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

Percentage Accurate: 91.1% → 96.7%

Time: 10.2s

Alternatives: 8

Speedup: 0.6×

• 49.3% 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: 91.1% 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: 96.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+265}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 4, t - z \cdot z, x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 4e+265)
   (fma (* y 4.0) (- t (* z z)) (* x x))
   (- (* x x) (* z (* z (* y 4.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 4e+265) {
		tmp = fma((y * 4.0), (t - (z * z)), (x * x));
	} else {
		tmp = (x * x) - (z * (z * (y * 4.0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 4e+265)
		tmp = fma(Float64(y * 4.0), Float64(t - Float64(z * z)), Float64(x * x));
	else
		tmp = Float64(Float64(x * x) - Float64(z * Float64(z * Float64(y * 4.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 4e+265], N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] - N[(z * N[(z * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 4.00000000000000027e265

   1. Initial program 99.4%

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

      1. cancel-sign-sub-inv 99.4%

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

      2. distribute-lft-neg-out 99.4%

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

      3. +-commutative 99.4%

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

      4. distribute-lft-neg-out 99.4%

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

      5. distribute-lft-neg-in 99.4%

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

      6. distribute-rgt-neg-in 99.4%

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

      7. fma-define 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. remove-double-neg 99.9%

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

      12. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   if 4.00000000000000027e265 < (*.f64 z z)

   1. Initial program 71.0%

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

   3. Taylor expanded in z around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. unsub-neg 71.0%

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

   5. Simplified 71.0%

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

      1. add-sqr-sqrt 33.6%

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

      2. pow2 33.6%

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

      3. sqrt-prod 33.6%

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

      4. *-commutative 33.6%

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

      5. sqrt-prod 33.6%

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

      6. metadata-eval 33.6%

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

      7. sqrt-prod 33.6%

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

      8. sqrt-pow1 46.5%

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

      9. metadata-eval 46.5%

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

      10. pow1 46.5%

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

      11. div-inv 46.5%

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

      12. pow-flip 46.5%

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

      13. metadata-eval 46.5%

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

   7. Applied egg-rr 46.5%

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

   8. Taylor expanded in z around inf 46.5%

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

      1. unpow2 46.5%

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

      2. swap-sqr 33.6%

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

      3. swap-sqr 33.6%

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

      4. metadata-eval 33.6%

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

      5. add-sqr-sqrt 71.0%

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

      6. *-commutative 71.0%

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

      7. associate-*r* 90.3%

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

   10. Applied egg-rr 90.3%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+265}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 4, t - z \cdot z, x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+265}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 4e+265)
   (fma x x (* (- (* z z) t) (* y -4.0)))
   (- (* x x) (* z (* z (* y 4.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 4e+265) {
		tmp = fma(x, x, (((z * z) - t) * (y * -4.0)));
	} else {
		tmp = (x * x) - (z * (z * (y * 4.0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 4e+265)
		tmp = fma(x, x, Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0)));
	else
		tmp = Float64(Float64(x * x) - Float64(z * Float64(z * Float64(y * 4.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 4e+265], N[(x * x + N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] - N[(z * N[(z * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 4.00000000000000027e265

   1. Initial program 99.4%

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

      1. fmm-def 99.4%

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

      2. distribute-lft-neg-in 99.4%

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

      3. *-commutative 99.4%

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

      4. distribute-rgt-neg-in 99.4%

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

      5. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   if 4.00000000000000027e265 < (*.f64 z z)

   1. Initial program 71.0%

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

   3. Taylor expanded in z around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. unsub-neg 71.0%

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

   5. Simplified 71.0%

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

      1. add-sqr-sqrt 33.6%

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

      2. pow2 33.6%

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

      3. sqrt-prod 33.6%

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

      4. *-commutative 33.6%

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

      5. sqrt-prod 33.6%

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

      6. metadata-eval 33.6%

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

      7. sqrt-prod 33.6%

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

      8. sqrt-pow1 46.5%

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

      9. metadata-eval 46.5%

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

      10. pow1 46.5%

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

      11. div-inv 46.5%

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

      12. pow-flip 46.5%

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

      13. metadata-eval 46.5%

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

   7. Applied egg-rr 46.5%

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

   8. Taylor expanded in z around inf 46.5%

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

      1. unpow2 46.5%

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

      2. swap-sqr 33.6%

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

      3. swap-sqr 33.6%

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

      4. metadata-eval 33.6%

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

      5. add-sqr-sqrt 71.0%

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

      6. *-commutative 71.0%

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

      7. associate-*r* 90.3%

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

   10. Applied egg-rr 90.3%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+265}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+265}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 4e+265)
   (+ (* x x) (* (* y 4.0) (- t (* z z))))
   (- (* x x) (* z (* z (* y 4.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 4e+265) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = (x * x) - (z * (z * (y * 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) <= 4d+265) then
        tmp = (x * x) + ((y * 4.0d0) * (t - (z * z)))
    else
        tmp = (x * x) - (z * (z * (y * 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) <= 4e+265) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = (x * x) - (z * (z * (y * 4.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * z) <= 4e+265:
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)))
	else:
		tmp = (x * x) - (z * (z * (y * 4.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 4e+265)
		tmp = Float64(Float64(x * x) + Float64(Float64(y * 4.0) * Float64(t - Float64(z * z))));
	else
		tmp = Float64(Float64(x * x) - Float64(z * Float64(z * Float64(y * 4.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * z) <= 4e+265)
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	else
		tmp = (x * x) - (z * (z * (y * 4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 4e+265], N[(N[(x * x), $MachinePrecision] + N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] - N[(z * N[(z * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 4.00000000000000027e265

   1. Initial program 99.4%

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

   if 4.00000000000000027e265 < (*.f64 z z)

   1. Initial program 71.0%

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

   3. Taylor expanded in z around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. unsub-neg 71.0%

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

   5. Simplified 71.0%

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

      1. add-sqr-sqrt 33.6%

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

      2. pow2 33.6%

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

      3. sqrt-prod 33.6%

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

      4. *-commutative 33.6%

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

      5. sqrt-prod 33.6%

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

      6. metadata-eval 33.6%

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

      7. sqrt-prod 33.6%

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

      8. sqrt-pow1 46.5%

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

      9. metadata-eval 46.5%

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

      10. pow1 46.5%

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

      11. div-inv 46.5%

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

      12. pow-flip 46.5%

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

      13. metadata-eval 46.5%

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

   7. Applied egg-rr 46.5%

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

   8. Taylor expanded in z around inf 46.5%

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

      1. unpow2 46.5%

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

      2. swap-sqr 33.6%

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

      3. swap-sqr 33.6%

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

      4. metadata-eval 33.6%

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

      5. add-sqr-sqrt 71.0%

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

      6. *-commutative 71.0%

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

      7. associate-*r* 90.3%

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

   10. Applied egg-rr 90.3%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+265}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 5e-14)
   (- (* x x) (* y (* t -4.0)))
   (- (* x x) (* z (* z (* y 4.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 5e-14) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = (x * x) - (z * (z * (y * 4.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * z) <= 5d-14) then
        tmp = (x * x) - (y * (t * (-4.0d0)))
    else
        tmp = (x * x) - (z * (z * (y * 4.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 5e-14) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = (x * x) - (z * (z * (y * 4.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * z) <= 5e-14:
		tmp = (x * x) - (y * (t * -4.0))
	else:
		tmp = (x * x) - (z * (z * (y * 4.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 5e-14)
		tmp = Float64(Float64(x * x) - Float64(y * Float64(t * -4.0)));
	else
		tmp = Float64(Float64(x * x) - Float64(z * Float64(z * Float64(y * 4.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * z) <= 5e-14)
		tmp = (x * x) - (y * (t * -4.0));
	else
		tmp = (x * x) - (z * (z * (y * 4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 5e-14], N[(N[(x * x), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] - N[(z * N[(z * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 5.0000000000000002e-14

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 97.6%

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

      1. *-commutative 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*l* 96.8%

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

   5. Simplified 96.8%

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

   if 5.0000000000000002e-14 < (*.f64 z z)

   1. Initial program 83.8%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. mul-1-neg 83.8%

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

      2. unsub-neg 83.8%

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

   5. Simplified 83.8%

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

      1. add-sqr-sqrt 39.3%

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

      2. pow2 39.2%

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

      3. sqrt-prod 37.7%

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

      4. *-commutative 37.7%

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

      5. sqrt-prod 37.7%

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

      6. metadata-eval 37.7%

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

      7. sqrt-prod 37.7%

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

      8. sqrt-pow1 44.9%

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

      9. metadata-eval 44.9%

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

      10. pow1 44.9%

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

      11. div-inv 44.9%

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

      12. pow-flip 44.9%

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

      13. metadata-eval 44.9%

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

   7. Applied egg-rr 44.9%

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

   8. Taylor expanded in z around inf 43.9%

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

      1. unpow2 43.9%

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

      2. swap-sqr 36.8%

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

      3. swap-sqr 36.8%

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

      4. metadata-eval 36.8%

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

      5. add-sqr-sqrt 77.5%

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

      6. *-commutative 77.5%

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

      7. associate-*r* 88.3%

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

   10. Applied egg-rr 88.3%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 44.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.38 \cdot 10^{-36}:\\ \;\;\;\;4 \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+91}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \left(y \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.38e-36)
   (* 4.0 (* y t))
   (if (<= z 9.2e+91) (* x x) (* (* z z) (* y -4.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.38e-36) {
		tmp = 4.0 * (y * t);
	} else if (z <= 9.2e+91) {
		tmp = x * x;
	} else {
		tmp = (z * z) * (y * -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 <= 1.38d-36) then
        tmp = 4.0d0 * (y * t)
    else if (z <= 9.2d+91) then
        tmp = x * x
    else
        tmp = (z * z) * (y * (-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 <= 1.38e-36) {
		tmp = 4.0 * (y * t);
	} else if (z <= 9.2e+91) {
		tmp = x * x;
	} else {
		tmp = (z * z) * (y * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 1.38e-36:
		tmp = 4.0 * (y * t)
	elif z <= 9.2e+91:
		tmp = x * x
	else:
		tmp = (z * z) * (y * -4.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.38e-36)
		tmp = Float64(4.0 * Float64(y * t));
	elseif (z <= 9.2e+91)
		tmp = Float64(x * x);
	else
		tmp = Float64(Float64(z * z) * Float64(y * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 1.38e-36)
		tmp = 4.0 * (y * t);
	elseif (z <= 9.2e+91)
		tmp = x * x;
	else
		tmp = (z * z) * (y * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 1.38e-36], N[(4.0 * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+91], N[(x * x), $MachinePrecision], N[(N[(z * z), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < 1.38e-36

   1. Initial program 93.7%

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

      1. fmm-def 96.4%

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

      2. distribute-lft-neg-in 96.4%

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

      3. *-commutative 96.4%

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

      4. distribute-rgt-neg-in 96.4%

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

      5. metadata-eval 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around inf 42.5%

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

      1. *-commutative 42.5%

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

   7. Simplified 42.5%

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

   if 1.38e-36 < z < 9.19999999999999965e91

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.8%

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

   5. Simplified 50.7%

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

      1. --rgt-identity 50.7%

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

   7. Applied egg-rr 50.7%

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

   if 9.19999999999999965e91 < z

   1. Initial program 75.2%

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

   3. Taylor expanded in z around inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. unsub-neg 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in z around inf 70.8%

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

      1. metadata-eval 70.8%

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

      2. distribute-lft-neg-in 70.8%

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

      3. associate-*r* 70.8%

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

      4. *-commutative 70.8%

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

      5. *-commutative 70.8%

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

      6. distribute-rgt-neg-in 70.8%

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

      7. distribute-rgt-neg-in 70.8%

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

      8. metadata-eval 70.8%

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

   8. Simplified 70.8%

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

      1. pow2 70.8%

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

   10. Applied egg-rr 70.8%

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

Alternative 6: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 3.4 \cdot 10^{+225}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \left(y \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 3.4e+225)
   (- (* x x) (* y (* t -4.0)))
   (* (* z z) (* y -4.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 3.4e+225) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = (z * z) * (y * -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) <= 3.4d+225) then
        tmp = (x * x) - (y * (t * (-4.0d0)))
    else
        tmp = (z * z) * (y * (-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) <= 3.4e+225) {
		tmp = (x * x) - (y * (t * -4.0));
	} else {
		tmp = (z * z) * (y * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * z) <= 3.4e+225:
		tmp = (x * x) - (y * (t * -4.0))
	else:
		tmp = (z * z) * (y * -4.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 3.4e+225)
		tmp = Float64(Float64(x * x) - Float64(y * Float64(t * -4.0)));
	else
		tmp = Float64(Float64(z * z) * Float64(y * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * z) <= 3.4e+225)
		tmp = (x * x) - (y * (t * -4.0));
	else
		tmp = (z * z) * (y * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 3.4e+225], N[(N[(x * x), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * z), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 3.40000000000000018e225

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 87.0%

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

      1. *-commutative 87.0%

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

      2. *-commutative 87.0%

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

      3. associate-*l* 86.5%

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

   5. Simplified 86.5%

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

   if 3.40000000000000018e225 < (*.f64 z z)

   1. Initial program 73.9%

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

   3. Taylor expanded in z around inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. unsub-neg 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in z around inf 79.0%

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

      1. metadata-eval 79.0%

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

      2. distribute-lft-neg-in 79.0%

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

      3. associate-*r* 79.0%

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

      4. *-commutative 79.0%

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

      5. *-commutative 79.0%

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

      6. distribute-rgt-neg-in 79.0%

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

      7. distribute-rgt-neg-in 79.0%

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

      8. metadata-eval 79.0%

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

   8. Simplified 79.0%

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

      1. pow2 79.0%

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

   10. Applied egg-rr 79.0%

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

Alternative 7: 59.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 8 \cdot 10^{+23}:\\ \;\;\;\;4 \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x x) 8e+23) (* 4.0 (* y t)) (* x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 8e+23) {
		tmp = 4.0 * (y * t);
	} 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) <= 8d+23) then
        tmp = 4.0d0 * (y * t)
    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) <= 8e+23) {
		tmp = 4.0 * (y * t);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x * x) <= 8e+23:
		tmp = 4.0 * (y * t)
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * x) <= 8e+23)
		tmp = Float64(4.0 * Float64(y * t));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * x) <= 8e+23)
		tmp = 4.0 * (y * t);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 8e+23], N[(4.0 * N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 7.9999999999999993e23

   1. Initial program 93.2%

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

      1. fmm-def 93.2%

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

      2. distribute-lft-neg-in 93.2%

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

      3. *-commutative 93.2%

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

      4. distribute-rgt-neg-in 93.2%

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

      5. metadata-eval 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in t around inf 51.8%

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

      1. *-commutative 51.8%

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

   7. Simplified 51.8%

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

   if 7.9999999999999993e23 < (*.f64 x x)

   1. Initial program 89.1%

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

   3. Taylor expanded in y around 0 89.1%

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

   5. Simplified 68.8%

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

      1. --rgt-identity 68.8%

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

   7. Applied egg-rr 68.8%

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

Alternative 8: 41.6% 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 91.3%

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

3. Taylor expanded in y around 0 91.3%

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

5. Simplified 38.1%

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

   1. --rgt-identity 38.1%

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

7. Applied egg-rr 38.1%

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

Developer Target 1: 91.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* x x) (* 4 (* y (- (* z z) t)))))

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