1p 77.7%

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

      3. associate-*r* 89.6%

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

   8. Simplified 89.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+34}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 2 \cdot 10^{+132}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 5 \cdot 10^{+206}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(z \cdot -4\right)\\ \end{array} \]

Alternative 3: 94.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+247}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(z \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 1e+247)
   (+ (* x x) (* (* y 4.0) (- t (* z z))))
   (* (* z y) (* z -4.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 1e+247) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = (z * 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 * z) <= 1d+247) then
        tmp = (x * x) + ((y * 4.0d0) * (t - (z * z)))
    else
        tmp = (z * 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 * z) <= 1e+247) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = (z * y) * (z * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * z) <= 1e+247:
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)))
	else:
		tmp = (z * y) * (z * -4.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 1e+247)
		tmp = Float64(Float64(x * x) + Float64(Float64(y * 4.0) * Float64(t - Float64(z * z))));
	else
		tmp = Float64(Float64(z * y) * Float64(z * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * z) <= 1e+247)
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	else
		tmp = (z * y) * (z * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 1e+247], N[(N[(x * x), $MachinePrecision] + N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 9.99999999999999952e246

   1. Initial program 96.6%

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

   if 9.99999999999999952e246 < (*.f64 z z)

   1. Initial program 69.8%

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

   2. Taylor expanded in z around inf 78.9%

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

      1. *-commutative 78.9%

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

      2. unpow2 78.9%

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

      3. associate-*l* 78.9%

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

   4. Simplified 78.9%

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

      1. expm1-log1p-u 34.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\right)\right)} \]

      2. expm1-udef 32.9%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\right)} - 1} \]

      3. associate-*l* 32.9%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\left(z \cdot \left(z \cdot -4\right)\right)}\right)} - 1 \]

   6. Applied egg-rr 32.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 34.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\right)\right)} \]

      2. expm1-log1p 78.9%

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

      3. associate-*r* 92.3%

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

   8. Simplified 92.3%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+247}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(z \cdot -4\right)\\ \end{array} \]

Alternative 4: 44.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \left(t \cdot 4\right)\\ \mathbf{elif}\;z \leq 11000000000 \lor \neg \left(z \leq 5.8 \cdot 10^{+66}\right) \land z \leq 1.75 \cdot 10^{+103}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 2e-105)
   (* y (* t 4.0))
   (if (or (<= z 11000000000.0) (and (not (<= z 5.8e+66)) (<= z 1.75e+103)))
     (* x x)
     (* y (* (* z z) -4.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2e-105) {
		tmp = y * (t * 4.0);
	} else if ((z <= 11000000000.0) || (!(z <= 5.8e+66) && (z <= 1.75e+103))) {
		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 <= 2d-105) then
        tmp = y * (t * 4.0d0)
    else if ((z <= 11000000000.0d0) .or. (.not. (z <= 5.8d+66)) .and. (z <= 1.75d+103)) 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 <= 2e-105) {
		tmp = y * (t * 4.0);
	} else if ((z <= 11000000000.0) || (!(z <= 5.8e+66) && (z <= 1.75e+103))) {
		tmp = x * x;
	} else {
		tmp = y * ((z * z) * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 2e-105:
		tmp = y * (t * 4.0)
	elif (z <= 11000000000.0) or (not (z <= 5.8e+66) and (z <= 1.75e+103)):
		tmp = x * x
	else:
		tmp = y * ((z * z) * -4.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 2e-105)
		tmp = Float64(y * Float64(t * 4.0));
	elseif ((z <= 11000000000.0) || (!(z <= 5.8e+66) && (z <= 1.75e+103)))
		tmp = Float64(x * x);
	else
		tmp = Float64(y * Float64(Float64(z * z) * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 2e-105)
		tmp = y * (t * 4.0);
	elseif ((z <= 11000000000.0) || (~((z <= 5.8e+66)) && (z <= 1.75e+103)))
		tmp = x * x;
	else
		tmp = y * ((z * z) * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 2e-105], N[(y * N[(t * 4.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 11000000000.0], And[N[Not[LessEqual[z, 5.8e+66]], $MachinePrecision], LessEqual[z, 1.75e+103]]], N[(x * x), $MachinePrecision], N[(y * N[(N[(z * z), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < 1.99999999999999993e-105

   1. Initial program 90.5%

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

   2. Taylor expanded in t around inf 41.5%

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

      1. associate-*r* 41.5%

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

      2. *-commutative 41.5%

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

   4. Simplified 41.5%

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

   if 1.99999999999999993e-105 < z < 1.1e10 or 5.79999999999999972e66 < z < 1.75e103

   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 73.0%

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

      1. unpow2 73.0%

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

   4. Simplified 73.0%

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

   if 1.1e10 < z < 5.79999999999999972e66 or 1.75e103 < z

   1. Initial program 76.3%

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

   2. Taylor expanded in z around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. unpow2 69.7%

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

      3. associate-*l* 69.7%

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

   4. Simplified 69.7%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \left(t \cdot 4\right)\\ \mathbf{elif}\;z \leq 11000000000 \lor \neg \left(z \leq 5.8 \cdot 10^{+66}\right) \land z \leq 1.75 \cdot 10^{+103}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\\ \end{array} \]

Alternative 5: 45.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.05 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \left(t \cdot 4\right)\\ \mathbf{elif}\;z \leq 10500000000:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(z \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.05e-105)
   (* y (* t 4.0))
   (if (<= z 10500000000.0)
     (* x x)
     (if (<= z 2.35e+66)
       (* y (* (* z z) -4.0))
       (if (<= z 2e+103) (* x x) (* (* z y) (* z -4.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.05e-105) {
		tmp = y * (t * 4.0);
	} else if (z <= 10500000000.0) {
		tmp = x * x;
	} else if (z <= 2.35e+66) {
		tmp = y * ((z * z) * -4.0);
	} else if (z <= 2e+103) {
		tmp = x * x;
	} else {
		tmp = (z * 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 <= 1.05d-105) then
        tmp = y * (t * 4.0d0)
    else if (z <= 10500000000.0d0) then
        tmp = x * x
    else if (z <= 2.35d+66) then
        tmp = y * ((z * z) * (-4.0d0))
    else if (z <= 2d+103) then
        tmp = x * x
    else
        tmp = (z * 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 <= 1.05e-105) {
		tmp = y * (t * 4.0);
	} else if (z <= 10500000000.0) {
		tmp = x * x;
	} else if (z <= 2.35e+66) {
		tmp = y * ((z * z) * -4.0);
	} else if (z <= 2e+103) {
		tmp = x * x;
	} else {
		tmp = (z * y) * (z * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 1.05e-105:
		tmp = y * (t * 4.0)
	elif z <= 10500000000.0:
		tmp = x * x
	elif z <= 2.35e+66:
		tmp = y * ((z * z) * -4.0)
	elif z <= 2e+103:
		tmp = x * x
	else:
		tmp = (z * y) * (z * -4.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.05e-105)
		tmp = Float64(y * Float64(t * 4.0));
	elseif (z <= 10500000000.0)
		tmp = Float64(x * x);
	elseif (z <= 2.35e+66)
		tmp = Float64(y * Float64(Float64(z * z) * -4.0));
	elseif (z <= 2e+103)
		tmp = Float64(x * x);
	else
		tmp = Float64(Float64(z * y) * Float64(z * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 1.05e-105)
		tmp = y * (t * 4.0);
	elseif (z <= 10500000000.0)
		tmp = x * x;
	elseif (z <= 2.35e+66)
		tmp = y * ((z * z) * -4.0);
	elseif (z <= 2e+103)
		tmp = x * x;
	else
		tmp = (z * y) * (z * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 1.05e-105], N[(y * N[(t * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 10500000000.0], N[(x * x), $MachinePrecision], If[LessEqual[z, 2.35e+66], N[(y * N[(N[(z * z), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+103], N[(x * x), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < 1.05e-105

   1. Initial program 90.5%

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

   2. Taylor expanded in t around inf 41.5%

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

      1. associate-*r* 41.5%

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

      2. *-commutative 41.5%

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

   4. Simplified 41.5%

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

   if 1.05e-105 < z < 1.05e10 or 2.3500000000000001e66 < z < 2e103

   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 73.0%

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

      1. unpow2 73.0%

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

   4. Simplified 73.0%

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

   if 1.05e10 < z < 2.3500000000000001e66

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. unpow2 55.7%

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

      3. associate-*l* 55.7%

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

   4. Simplified 55.7%

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

   if 2e103 < z

   1. Initial program 70.8%

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

   2. Taylor expanded in z around inf 73.0%

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

      1. *-commutative 73.0%

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

      2. unpow2 73.0%

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

      3. associate-*l* 73.0%

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

   4. Simplified 73.0%

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

      1. expm1-log1p-u 37.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\right)\right)} \]

      2. expm1-udef 34.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\right)} - 1} \]

      3. associate-*l* 34.3%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\left(z \cdot \left(z \cdot -4\right)\right)}\right)} - 1 \]

   6. Applied egg-rr 34.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 37.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\right)\right)} \]

      2. expm1-log1p 73.0%

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

      3. associate-*r* 87.1%

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

   8. Simplified 87.1%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.05 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \left(t \cdot 4\right)\\ \mathbf{elif}\;z \leq 10500000000:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(z \cdot -4\right)\\ \end{array} \]

Alternative 6: 77.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.1 \cdot 10^{-24}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+124}:\\ \;\;\;\;x \cdot x - 4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(z \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 4.1e-24)
   (- (* x x) (* y (* t -4.0)))
   (if (<= z 6.8e+124)
     (- (* x x) (* 4.0 (* (* z z) y)))
     (* (* z y) (* z -4.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 4.1e-24) {
		tmp = (x * x) - (y * (t * -4.0));
	} else if (z <= 6.8e+124) {
		tmp = (x * x) - (4.0 * ((z * z) * y));
	} else {
		tmp = (z * 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 <= 4.1d-24) then
        tmp = (x * x) - (y * (t * (-4.0d0)))
    else if (z <= 6.8d+124) then
        tmp = (x * x) - (4.0d0 * ((z * z) * y))
    else
        tmp = (z * 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 <= 4.1e-24) {
		tmp = (x * x) - (y * (t * -4.0));
	} else if (z <= 6.8e+124) {
		tmp = (x * x) - (4.0 * ((z * z) * y));
	} else {
		tmp = (z * y) * (z * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 4.1e-24:
		tmp = (x * x) - (y * (t * -4.0))
	elif z <= 6.8e+124:
		tmp = (x * x) - (4.0 * ((z * z) * y))
	else:
		tmp = (z * y) * (z * -4.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 4.1e-24)
		tmp = Float64(Float64(x * x) - Float64(y * Float64(t * -4.0)));
	elseif (z <= 6.8e+124)
		tmp = Float64(Float64(x * x) - Float64(4.0 * Float64(Float64(z * z) * y)));
	else
		tmp = Float64(Float64(z * y) * Float64(z * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 4.1e-24)
		tmp = (x * x) - (y * (t * -4.0));
	elseif (z <= 6.8e+124)
		tmp = (x * x) - (4.0 * ((z * z) * y));
	else
		tmp = (z * y) * (z * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 4.1e-24], N[(N[(x * x), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+124], N[(N[(x * x), $MachinePrecision] - N[(4.0 * N[(N[(z * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < 4.10000000000000015e-24

   1. Initial program 91.6%

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

   2. Taylor expanded in z around 0 73.9%

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

      1. associate-*l* 73.9%

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

   4. Simplified 73.9%

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

   if 4.10000000000000015e-24 < z < 6.8e124

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 83.5%

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

      1. unpow2 83.5%

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

   4. Simplified 83.5%

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

   if 6.8e124 < z

   1. Initial program 65.5%

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

   2. Taylor expanded in z around inf 73.2%

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

      1. *-commutative 73.2%

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

      2. unpow2 73.2%

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

      3. associate-*l* 73.2%

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

   4. Simplified 73.2%

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

      1. expm1-log1p-u 34.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\right)\right)} \]

      2. expm1-udef 34.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\right)} - 1} \]

      3. associate-*l* 34.1%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\left(z \cdot \left(z \cdot -4\right)\right)}\right)} - 1 \]

   6. Applied egg-rr 34.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 34.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\right)\right)} \]

      2. expm1-log1p 73.2%

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

      3. associate-*r* 89.9%

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

   8. Simplified 89.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.1 \cdot 10^{-24}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+124}:\\ \;\;\;\;x \cdot x - 4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(z \cdot -4\right)\\ \end{array} \]

Alternative 7: 78.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.05 \cdot 10^{-24}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+188}:\\ \;\;\;\;x \cdot x - 4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(z \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 2.05e-24)
   (- (* x x) (* y (* t -4.0)))
   (if (<= z 1.35e+188)
     (- (* x x) (* 4.0 (* z (* z y))))
     (* (* z y) (* z -4.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2.05e-24) {
		tmp = (x * x) - (y * (t * -4.0));
	} else if (z <= 1.35e+188) {
		tmp = (x * x) - (4.0 * (z * (z * y)));
	} else {
		tmp = (z * 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 <= 2.05d-24) then
        tmp = (x * x) - (y * (t * (-4.0d0)))
    else if (z <= 1.35d+188) then
        tmp = (x * x) - (4.0d0 * (z * (z * y)))
    else
        tmp = (z * 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 <= 2.05e-24) {
		tmp = (x * x) - (y * (t * -4.0));
	} else if (z <= 1.35e+188) {
		tmp = (x * x) - (4.0 * (z * (z * y)));
	} else {
		tmp = (z * y) * (z * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 2.05e-24:
		tmp = (x * x) - (y * (t * -4.0))
	elif z <= 1.35e+188:
		tmp = (x * x) - (4.0 * (z * (z * y)))
	else:
		tmp = (z * y) * (z * -4.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 2.05e-24)
		tmp = Float64(Float64(x * x) - Float64(y * Float64(t * -4.0)));
	elseif (z <= 1.35e+188)
		tmp = Float64(Float64(x * x) - Float64(4.0 * Float64(z * Float64(z * y))));
	else
		tmp = Float64(Float64(z * y) * Float64(z * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 2.05e-24)
		tmp = (x * x) - (y * (t * -4.0));
	elseif (z <= 1.35e+188)
		tmp = (x * x) - (4.0 * (z * (z * y)));
	else
		tmp = (z * y) * (z * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 2.05e-24], N[(N[(x * x), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+188], N[(N[(x * x), $MachinePrecision] - N[(4.0 * N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < 2.05000000000000007e-24

   1. Initial program 91.6%

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

   2. Taylor expanded in z around 0 73.9%

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

      1. associate-*l* 73.9%

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

   4. Simplified 73.9%

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

   if 2.05000000000000007e-24 < z < 1.35e188

   1. Initial program 83.0%

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

      1. add-cube-cbrt 82.6%

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

      2. pow3 82.6%

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

      3. associate-*l* 82.6%

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

   3. Applied egg-rr 82.6%

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

      1. associate-*r* 82.6%

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

      2. cbrt-prod 82.2%

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

   5. Applied egg-rr 82.2%

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

      1. /-rgt-identity 82.2%

         \[\leadsto x \cdot x - {\left(\sqrt[3]{\color{blue}{\frac{y \cdot 4}{1}}} \cdot \sqrt[3]{z \cdot z - t}\right)}^{3} \]

      2. associate-/l* 82.2%

         \[\leadsto x \cdot x - {\left(\sqrt[3]{\color{blue}{\frac{y}{\frac{1}{4}}}} \cdot \sqrt[3]{z \cdot z - t}\right)}^{3} \]

      3. metadata-eval 82.2%

         \[\leadsto x \cdot x - {\left(\sqrt[3]{\frac{y}{\color{blue}{0.25}}} \cdot \sqrt[3]{z \cdot z - t}\right)}^{3} \]

   7. Simplified 82.2%

      \[\leadsto x \cdot x - {\color{blue}{\left(\sqrt[3]{\frac{y}{0.25}} \cdot \sqrt[3]{z \cdot z - t}\right)}}^{3} \]

   8. Taylor expanded in t around 0 72.4%

      \[\leadsto x \cdot x - \color{blue}{4 \cdot \left({1}^{0.3333333333333333} \cdot \left(y \cdot {z}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. pow-base-1 72.4%

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

      2. *-lft-identity 72.4%

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

      3. *-commutative 72.4%

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

      4. unpow2 72.4%

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

      5. associate-*r* 84.9%

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

   10. Simplified 84.9%

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

   if 1.35e188 < z

   1. Initial program 74.6%

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

   2. Taylor expanded in z around inf 83.3%

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

      1. *-commutative 83.3%

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

      2. unpow2 83.3%

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

      3. associate-*l* 83.3%

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

   4. Simplified 83.3%

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

      1. expm1-log1p-u 31.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\right)\right)} \]

      2. expm1-udef 31.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \left(\left(z \cdot z\right) \cdot -4\right)\right)} - 1} \]

      3. associate-*l* 31.2%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\left(z \cdot \left(z \cdot -4\right)\right)}\right)} - 1 \]

   6. Applied egg-rr 31.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 31.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\right)\right)} \]

      2. expm1-log1p 83.3%

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

      3. associate-*r* 91.3%

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

   8. Simplified 91.3%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.05 \cdot 10^{-24}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+188}:\\ \;\;\;\;x \cdot x - 4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(z \cdot -4\right)\\ \end{array} \]

Alternative 8: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 5.6 \cdot 10^{+249}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x x) 5.6e+249) (* (- (* z z) t) (* y -4.0)) (* x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 5.6e+249) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x * x) <= 5.6d+249) then
        tmp = ((z * z) - t) * (y * (-4.0d0))
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 5.6e+249) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x * x) <= 5.6e+249:
		tmp = ((z * z) - t) * (y * -4.0)
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * x) <= 5.6e+249)
		tmp = Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * x) <= 5.6e+249)
		tmp = ((z * z) - t) * (y * -4.0);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 5.6e+249], N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision], N[(x * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 5.60000000000000035e249

   1. Initial program 93.5%

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

   2. Taylor expanded in x around 0 78.4%

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

      1. associate-*r* 78.4%

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

      2. unpow2 78.4%

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

      3. *-commutative 78.4%

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

      4. *-commutative 78.4%

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

   4. Simplified 78.4%

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

   if 5.60000000000000035e249 < (*.f64 x x)

   1. Initial program 77.6%

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

   2. Taylor expanded in x around inf 81.7%

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

      1. unpow2 81.7%

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

   4. Simplified 81.7%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 5.6 \cdot 10^{+249}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 9: 58.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2.5 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \left(t \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x x) 2.5e+91) (* y (* t 4.0)) (* x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 2.5e+91) {
		tmp = y * (t * 4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x * x) <= 2.5d+91) then
        tmp = y * (t * 4.0d0)
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 2.5e+91) {
		tmp = y * (t * 4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x * x) <= 2.5e+91:
		tmp = y * (t * 4.0)
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * x) <= 2.5e+91)
		tmp = Float64(y * Float64(t * 4.0));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * x) <= 2.5e+91)
		tmp = y * (t * 4.0);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 2.5e+91], N[(y * N[(t * 4.0), $MachinePrecision]), $MachinePrecision], N[(x * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 2.5000000000000001e91

   1. Initial program 93.5%

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

   2. Taylor expanded in t around inf 44.9%

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

      1. associate-*r* 44.9%

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

      2. *-commutative 44.9%

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

   4. Simplified 44.9%

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

   if 2.5000000000000001e91 < (*.f64 x x)

   1. Initial program 82.0%

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

   2. Taylor expanded in x around inf 70.7%

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

      1. unpow2 70.7%

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

   4. Simplified 70.7%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2.5 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \left(t \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 10: 40.7% 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 88.6%

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

2. Taylor expanded in x around inf 40.0%

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

   1. unpow2 40.0%

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

4. Simplified 40.0%

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

5. Final simplification 40.0%

   \[\leadsto x \cdot x \]

Developer target: 91.3% 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 2023293 
(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))))