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

Percentage Accurate: 99.7% → 99.8%

Time: 9.3s

Alternatives: 8

Speedup: 1.1×

• 21.5% 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, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative N/A

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

   2. associate-*l* N/A

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

   3. *-commutative N/A

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

   4. associate-*r* N/A

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

   5. accelerator-lowering-fma.f64 N/A

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

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

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

   7. --lowering--.f64 99.8

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

4. Applied egg-rr 99.8%

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

Alternative 2: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-38}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+78}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.5e-38)
   (* 6.0 (* y z))
   (if (<= z 2.2e-127)
     x
     (if (<= z 1.2e+78) (* z (* y 6.0)) (* x (* z -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.5e-38) {
		tmp = 6.0 * (y * z);
	} else if (z <= 2.2e-127) {
		tmp = x;
	} else if (z <= 1.2e+78) {
		tmp = z * (y * 6.0);
	} else {
		tmp = x * (z * -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 <= (-3.5d-38)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 2.2d-127) then
        tmp = x
    else if (z <= 1.2d+78) then
        tmp = z * (y * 6.0d0)
    else
        tmp = x * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.5e-38) {
		tmp = 6.0 * (y * z);
	} else if (z <= 2.2e-127) {
		tmp = x;
	} else if (z <= 1.2e+78) {
		tmp = z * (y * 6.0);
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.5e-38:
		tmp = 6.0 * (y * z)
	elif z <= 2.2e-127:
		tmp = x
	elif z <= 1.2e+78:
		tmp = z * (y * 6.0)
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.5e-38)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 2.2e-127)
		tmp = x;
	elseif (z <= 1.2e+78)
		tmp = Float64(z * Float64(y * 6.0));
	else
		tmp = Float64(x * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.5e-38)
		tmp = 6.0 * (y * z);
	elseif (z <= 2.2e-127)
		tmp = x;
	elseif (z <= 1.2e+78)
		tmp = z * (y * 6.0);
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.5e-38], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-127], x, If[LessEqual[z, 1.2e+78], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5000000000000001e-38

   1. Initial program 98.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 62.6

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

   5. Simplified 62.6%

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

   if -3.5000000000000001e-38 < z < 2.2000000000000001e-127

   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 83.5%

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

   if 2.2000000000000001e-127 < z < 1.1999999999999999e78

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

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

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

      7. --lowering--.f64 99.7

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-lowering-*.f64 58.9

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

   7. Simplified 58.9%

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

   if 1.1999999999999999e78 < 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 inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. *-lft-identity N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 70.9

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

   5. Simplified 70.9%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 71.0

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

   8. Simplified 71.0%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-38}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+78}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+77}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= z -5.8e-43)
     t_0
     (if (<= z 2.2e-127) x (if (<= z 1.6e+77) t_0 (* x (* z -6.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -5.8e-43) {
		tmp = t_0;
	} else if (z <= 2.2e-127) {
		tmp = x;
	} else if (z <= 1.6e+77) {
		tmp = t_0;
	} else {
		tmp = x * (z * -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) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    if (z <= (-5.8d-43)) then
        tmp = t_0
    else if (z <= 2.2d-127) then
        tmp = x
    else if (z <= 1.6d+77) then
        tmp = t_0
    else
        tmp = x * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -5.8e-43) {
		tmp = t_0;
	} else if (z <= 2.2e-127) {
		tmp = x;
	} else if (z <= 1.6e+77) {
		tmp = t_0;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	tmp = 0
	if z <= -5.8e-43:
		tmp = t_0
	elif z <= 2.2e-127:
		tmp = x
	elif z <= 1.6e+77:
		tmp = t_0
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -5.8e-43)
		tmp = t_0;
	elseif (z <= 2.2e-127)
		tmp = x;
	elseif (z <= 1.6e+77)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -5.8e-43)
		tmp = t_0;
	elseif (z <= 2.2e-127)
		tmp = x;
	elseif (z <= 1.6e+77)
		tmp = t_0;
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e-43], t$95$0, If[LessEqual[z, 2.2e-127], x, If[LessEqual[z, 1.6e+77], t$95$0, N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000003e-43 or 2.2000000000000001e-127 < z < 1.6000000000000001e77

   1. Initial program 99.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 61.2

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

   5. Simplified 61.2%

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

   if -5.8000000000000003e-43 < z < 2.2000000000000001e-127

   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 83.5%

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

   if 1.6000000000000001e77 < 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 inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. *-lft-identity N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 70.9

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

   5. Simplified 70.9%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 71.0

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

   8. Simplified 71.0%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-43}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+77}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - y\right) \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 6, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x y) (* z -6.0))))
   (if (<= z -0.17) t_0 (if (<= z 1.95e-11) (fma (* z 6.0) y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - y) * (z * -6.0);
	double tmp;
	if (z <= -0.17) {
		tmp = t_0;
	} else if (z <= 1.95e-11) {
		tmp = fma((z * 6.0), y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - y) * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -0.17)
		tmp = t_0;
	elseif (z <= 1.95e-11)
		tmp = fma(Float64(z * 6.0), y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.17], t$95$0, If[LessEqual[z, 1.95e-11], N[(N[(z * 6.0), $MachinePrecision] * y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.170000000000000012 or 1.95000000000000005e-11 < 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. associate-*r* N/A

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

      2. distribute-lft-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. metadata-eval N/A

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

      13. distribute-lft-neg-in N/A

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

      14. distribute-rgt-neg-in N/A

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

      15. distribute-lft-neg-in N/A

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

      16. mul-1-neg N/A

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

      17. distribute-rgt-out-- N/A

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

      18. distribute-lft-out-- N/A

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

      19. neg-mul-1 N/A

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

      20. neg-sub0 N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

      21. associate-+l- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

      22. neg-sub0 N/A

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

      23. mul-1-neg N/A

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

      24. *-lft-identity N/A

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

      25. *-inverses N/A

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

      26. associate-*l/ N/A

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

      27. associate-*r/ N/A

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

      28. associate-*r/ N/A

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

      29. *-rgt-identity N/A

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

   5. Simplified 99.1%

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

   if -0.170000000000000012 < z < 1.95000000000000005e-11

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 99.1%

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

      1. +-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 99.8

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

   7. Applied egg-rr 99.8%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;\left(x - y\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 6, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6100:\\ \;\;\;\;\mathsf{fma}\left(z, x \cdot -6, x\right)\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 6, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot z, -6, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6100.0)
   (fma z (* x -6.0) x)
   (if (<= x 3.25e-38) (fma (* z 6.0) y x) (fma (* x z) -6.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6100.0) {
		tmp = fma(z, (x * -6.0), x);
	} else if (x <= 3.25e-38) {
		tmp = fma((z * 6.0), y, x);
	} else {
		tmp = fma((x * z), -6.0, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6100.0)
		tmp = fma(z, Float64(x * -6.0), x);
	elseif (x <= 3.25e-38)
		tmp = fma(Float64(z * 6.0), y, x);
	else
		tmp = fma(Float64(x * z), -6.0, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6100.0], N[(z * N[(x * -6.0), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[x, 3.25e-38], N[(N[(z * 6.0), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * -6.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6100

   1. Initial program 100.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. *-lft-identity N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 91.5

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

   5. Simplified 91.5%

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

   if -6100 < x < 3.24999999999999975e-38

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 90.2%

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

      1. +-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 91.0

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

   7. Applied egg-rr 91.0%

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

   if 3.24999999999999975e-38 < x

   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. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. *-lft-identity N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 87.5

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

   5. Simplified 87.5%

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

      1. associate-*r* N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 87.5

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

   7. Applied egg-rr 87.5%

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

Alternative 6: 75.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(z, x \cdot -6, x\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.6e+72)
   (* y (* z 6.0))
   (if (<= y 1.02e+86) (fma z (* x -6.0) x) (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.6e+72) {
		tmp = y * (z * 6.0);
	} else if (y <= 1.02e+86) {
		tmp = fma(z, (x * -6.0), x);
	} else {
		tmp = 6.0 * (y * z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.6e+72)
		tmp = Float64(y * Float64(z * 6.0));
	elseif (y <= 1.02e+86)
		tmp = fma(z, Float64(x * -6.0), x);
	else
		tmp = Float64(6.0 * Float64(y * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.6e+72], N[(y * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e+86], N[(z * N[(x * -6.0), $MachinePrecision] + x), $MachinePrecision], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6000000000000001e72

   1. Initial program 97.1%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 80.4

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

   5. Simplified 80.4%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 80.5

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

   7. Applied egg-rr 80.5%

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

   if -1.6000000000000001e72 < y < 1.01999999999999996e86

   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. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. *-lft-identity N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 82.4

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

   5. Simplified 82.4%

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

   if 1.01999999999999996e86 < y

   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. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 73.4

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

   5. Simplified 73.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(z, x \cdot -6, x\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-45}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= z -8.5e-45) t_0 (if (<= z 2.2e-127) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -8.5e-45) {
		tmp = t_0;
	} else if (z <= 2.2e-127) {
		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 * z)
    if (z <= (-8.5d-45)) then
        tmp = t_0
    else if (z <= 2.2d-127) 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 * z);
	double tmp;
	if (z <= -8.5e-45) {
		tmp = t_0;
	} else if (z <= 2.2e-127) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	tmp = 0
	if z <= -8.5e-45:
		tmp = t_0
	elif z <= 2.2e-127:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -8.5e-45)
		tmp = t_0;
	elseif (z <= 2.2e-127)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -8.5e-45)
		tmp = t_0;
	elseif (z <= 2.2e-127)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e-45], t$95$0, If[LessEqual[z, 2.2e-127], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000041e-45 or 2.2000000000000001e-127 < z

   1. Initial program 99.2%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 53.3

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

   5. Simplified 53.3%

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

   if -8.50000000000000041e-45 < z < 2.2000000000000001e-127

   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 83.5%

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

Alternative 8: 36.4% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

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

3. Taylor expanded in z around 0

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

5. Simplified 39.1%

   \[\leadsto \color{blue}{x} \]
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 2024204 
(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)))