Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E

Percentage Accurate: 99.7% → 99.8%

Time: 9.4s

Alternatives: 11

Speedup: 1.0×

• 20.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \left(6 \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (- y x) (* 6.0 z))))

C

double code(double x, double y, double z) {
	return x + ((y - x) * (6.0 * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) * (6.0d0 * z))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * (6.0 * z));
}

Python

def code(x, y, z):
	return x + ((y - x) * (6.0 * z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * Float64(6.0 * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * (6.0 * z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Step-by-step derivation

   1. associate-*l* 99.8%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(6 \cdot z\right)} \]

4. Final simplification 99.8%

   \[\leadsto x + \left(y - x\right) \cdot \left(6 \cdot z\right) \]

Alternative 2: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(6 \cdot z\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+247}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+212}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-22}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+166} \lor \neg \left(z \leq 6.5 \cdot 10^{+207}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* 6.0 z))) (t_1 (* -6.0 (* x z))))
   (if (<= z -2.45e+247)
     t_0
     (if (<= z -9.5e+228)
       (* x (* z -6.0))
       (if (<= z -3.1e+212)
         t_0
         (if (<= z -1.85e+98)
           t_1
           (if (<= z -6.6e-22)
             t_0
             (if (<= z 4.6e-16)
               x
               (if (or (<= z 2.3e+166) (not (<= z 6.5e+207))) t_0 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -2.45e+247) {
		tmp = t_0;
	} else if (z <= -9.5e+228) {
		tmp = x * (z * -6.0);
	} else if (z <= -3.1e+212) {
		tmp = t_0;
	} else if (z <= -1.85e+98) {
		tmp = t_1;
	} else if (z <= -6.6e-22) {
		tmp = t_0;
	} else if (z <= 4.6e-16) {
		tmp = x;
	} else if ((z <= 2.3e+166) || !(z <= 6.5e+207)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (6.0d0 * z)
    t_1 = (-6.0d0) * (x * z)
    if (z <= (-2.45d+247)) then
        tmp = t_0
    else if (z <= (-9.5d+228)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= (-3.1d+212)) then
        tmp = t_0
    else if (z <= (-1.85d+98)) then
        tmp = t_1
    else if (z <= (-6.6d-22)) then
        tmp = t_0
    else if (z <= 4.6d-16) then
        tmp = x
    else if ((z <= 2.3d+166) .or. (.not. (z <= 6.5d+207))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -2.45e+247) {
		tmp = t_0;
	} else if (z <= -9.5e+228) {
		tmp = x * (z * -6.0);
	} else if (z <= -3.1e+212) {
		tmp = t_0;
	} else if (z <= -1.85e+98) {
		tmp = t_1;
	} else if (z <= -6.6e-22) {
		tmp = t_0;
	} else if (z <= 4.6e-16) {
		tmp = x;
	} else if ((z <= 2.3e+166) || !(z <= 6.5e+207)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (6.0 * z)
	t_1 = -6.0 * (x * z)
	tmp = 0
	if z <= -2.45e+247:
		tmp = t_0
	elif z <= -9.5e+228:
		tmp = x * (z * -6.0)
	elif z <= -3.1e+212:
		tmp = t_0
	elif z <= -1.85e+98:
		tmp = t_1
	elif z <= -6.6e-22:
		tmp = t_0
	elif z <= 4.6e-16:
		tmp = x
	elif (z <= 2.3e+166) or not (z <= 6.5e+207):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(6.0 * z))
	t_1 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.45e+247)
		tmp = t_0;
	elseif (z <= -9.5e+228)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= -3.1e+212)
		tmp = t_0;
	elseif (z <= -1.85e+98)
		tmp = t_1;
	elseif (z <= -6.6e-22)
		tmp = t_0;
	elseif (z <= 4.6e-16)
		tmp = x;
	elseif ((z <= 2.3e+166) || !(z <= 6.5e+207))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (6.0 * z);
	t_1 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.45e+247)
		tmp = t_0;
	elseif (z <= -9.5e+228)
		tmp = x * (z * -6.0);
	elseif (z <= -3.1e+212)
		tmp = t_0;
	elseif (z <= -1.85e+98)
		tmp = t_1;
	elseif (z <= -6.6e-22)
		tmp = t_0;
	elseif (z <= 4.6e-16)
		tmp = x;
	elseif ((z <= 2.3e+166) || ~((z <= 6.5e+207)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.45e+247], t$95$0, If[LessEqual[z, -9.5e+228], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e+212], t$95$0, If[LessEqual[z, -1.85e+98], t$95$1, If[LessEqual[z, -6.6e-22], t$95$0, If[LessEqual[z, 4.6e-16], x, If[Or[LessEqual[z, 2.3e+166], N[Not[LessEqual[z, 6.5e+207]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4499999999999999e247 or -9.50000000000000046e228 < z < -3.09999999999999998e212 or -1.8499999999999999e98 < z < -6.6000000000000002e-22 or 4.5999999999999998e-16 < z < 2.30000000000000008e166 or 6.5000000000000001e207 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 98.2%

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

      1. add-sqr-sqrt 48.7%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 48.7%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 48.7%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in z around 0 98.2%

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

      1. associate-*r* 98.1%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(x - y\right)} \]

      2. *-commutative 98.1%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(x - y\right) \]

   9. Simplified 98.1%

      \[\leadsto \color{blue}{\left(z \cdot -6\right) \cdot \left(x - y\right)} \]

   10. Taylor expanded in x around 0 73.8%

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

       1. *-commutative 73.8%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

       2. associate-*l* 73.7%

          \[\leadsto \color{blue}{y \cdot \left(z \cdot 6\right)} \]

   12. Simplified 73.7%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot 6\right)} \]

   if -2.4499999999999999e247 < z < -9.50000000000000046e228

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.6%

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

      1. add-sqr-sqrt 62.3%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 62.3%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 62.3%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in x around inf 76.2%

      \[\leadsto \color{blue}{-6 \cdot \left(x \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 76.2%

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot -6} \]

      2. associate-*r* 76.4%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot -6\right)} \]

   9. Simplified 76.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot -6\right)} \]

   if -3.09999999999999998e212 < z < -1.8499999999999999e98 or 2.30000000000000008e166 < z < 6.5000000000000001e207

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.9%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.9%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(x - y\right)\right)} \]

   5. Taylor expanded in x around inf 74.0%

      \[\leadsto -6 \cdot \color{blue}{\left(x \cdot z\right)} \]

   if -6.6000000000000002e-22 < z < 4.5999999999999998e-16

   1. Initial program 99.1%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 74.4%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+247}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+212}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+98}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+166} \lor \neg \left(z \leq 6.5 \cdot 10^{+207}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+247}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+212}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+166} \lor \neg \left(z \leq 4 \cdot 10^{+206}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* 6.0 z))))
   (if (<= z -2.35e+247)
     t_0
     (if (<= z -4e+228)
       (* x (* z -6.0))
       (if (<= z -6.6e+212)
         t_0
         (if (<= z -3.5e+103)
           (* z (* x -6.0))
           (if (<= z -5.2e-20)
             t_0
             (if (<= z 2.6e-14)
               x
               (if (or (<= z 2.15e+166) (not (<= z 4e+206)))
                 t_0
                 (* -6.0 (* x z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double tmp;
	if (z <= -2.35e+247) {
		tmp = t_0;
	} else if (z <= -4e+228) {
		tmp = x * (z * -6.0);
	} else if (z <= -6.6e+212) {
		tmp = t_0;
	} else if (z <= -3.5e+103) {
		tmp = z * (x * -6.0);
	} else if (z <= -5.2e-20) {
		tmp = t_0;
	} else if (z <= 2.6e-14) {
		tmp = x;
	} else if ((z <= 2.15e+166) || !(z <= 4e+206)) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (6.0d0 * z)
    if (z <= (-2.35d+247)) then
        tmp = t_0
    else if (z <= (-4d+228)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= (-6.6d+212)) then
        tmp = t_0
    else if (z <= (-3.5d+103)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= (-5.2d-20)) then
        tmp = t_0
    else if (z <= 2.6d-14) then
        tmp = x
    else if ((z <= 2.15d+166) .or. (.not. (z <= 4d+206))) then
        tmp = t_0
    else
        tmp = (-6.0d0) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double tmp;
	if (z <= -2.35e+247) {
		tmp = t_0;
	} else if (z <= -4e+228) {
		tmp = x * (z * -6.0);
	} else if (z <= -6.6e+212) {
		tmp = t_0;
	} else if (z <= -3.5e+103) {
		tmp = z * (x * -6.0);
	} else if (z <= -5.2e-20) {
		tmp = t_0;
	} else if (z <= 2.6e-14) {
		tmp = x;
	} else if ((z <= 2.15e+166) || !(z <= 4e+206)) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (6.0 * z)
	tmp = 0
	if z <= -2.35e+247:
		tmp = t_0
	elif z <= -4e+228:
		tmp = x * (z * -6.0)
	elif z <= -6.6e+212:
		tmp = t_0
	elif z <= -3.5e+103:
		tmp = z * (x * -6.0)
	elif z <= -5.2e-20:
		tmp = t_0
	elif z <= 2.6e-14:
		tmp = x
	elif (z <= 2.15e+166) or not (z <= 4e+206):
		tmp = t_0
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(6.0 * z))
	tmp = 0.0
	if (z <= -2.35e+247)
		tmp = t_0;
	elseif (z <= -4e+228)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= -6.6e+212)
		tmp = t_0;
	elseif (z <= -3.5e+103)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= -5.2e-20)
		tmp = t_0;
	elseif (z <= 2.6e-14)
		tmp = x;
	elseif ((z <= 2.15e+166) || !(z <= 4e+206))
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (6.0 * z);
	tmp = 0.0;
	if (z <= -2.35e+247)
		tmp = t_0;
	elseif (z <= -4e+228)
		tmp = x * (z * -6.0);
	elseif (z <= -6.6e+212)
		tmp = t_0;
	elseif (z <= -3.5e+103)
		tmp = z * (x * -6.0);
	elseif (z <= -5.2e-20)
		tmp = t_0;
	elseif (z <= 2.6e-14)
		tmp = x;
	elseif ((z <= 2.15e+166) || ~((z <= 4e+206)))
		tmp = t_0;
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e+247], t$95$0, If[LessEqual[z, -4e+228], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.6e+212], t$95$0, If[LessEqual[z, -3.5e+103], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.2e-20], t$95$0, If[LessEqual[z, 2.6e-14], x, If[Or[LessEqual[z, 2.15e+166], N[Not[LessEqual[z, 4e+206]], $MachinePrecision]], t$95$0, N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.3500000000000001e247 or -3.9999999999999997e228 < z < -6.6e212 or -3.5e103 < z < -5.1999999999999999e-20 or 2.59999999999999997e-14 < z < 2.15e166 or 4.0000000000000002e206 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 98.2%

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

      1. add-sqr-sqrt 48.7%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 48.7%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 48.7%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in z around 0 98.2%

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

      1. associate-*r* 98.1%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(x - y\right)} \]

      2. *-commutative 98.1%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(x - y\right) \]

   9. Simplified 98.1%

      \[\leadsto \color{blue}{\left(z \cdot -6\right) \cdot \left(x - y\right)} \]

   10. Taylor expanded in x around 0 73.8%

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

       1. *-commutative 73.8%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

       2. associate-*l* 73.7%

          \[\leadsto \color{blue}{y \cdot \left(z \cdot 6\right)} \]

   12. Simplified 73.7%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot 6\right)} \]

   if -2.3500000000000001e247 < z < -3.9999999999999997e228

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.6%

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

      1. add-sqr-sqrt 62.3%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 62.3%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 62.3%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in x around inf 76.2%

      \[\leadsto \color{blue}{-6 \cdot \left(x \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 76.2%

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot -6} \]

      2. associate-*r* 76.4%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot -6\right)} \]

   9. Simplified 76.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot -6\right)} \]

   if -6.6e212 < z < -3.5e103

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.9%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.9%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.7%

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

      1. add-sqr-sqrt 37.4%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 37.4%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 37.4%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in x around inf 72.2%

      \[\leadsto \color{blue}{-6 \cdot \left(x \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 72.2%

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot -6} \]

      2. *-commutative 72.2%

         \[\leadsto \color{blue}{\left(z \cdot x\right)} \cdot -6 \]

      3. associate-*l* 72.4%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot -6\right)} \]

   9. Simplified 72.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot -6\right)} \]

   if -5.1999999999999999e-20 < z < 2.59999999999999997e-14

   1. Initial program 99.1%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 74.4%

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

   if 2.15e166 < z < 4.0000000000000002e206

   1. Initial program 100.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 100.0%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(x - y\right)\right)} \]

   5. Taylor expanded in x around inf 78.7%

      \[\leadsto -6 \cdot \color{blue}{\left(x \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+247}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+212}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+166} \lor \neg \left(z \leq 4 \cdot 10^{+206}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+247}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+212}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+166} \lor \neg \left(z \leq 2.52 \cdot 10^{+207}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* 6.0 z))))
   (if (<= z -3.2e+247)
     t_0
     (if (<= z -4.2e+228)
       (* x (* z -6.0))
       (if (<= z -1.05e+212)
         t_0
         (if (<= z -1.7e+99)
           (* z (* x -6.0))
           (if (<= z -3.3e-20)
             (* z (* y 6.0))
             (if (<= z 1.56e-15)
               x
               (if (or (<= z 1.8e+166) (not (<= z 2.52e+207)))
                 t_0
                 (* -6.0 (* x z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double tmp;
	if (z <= -3.2e+247) {
		tmp = t_0;
	} else if (z <= -4.2e+228) {
		tmp = x * (z * -6.0);
	} else if (z <= -1.05e+212) {
		tmp = t_0;
	} else if (z <= -1.7e+99) {
		tmp = z * (x * -6.0);
	} else if (z <= -3.3e-20) {
		tmp = z * (y * 6.0);
	} else if (z <= 1.56e-15) {
		tmp = x;
	} else if ((z <= 1.8e+166) || !(z <= 2.52e+207)) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (6.0d0 * z)
    if (z <= (-3.2d+247)) then
        tmp = t_0
    else if (z <= (-4.2d+228)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= (-1.05d+212)) then
        tmp = t_0
    else if (z <= (-1.7d+99)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= (-3.3d-20)) then
        tmp = z * (y * 6.0d0)
    else if (z <= 1.56d-15) then
        tmp = x
    else if ((z <= 1.8d+166) .or. (.not. (z <= 2.52d+207))) then
        tmp = t_0
    else
        tmp = (-6.0d0) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double tmp;
	if (z <= -3.2e+247) {
		tmp = t_0;
	} else if (z <= -4.2e+228) {
		tmp = x * (z * -6.0);
	} else if (z <= -1.05e+212) {
		tmp = t_0;
	} else if (z <= -1.7e+99) {
		tmp = z * (x * -6.0);
	} else if (z <= -3.3e-20) {
		tmp = z * (y * 6.0);
	} else if (z <= 1.56e-15) {
		tmp = x;
	} else if ((z <= 1.8e+166) || !(z <= 2.52e+207)) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (6.0 * z)
	tmp = 0
	if z <= -3.2e+247:
		tmp = t_0
	elif z <= -4.2e+228:
		tmp = x * (z * -6.0)
	elif z <= -1.05e+212:
		tmp = t_0
	elif z <= -1.7e+99:
		tmp = z * (x * -6.0)
	elif z <= -3.3e-20:
		tmp = z * (y * 6.0)
	elif z <= 1.56e-15:
		tmp = x
	elif (z <= 1.8e+166) or not (z <= 2.52e+207):
		tmp = t_0
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(6.0 * z))
	tmp = 0.0
	if (z <= -3.2e+247)
		tmp = t_0;
	elseif (z <= -4.2e+228)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= -1.05e+212)
		tmp = t_0;
	elseif (z <= -1.7e+99)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= -3.3e-20)
		tmp = Float64(z * Float64(y * 6.0));
	elseif (z <= 1.56e-15)
		tmp = x;
	elseif ((z <= 1.8e+166) || !(z <= 2.52e+207))
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (6.0 * z);
	tmp = 0.0;
	if (z <= -3.2e+247)
		tmp = t_0;
	elseif (z <= -4.2e+228)
		tmp = x * (z * -6.0);
	elseif (z <= -1.05e+212)
		tmp = t_0;
	elseif (z <= -1.7e+99)
		tmp = z * (x * -6.0);
	elseif (z <= -3.3e-20)
		tmp = z * (y * 6.0);
	elseif (z <= 1.56e-15)
		tmp = x;
	elseif ((z <= 1.8e+166) || ~((z <= 2.52e+207)))
		tmp = t_0;
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+247], t$95$0, If[LessEqual[z, -4.2e+228], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.05e+212], t$95$0, If[LessEqual[z, -1.7e+99], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-20], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.56e-15], x, If[Or[LessEqual[z, 1.8e+166], N[Not[LessEqual[z, 2.52e+207]], $MachinePrecision]], t$95$0, N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.20000000000000022e247 or -4.19999999999999988e228 < z < -1.05e212 or 1.55999999999999991e-15 < z < 1.7999999999999999e166 or 2.51999999999999998e207 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.7%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.7%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.7%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.7%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.7%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 98.3%

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

      1. add-sqr-sqrt 46.9%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 46.9%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 46.9%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in z around 0 98.3%

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

      1. associate-*r* 98.3%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(x - y\right)} \]

      2. *-commutative 98.3%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(x - y\right) \]

   9. Simplified 98.3%

      \[\leadsto \color{blue}{\left(z \cdot -6\right) \cdot \left(x - y\right)} \]

   10. Taylor expanded in x around 0 77.9%

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

       1. *-commutative 77.9%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

       2. associate-*l* 77.9%

          \[\leadsto \color{blue}{y \cdot \left(z \cdot 6\right)} \]

   12. Simplified 77.9%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot 6\right)} \]

   if -3.20000000000000022e247 < z < -4.19999999999999988e228

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.6%

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

      1. add-sqr-sqrt 62.3%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 62.3%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 62.3%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in x around inf 76.2%

      \[\leadsto \color{blue}{-6 \cdot \left(x \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 76.2%

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot -6} \]

      2. associate-*r* 76.4%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot -6\right)} \]

   9. Simplified 76.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot -6\right)} \]

   if -1.05e212 < z < -1.69999999999999992e99

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.9%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.9%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.7%

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

      1. add-sqr-sqrt 37.4%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 37.4%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 37.4%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in x around inf 72.2%

      \[\leadsto \color{blue}{-6 \cdot \left(x \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 72.2%

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot -6} \]

      2. *-commutative 72.2%

         \[\leadsto \color{blue}{\left(z \cdot x\right)} \cdot -6 \]

      3. associate-*l* 72.4%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot -6\right)} \]

   9. Simplified 72.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot -6\right)} \]

   if -1.69999999999999992e99 < z < -3.3e-20

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 97.7%

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

      1. add-sqr-sqrt 53.9%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 53.9%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 53.9%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in z around 0 97.7%

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

      1. associate-*r* 97.6%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(x - y\right)} \]

      2. *-commutative 97.6%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(x - y\right) \]

   9. Simplified 97.6%

      \[\leadsto \color{blue}{\left(z \cdot -6\right) \cdot \left(x - y\right)} \]

   10. Taylor expanded in x around 0 61.5%

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

       1. *-commutative 61.5%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

       2. *-commutative 61.5%

          \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

       3. associate-*l* 61.5%

          \[\leadsto \color{blue}{z \cdot \left(y \cdot 6\right)} \]

   12. Simplified 61.5%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot 6\right)} \]

   if -3.3e-20 < z < 1.55999999999999991e-15

   1. Initial program 99.1%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 74.4%

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

   if 1.7999999999999999e166 < z < 2.51999999999999998e207

   1. Initial program 100.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 100.0%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(x - y\right)\right)} \]

   5. Taylor expanded in x around inf 78.7%

      \[\leadsto -6 \cdot \color{blue}{\left(x \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+247}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+212}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+166} \lor \neg \left(z \leq 2.52 \cdot 10^{+207}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 5: 61.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+247}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+210}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+166} \lor \neg \left(z \leq 7.6 \cdot 10^{+207}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* 6.0 z))))
   (if (<= z -2.4e+247)
     t_0
     (if (<= z -8e+228)
       (* x (* z -6.0))
       (if (<= z -3e+210)
         t_0
         (if (<= z -9.2e+97)
           (* z (* x -6.0))
           (if (<= z -7.5e-20)
             (* z (* y 6.0))
             (if (<= z 3e-20)
               x
               (if (or (<= z 2.1e+166) (not (<= z 7.6e+207)))
                 (* 6.0 (* y z))
                 (* -6.0 (* x z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double tmp;
	if (z <= -2.4e+247) {
		tmp = t_0;
	} else if (z <= -8e+228) {
		tmp = x * (z * -6.0);
	} else if (z <= -3e+210) {
		tmp = t_0;
	} else if (z <= -9.2e+97) {
		tmp = z * (x * -6.0);
	} else if (z <= -7.5e-20) {
		tmp = z * (y * 6.0);
	} else if (z <= 3e-20) {
		tmp = x;
	} else if ((z <= 2.1e+166) || !(z <= 7.6e+207)) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (6.0d0 * z)
    if (z <= (-2.4d+247)) then
        tmp = t_0
    else if (z <= (-8d+228)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= (-3d+210)) then
        tmp = t_0
    else if (z <= (-9.2d+97)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= (-7.5d-20)) then
        tmp = z * (y * 6.0d0)
    else if (z <= 3d-20) then
        tmp = x
    else if ((z <= 2.1d+166) .or. (.not. (z <= 7.6d+207))) then
        tmp = 6.0d0 * (y * z)
    else
        tmp = (-6.0d0) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double tmp;
	if (z <= -2.4e+247) {
		tmp = t_0;
	} else if (z <= -8e+228) {
		tmp = x * (z * -6.0);
	} else if (z <= -3e+210) {
		tmp = t_0;
	} else if (z <= -9.2e+97) {
		tmp = z * (x * -6.0);
	} else if (z <= -7.5e-20) {
		tmp = z * (y * 6.0);
	} else if (z <= 3e-20) {
		tmp = x;
	} else if ((z <= 2.1e+166) || !(z <= 7.6e+207)) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (6.0 * z)
	tmp = 0
	if z <= -2.4e+247:
		tmp = t_0
	elif z <= -8e+228:
		tmp = x * (z * -6.0)
	elif z <= -3e+210:
		tmp = t_0
	elif z <= -9.2e+97:
		tmp = z * (x * -6.0)
	elif z <= -7.5e-20:
		tmp = z * (y * 6.0)
	elif z <= 3e-20:
		tmp = x
	elif (z <= 2.1e+166) or not (z <= 7.6e+207):
		tmp = 6.0 * (y * z)
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(6.0 * z))
	tmp = 0.0
	if (z <= -2.4e+247)
		tmp = t_0;
	elseif (z <= -8e+228)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= -3e+210)
		tmp = t_0;
	elseif (z <= -9.2e+97)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= -7.5e-20)
		tmp = Float64(z * Float64(y * 6.0));
	elseif (z <= 3e-20)
		tmp = x;
	elseif ((z <= 2.1e+166) || !(z <= 7.6e+207))
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = Float64(-6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (6.0 * z);
	tmp = 0.0;
	if (z <= -2.4e+247)
		tmp = t_0;
	elseif (z <= -8e+228)
		tmp = x * (z * -6.0);
	elseif (z <= -3e+210)
		tmp = t_0;
	elseif (z <= -9.2e+97)
		tmp = z * (x * -6.0);
	elseif (z <= -7.5e-20)
		tmp = z * (y * 6.0);
	elseif (z <= 3e-20)
		tmp = x;
	elseif ((z <= 2.1e+166) || ~((z <= 7.6e+207)))
		tmp = 6.0 * (y * z);
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+247], t$95$0, If[LessEqual[z, -8e+228], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e+210], t$95$0, If[LessEqual[z, -9.2e+97], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-20], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-20], x, If[Or[LessEqual[z, 2.1e+166], N[Not[LessEqual[z, 7.6e+207]], $MachinePrecision]], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2.4e247 or -7.9999999999999994e228 < z < -3.00000000000000022e210

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.7%

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

      1. add-sqr-sqrt 49.9%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 49.9%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 49.9%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in z around 0 99.7%

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

      1. associate-*r* 99.9%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(x - y\right)} \]

      2. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(x - y\right) \]

   9. Simplified 99.9%

      \[\leadsto \color{blue}{\left(z \cdot -6\right) \cdot \left(x - y\right)} \]

   10. Taylor expanded in x around 0 92.6%

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

       1. *-commutative 92.6%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

       2. associate-*l* 92.8%

          \[\leadsto \color{blue}{y \cdot \left(z \cdot 6\right)} \]

   12. Simplified 92.8%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot 6\right)} \]

   if -2.4e247 < z < -7.9999999999999994e228

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.6%

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

      1. add-sqr-sqrt 62.3%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 62.3%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 62.3%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in x around inf 76.2%

      \[\leadsto \color{blue}{-6 \cdot \left(x \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 76.2%

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot -6} \]

      2. associate-*r* 76.4%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot -6\right)} \]

   9. Simplified 76.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot -6\right)} \]

   if -3.00000000000000022e210 < z < -9.20000000000000022e97

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.9%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.9%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.7%

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

      1. add-sqr-sqrt 37.4%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 37.4%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 37.4%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in x around inf 72.2%

      \[\leadsto \color{blue}{-6 \cdot \left(x \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 72.2%

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot -6} \]

      2. *-commutative 72.2%

         \[\leadsto \color{blue}{\left(z \cdot x\right)} \cdot -6 \]

      3. associate-*l* 72.4%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot -6\right)} \]

   9. Simplified 72.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot -6\right)} \]

   if -9.20000000000000022e97 < z < -7.49999999999999981e-20

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 97.7%

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

      1. add-sqr-sqrt 53.9%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 53.9%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 53.9%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in z around 0 97.7%

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

      1. associate-*r* 97.6%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(x - y\right)} \]

      2. *-commutative 97.6%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(x - y\right) \]

   9. Simplified 97.6%

      \[\leadsto \color{blue}{\left(z \cdot -6\right) \cdot \left(x - y\right)} \]

   10. Taylor expanded in x around 0 61.5%

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

       1. *-commutative 61.5%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

       2. *-commutative 61.5%

          \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

       3. associate-*l* 61.5%

          \[\leadsto \color{blue}{z \cdot \left(y \cdot 6\right)} \]

   12. Simplified 61.5%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot 6\right)} \]

   if -7.49999999999999981e-20 < z < 3.00000000000000029e-20

   1. Initial program 99.1%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 74.4%

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

   if 3.00000000000000029e-20 < z < 2.1000000000000001e166 or 7.59999999999999973e207 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.7%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.7%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.7%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.7%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.7%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 98.0%

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

      1. add-sqr-sqrt 46.1%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 46.1%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 46.1%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in z around 0 98.0%

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

      1. associate-*r* 97.9%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(x - y\right)} \]

      2. *-commutative 97.9%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(x - y\right) \]

   9. Simplified 97.9%

      \[\leadsto \color{blue}{\left(z \cdot -6\right) \cdot \left(x - y\right)} \]

   10. Taylor expanded in x around 0 74.1%

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

       1. *-commutative 74.1%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

       2. *-commutative 74.1%

          \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   12. Simplified 74.1%

       \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot 6} \]

   if 2.1000000000000001e166 < z < 7.59999999999999973e207

   1. Initial program 100.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 100.0%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(x - y\right)\right)} \]

   5. Taylor expanded in x around inf 78.7%

      \[\leadsto -6 \cdot \color{blue}{\left(x \cdot z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+247}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+210}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+166} \lor \neg \left(z \leq 7.6 \cdot 10^{+207}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 6: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-20} \lor \neg \left(z \leq 9.2 \cdot 10^{-18}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.3e-20) (not (<= z 9.2e-18))) (* -6.0 (* z (- x y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.3e-20) || !(z <= 9.2e-18)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.3d-20)) .or. (.not. (z <= 9.2d-18))) then
        tmp = (-6.0d0) * (z * (x - y))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.3e-20) || !(z <= 9.2e-18)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.3e-20) or not (z <= 9.2e-18):
		tmp = -6.0 * (z * (x - y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.3e-20) || !(z <= 9.2e-18))
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.3e-20) || ~((z <= 9.2e-18)))
		tmp = -6.0 * (z * (x - y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.3e-20], N[Not[LessEqual[z, 9.2e-18]], $MachinePrecision]], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e-20 or 9.2000000000000004e-18 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 98.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(x - y\right)\right)} \]

   if -3.3e-20 < z < 9.2000000000000004e-18

   1. Initial program 99.1%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 74.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-20} \lor \neg \left(z \leq 9.2 \cdot 10^{-18}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-20}:\\ \;\;\;\;\left(z \cdot -6\right) \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.15e-20)
   (* (* z -6.0) (- x y))
   (if (<= z 4.3e-17) x (* -6.0 (* z (- x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e-20) {
		tmp = (z * -6.0) * (x - y);
	} else if (z <= 4.3e-17) {
		tmp = x;
	} else {
		tmp = -6.0 * (z * (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.15d-20)) then
        tmp = (z * (-6.0d0)) * (x - y)
    else if (z <= 4.3d-17) then
        tmp = x
    else
        tmp = (-6.0d0) * (z * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e-20) {
		tmp = (z * -6.0) * (x - y);
	} else if (z <= 4.3e-17) {
		tmp = x;
	} else {
		tmp = -6.0 * (z * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.15e-20:
		tmp = (z * -6.0) * (x - y)
	elif z <= 4.3e-17:
		tmp = x
	else:
		tmp = -6.0 * (z * (x - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.15e-20)
		tmp = Float64(Float64(z * -6.0) * Float64(x - y));
	elseif (z <= 4.3e-17)
		tmp = x;
	else
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.15e-20)
		tmp = (z * -6.0) * (x - y);
	elseif (z <= 4.3e-17)
		tmp = x;
	else
		tmp = -6.0 * (z * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.15e-20], N[(N[(z * -6.0), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e-17], x, N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e-20

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.0%

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

      1. add-sqr-sqrt 48.3%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 48.3%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 48.3%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in z around 0 99.0%

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

      1. associate-*r* 99.1%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(x - y\right)} \]

      2. *-commutative 99.1%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(x - y\right) \]

   9. Simplified 99.1%

      \[\leadsto \color{blue}{\left(z \cdot -6\right) \cdot \left(x - y\right)} \]

   if -1.15e-20 < z < 4.30000000000000023e-17

   1. Initial program 99.1%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 74.4%

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

   if 4.30000000000000023e-17 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 98.2%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(x - y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-20}:\\ \;\;\;\;\left(z \cdot -6\right) \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \]

Alternative 8: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.116:\\ \;\;\;\;\left(z \cdot -6\right) \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.116)
   (* (* z -6.0) (- x y))
   (if (<= z 0.17) (+ x (* 6.0 (* y z))) (* -6.0 (* z (- x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.116) {
		tmp = (z * -6.0) * (x - y);
	} else if (z <= 0.17) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = -6.0 * (z * (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.116d0)) then
        tmp = (z * (-6.0d0)) * (x - y)
    else if (z <= 0.17d0) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = (-6.0d0) * (z * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.116) {
		tmp = (z * -6.0) * (x - y);
	} else if (z <= 0.17) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = -6.0 * (z * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.116:
		tmp = (z * -6.0) * (x - y)
	elif z <= 0.17:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = -6.0 * (z * (x - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.116)
		tmp = Float64(Float64(z * -6.0) * Float64(x - y));
	elseif (z <= 0.17)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.116)
		tmp = (z * -6.0) * (x - y);
	elseif (z <= 0.17)
		tmp = x + (6.0 * (y * z));
	else
		tmp = -6.0 * (z * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.116], N[(N[(z * -6.0), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.116000000000000006

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.0%

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

      1. add-sqr-sqrt 48.3%

         \[\leadsto -6 \cdot \color{blue}{\left(\sqrt{z \cdot \left(x - y\right)} \cdot \sqrt{z \cdot \left(x - y\right)}\right)} \]

      2. pow2 48.3%

         \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   6. Applied egg-rr 48.3%

      \[\leadsto -6 \cdot \color{blue}{{\left(\sqrt{z \cdot \left(x - y\right)}\right)}^{2}} \]

   7. Taylor expanded in z around 0 99.0%

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

      1. associate-*r* 99.1%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(x - y\right)} \]

      2. *-commutative 99.1%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(x - y\right) \]

   9. Simplified 99.1%

      \[\leadsto \color{blue}{\left(z \cdot -6\right) \cdot \left(x - y\right)} \]

   if -0.116000000000000006 < z < 0.170000000000000012

   1. Initial program 99.2%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in y around inf 99.7%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot z\right)} \]

   if 0.170000000000000012 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(x - y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.116:\\ \;\;\;\;\left(z \cdot -6\right) \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \]

Alternative 9: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-9} \lor \neg \left(z \leq 62000\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.25e-9) (not (<= z 62000.0))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.25e-9) || !(z <= 62000.0)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.25d-9)) .or. (.not. (z <= 62000.0d0))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.25e-9) || !(z <= 62000.0)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.25e-9) or not (z <= 62000.0):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.25e-9) || !(z <= 62000.0))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.25e-9) || ~((z <= 62000.0)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.25e-9], N[Not[LessEqual[z, 62000.0]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.24999999999999988e-9 or 62000 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)} \]

      4. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{-\left(-\left(y - x\right) \cdot 6\right)}, x\right) \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, -\color{blue}{\left(-\left(y - x\right)\right) \cdot 6}, x\right) \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(-\left(y - x\right)\right) \cdot \left(-6\right)}, x\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(-\color{blue}{\left(y + \left(-x\right)\right)}\right) \cdot \left(-6\right), x\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(\left(-y\right) + \left(-\left(-x\right)\right)\right)} \cdot \left(-6\right), x\right) \]

      9. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(z, \left(\left(-y\right) + \color{blue}{x}\right) \cdot \left(-6\right), x\right) \]

      10. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(-6\right), x\right) \]

      11. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(x - y\right)} \cdot \left(-6\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(z, \left(x - y\right) \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \left(x - y\right) \cdot -6, x\right)} \]

   4. Taylor expanded in z around inf 99.4%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(x - y\right)\right)} \]

   5. Taylor expanded in x around inf 45.5%

      \[\leadsto -6 \cdot \color{blue}{\left(x \cdot z\right)} \]

   if -2.24999999999999988e-9 < z < 62000

   1. Initial program 99.1%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 71.7%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-9} \lor \neg \left(z \leq 62000\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + z \cdot \left(\left(y - x\right) \cdot 6\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* z (* (- y x) 6.0))))

C

double code(double x, double y, double z) {
	return x + (z * ((y - x) * 6.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (z * ((y - x) * 6.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + (z * ((y - x) * 6.0));
}

Python

def code(x, y, z):
	return x + (z * ((y - x) * 6.0))

Julia

function code(x, y, z)
	return Float64(x + Float64(z * Float64(Float64(y - x) * 6.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (z * ((y - x) * 6.0));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

2. Final simplification 99.5%

   \[\leadsto x + z \cdot \left(\left(y - x\right) \cdot 6\right) \]

Alternative 11: 36.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

2. Taylor expanded in z around 0 37.9%

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

3. Final simplification 37.9%

   \[\leadsto x \]

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \left(6 \cdot z\right) \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* 6.0 z) (- x y))))

C

double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - ((6.0d0 * z) * (x - y))
end function

Java

public static double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

Python

def code(x, y, z):
	return x - ((6.0 * z) * (x - y))

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(6.0 * z) * Float64(x - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((6.0 * z) * (x - y));
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(6.0 * z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023335 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))