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

Percentage Accurate: 99.6% → 99.8%

Time: 7.3s

Alternatives: 9

Speedup: 1.0×

• 21.3% 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: 99.6% 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 99.8%

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

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot z\right)}\right) \]

   2. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot z\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot z\right)}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot z\right)\right)\right) \]

   5. *-lowering-*.f64 99.9%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{*.f64}\left(6, \color{blue}{z}\right)\right)\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(6 \cdot z\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6\right)\\ t_1 := y \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;z \leq -1.92 \cdot 10^{+211}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+170}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z -6.0))) (t_1 (* y (* 6.0 z))))
   (if (<= z -1.92e+211)
     t_0
     (if (<= z -3.9e-14)
       t_1
       (if (<= z 0.17) x (if (<= z 4.3e+170) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = y * (6.0 * z);
	double tmp;
	if (z <= -1.92e+211) {
		tmp = t_0;
	} else if (z <= -3.9e-14) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if (z <= 4.3e+170) {
		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 = x * (z * (-6.0d0))
    t_1 = y * (6.0d0 * z)
    if (z <= (-1.92d+211)) then
        tmp = t_0
    else if (z <= (-3.9d-14)) then
        tmp = t_1
    else if (z <= 0.17d0) then
        tmp = x
    else if (z <= 4.3d+170) 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 = x * (z * -6.0);
	double t_1 = y * (6.0 * z);
	double tmp;
	if (z <= -1.92e+211) {
		tmp = t_0;
	} else if (z <= -3.9e-14) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if (z <= 4.3e+170) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * -6.0)
	t_1 = y * (6.0 * z)
	tmp = 0
	if z <= -1.92e+211:
		tmp = t_0
	elif z <= -3.9e-14:
		tmp = t_1
	elif z <= 0.17:
		tmp = x
	elif z <= 4.3e+170:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * -6.0))
	t_1 = Float64(y * Float64(6.0 * z))
	tmp = 0.0
	if (z <= -1.92e+211)
		tmp = t_0;
	elseif (z <= -3.9e-14)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif (z <= 4.3e+170)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * -6.0);
	t_1 = y * (6.0 * z);
	tmp = 0.0;
	if (z <= -1.92e+211)
		tmp = t_0;
	elseif (z <= -3.9e-14)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif (z <= 4.3e+170)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.92e+211], t$95$0, If[LessEqual[z, -3.9e-14], t$95$1, If[LessEqual[z, 0.17], x, If[LessEqual[z, 4.3e+170], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.91999999999999991e211 or 0.170000000000000012 < z < 4.2999999999999999e170

   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 inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -6 \cdot z\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(z \cdot \color{blue}{-6}\right)\right)\right) \]

      4. *-lowering-*.f64 62.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right) \]

   5. Simplified 62.2%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-6 \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{-6}\right)\right) \]

      2. *-lowering-*.f64 60.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right) \]

   8. Simplified 60.2%

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

   if -1.91999999999999991e211 < z < -3.8999999999999998e-14 or 4.2999999999999999e170 < z

   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

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot y\right)}\right) \]

      4. *-lowering-*.f64 64.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(6, \color{blue}{y}\right)\right) \]

   5. Simplified 64.2%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(6 \cdot z\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 64.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(6, z\right), y\right) \]

   7. Applied egg-rr 64.2%

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

   if -3.8999999999999998e-14 < z < 0.170000000000000012

   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

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 75.0%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.92 \cdot 10^{+211}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6\right)\\ t_1 := z \cdot \left(y \cdot 6\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+211}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+170}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z -6.0))) (t_1 (* z (* y 6.0))))
   (if (<= z -2.5e+211)
     t_0
     (if (<= z -1.35e-9)
       t_1
       (if (<= z 0.17) x (if (<= z 6.8e+170) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = z * (y * 6.0);
	double tmp;
	if (z <= -2.5e+211) {
		tmp = t_0;
	} else if (z <= -1.35e-9) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if (z <= 6.8e+170) {
		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 = x * (z * (-6.0d0))
    t_1 = z * (y * 6.0d0)
    if (z <= (-2.5d+211)) then
        tmp = t_0
    else if (z <= (-1.35d-9)) then
        tmp = t_1
    else if (z <= 0.17d0) then
        tmp = x
    else if (z <= 6.8d+170) 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 = x * (z * -6.0);
	double t_1 = z * (y * 6.0);
	double tmp;
	if (z <= -2.5e+211) {
		tmp = t_0;
	} else if (z <= -1.35e-9) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if (z <= 6.8e+170) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * -6.0)
	t_1 = z * (y * 6.0)
	tmp = 0
	if z <= -2.5e+211:
		tmp = t_0
	elif z <= -1.35e-9:
		tmp = t_1
	elif z <= 0.17:
		tmp = x
	elif z <= 6.8e+170:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * -6.0))
	t_1 = Float64(z * Float64(y * 6.0))
	tmp = 0.0
	if (z <= -2.5e+211)
		tmp = t_0;
	elseif (z <= -1.35e-9)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif (z <= 6.8e+170)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * -6.0);
	t_1 = z * (y * 6.0);
	tmp = 0.0;
	if (z <= -2.5e+211)
		tmp = t_0;
	elseif (z <= -1.35e-9)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif (z <= 6.8e+170)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+211], t$95$0, If[LessEqual[z, -1.35e-9], t$95$1, If[LessEqual[z, 0.17], x, If[LessEqual[z, 6.8e+170], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4999999999999998e211 or 0.170000000000000012 < z < 6.8000000000000003e170

   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 inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -6 \cdot z\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(z \cdot \color{blue}{-6}\right)\right)\right) \]

      4. *-lowering-*.f64 62.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right) \]

   5. Simplified 62.2%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-6 \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{-6}\right)\right) \]

      2. *-lowering-*.f64 60.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right) \]

   8. Simplified 60.2%

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

   if -2.4999999999999998e211 < z < -1.3500000000000001e-9 or 6.8000000000000003e170 < z

   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

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot y\right)}\right) \]

      4. *-lowering-*.f64 64.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(6, \color{blue}{y}\right)\right) \]

   5. Simplified 64.2%

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

   if -1.3500000000000001e-9 < z < 0.170000000000000012

   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

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 75.0%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+211}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.2:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* (- y x) z))))
   (if (<= z -0.2) t_0 (if (<= z 0.17) (+ x (* y (* 6.0 z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.2) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x + (y * (6.0 * 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 * ((y - x) * z)
    if (z <= (-0.2d0)) then
        tmp = t_0
    else if (z <= 0.17d0) then
        tmp = x + (y * (6.0d0 * 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 * ((y - x) * z);
	double tmp;
	if (z <= -0.2) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.2:
		tmp = t_0
	elif z <= 0.17:
		tmp = x + (y * (6.0 * z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.2)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.2)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x + (y * (6.0 * z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.2], t$95$0, If[LessEqual[z, 0.17], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.20000000000000001 or 0.170000000000000012 < z

   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 inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 98.5%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 98.5%

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

   if -0.20000000000000001 < z < 0.170000000000000012

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot z\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot z\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot z\right)\right)\right) \]

      5. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{*.f64}\left(6, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(6, z\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 99.5%

      \[\leadsto x + \color{blue}{y} \cdot \left(6 \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.2:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -9.1 \cdot 10^{-20}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 245:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* (- y x) z))))
   (if (<= z -9.1e-20) t_0 (if (<= z 245.0) (* x (+ 1.0 (* z -6.0))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * ((y - x) * z);
	double tmp;
	if (z <= -9.1e-20) {
		tmp = t_0;
	} else if (z <= 245.0) {
		tmp = x * (1.0 + (z * -6.0));
	} 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 * ((y - x) * z)
    if (z <= (-9.1d-20)) then
        tmp = t_0
    else if (z <= 245.0d0) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    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 * ((y - x) * z);
	double tmp;
	if (z <= -9.1e-20) {
		tmp = t_0;
	} else if (z <= 245.0) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * ((y - x) * z)
	tmp = 0
	if z <= -9.1e-20:
		tmp = t_0
	elif z <= 245.0:
		tmp = x * (1.0 + (z * -6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -9.1e-20)
		tmp = t_0;
	elseif (z <= 245.0)
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -9.1e-20)
		tmp = t_0;
	elseif (z <= 245.0)
		tmp = x * (1.0 + (z * -6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.1e-20], t$95$0, If[LessEqual[z, 245.0], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.09999999999999997e-20 or 245 < z

   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 inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 98.9%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 98.9%

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

   if -9.09999999999999997e-20 < z < 245

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -6 \cdot z\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(z \cdot \color{blue}{-6}\right)\right)\right) \]

      4. *-lowering-*.f64 75.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right) \]

   5. Simplified 75.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + z \cdot -6\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.1 \cdot 10^{-20}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 245:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -3.95 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* (- y x) z))))
   (if (<= z -3.95e-19) t_0 (if (<= z 5.7e-30) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * ((y - x) * z);
	double tmp;
	if (z <= -3.95e-19) {
		tmp = t_0;
	} else if (z <= 5.7e-30) {
		tmp = x;
	} 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 * ((y - x) * z)
    if (z <= (-3.95d-19)) then
        tmp = t_0
    else if (z <= 5.7d-30) then
        tmp = x
    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 * ((y - x) * z);
	double tmp;
	if (z <= -3.95e-19) {
		tmp = t_0;
	} else if (z <= 5.7e-30) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * ((y - x) * z)
	tmp = 0
	if z <= -3.95e-19:
		tmp = t_0
	elif z <= 5.7e-30:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -3.95e-19)
		tmp = t_0;
	elseif (z <= 5.7e-30)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -3.95e-19)
		tmp = t_0;
	elseif (z <= 5.7e-30)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.95e-19], t$95$0, If[LessEqual[z, 5.7e-30], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9500000000000002e-19 or 5.69999999999999977e-30 < z

   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 inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 97.2%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 97.2%

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

   if -3.9500000000000002e-19 < z < 5.69999999999999977e-30

   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

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 76.4%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.95 \cdot 10^{-19}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -0.166:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z -6.0)))) (if (<= z -0.166) t_0 (if (<= z 0.17) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double tmp;
	if (z <= -0.166) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} 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 = x * (z * (-6.0d0))
    if (z <= (-0.166d0)) then
        tmp = t_0
    else if (z <= 0.17d0) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double tmp;
	if (z <= -0.166) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * -6.0)
	tmp = 0
	if z <= -0.166:
		tmp = t_0
	elif z <= 0.17:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -0.166)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * -6.0);
	tmp = 0.0;
	if (z <= -0.166)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.166], t$95$0, If[LessEqual[z, 0.17], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.166000000000000009 or 0.170000000000000012 < z

   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 inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -6 \cdot z\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(z \cdot \color{blue}{-6}\right)\right)\right) \]

      4. *-lowering-*.f64 52.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right) \]

   5. Simplified 52.0%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-6 \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{-6}\right)\right) \]

      2. *-lowering-*.f64 50.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right) \]

   8. Simplified 50.6%

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

   if -0.166000000000000009 < z < 0.170000000000000012

   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

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 74.4%

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

Alternative 8: 99.6% 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 99.8%

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

3. Final simplification 99.8%

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

Alternative 9: 35.7% 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 99.8%

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

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 34.4%

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

Developer Target 1: 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 2024161 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (* 6 z) (- x y))))

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