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

Percentage Accurate: 99.7% → 99.8%

Time: 7.2s

Alternatives: 9

Speedup: 1.0×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
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 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.00052:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.165)
   (* (- y x) (* 6.0 z))
   (if (<= z 0.00052) (+ x (* y (* 6.0 z))) (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.00052) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	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) :: tmp
    if (z <= (-0.165d0)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 0.00052d0) then
        tmp = x + (y * (6.0d0 * z))
    else
        tmp = z * ((y - x) * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.00052) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.165:
		tmp = (y - x) * (6.0 * z)
	elif z <= 0.00052:
		tmp = x + (y * (6.0 * z))
	else:
		tmp = z * ((y - x) * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.165)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 0.00052)
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	else
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.165)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 0.00052)
		tmp = x + (y * (6.0 * z));
	else
		tmp = z * ((y - x) * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.165], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00052], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.165000000000000008

   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 97.8%

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

   5. Simplified 97.8%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 97.9%

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

   7. Applied egg-rr 97.9%

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

   if -0.165000000000000008 < z < 5.19999999999999954e-4

   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. 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 98.7%

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

   if 5.19999999999999954e-4 < 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 97.7%

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

   5. Simplified 97.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. --lowering--.f64 97.9%

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

   7. Applied egg-rr 97.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.00052:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.7e+20)
   (* z (* (- y x) 6.0))
   (if (<= y 2.3e+28) (* x (+ 1.0 (* z -6.0))) (* (- y x) (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e+20) {
		tmp = z * ((y - x) * 6.0);
	} else if (y <= 2.3e+28) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = (y - x) * (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 (y <= (-3.7d+20)) then
        tmp = z * ((y - x) * 6.0d0)
    else if (y <= 2.3d+28) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    else
        tmp = (y - x) * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e+20) {
		tmp = z * ((y - x) * 6.0);
	} else if (y <= 2.3e+28) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.7e+20:
		tmp = z * ((y - x) * 6.0)
	elif y <= 2.3e+28:
		tmp = x * (1.0 + (z * -6.0))
	else:
		tmp = (y - x) * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.7e+20)
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	elseif (y <= 2.3e+28)
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	else
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.7e+20)
		tmp = z * ((y - x) * 6.0);
	elseif (y <= 2.3e+28)
		tmp = x * (1.0 + (z * -6.0));
	else
		tmp = (y - x) * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.7e+20], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+28], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7e20

   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 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 81.2%

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

   5. Simplified 81.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. --lowering--.f64 81.5%

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

   7. Applied egg-rr 81.5%

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

   if -3.7e20 < y < 2.29999999999999984e28

   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 84.0%

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

   5. Simplified 84.0%

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

   if 2.29999999999999984e28 < y

   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 79.8%

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

   5. Simplified 79.8%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 79.9%

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

   7. Applied egg-rr 79.9%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) 6.0))))
   (if (<= y -9.8e+19) t_0 (if (<= y 9.6e+28) (* x (+ 1.0 (* z -6.0))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * 6.0);
	double tmp;
	if (y <= -9.8e+19) {
		tmp = t_0;
	} else if (y <= 9.6e+28) {
		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 = z * ((y - x) * 6.0d0)
    if (y <= (-9.8d+19)) then
        tmp = t_0
    else if (y <= 9.6d+28) 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 = z * ((y - x) * 6.0);
	double tmp;
	if (y <= -9.8e+19) {
		tmp = t_0;
	} else if (y <= 9.6e+28) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y - x) * 6.0)
	tmp = 0
	if y <= -9.8e+19:
		tmp = t_0
	elif y <= 9.6e+28:
		tmp = x * (1.0 + (z * -6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(y - x) * 6.0))
	tmp = 0.0
	if (y <= -9.8e+19)
		tmp = t_0;
	elseif (y <= 9.6e+28)
		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 = z * ((y - x) * 6.0);
	tmp = 0.0;
	if (y <= -9.8e+19)
		tmp = t_0;
	elseif (y <= 9.6e+28)
		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[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.8e+19], t$95$0, If[LessEqual[y, 9.6e+28], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.8e19 or 9.59999999999999925e28 < y

   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 80.4%

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

   5. Simplified 80.4%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. --lowering--.f64 80.5%

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

   7. Applied egg-rr 80.5%

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

   if -9.8e19 < y < 9.59999999999999925e28

   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 84.0%

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

   5. Simplified 84.0%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* (- y x) z))))
   (if (<= y -1.05e+20) t_0 (if (<= y 1.3e+28) (* 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 (y <= -1.05e+20) {
		tmp = t_0;
	} else if (y <= 1.3e+28) {
		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 (y <= (-1.05d+20)) then
        tmp = t_0
    else if (y <= 1.3d+28) 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 (y <= -1.05e+20) {
		tmp = t_0;
	} else if (y <= 1.3e+28) {
		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 y <= -1.05e+20:
		tmp = t_0
	elif y <= 1.3e+28:
		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 (y <= -1.05e+20)
		tmp = t_0;
	elseif (y <= 1.3e+28)
		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 (y <= -1.05e+20)
		tmp = t_0;
	elseif (y <= 1.3e+28)
		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[y, -1.05e+20], t$95$0, If[LessEqual[y, 1.3e+28], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e20 or 1.3000000000000001e28 < y

   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 80.4%

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

   5. Simplified 80.4%

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

   if -1.05e20 < y < 1.3000000000000001e28

   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 84.0%

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

   5. Simplified 84.0%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* (- y x) z))))
   (if (<= z -3.8e-13) t_0 (if (<= z 7e-28) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * ((y - x) * z);
	double tmp;
	if (z <= -3.8e-13) {
		tmp = t_0;
	} else if (z <= 7e-28) {
		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 <= (-3.8d-13)) then
        tmp = t_0
    else if (z <= 7d-28) 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 <= -3.8e-13) {
		tmp = t_0;
	} else if (z <= 7e-28) {
		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 <= -3.8e-13:
		tmp = t_0
	elif z <= 7e-28:
		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 <= -3.8e-13)
		tmp = t_0;
	elseif (z <= 7e-28)
		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 <= -3.8e-13)
		tmp = t_0;
	elseif (z <= 7e-28)
		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, -3.8e-13], t$95$0, If[LessEqual[z, 7e-28], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8e-13 or 6.9999999999999999e-28 < 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 95.1%

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

   5. Simplified 95.1%

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

   if -3.8e-13 < z < 6.9999999999999999e-28

   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 65.0%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-13}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z -6.0)))) (if (<= z -0.165) 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 <= -0.165) {
		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 <= (-0.165d0)) 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 <= -0.165) {
		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 <= -0.165:
		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 <= -0.165)
		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 <= -0.165)
		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, -0.165], t$95$0, If[LessEqual[z, 0.17], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 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 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 58.0%

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

   8. Simplified 58.0%

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

   if -0.165000000000000008 < 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 62.2%

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

Alternative 8: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
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: 37.0% 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 32.2%

   \[\leadsto \color{blue}{x} \]
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 2024145 
(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)))