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

Percentage Accurate: 90.6% → 96.7%

Time: 10.5s

Alternatives: 9

Speedup: 0.8×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.6% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 4, \mathsf{fma}\left(z, -z, t\right), x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 5e+276)
   (fma (* y 4.0) (fma z (- z) t) (* 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) <= 5e+276) {
		tmp = fma((y * 4.0), fma(z, -z, t), (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) <= 5e+276)
		tmp = fma(Float64(y * 4.0), fma(z, Float64(-z), t), 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], 5e+276], N[(N[(y * 4.0), $MachinePrecision] * N[(z * (-z) + t), $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) < 5.00000000000000001e276

   1. Initial program 96.3%

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

      1. cancel-sign-sub-inv 96.3%

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

      2. distribute-lft-neg-out 96.3%

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

      3. +-commutative 96.3%

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

      4. distribute-lft-neg-out 96.3%

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

      5. distribute-lft-neg-in 96.3%

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

      6. distribute-rgt-neg-in 96.3%

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

      7. fma-def 98.1%

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

      8. sub-neg 98.1%

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

      9. distribute-neg-in 98.1%

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

      10. distribute-rgt-neg-out 98.1%

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

      11. remove-double-neg 98.1%

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

      12. fma-def 98.1%

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

   3. Simplified 98.1%

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

   if 5.00000000000000001e276 < (*.f64 z z)

   1. Initial program 69.3%

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

      1. fma-neg 69.3%

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

   3. Applied egg-rr 69.3%

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

      1. fma-udef 69.3%

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

      2. unpow2 69.3%

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

      3. sub-neg 69.3%

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

      4. flip-- 3.4%

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

      5. pow-prod-up 3.4%

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

      6. metadata-eval 3.4%

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

      7. sqr-neg 3.4%

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

      8. remove-double-neg 3.4%

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

      9. sub-neg 3.4%

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

      10. clear-num 3.4%

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

      11. un-div-inv 3.4%

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

      12. clear-num 3.4%

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

      13. metadata-eval 3.4%

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

      14. pow-sqr 3.4%

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

      15. add-sqr-sqrt 2.3%

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

      16. sqrt-prod 3.4%

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

   5. Applied egg-rr 69.3%

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

   6. Taylor expanded in z around inf 69.3%

      \[\leadsto x \cdot x - \frac{y \cdot 4}{\color{blue}{\frac{1}{{z}^{2}}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 69.3%

         \[\leadsto x \cdot x - \color{blue}{\frac{y \cdot 4}{1} \cdot {z}^{2}} \]

      2. /-rgt-identity 69.3%

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

      3. unpow2 69.3%

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

      4. associate-*r* 90.9%

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

   8. Applied egg-rr 90.9%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 4, \mathsf{fma}\left(z, -z, t\right), x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \]

Alternative 2: 96.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 5e+276)
   (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) <= 5e+276) {
		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) <= 5e+276)
		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], 5e+276], 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) < 5.00000000000000001e276

   1. Initial program 96.3%

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

      1. fma-neg 98.1%

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

      2. distribute-lft-neg-in 98.1%

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

      3. *-commutative 98.1%

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

      4. distribute-rgt-neg-in 98.1%

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

      5. metadata-eval 98.1%

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

   3. Simplified 98.1%

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

   if 5.00000000000000001e276 < (*.f64 z z)

   1. Initial program 69.3%

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

      1. fma-neg 69.3%

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

   3. Applied egg-rr 69.3%

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

      1. fma-udef 69.3%

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

      2. unpow2 69.3%

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

      3. sub-neg 69.3%

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

      4. flip-- 3.4%

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

      5. pow-prod-up 3.4%

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

      6. metadata-eval 3.4%

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

      7. sqr-neg 3.4%

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

      8. remove-double-neg 3.4%

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

      9. sub-neg 3.4%

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

      10. clear-num 3.4%

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

      11. un-div-inv 3.4%

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

      12. clear-num 3.4%

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

      13. metadata-eval 3.4%

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

      14. pow-sqr 3.4%

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

      15. add-sqr-sqrt 2.3%

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

      16. sqrt-prod 3.4%

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

   5. Applied egg-rr 69.3%

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

   6. Taylor expanded in z around inf 69.3%

      \[\leadsto x \cdot x - \frac{y \cdot 4}{\color{blue}{\frac{1}{{z}^{2}}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 69.3%

         \[\leadsto x \cdot x - \color{blue}{\frac{y \cdot 4}{1} \cdot {z}^{2}} \]

      2. /-rgt-identity 69.3%

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

      3. unpow2 69.3%

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

      4. associate-*r* 90.9%

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

   8. Applied egg-rr 90.9%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \]

Alternative 3: 96.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 4, t - z \cdot z, x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 5e+276)
   (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) <= 5e+276) {
		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) <= 5e+276)
		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], 5e+276], 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) < 5.00000000000000001e276

   1. Initial program 96.3%

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

      1. cancel-sign-sub-inv 96.3%

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

      2. distribute-lft-neg-out 96.3%

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

      3. +-commutative 96.3%

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

      4. distribute-lft-neg-out 96.3%

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

      5. distribute-lft-neg-in 96.3%

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

      6. distribute-rgt-neg-in 96.3%

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

      7. fma-def 98.1%

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

      8. sub-neg 98.1%

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

      9. +-commutative 98.1%

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

      10. distribute-neg-in 98.1%

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

      11. remove-double-neg 98.1%

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

      12. sub-neg 98.1%

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

   3. Simplified 98.1%

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

   if 5.00000000000000001e276 < (*.f64 z z)

   1. Initial program 69.3%

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

      1. fma-neg 69.3%

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

   3. Applied egg-rr 69.3%

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

      1. fma-udef 69.3%

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

      2. unpow2 69.3%

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

      3. sub-neg 69.3%

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

      4. flip-- 3.4%

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

      5. pow-prod-up 3.4%

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

      6. metadata-eval 3.4%

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

      7. sqr-neg 3.4%

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

      8. remove-double-neg 3.4%

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

      9. sub-neg 3.4%

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

      10. clear-num 3.4%

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

      11. un-div-inv 3.4%

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

      12. clear-num 3.4%

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

      13. metadata-eval 3.4%

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

      14. pow-sqr 3.4%

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

      15. add-sqr-sqrt 2.3%

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

      16. sqrt-prod 3.4%

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

   5. Applied egg-rr 69.3%

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

   6. Taylor expanded in z around inf 69.3%

      \[\leadsto x \cdot x - \frac{y \cdot 4}{\color{blue}{\frac{1}{{z}^{2}}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 69.3%

         \[\leadsto x \cdot x - \color{blue}{\frac{y \cdot 4}{1} \cdot {z}^{2}} \]

      2. /-rgt-identity 69.3%

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

      3. unpow2 69.3%

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

      4. associate-*r* 90.9%

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

   8. Applied egg-rr 90.9%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 4, t - z \cdot z, x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \]

Alternative 4: 95.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+276}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 5e+276)
   (+ (* 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) <= 5e+276) {
		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) <= 5d+276) 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) <= 5e+276) {
		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) <= 5e+276:
		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) <= 5e+276)
		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) <= 5e+276)
		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], 5e+276], 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) < 5.00000000000000001e276

   1. Initial program 96.3%

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

   if 5.00000000000000001e276 < (*.f64 z z)

   1. Initial program 69.3%

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

      1. fma-neg 69.3%

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

   3. Applied egg-rr 69.3%

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

      1. fma-udef 69.3%

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

      2. unpow2 69.3%

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

      3. sub-neg 69.3%

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

      4. flip-- 3.4%

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

      5. pow-prod-up 3.4%

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

      6. metadata-eval 3.4%

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

      7. sqr-neg 3.4%

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

      8. remove-double-neg 3.4%

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

      9. sub-neg 3.4%

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

      10. clear-num 3.4%

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

      11. un-div-inv 3.4%

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

      12. clear-num 3.4%

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

      13. metadata-eval 3.4%

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

      14. pow-sqr 3.4%

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

      15. add-sqr-sqrt 2.3%

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

      16. sqrt-prod 3.4%

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

   5. Applied egg-rr 69.3%

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

   6. Taylor expanded in z around inf 69.3%

      \[\leadsto x \cdot x - \frac{y \cdot 4}{\color{blue}{\frac{1}{{z}^{2}}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 69.3%

         \[\leadsto x \cdot x - \color{blue}{\frac{y \cdot 4}{1} \cdot {z}^{2}} \]

      2. /-rgt-identity 69.3%

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

      3. unpow2 69.3%

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

      4. associate-*r* 90.9%

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

   8. Applied egg-rr 90.9%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+276}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \]

Alternative 5: 78.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 6 \cdot 10^{+15}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 6e+15)
   (- (* 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 <= 6e+15) {
		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 <= 6d+15) 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 <= 6e+15) {
		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 <= 6e+15:
		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 (z <= 6e+15)
		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 <= 6e+15)
		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[z, 6e+15], 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 z < 6e15

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. *-commutative 71.9%

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

      3. associate-*l* 71.3%

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

   4. Simplified 71.3%

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

   if 6e15 < z

   1. Initial program 73.1%

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

      1. fma-neg 73.1%

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

   3. Applied egg-rr 73.1%

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

      1. fma-udef 73.1%

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

      2. unpow2 73.1%

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

      3. sub-neg 73.1%

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

      4. flip-- 22.0%

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

      5. pow-prod-up 22.0%

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

      6. metadata-eval 22.0%

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

      7. sqr-neg 22.0%

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

      8. remove-double-neg 22.0%

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

      9. sub-neg 22.0%

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

      10. clear-num 22.0%

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

      11. un-div-inv 22.0%

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

      12. clear-num 22.0%

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

      13. metadata-eval 22.0%

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

      14. pow-sqr 22.0%

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

      15. add-sqr-sqrt 11.0%

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

      16. sqrt-prod 19.5%

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

   5. Applied egg-rr 68.2%

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

   6. Taylor expanded in z around inf 70.8%

      \[\leadsto x \cdot x - \frac{y \cdot 4}{\color{blue}{\frac{1}{{z}^{2}}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 70.8%

         \[\leadsto x \cdot x - \color{blue}{\frac{y \cdot 4}{1} \cdot {z}^{2}} \]

      2. /-rgt-identity 70.8%

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

      3. unpow2 70.8%

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

      4. associate-*r* 88.0%

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

   8. Applied egg-rr 88.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6 \cdot 10^{+15}:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - z \cdot \left(z \cdot \left(y \cdot 4\right)\right)\\ \end{array} \]

Alternative 6: 45.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(y \cdot t\right)\\ \mathbf{if}\;x \leq 5.7 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 4.0 (* y t)))) (if (<= x 5.7e+48) t_1 (- (* x x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 4.0 * (y * t);
	double tmp;
	if (x <= 5.7e+48) {
		tmp = t_1;
	} else {
		tmp = (x * x) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 4.0d0 * (y * t)
    if (x <= 5.7d+48) then
        tmp = t_1
    else
        tmp = (x * x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 4.0 * (y * t);
	double tmp;
	if (x <= 5.7e+48) {
		tmp = t_1;
	} else {
		tmp = (x * x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 4.0 * (y * t)
	tmp = 0
	if x <= 5.7e+48:
		tmp = t_1
	else:
		tmp = (x * x) - t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(4.0 * Float64(y * t))
	tmp = 0.0
	if (x <= 5.7e+48)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 4.0 * (y * t);
	tmp = 0.0;
	if (x <= 5.7e+48)
		tmp = t_1;
	else
		tmp = (x * x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(4.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 5.7e+48], t$95$1, N[(N[(x * x), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 5.69999999999999968e48

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf 30.5%

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

      1. *-commutative 30.5%

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

   4. Simplified 30.5%

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

   if 5.69999999999999968e48 < x

   1. Initial program 91.5%

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

      1. fma-neg 91.5%

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

   3. Applied egg-rr 91.5%

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

      1. fma-udef 91.5%

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

      2. unpow2 91.5%

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

      3. sub-neg 91.5%

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

      4. flip-- 54.8%

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

      5. pow-prod-up 54.8%

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

      6. metadata-eval 54.8%

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

      7. sqr-neg 54.8%

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

      8. remove-double-neg 54.8%

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

      9. sub-neg 54.8%

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

      10. clear-num 54.8%

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

      11. un-div-inv 54.8%

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

      12. clear-num 54.8%

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

      13. metadata-eval 54.8%

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

      14. pow-sqr 54.8%

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

      15. add-sqr-sqrt 22.2%

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

      16. sqrt-prod 42.4%

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

   5. Applied egg-rr 84.7%

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

   6. Taylor expanded in z around 0 73.2%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.7 \cdot 10^{+48}:\\ \;\;\;\;4 \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x - 4 \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 7: 67.1% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.0%

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

2. Taylor expanded in z around 0 58.7%

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

   1. *-commutative 58.7%

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

   2. *-commutative 58.7%

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

   3. associate-*l* 58.3%

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

4. Simplified 58.3%

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

5. Final simplification 58.3%

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

Alternative 8: 6.0% accurate, 2.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.0%

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

   1. fma-neg 87.1%

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

3. Applied egg-rr 87.1%

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

   1. fma-udef 87.0%

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

   2. unpow2 87.0%

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

   3. sub-neg 87.0%

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

   4. flip-- 48.9%

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

   5. pow-prod-up 48.9%

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

   6. metadata-eval 48.9%

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

   7. sqr-neg 48.9%

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

   8. remove-double-neg 48.9%

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

   9. sub-neg 48.9%

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

   10. clear-num 48.9%

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

   11. un-div-inv 48.8%

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

   12. clear-num 48.8%

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

   13. metadata-eval 48.8%

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

   14. pow-sqr 48.8%

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

   15. add-sqr-sqrt 23.2%

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

   16. sqrt-prod 33.7%

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

5. Applied egg-rr 66.8%

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

6. Taylor expanded in z around 0 39.4%

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

7. Taylor expanded in x around 0 6.1%

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

8. Final simplification 6.1%

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

Alternative 9: 31.8% accurate, 2.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.0%

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

2. Taylor expanded in t around inf 26.7%

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

   1. *-commutative 26.7%

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

4. Simplified 26.7%

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

5. Final simplification 26.7%

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

Developer target: 90.6% 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 2023308 
(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))))