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

Percentage Accurate: 90.7% → 92.7%

Time: 10.2s

Alternatives: 7

Speedup: 0.5×

• 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: 90.7% 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: 92.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.2%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around 0 0.0%

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

   3. Taylor expanded in x around 0 57.1%

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

      1. +-commutative 57.1%

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

      2. add-sqr-sqrt 50.0%

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

      3. *-commutative 50.0%

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

      4. fma-def 50.0%

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

      5. sqrt-prod 50.0%

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

      6. metadata-eval 50.0%

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

      7. *-commutative 50.0%

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

      8. sqrt-prod 42.9%

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

      9. unpow2 42.9%

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

      10. sqrt-prod 21.4%

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

      11. add-sqr-sqrt 35.7%

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

      12. sqrt-prod 35.7%

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

      13. metadata-eval 35.7%

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

      14. *-commutative 35.7%

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

      15. sqrt-prod 35.7%

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

      16. unpow2 35.7%

          \[\leadsto -1 \cdot \mathsf{fma}\left(2 \cdot \left(z \cdot \sqrt{y}\right), 2 \cdot \left(\sqrt{\color{blue}{z \cdot z}} \cdot \sqrt{y}\right), -4 \cdot \left(y \cdot t\right)\right) \]

      17. sqrt-prod 21.4%

          \[\leadsto -1 \cdot \mathsf{fma}\left(2 \cdot \left(z \cdot \sqrt{y}\right), 2 \cdot \left(\color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)} \cdot \sqrt{y}\right), -4 \cdot \left(y \cdot t\right)\right) \]

      18. add-sqr-sqrt 42.9%

          \[\leadsto -1 \cdot \mathsf{fma}\left(2 \cdot \left(z \cdot \sqrt{y}\right), 2 \cdot \left(\color{blue}{z} \cdot \sqrt{y}\right), -4 \cdot \left(y \cdot t\right)\right) \]

      19. *-commutative 42.9%

          \[\leadsto -1 \cdot \mathsf{fma}\left(2 \cdot \left(z \cdot \sqrt{y}\right), 2 \cdot \left(z \cdot \sqrt{y}\right), \color{blue}{\left(y \cdot t\right) \cdot -4}\right) \]

   5. Applied egg-rr 42.9%

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

      1. fma-udef 42.9%

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

      2. unpow2 42.9%

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

      3. associate-*r* 42.9%

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

      4. associate-*r* 42.9%

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

      5. *-commutative 42.9%

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

      6. *-commutative 42.9%

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

   7. Simplified 42.9%

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

      1. unpow2 42.9%

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

      2. *-commutative 42.9%

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

      3. *-commutative 42.9%

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

      4. associate-*r* 42.9%

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

      5. metadata-eval 42.9%

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

      6. sqrt-prod 42.9%

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

      7. associate-*r* 42.9%

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

      8. metadata-eval 42.9%

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

      9. sqrt-prod 42.9%

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

      10. unswap-sqr 42.9%

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

      11. add-sqr-sqrt 57.1%

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

      12. associate-*r* 57.2%

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

   9. Applied egg-rr 57.2%

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

4. Final simplification 95.0%

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

Alternative 2: 92.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 91.9%

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

   1. fma-neg 95.0%

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

   2. distribute-lft-neg-in 95.0%

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

   3. *-commutative 95.0%

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

   4. distribute-rgt-neg-in 95.0%

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

   5. metadata-eval 95.0%

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

3. Simplified 95.0%

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

4. Final simplification 95.0%

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

Alternative 3: 92.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.2%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around inf 36.1%

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

      1. *-commutative 36.1%

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

      2. associate-*l* 36.1%

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

   4. Simplified 36.1%

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

      1. add-cube-cbrt 36.1%

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

      2. pow3 36.1%

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

      3. *-commutative 36.1%

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

   6. Applied egg-rr 36.1%

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

      1. rem-cube-cbrt 36.1%

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

      2. unpow2 36.1%

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

      3. associate-*r* 36.1%

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

   8. Applied egg-rr 36.1%

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

4. Final simplification 93.9%

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

Alternative 4: 86.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+54}:\\ \;\;\;\;x \cdot x - -4 \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;z \cdot z \leq 10^{+303}:\\ \;\;\;\;x \cdot x - \left(z \cdot z\right) \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 2e+54)
   (- (* x x) (* -4.0 (* t y)))
   (if (<= (* z z) 1e+303)
     (- (* x x) (* (* z z) (* y 4.0)))
     (* y (* z (* z -4.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 2e+54) {
		tmp = (x * x) - (-4.0 * (t * y));
	} else if ((z * z) <= 1e+303) {
		tmp = (x * x) - ((z * z) * (y * 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) <= 2d+54) then
        tmp = (x * x) - ((-4.0d0) * (t * y))
    else if ((z * z) <= 1d+303) then
        tmp = (x * x) - ((z * z) * (y * 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) <= 2e+54) {
		tmp = (x * x) - (-4.0 * (t * y));
	} else if ((z * z) <= 1e+303) {
		tmp = (x * x) - ((z * z) * (y * 4.0));
	} else {
		tmp = y * (z * (z * -4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * z) <= 2e+54:
		tmp = (x * x) - (-4.0 * (t * y))
	elif (z * z) <= 1e+303:
		tmp = (x * x) - ((z * z) * (y * 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) <= 2e+54)
		tmp = Float64(Float64(x * x) - Float64(-4.0 * Float64(t * y)));
	elseif (Float64(z * z) <= 1e+303)
		tmp = Float64(Float64(x * x) - Float64(Float64(z * z) * Float64(y * 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) <= 2e+54)
		tmp = (x * x) - (-4.0 * (t * y));
	elseif ((z * z) <= 1e+303)
		tmp = (x * x) - ((z * z) * (y * 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], 2e+54], N[(N[(x * x), $MachinePrecision] - N[(-4.0 * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * z), $MachinePrecision], 1e+303], N[(N[(x * x), $MachinePrecision] - N[(N[(z * z), $MachinePrecision] * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z z) < 2.0000000000000002e54

   1. Initial program 96.5%

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

   2. Taylor expanded in z around 0 90.2%

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

      1. *-commutative 90.2%

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

   4. Simplified 90.2%

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

   if 2.0000000000000002e54 < (*.f64 z z) < 1e303

   1. Initial program 91.9%

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

      1. add-cube-cbrt 91.3%

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

      2. pow3 91.3%

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

      3. pow2 91.3%

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

   3. Applied egg-rr 91.3%

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

   4. Taylor expanded in t around 0 75.7%

      \[\leadsto x \cdot x - \left(y \cdot 4\right) \cdot {\color{blue}{\left({\left({z}^{2}\right)}^{0.3333333333333333}\right)}}^{3} \]
   5. Step-by-step derivation

      1. unpow1/3 78.6%

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

   6. Simplified 78.6%

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

      1. unpow3 78.6%

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

      2. add-cube-cbrt 79.1%

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

      3. unpow2 79.1%

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

   8. Applied egg-rr 79.1%

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

   if 1e303 < (*.f64 z z)

   1. Initial program 80.1%

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

   2. Taylor expanded in z around inf 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-*l* 87.0%

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

   4. Simplified 87.0%

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

      1. add-cube-cbrt 87.0%

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

      2. pow3 87.0%

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

      3. *-commutative 87.0%

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

   6. Applied egg-rr 87.0%

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

      1. rem-cube-cbrt 87.0%

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

      2. unpow2 87.0%

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

      3. associate-*r* 87.0%

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

   8. Applied egg-rr 87.0%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+54}:\\ \;\;\;\;x \cdot x - -4 \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;z \cdot z \leq 10^{+303}:\\ \;\;\;\;x \cdot x - \left(z \cdot z\right) \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\\ \end{array} \]

Alternative 5: 74.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.2 \cdot 10^{+114}:\\ \;\;\;\;x \cdot x - -4 \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 3.2e+114) (- (* x x) (* -4.0 (* t y))) (* y (* z (* z -4.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3.2e+114) {
		tmp = (x * x) - (-4.0 * (t * y));
	} 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 <= 3.2d+114) then
        tmp = (x * x) - ((-4.0d0) * (t * y))
    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 <= 3.2e+114) {
		tmp = (x * x) - (-4.0 * (t * y));
	} else {
		tmp = y * (z * (z * -4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 3.2e+114:
		tmp = (x * x) - (-4.0 * (t * y))
	else:
		tmp = y * (z * (z * -4.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 3.2e+114)
		tmp = Float64(Float64(x * x) - Float64(-4.0 * Float64(t * y)));
	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 <= 3.2e+114)
		tmp = (x * x) - (-4.0 * (t * y));
	else
		tmp = y * (z * (z * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 3.2e+114], N[(N[(x * x), $MachinePrecision] - N[(-4.0 * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.2e114

   1. Initial program 92.8%

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

   2. Taylor expanded in z around 0 74.5%

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

      1. *-commutative 74.5%

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

   4. Simplified 74.5%

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

   if 3.2e114 < z

   1. Initial program 86.4%

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

   2. Taylor expanded in z around inf 92.0%

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

      1. *-commutative 92.0%

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

      2. associate-*l* 92.0%

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

   4. Simplified 92.0%

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

      1. add-cube-cbrt 92.0%

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

      2. pow3 92.0%

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

      3. *-commutative 92.0%

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

   6. Applied egg-rr 92.0%

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

      1. rem-cube-cbrt 92.0%

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

      2. unpow2 92.0%

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

      3. associate-*r* 92.0%

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

   8. Applied egg-rr 92.0%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.2 \cdot 10^{+114}:\\ \;\;\;\;x \cdot x - -4 \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\\ \end{array} \]

Alternative 6: 45.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.95 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(t \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.95e+27) (* y (* t 4.0)) (* y (* z (* z -4.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.95e+27) {
		tmp = 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 <= 1.95d+27) then
        tmp = 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 <= 1.95e+27) {
		tmp = y * (t * 4.0);
	} else {
		tmp = y * (z * (z * -4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 1.95e+27:
		tmp = y * (t * 4.0)
	else:
		tmp = y * (z * (z * -4.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.95e+27)
		tmp = 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 <= 1.95e+27)
		tmp = y * (t * 4.0);
	else
		tmp = y * (z * (z * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 1.95e+27], N[(y * N[(t * 4.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.9499999999999999e27

   1. Initial program 92.8%

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

   2. Taylor expanded in t around inf 33.9%

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

      1. *-commutative 33.9%

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

      2. *-commutative 33.9%

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

      3. associate-*l* 33.9%

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

   4. Simplified 33.9%

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

   if 1.9499999999999999e27 < z

   1. Initial program 88.1%

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

   2. Taylor expanded in z around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*l* 78.5%

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

   4. Simplified 78.5%

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

      1. add-cube-cbrt 78.3%

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

      2. pow3 78.3%

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

      3. *-commutative 78.3%

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

   6. Applied egg-rr 78.3%

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

      1. rem-cube-cbrt 78.5%

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

      2. unpow2 78.5%

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

      3. associate-*r* 78.5%

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

   8. Applied egg-rr 78.5%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.95 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(t \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(z \cdot -4\right)\right)\\ \end{array} \]

Alternative 7: 32.7% accurate, 2.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.9%

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

2. Taylor expanded in t around inf 30.0%

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

   1. *-commutative 30.0%

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

   2. *-commutative 30.0%

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

   3. associate-*l* 30.0%

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

4. Simplified 30.0%

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

5. Final simplification 30.0%

   \[\leadsto y \cdot \left(t \cdot 4\right) \]

Developer target: 90.7% 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 2023302 
(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))))