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

Percentage Accurate: 99.8% → 99.8%

Time: 9.8s

Alternatives: 14

Speedup: 1.0×

• 22.0% 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: 99.8% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in y around 0 99.8%

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

   1. fma-define 99.8%

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

5. Simplified 99.8%

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

6. Final simplification 99.8%

   \[\leadsto x + \mathsf{fma}\left(-6, x, 6 \cdot y\right) \cdot z \]
7. Add Preprocessing

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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-define 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. Add Preprocessing

5. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(z, -6 \cdot \left(x - y\right), x\right) \]
6. Add Preprocessing

Alternative 3: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 22500000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* y z))))
   (if (<= z -2.8e+33)
     t_0
     (if (<= z -5.7e-58)
       t_1
       (if (<= z 1.75e-96) x (if (<= z 22500000000000.0) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -2.8e+33) {
		tmp = t_0;
	} else if (z <= -5.7e-58) {
		tmp = t_1;
	} else if (z <= 1.75e-96) {
		tmp = x;
	} else if (z <= 22500000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	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 = (-6.0d0) * (x * z)
    t_1 = 6.0d0 * (y * z)
    if (z <= (-2.8d+33)) then
        tmp = t_0
    else if (z <= (-5.7d-58)) then
        tmp = t_1
    else if (z <= 1.75d-96) then
        tmp = x
    else if (z <= 22500000000000.0d0) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -2.8e+33) {
		tmp = t_0;
	} else if (z <= -5.7e-58) {
		tmp = t_1;
	} else if (z <= 1.75e-96) {
		tmp = x;
	} else if (z <= 22500000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -2.8e+33:
		tmp = t_0
	elif z <= -5.7e-58:
		tmp = t_1
	elif z <= 1.75e-96:
		tmp = x
	elif z <= 22500000000000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -2.8e+33)
		tmp = t_0;
	elseif (z <= -5.7e-58)
		tmp = t_1;
	elseif (z <= 1.75e-96)
		tmp = x;
	elseif (z <= 22500000000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -2.8e+33)
		tmp = t_0;
	elseif (z <= -5.7e-58)
		tmp = t_1;
	elseif (z <= 1.75e-96)
		tmp = x;
	elseif (z <= 22500000000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+33], t$95$0, If[LessEqual[z, -5.7e-58], t$95$1, If[LessEqual[z, 1.75e-96], x, If[LessEqual[z, 22500000000000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8000000000000001e33 or 2.25e13 < 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-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in x around inf 60.4%

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

   if -2.8000000000000001e33 < z < -5.70000000000000032e-58 or 1.7499999999999999e-96 < z < 2.25e13

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

   4. Taylor expanded in y around inf 62.9%

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

      1. *-commutative 62.9%

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

   6. Simplified 62.9%

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

   if -5.70000000000000032e-58 < z < 1.7499999999999999e-96

   1. Initial program 100.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 81.5%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-58}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 22500000000000:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-57}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 85000000000000:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))))
   (if (<= z -4.4e+33)
     t_0
     (if (<= z -1e-57)
       (* (* 6.0 y) z)
       (if (<= z 1.8e-96)
         x
         (if (<= z 85000000000000.0) (* 6.0 (* y z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double tmp;
	if (z <= -4.4e+33) {
		tmp = t_0;
	} else if (z <= -1e-57) {
		tmp = (6.0 * y) * z;
	} else if (z <= 1.8e-96) {
		tmp = x;
	} else if (z <= 85000000000000.0) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	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 = (-6.0d0) * (x * z)
    if (z <= (-4.4d+33)) then
        tmp = t_0
    else if (z <= (-1d-57)) then
        tmp = (6.0d0 * y) * z
    else if (z <= 1.8d-96) then
        tmp = x
    else if (z <= 85000000000000.0d0) then
        tmp = 6.0d0 * (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double tmp;
	if (z <= -4.4e+33) {
		tmp = t_0;
	} else if (z <= -1e-57) {
		tmp = (6.0 * y) * z;
	} else if (z <= 1.8e-96) {
		tmp = x;
	} else if (z <= 85000000000000.0) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	tmp = 0
	if z <= -4.4e+33:
		tmp = t_0
	elif z <= -1e-57:
		tmp = (6.0 * y) * z
	elif z <= 1.8e-96:
		tmp = x
	elif z <= 85000000000000.0:
		tmp = 6.0 * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -4.4e+33)
		tmp = t_0;
	elseif (z <= -1e-57)
		tmp = Float64(Float64(6.0 * y) * z);
	elseif (z <= 1.8e-96)
		tmp = x;
	elseif (z <= 85000000000000.0)
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -4.4e+33)
		tmp = t_0;
	elseif (z <= -1e-57)
		tmp = (6.0 * y) * z;
	elseif (z <= 1.8e-96)
		tmp = x;
	elseif (z <= 85000000000000.0)
		tmp = 6.0 * (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+33], t$95$0, If[LessEqual[z, -1e-57], N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 1.8e-96], x, If[LessEqual[z, 85000000000000.0], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.39999999999999988e33 or 8.5e13 < 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-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in x around inf 60.4%

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

   if -4.39999999999999988e33 < z < -9.99999999999999955e-58

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

   4. Taylor expanded in y around inf 63.4%

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

      1. associate-*r* 63.7%

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

      2. *-commutative 63.7%

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

   6. Simplified 63.7%

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

   if -9.99999999999999955e-58 < z < 1.80000000000000004e-96

   1. Initial program 100.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 81.5%

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

   if 1.80000000000000004e-96 < z < 8.5e13

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

   4. Taylor expanded in y around inf 62.3%

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

      1. *-commutative 62.3%

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

   6. Simplified 62.3%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-57}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 85000000000000:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-57}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1850000000000:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.2e+33)
   (* z (* x -6.0))
   (if (<= z -1.02e-57)
     (* (* 6.0 y) z)
     (if (<= z 2.5e-97)
       x
       (if (<= z 1850000000000.0) (* 6.0 (* y z)) (* -6.0 (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.2e+33) {
		tmp = z * (x * -6.0);
	} else if (z <= -1.02e-57) {
		tmp = (6.0 * y) * z;
	} else if (z <= 2.5e-97) {
		tmp = x;
	} else if (z <= 1850000000000.0) {
		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) :: tmp
    if (z <= (-4.2d+33)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= (-1.02d-57)) then
        tmp = (6.0d0 * y) * z
    else if (z <= 2.5d-97) then
        tmp = x
    else if (z <= 1850000000000.0d0) 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 tmp;
	if (z <= -4.2e+33) {
		tmp = z * (x * -6.0);
	} else if (z <= -1.02e-57) {
		tmp = (6.0 * y) * z;
	} else if (z <= 2.5e-97) {
		tmp = x;
	} else if (z <= 1850000000000.0) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.2e+33:
		tmp = z * (x * -6.0)
	elif z <= -1.02e-57:
		tmp = (6.0 * y) * z
	elif z <= 2.5e-97:
		tmp = x
	elif z <= 1850000000000.0:
		tmp = 6.0 * (y * z)
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.2e+33)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= -1.02e-57)
		tmp = Float64(Float64(6.0 * y) * z);
	elseif (z <= 2.5e-97)
		tmp = x;
	elseif (z <= 1850000000000.0)
		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)
	tmp = 0.0;
	if (z <= -4.2e+33)
		tmp = z * (x * -6.0);
	elseif (z <= -1.02e-57)
		tmp = (6.0 * y) * z;
	elseif (z <= 2.5e-97)
		tmp = x;
	elseif (z <= 1850000000000.0)
		tmp = 6.0 * (y * z);
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.2e+33], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.02e-57], N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 2.5e-97], x, If[LessEqual[z, 1850000000000.0], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.2000000000000001e33

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.3%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

   4. Taylor expanded in z around inf 99.8%

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

      1. metadata-eval 99.8%

         \[\leadsto z \cdot \left(-6 \cdot x + \color{blue}{\left(-6 \cdot -1\right)} \cdot y\right) \]

      2. associate-*r* 99.8%

         \[\leadsto z \cdot \left(-6 \cdot x + \color{blue}{-6 \cdot \left(-1 \cdot y\right)}\right) \]

      3. neg-mul-1 99.8%

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

      4. distribute-lft-in 99.7%

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

      5. sub-neg 99.7%

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

      6. associate-*r* 99.7%

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

      7. *-commutative 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in x around inf 59.4%

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

      1. associate-*r* 59.5%

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

      2. *-commutative 59.5%

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

      3. *-commutative 59.5%

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

   9. Simplified 59.5%

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

   if -4.2000000000000001e33 < z < -1.02e-57

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

   4. Taylor expanded in y around inf 63.4%

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

      1. associate-*r* 63.7%

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

      2. *-commutative 63.7%

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

   6. Simplified 63.7%

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

   if -1.02e-57 < z < 2.4999999999999998e-97

   1. Initial program 100.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 81.5%

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

   if 2.4999999999999998e-97 < z < 1.85e12

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

   4. Taylor expanded in y around inf 62.3%

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

      1. *-commutative 62.3%

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

   6. Simplified 62.3%

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

   if 1.85e12 < 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-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 99.6%

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

   6. Taylor expanded in x around inf 61.5%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-57}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1850000000000:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-57} \lor \neg \left(z \leq 1.8 \cdot 10^{-96}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.02e-57) (not (<= z 1.8e-96))) (* -6.0 (* z (- x y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.02e-57) || !(z <= 1.8e-96)) {
		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 <= (-1.02d-57)) .or. (.not. (z <= 1.8d-96))) 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 <= -1.02e-57) || !(z <= 1.8e-96)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.02e-57) or not (z <= 1.8e-96):
		tmp = -6.0 * (z * (x - y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.02e-57) || !(z <= 1.8e-96))
		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 <= -1.02e-57) || ~((z <= 1.8e-96)))
		tmp = -6.0 * (z * (x - y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.02e-57], N[Not[LessEqual[z, 1.8e-96]], $MachinePrecision]], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e-57 or 1.80000000000000004e-96 < 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-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 92.5%

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

   if -1.02e-57 < z < 1.80000000000000004e-96

   1. Initial program 100.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 81.5%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-57} \lor \neg \left(z \leq 1.8 \cdot 10^{-96}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-58}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \left(-6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.26e-58)
   (* -6.0 (* z (- x y)))
   (if (<= z 1.45e-96) x (* (- x y) (* -6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.26e-58) {
		tmp = -6.0 * (z * (x - y));
	} else if (z <= 1.45e-96) {
		tmp = x;
	} else {
		tmp = (x - y) * (-6.0 * 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) :: tmp
    if (z <= (-1.26d-58)) then
        tmp = (-6.0d0) * (z * (x - y))
    else if (z <= 1.45d-96) then
        tmp = x
    else
        tmp = (x - y) * ((-6.0d0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.26e-58) {
		tmp = -6.0 * (z * (x - y));
	} else if (z <= 1.45e-96) {
		tmp = x;
	} else {
		tmp = (x - y) * (-6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.26e-58:
		tmp = -6.0 * (z * (x - y))
	elif z <= 1.45e-96:
		tmp = x
	else:
		tmp = (x - y) * (-6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.26e-58)
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	elseif (z <= 1.45e-96)
		tmp = x;
	else
		tmp = Float64(Float64(x - y) * Float64(-6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.26e-58)
		tmp = -6.0 * (z * (x - y));
	elseif (z <= 1.45e-96)
		tmp = x;
	else
		tmp = (x - y) * (-6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.26e-58], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-96], x, N[(N[(x - y), $MachinePrecision] * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2600000000000001e-58

   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-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 94.0%

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

   if -1.2600000000000001e-58 < z < 1.44999999999999997e-96

   1. Initial program 100.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 81.5%

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

   if 1.44999999999999997e-96 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.0%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

   4. Taylor expanded in z around inf 90.8%

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

      1. metadata-eval 90.8%

         \[\leadsto z \cdot \left(-6 \cdot x + \color{blue}{\left(-6 \cdot -1\right)} \cdot y\right) \]

      2. associate-*r* 90.8%

         \[\leadsto z \cdot \left(-6 \cdot x + \color{blue}{-6 \cdot \left(-1 \cdot y\right)}\right) \]

      3. neg-mul-1 90.8%

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

      4. distribute-lft-in 90.8%

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

      5. sub-neg 90.8%

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

      6. associate-*r* 90.8%

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

      7. *-commutative 90.8%

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

   6. Simplified 90.8%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-58}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \left(-6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \left(-6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.165)
   (* -6.0 (* z (- x y)))
   (if (<= z 0.165) (+ x (* 6.0 (* y z))) (* (- x y) (* -6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = -6.0 * (z * (x - y));
	} else if (z <= 0.165) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = (x - y) * (-6.0 * 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) :: tmp
    if (z <= (-0.165d0)) then
        tmp = (-6.0d0) * (z * (x - y))
    else if (z <= 0.165d0) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = (x - y) * ((-6.0d0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = -6.0 * (z * (x - y));
	} else if (z <= 0.165) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = (x - y) * (-6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.165:
		tmp = -6.0 * (z * (x - y))
	elif z <= 0.165:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = (x - y) * (-6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.165)
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	elseif (z <= 0.165)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(Float64(x - y) * Float64(-6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.165)
		tmp = -6.0 * (z * (x - y));
	elseif (z <= 0.165)
		tmp = x + (6.0 * (y * z));
	else
		tmp = (x - y) * (-6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.165], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.165], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.165000000000000008

   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-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 99.4%

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

   if -0.165000000000000008 < z < 0.165000000000000008

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.8%

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

      1. *-commutative 98.8%

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

   5. Simplified 98.8%

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

   if 0.165000000000000008 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.2%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

   4. Taylor expanded in z around inf 98.5%

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

      1. metadata-eval 98.5%

         \[\leadsto z \cdot \left(-6 \cdot x + \color{blue}{\left(-6 \cdot -1\right)} \cdot y\right) \]

      2. associate-*r* 98.5%

         \[\leadsto z \cdot \left(-6 \cdot x + \color{blue}{-6 \cdot \left(-1 \cdot y\right)}\right) \]

      3. neg-mul-1 98.5%

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

      4. distribute-lft-in 98.5%

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

      5. sub-neg 98.5%

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

      6. associate-*r* 98.5%

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

      7. *-commutative 98.5%

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

   6. Simplified 98.5%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \left(-6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-7}:\\ \;\;\;\;x + \left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \left(-6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.17)
   (* -6.0 (* z (- x y)))
   (if (<= z 1.8e-7) (+ x (* (* 6.0 y) z)) (* (- x y) (* -6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = -6.0 * (z * (x - y));
	} else if (z <= 1.8e-7) {
		tmp = x + ((6.0 * y) * z);
	} else {
		tmp = (x - y) * (-6.0 * 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) :: tmp
    if (z <= (-0.17d0)) then
        tmp = (-6.0d0) * (z * (x - y))
    else if (z <= 1.8d-7) then
        tmp = x + ((6.0d0 * y) * z)
    else
        tmp = (x - y) * ((-6.0d0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = -6.0 * (z * (x - y));
	} else if (z <= 1.8e-7) {
		tmp = x + ((6.0 * y) * z);
	} else {
		tmp = (x - y) * (-6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.17:
		tmp = -6.0 * (z * (x - y))
	elif z <= 1.8e-7:
		tmp = x + ((6.0 * y) * z)
	else:
		tmp = (x - y) * (-6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.17)
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	elseif (z <= 1.8e-7)
		tmp = Float64(x + Float64(Float64(6.0 * y) * z));
	else
		tmp = Float64(Float64(x - y) * Float64(-6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.17)
		tmp = -6.0 * (z * (x - y));
	elseif (z <= 1.8e-7)
		tmp = x + ((6.0 * y) * z);
	else
		tmp = (x - y) * (-6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.17], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-7], N[(x + N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.170000000000000012

   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-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 99.4%

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

   if -0.170000000000000012 < z < 1.79999999999999997e-7

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.8%

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

   if 1.79999999999999997e-7 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.4%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

   4. Taylor expanded in z around inf 98.5%

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

      1. metadata-eval 98.5%

         \[\leadsto z \cdot \left(-6 \cdot x + \color{blue}{\left(-6 \cdot -1\right)} \cdot y\right) \]

      2. associate-*r* 98.5%

         \[\leadsto z \cdot \left(-6 \cdot x + \color{blue}{-6 \cdot \left(-1 \cdot y\right)}\right) \]

      3. neg-mul-1 98.5%

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

      4. distribute-lft-in 98.5%

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

      5. sub-neg 98.5%

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

      6. associate-*r* 98.5%

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

      7. *-commutative 98.5%

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

   6. Simplified 98.5%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-7}:\\ \;\;\;\;x + \left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \left(-6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;z \cdot \left(6 \cdot y + x \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-7}:\\ \;\;\;\;x + \left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \left(-6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.165)
   (* z (+ (* 6.0 y) (* x -6.0)))
   (if (<= z 1.8e-7) (+ x (* (* 6.0 y) z)) (* (- x y) (* -6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = z * ((6.0 * y) + (x * -6.0));
	} else if (z <= 1.8e-7) {
		tmp = x + ((6.0 * y) * z);
	} else {
		tmp = (x - y) * (-6.0 * 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) :: tmp
    if (z <= (-0.165d0)) then
        tmp = z * ((6.0d0 * y) + (x * (-6.0d0)))
    else if (z <= 1.8d-7) then
        tmp = x + ((6.0d0 * y) * z)
    else
        tmp = (x - y) * ((-6.0d0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = z * ((6.0 * y) + (x * -6.0));
	} else if (z <= 1.8e-7) {
		tmp = x + ((6.0 * y) * z);
	} else {
		tmp = (x - y) * (-6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.165:
		tmp = z * ((6.0 * y) + (x * -6.0))
	elif z <= 1.8e-7:
		tmp = x + ((6.0 * y) * z)
	else:
		tmp = (x - y) * (-6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.165)
		tmp = Float64(z * Float64(Float64(6.0 * y) + Float64(x * -6.0)));
	elseif (z <= 1.8e-7)
		tmp = Float64(x + Float64(Float64(6.0 * y) * z));
	else
		tmp = Float64(Float64(x - y) * Float64(-6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.165)
		tmp = z * ((6.0 * y) + (x * -6.0));
	elseif (z <= 1.8e-7)
		tmp = x + ((6.0 * y) * z);
	else
		tmp = (x - y) * (-6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.165], N[(z * N[(N[(6.0 * y), $MachinePrecision] + N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-7], N[(x + N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.165000000000000008

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

   4. Taylor expanded in z around inf 99.4%

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

   if -0.165000000000000008 < z < 1.79999999999999997e-7

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.8%

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

   if 1.79999999999999997e-7 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.4%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right) + x \cdot \left(1 + -6 \cdot z\right)} \]

   4. Taylor expanded in z around inf 98.5%

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

      1. metadata-eval 98.5%

         \[\leadsto z \cdot \left(-6 \cdot x + \color{blue}{\left(-6 \cdot -1\right)} \cdot y\right) \]

      2. associate-*r* 98.5%

         \[\leadsto z \cdot \left(-6 \cdot x + \color{blue}{-6 \cdot \left(-1 \cdot y\right)}\right) \]

      3. neg-mul-1 98.5%

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

      4. distribute-lft-in 98.5%

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

      5. sub-neg 98.5%

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

      6. associate-*r* 98.5%

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

      7. *-commutative 98.5%

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

   6. Simplified 98.5%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;z \cdot \left(6 \cdot y + x \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-7}:\\ \;\;\;\;x + \left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \left(-6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 1600000\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 1600000.0))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 1600000.0)) {
		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 <= (-0.165d0)) .or. (.not. (z <= 1600000.0d0))) 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 <= -0.165) || !(z <= 1600000.0)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 1600000.0):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 1600000.0))
		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 <= -0.165) || ~((z <= 1600000.0)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 1600000.0]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 1.6e6 < 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-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 99.0%

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

   6. Taylor expanded in x around inf 57.9%

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

   if -0.165000000000000008 < z < 1.6e6

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 69.3%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 1600000\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + (z * ((6.0 * 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 * ((6.0d0 * y) + (x * (-6.0d0))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in y around 0 99.8%

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

4. Final simplification 99.8%

   \[\leadsto x + z \cdot \left(6 \cdot y + x \cdot -6\right) \]
5. Add Preprocessing

Alternative 13: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + (z * (6.0 * (y - 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 + (z * (6.0d0 * (y - x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing

3. Final simplification 99.8%

   \[\leadsto x + z \cdot \left(6 \cdot \left(y - x\right)\right) \]
4. Add Preprocessing

Alternative 14: 36.2% 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 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in z around 0 36.7%

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

4. Final simplification 36.7%

   \[\leadsto x \]
5. Add Preprocessing

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 2024055 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (- x (* (* 6.0 z) (- x y)))

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