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

Percentage Accurate: 99.7% → 99.7%

Time: 6.5s

Alternatives: 9

Speedup: 1.0×

• 20.5% 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: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. *-commutative 99.9%

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

   3. fma-def 99.9%

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

   4. remove-double-neg 99.9%

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

   5. distribute-lft-neg-in 99.9%

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

   6. distribute-rgt-neg-in 99.9%

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

   7. sub-neg 99.9%

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

   8. distribute-neg-in 99.9%

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

   9. remove-double-neg 99.9%

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

   10. +-commutative 99.9%

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

   11. sub-neg 99.9%

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

   12. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-5} \lor \neg \left(z \leq 6.4 \cdot 10^{-68}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5e-5) (not (<= z 6.4e-68))) (* -6.0 (* z (- x y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-5) || !(z <= 6.4e-68)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.5d-5)) .or. (.not. (z <= 6.4d-68))) then
        tmp = (-6.0d0) * (z * (x - y))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-5) || !(z <= 6.4e-68)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.5e-5) or not (z <= 6.4e-68):
		tmp = -6.0 * (z * (x - y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.5e-5) || !(z <= 6.4e-68))
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.5e-5) || ~((z <= 6.4e-68)))
		tmp = -6.0 * (z * (x - y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.5e-5], N[Not[LessEqual[z, 6.4e-68]], $MachinePrecision]], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.50000000000000028e-5 or 6.3999999999999998e-68 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-def 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sub-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 96.0%

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

   if -4.50000000000000028e-5 < z < 6.3999999999999998e-68

   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 78.2%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-5} \lor \neg \left(z \leq 6.4 \cdot 10^{-68}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -47000 \lor \neg \left(z \leq 3.05 \cdot 10^{-69}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -47000.0) (not (<= z 3.05e-69)))
   (* -6.0 (* z (- x y)))
   (* x (+ 1.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -47000.0) || !(z <= 3.05e-69)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x * (1.0 + (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 <= (-47000.0d0)) .or. (.not. (z <= 3.05d-69))) then
        tmp = (-6.0d0) * (z * (x - y))
    else
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -47000.0) || !(z <= 3.05e-69)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x * (1.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -47000.0) or not (z <= 3.05e-69):
		tmp = -6.0 * (z * (x - y))
	else:
		tmp = x * (1.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -47000.0) || !(z <= 3.05e-69))
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -47000.0) || ~((z <= 3.05e-69)))
		tmp = -6.0 * (z * (x - y));
	else
		tmp = x * (1.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -47000.0], N[Not[LessEqual[z, 3.05e-69]], $MachinePrecision]], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -47000 or 3.0500000000000002e-69 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-def 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sub-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 96.9%

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

   if -47000 < z < 3.0500000000000002e-69

   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 79.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -47000 \lor \neg \left(z \leq 3.05 \cdot 10^{-69}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.18 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.18) (not (<= z 0.17)))
   (* -6.0 (* z (- x y)))
   (+ x (* z (* y 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.18) || !(z <= 0.17)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x + (z * (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 <= (-0.18d0)) .or. (.not. (z <= 0.17d0))) then
        tmp = (-6.0d0) * (z * (x - y))
    else
        tmp = x + (z * (y * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.18) || !(z <= 0.17)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.18) or not (z <= 0.17):
		tmp = -6.0 * (z * (x - y))
	else:
		tmp = x + (z * (y * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.18) || !(z <= 0.17))
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	else
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.18) || ~((z <= 0.17)))
		tmp = -6.0 * (z * (x - y));
	else
		tmp = x + (z * (y * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.18], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.17999999999999999 or 0.170000000000000012 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-def 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sub-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 97.3%

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

   if -0.17999999999999999 < 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 y around inf 98.9%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.18 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 5.6 \cdot 10^{-18}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 5.6e-18))) (* -6.0 (* z x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 5.6e-18)) {
		tmp = -6.0 * (z * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.165d0)) .or. (.not. (z <= 5.6d-18))) then
        tmp = (-6.0d0) * (z * x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 5.6e-18)) {
		tmp = -6.0 * (z * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 5.6e-18):
		tmp = -6.0 * (z * x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 5.6e-18))
		tmp = Float64(-6.0 * Float64(z * x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.165) || ~((z <= 5.6e-18)))
		tmp = -6.0 * (z * x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 5.6e-18]], $MachinePrecision]], N[(-6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 5.60000000000000025e-18 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-def 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sub-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 97.4%

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

   6. Taylor expanded in x around inf 53.9%

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

   if -0.165000000000000008 < z < 5.60000000000000025e-18

   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 75.7%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 5.6 \cdot 10^{-18}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.165) (* x (* z -6.0)) (if (<= z 5.6e-18) x (* -6.0 (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = x * (z * -6.0);
	} else if (z <= 5.6e-18) {
		tmp = x;
	} else {
		tmp = -6.0 * (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.165d0)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= 5.6d-18) then
        tmp = x
    else
        tmp = (-6.0d0) * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = x * (z * -6.0);
	} else if (z <= 5.6e-18) {
		tmp = x;
	} else {
		tmp = -6.0 * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.165:
		tmp = x * (z * -6.0)
	elif z <= 5.6e-18:
		tmp = x
	else:
		tmp = -6.0 * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.165)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= 5.6e-18)
		tmp = x;
	else
		tmp = Float64(-6.0 * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.165)
		tmp = x * (z * -6.0);
	elseif (z <= 5.6e-18)
		tmp = x;
	else
		tmp = -6.0 * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.165], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-18], x, N[(-6.0 * N[(z * x), $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 x around inf 51.2%

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

   4. Taylor expanded in z around inf 48.8%

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

      1. *-commutative 48.8%

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

   6. Simplified 48.8%

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

   if -0.165000000000000008 < z < 5.60000000000000025e-18

   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 75.7%

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

   if 5.60000000000000025e-18 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-def 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sub-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 98.3%

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

   6. Taylor expanded in x around inf 60.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.16:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.16) (* z (* x -6.0)) (if (<= z 5.6e-18) x (* -6.0 (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.16) {
		tmp = z * (x * -6.0);
	} else if (z <= 5.6e-18) {
		tmp = x;
	} else {
		tmp = -6.0 * (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.16d0)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= 5.6d-18) then
        tmp = x
    else
        tmp = (-6.0d0) * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.16) {
		tmp = z * (x * -6.0);
	} else if (z <= 5.6e-18) {
		tmp = x;
	} else {
		tmp = -6.0 * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.16:
		tmp = z * (x * -6.0)
	elif z <= 5.6e-18:
		tmp = x
	else:
		tmp = -6.0 * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.16)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= 5.6e-18)
		tmp = x;
	else
		tmp = Float64(-6.0 * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.16)
		tmp = z * (x * -6.0);
	elseif (z <= 5.6e-18)
		tmp = x;
	else
		tmp = -6.0 * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.16], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-18], x, N[(-6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.160000000000000003

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-def 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sub-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 96.6%

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

   6. Taylor expanded in x around inf 48.7%

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

      1. associate-*r* 48.9%

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

      2. *-commutative 48.9%

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

   8. Simplified 48.9%

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

   if -0.160000000000000003 < z < 5.60000000000000025e-18

   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 75.7%

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

   if 5.60000000000000025e-18 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-def 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sub-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 98.3%

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

   6. Taylor expanded in x around inf 60.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.16:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \end{array} \]
5. 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 99.9%

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

3. Final simplification 99.9%

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

Alternative 9: 36.5% 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 99.9%

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

3. Taylor expanded in z around 0 39.5%

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

4. Final simplification 39.5%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024021 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

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