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

Percentage Accurate: 99.7% → 99.8%

Time: 16.2s

Alternatives: 13

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13500000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.108:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6 + y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -13500000.0)
   (* z (* (- y x) 6.0))
   (if (<= z 0.108) (+ x (* y (* 6.0 z))) (* z (+ (* x -6.0) (* y 6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -13500000.0) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 0.108) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = z * ((x * -6.0) + (y * 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 <= (-13500000.0d0)) then
        tmp = z * ((y - x) * 6.0d0)
    else if (z <= 0.108d0) then
        tmp = x + (y * (6.0d0 * z))
    else
        tmp = z * ((x * (-6.0d0)) + (y * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -13500000.0) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 0.108) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = z * ((x * -6.0) + (y * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -13500000.0:
		tmp = z * ((y - x) * 6.0)
	elif z <= 0.108:
		tmp = x + (y * (6.0 * z))
	else:
		tmp = z * ((x * -6.0) + (y * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -13500000.0)
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	elseif (z <= 0.108)
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	else
		tmp = Float64(z * Float64(Float64(x * -6.0) + Float64(y * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -13500000.0)
		tmp = z * ((y - x) * 6.0);
	elseif (z <= 0.108)
		tmp = x + (y * (6.0 * z));
	else
		tmp = z * ((x * -6.0) + (y * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -13500000.0], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.108], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * -6.0), $MachinePrecision] + N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e7

   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. associate-*r* 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.8%

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

      5. fma-define 99.7%

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

   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 z around inf 99.3%

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

      1. associate-*r* 99.3%

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

      2. *-commutative 99.3%

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

      3. associate-*r* 99.1%

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

   7. Simplified 99.1%

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

   if -1.35e7 < z < 0.107999999999999999

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 98.7%

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

      1. *-commutative 98.7%

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

      2. associate-*r* 98.8%

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

   5. Simplified 98.8%

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

   if 0.107999999999999999 < 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 97.3%

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

      1. fma-define 97.3%

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

      2. *-commutative 97.3%

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

      3. +-commutative 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in z around inf 98.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13500000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.108:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6 + y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13500000 \lor \neg \left(z \leq 0.108\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -13500000.0) (not (<= z 0.108)))
   (* z (* (- y x) 6.0))
   (+ x (* y (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -13500000.0) || !(z <= 0.108)) {
		tmp = z * ((y - x) * 6.0);
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-13500000.0d0)) .or. (.not. (z <= 0.108d0))) then
        tmp = z * ((y - x) * 6.0d0)
    else
        tmp = x + (y * (6.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -13500000.0) || !(z <= 0.108)) {
		tmp = z * ((y - x) * 6.0);
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -13500000.0) or not (z <= 0.108):
		tmp = z * ((y - x) * 6.0)
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -13500000.0) || !(z <= 0.108))
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	else
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -13500000.0) || ~((z <= 0.108)))
		tmp = z * ((y - x) * 6.0);
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -13500000.0], N[Not[LessEqual[z, 0.108]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e7 or 0.107999999999999999 < z

   1. Initial program 99.7%

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

      1. associate-*r* 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.7%

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

      5. fma-define 99.7%

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

   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 z around inf 98.7%

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

      1. associate-*r* 98.8%

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

      2. *-commutative 98.8%

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

      3. associate-*r* 98.7%

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

   7. Simplified 98.7%

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

   if -1.35e7 < z < 0.107999999999999999

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 98.7%

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

      1. *-commutative 98.7%

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

      2. associate-*r* 98.8%

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

   5. Simplified 98.8%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13500000 \lor \neg \left(z \leq 0.108\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13500000 \lor \neg \left(z \leq 0.108\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -13500000.0) (not (<= z 0.108)))
   (* z (* (- y x) 6.0))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -13500000.0) || !(z <= 0.108)) {
		tmp = z * ((y - x) * 6.0);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-13500000.0d0)) .or. (.not. (z <= 0.108d0))) then
        tmp = z * ((y - x) * 6.0d0)
    else
        tmp = x + (6.0d0 * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -13500000.0) || !(z <= 0.108)) {
		tmp = z * ((y - x) * 6.0);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -13500000.0) or not (z <= 0.108):
		tmp = z * ((y - x) * 6.0)
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -13500000.0) || !(z <= 0.108))
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	else
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -13500000.0) || ~((z <= 0.108)))
		tmp = z * ((y - x) * 6.0);
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -13500000.0], N[Not[LessEqual[z, 0.108]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e7 or 0.107999999999999999 < z

   1. Initial program 99.7%

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

      1. associate-*r* 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.7%

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

      5. fma-define 99.7%

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

   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 z around inf 98.7%

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

      1. associate-*r* 98.8%

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

      2. *-commutative 98.8%

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

      3. associate-*r* 98.7%

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

   7. Simplified 98.7%

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

   if -1.35e7 < z < 0.107999999999999999

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 98.7%

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

      1. *-commutative 98.7%

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

   5. Simplified 98.7%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13500000 \lor \neg \left(z \leq 0.108\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-153} \lor \neg \left(z \leq 0.00175\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.8e-153) (not (<= z 0.00175)))
   (* z (* (- y x) 6.0))
   (* x (+ (* z -6.0) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.8e-153) || !(z <= 0.00175)) {
		tmp = z * ((y - x) * 6.0);
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	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 <= (-7.8d-153)) .or. (.not. (z <= 0.00175d0))) then
        tmp = z * ((y - x) * 6.0d0)
    else
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.8e-153) || !(z <= 0.00175)) {
		tmp = z * ((y - x) * 6.0);
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.8e-153) or not (z <= 0.00175):
		tmp = z * ((y - x) * 6.0)
	else:
		tmp = x * ((z * -6.0) + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.8e-153) || !(z <= 0.00175))
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	else
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.8e-153) || ~((z <= 0.00175)))
		tmp = z * ((y - x) * 6.0);
	else
		tmp = x * ((z * -6.0) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.8e-153], N[Not[LessEqual[z, 0.00175]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000004e-153 or 0.00175000000000000004 < z

   1. Initial program 99.7%

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

      1. associate-*r* 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.7%

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

      5. fma-define 99.7%

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

   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 z around inf 94.2%

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

      1. associate-*r* 94.3%

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

      2. *-commutative 94.3%

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

      3. associate-*r* 94.2%

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

   7. Simplified 94.2%

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

   if -7.8000000000000004e-153 < z < 0.00175000000000000004

   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 75.8%

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

      1. +-commutative 75.8%

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

   5. Simplified 75.8%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-153} \lor \neg \left(z \leq 0.00175\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.35e+91)
   (* z (* y 6.0))
   (if (<= y 5.8e+36) (* x (+ (* z -6.0) 1.0)) (* y (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+91) {
		tmp = z * (y * 6.0);
	} else if (y <= 5.8e+36) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = y * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.35d+91)) then
        tmp = z * (y * 6.0d0)
    else if (y <= 5.8d+36) then
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    else
        tmp = y * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+91) {
		tmp = z * (y * 6.0);
	} else if (y <= 5.8e+36) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = y * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.35e+91:
		tmp = z * (y * 6.0)
	elif y <= 5.8e+36:
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = y * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.35e+91)
		tmp = Float64(z * Float64(y * 6.0));
	elseif (y <= 5.8e+36)
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	else
		tmp = Float64(y * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.35e+91)
		tmp = z * (y * 6.0);
	elseif (y <= 5.8e+36)
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = y * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.35e+91], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+36], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35e91

   1. Initial program 99.9%

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

      1. associate-*r* 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.6%

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

      5. fma-define 99.7%

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

   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 79.7%

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

      1. *-commutative 79.7%

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

      2. associate-*r* 79.8%

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

      3. *-commutative 79.8%

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

      4. associate-*r* 79.9%

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

   7. Simplified 79.9%

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

   if -1.35e91 < y < 5.8e36

   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 82.6%

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

      1. +-commutative 82.6%

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

   5. Simplified 82.6%

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

   if 5.8e36 < 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 98.1%

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

      1. fma-define 98.1%

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

      2. *-commutative 98.1%

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

      3. +-commutative 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in y around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-*r* 74.0%

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

   8. Simplified 74.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13500000 \lor \neg \left(z \leq 3350\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -13500000.0) (not (<= z 3350.0))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -13500000.0) || !(z <= 3350.0)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-13500000.0d0)) .or. (.not. (z <= 3350.0d0))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -13500000.0) || !(z <= 3350.0)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -13500000.0) or not (z <= 3350.0):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -13500000.0) || !(z <= 3350.0))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -13500000.0) || ~((z <= 3350.0)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -13500000.0], N[Not[LessEqual[z, 3350.0]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e7 or 3350 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 56.3%

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

   4. Taylor expanded in z around inf 55.4%

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

   if -1.35e7 < z < 3350

   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 66.5%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13500000 \lor \neg \left(z \leq 3350\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 3350:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.8e-153) (* y (* 6.0 z)) (if (<= z 3350.0) x (* x (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.8e-153) {
		tmp = y * (6.0 * z);
	} else if (z <= 3350.0) {
		tmp = x;
	} 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 <= (-7.8d-153)) then
        tmp = y * (6.0d0 * z)
    else if (z <= 3350.0d0) then
        tmp = x
    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 <= -7.8e-153) {
		tmp = y * (6.0 * z);
	} else if (z <= 3350.0) {
		tmp = x;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.8e-153:
		tmp = y * (6.0 * z)
	elif z <= 3350.0:
		tmp = x
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.8e-153)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (z <= 3350.0)
		tmp = x;
	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 <= -7.8e-153)
		tmp = y * (6.0 * z);
	elseif (z <= 3350.0)
		tmp = x;
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.8e-153], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3350.0], x, N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8000000000000004e-153

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 98.5%

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

      1. fma-define 98.5%

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

      2. *-commutative 98.5%

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

      3. +-commutative 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in y around inf 54.7%

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

      1. *-commutative 54.7%

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

      2. associate-*r* 54.8%

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

   8. Simplified 54.8%

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

   if -7.8000000000000004e-153 < z < 3350

   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 71.5%

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

   if 3350 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 62.4%

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

   4. Taylor expanded in z around inf 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-*r* 61.1%

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

      3. *-commutative 61.1%

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

   6. Simplified 61.1%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 3350:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-153}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3350:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.2e-153) (* 6.0 (* y z)) (if (<= z 3350.0) x (* x (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.2e-153) {
		tmp = 6.0 * (y * z);
	} else if (z <= 3350.0) {
		tmp = x;
	} 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 <= (-7.2d-153)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 3350.0d0) then
        tmp = x
    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 <= -7.2e-153) {
		tmp = 6.0 * (y * z);
	} else if (z <= 3350.0) {
		tmp = x;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.2e-153:
		tmp = 6.0 * (y * z)
	elif z <= 3350.0:
		tmp = x
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.2e-153)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 3350.0)
		tmp = x;
	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 <= -7.2e-153)
		tmp = 6.0 * (y * z);
	elseif (z <= 3350.0)
		tmp = x;
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.2e-153], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3350.0], x, N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.1999999999999995e-153

   1. Initial program 99.6%

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

      1. associate-*r* 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.7%

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

      5. fma-define 99.7%

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

   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 54.7%

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

      1. *-commutative 54.7%

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

   7. Simplified 54.7%

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

   if -7.1999999999999995e-153 < z < 3350

   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 71.5%

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

   if 3350 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 62.4%

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

   4. Taylor expanded in z around inf 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-*r* 61.1%

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

      3. *-commutative 61.1%

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

   6. Simplified 61.1%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-153}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3350:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-153}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3350:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.8e-153) (* 6.0 (* y z)) (if (<= z 3350.0) x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.8e-153) {
		tmp = 6.0 * (y * z);
	} else if (z <= 3350.0) {
		tmp = x;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-7.8d-153)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 3350.0d0) then
        tmp = x
    else
        tmp = (-6.0d0) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.8e-153) {
		tmp = 6.0 * (y * z);
	} else if (z <= 3350.0) {
		tmp = x;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.8e-153:
		tmp = 6.0 * (y * z)
	elif z <= 3350.0:
		tmp = x
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.8e-153)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 3350.0)
		tmp = x;
	else
		tmp = Float64(-6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.8e-153)
		tmp = 6.0 * (y * z);
	elseif (z <= 3350.0)
		tmp = x;
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.8e-153], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3350.0], x, N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8000000000000004e-153

   1. Initial program 99.6%

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

      1. associate-*r* 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.7%

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

      5. fma-define 99.7%

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

   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 54.7%

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

      1. *-commutative 54.7%

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

   7. Simplified 54.7%

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

   if -7.8000000000000004e-153 < z < 3350

   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 71.5%

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

   if 3350 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 62.4%

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

   4. Taylor expanded in z around inf 61.0%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-153}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3350:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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. associate-*l* 99.8%

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

3. Simplified 99.8%

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

Alternative 12: 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 13: 37.1% 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 31.8%

   \[\leadsto \color{blue}{x} \]
4. 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 2024163 
(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)))