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

Percentage Accurate: 99.5% → 99.8%

Time: 14.4s

Alternatives: 11

Speedup: 1.2×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- y x) (+ 4.0 (* z -6.0)) x))

C

double code(double x, double y, double z) {
	return fma((y - x), (4.0 + (z * -6.0)), x);
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), Float64(4.0 + Float64(z * -6.0)), x)
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

   2. associate-*l* 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

   3. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

   4. sub-neg 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

   5. distribute-rgt-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.66 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.66) (not (<= z 0.5)))
   (+ x (* (- y x) (* z -6.0)))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.66) || !(z <= 0.5)) {
		tmp = x + ((y - x) * (z * -6.0));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	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 <= (-0.66d0)) .or. (.not. (z <= 0.5d0))) then
        tmp = x + ((y - x) * (z * (-6.0d0)))
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.66) || !(z <= 0.5)) {
		tmp = x + ((y - x) * (z * -6.0));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.66) or not (z <= 0.5):
		tmp = x + ((y - x) * (z * -6.0))
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.66) || !(z <= 0.5))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z * -6.0)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.66) || ~((z <= 0.5)))
		tmp = x + ((y - x) * (z * -6.0));
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.66], N[Not[LessEqual[z, 0.5]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.660000000000000031 or 0.5 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \left(\color{blue}{0.6666666666666666} - z\right), x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + x} \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + x} \]

   7. Taylor expanded in z around inf 98.8%

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

   if -0.660000000000000031 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 96.2%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.66 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.66 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.66) (not (<= z 0.52)))
   (+ x (* -6.0 (* (- y x) z)))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.66) || !(z <= 0.52)) {
		tmp = x + (-6.0 * ((y - x) * z));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	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 <= (-0.66d0)) .or. (.not. (z <= 0.52d0))) then
        tmp = x + ((-6.0d0) * ((y - x) * z))
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.66) || !(z <= 0.52)) {
		tmp = x + (-6.0 * ((y - x) * z));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.66) or not (z <= 0.52):
		tmp = x + (-6.0 * ((y - x) * z))
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.66) || !(z <= 0.52))
		tmp = Float64(x + Float64(-6.0 * Float64(Float64(y - x) * z)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.66) || ~((z <= 0.52)))
		tmp = x + (-6.0 * ((y - x) * z));
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.66], N[Not[LessEqual[z, 0.52]], $MachinePrecision]], N[(x + N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.660000000000000031 or 0.52000000000000002 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 98.7%

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

   if -0.660000000000000031 < z < 0.52000000000000002

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 96.2%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.66 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-11} \lor \neg \left(y \leq 2.46 \cdot 10^{+61}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.2e-11) (not (<= y 2.46e+61)))
   (* y (+ 4.0 (* z -6.0)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e-11) || !(y <= 2.46e+61)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 + (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 ((y <= (-3.2d-11)) .or. (.not. (y <= 2.46d+61))) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e-11) || !(y <= 2.46e+61)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.2e-11) or not (y <= 2.46e+61):
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.2e-11) || !(y <= 2.46e+61))
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.2e-11) || ~((y <= 2.46e+61)))
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.2e-11], N[Not[LessEqual[y, 2.46e+61]], $MachinePrecision]], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999994e-11 or 2.46e61 < y

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 83.1%

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

   if -3.19999999999999994e-11 < y < 2.46e61

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \left(\color{blue}{0.6666666666666666} - z\right), x\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 79.4%

      \[\leadsto \color{blue}{x + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 79.4%

         \[\leadsto \color{blue}{1 \cdot x} + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. *-commutative 79.4%

         \[\leadsto 1 \cdot x + -6 \cdot \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot x\right)} \]

      3. associate-*r* 79.7%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x} \]

      4. sub-neg 79.7%

         \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      5. distribute-rgt-in 79.6%

         \[\leadsto 1 \cdot x + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)} \cdot x \]

      6. metadata-eval 79.6%

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

      7. neg-mul-1 79.6%

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

      8. associate-*r* 79.6%

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

      9. *-commutative 79.6%

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

      10. metadata-eval 79.6%

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

      11. distribute-lft-in 79.6%

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

      12. distribute-rgt-in 79.7%

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

      13. distribute-lft-in 79.7%

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

      14. metadata-eval 79.7%

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

      15. associate-+r+ 79.7%

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

      16. metadata-eval 79.7%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. associate-*r* 79.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      18. metadata-eval 79.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

   7. Simplified 79.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-11} \lor \neg \left(y \leq 2.46 \cdot 10^{+61}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.5 \lor \neg \left(z \leq 12800\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.5) (not (<= z 12800.0))) (* 6.0 (* x z)) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.5) || !(z <= 12800.0)) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = x * -3.0;
	}
	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 <= (-0.5d0)) .or. (.not. (z <= 12800.0d0))) then
        tmp = 6.0d0 * (x * z)
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.5) || !(z <= 12800.0)) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.5) or not (z <= 12800.0):
		tmp = 6.0 * (x * z)
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.5) || !(z <= 12800.0))
		tmp = Float64(6.0 * Float64(x * z));
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.5) || ~((z <= 12800.0)))
		tmp = 6.0 * (x * z);
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.5], N[Not[LessEqual[z, 12800.0]], $MachinePrecision]], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.5 or 12800 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \left(\color{blue}{0.6666666666666666} - z\right), x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 61.2%

      \[\leadsto \color{blue}{x + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 61.2%

         \[\leadsto \color{blue}{1 \cdot x} + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. *-commutative 61.2%

         \[\leadsto 1 \cdot x + -6 \cdot \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot x\right)} \]

      3. associate-*r* 61.3%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x} \]

      4. sub-neg 61.3%

         \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      5. distribute-rgt-in 61.3%

         \[\leadsto 1 \cdot x + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)} \cdot x \]

      6. metadata-eval 61.3%

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

      7. neg-mul-1 61.3%

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

      8. associate-*r* 61.3%

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

      9. *-commutative 61.3%

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

      10. metadata-eval 61.3%

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

      11. distribute-lft-in 61.3%

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

      12. distribute-rgt-in 61.3%

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

      13. distribute-lft-in 61.3%

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

      14. metadata-eval 61.3%

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

      15. associate-+r+ 61.3%

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

      16. metadata-eval 61.3%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. associate-*r* 61.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      18. metadata-eval 61.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

   7. Simplified 61.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   8. Taylor expanded in z around inf 60.9%

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

   if -0.5 < z < 12800

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \left(\color{blue}{0.6666666666666666} - z\right), x\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 52.0%

      \[\leadsto \color{blue}{x + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 52.0%

         \[\leadsto \color{blue}{1 \cdot x} + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. *-commutative 52.0%

         \[\leadsto 1 \cdot x + -6 \cdot \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot x\right)} \]

      3. associate-*r* 52.2%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x} \]

      4. sub-neg 52.2%

         \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      5. distribute-rgt-in 52.2%

         \[\leadsto 1 \cdot x + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)} \cdot x \]

      6. metadata-eval 52.2%

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

      7. neg-mul-1 52.2%

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

      8. associate-*r* 52.2%

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

      9. *-commutative 52.2%

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

      10. metadata-eval 52.2%

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

      11. distribute-lft-in 52.2%

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

      12. distribute-rgt-in 52.2%

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

      13. distribute-lft-in 52.2%

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

      14. metadata-eval 52.2%

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

      15. associate-+r+ 52.3%

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

      16. metadata-eval 52.3%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. associate-*r* 52.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      18. metadata-eval 52.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

   7. Simplified 52.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   8. Taylor expanded in z around 0 50.2%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 50.2%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 50.2%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.5 \lor \neg \left(z \leq 12800\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 12800:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.5)
   (* 6.0 (* x z))
   (if (<= z 12800.0) (* x -3.0) (* x (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = 6.0 * (x * z);
	} else if (z <= 12800.0) {
		tmp = x * -3.0;
	} 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 <= (-0.5d0)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= 12800.0d0) then
        tmp = x * (-3.0d0)
    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 <= -0.5) {
		tmp = 6.0 * (x * z);
	} else if (z <= 12800.0) {
		tmp = x * -3.0;
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.5:
		tmp = 6.0 * (x * z)
	elif z <= 12800.0:
		tmp = x * -3.0
	else:
		tmp = x * (z * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.5)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= 12800.0)
		tmp = Float64(x * -3.0);
	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 <= -0.5)
		tmp = 6.0 * (x * z);
	elseif (z <= 12800.0)
		tmp = x * -3.0;
	else
		tmp = x * (z * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.5], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 12800.0], N[(x * -3.0), $MachinePrecision], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.5

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \left(\color{blue}{0.6666666666666666} - z\right), x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 59.8%

      \[\leadsto \color{blue}{x + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 59.8%

         \[\leadsto \color{blue}{1 \cdot x} + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. *-commutative 59.8%

         \[\leadsto 1 \cdot x + -6 \cdot \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot x\right)} \]

      3. associate-*r* 59.7%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x} \]

      4. sub-neg 59.7%

         \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      5. distribute-rgt-in 59.7%

         \[\leadsto 1 \cdot x + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)} \cdot x \]

      6. metadata-eval 59.7%

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

      7. neg-mul-1 59.7%

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

      8. associate-*r* 59.7%

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

      9. *-commutative 59.7%

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

      10. metadata-eval 59.7%

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

      11. distribute-lft-in 59.7%

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

      12. distribute-rgt-in 59.7%

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

      13. distribute-lft-in 59.7%

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

      14. metadata-eval 59.7%

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

      15. associate-+r+ 59.7%

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

      16. metadata-eval 59.7%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. associate-*r* 59.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      18. metadata-eval 59.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

   7. Simplified 59.7%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   8. Taylor expanded in z around inf 59.4%

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

   if -0.5 < z < 12800

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \left(\color{blue}{0.6666666666666666} - z\right), x\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 52.0%

      \[\leadsto \color{blue}{x + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 52.0%

         \[\leadsto \color{blue}{1 \cdot x} + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. *-commutative 52.0%

         \[\leadsto 1 \cdot x + -6 \cdot \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot x\right)} \]

      3. associate-*r* 52.2%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x} \]

      4. sub-neg 52.2%

         \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      5. distribute-rgt-in 52.2%

         \[\leadsto 1 \cdot x + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)} \cdot x \]

      6. metadata-eval 52.2%

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

      7. neg-mul-1 52.2%

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

      8. associate-*r* 52.2%

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

      9. *-commutative 52.2%

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

      10. metadata-eval 52.2%

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

      11. distribute-lft-in 52.2%

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

      12. distribute-rgt-in 52.2%

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

      13. distribute-lft-in 52.2%

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

      14. metadata-eval 52.2%

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

      15. associate-+r+ 52.3%

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

      16. metadata-eval 52.3%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. associate-*r* 52.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      18. metadata-eval 52.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

   7. Simplified 52.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   8. Taylor expanded in z around 0 50.2%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 50.2%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 50.2%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if 12800 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \left(\color{blue}{0.6666666666666666} - z\right), x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 62.7%

      \[\leadsto \color{blue}{x + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 62.7%

         \[\leadsto \color{blue}{1 \cdot x} + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right) \]

      2. *-commutative 62.7%

         \[\leadsto 1 \cdot x + -6 \cdot \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot x\right)} \]

      3. associate-*r* 62.8%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x} \]

      4. sub-neg 62.8%

         \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      5. distribute-rgt-in 62.8%

         \[\leadsto 1 \cdot x + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)} \cdot x \]

      6. metadata-eval 62.8%

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

      7. neg-mul-1 62.8%

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

      8. associate-*r* 62.8%

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

      9. *-commutative 62.8%

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

      10. metadata-eval 62.8%

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

      11. distribute-lft-in 62.8%

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

      12. distribute-rgt-in 62.8%

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

      13. distribute-lft-in 62.8%

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

      14. metadata-eval 62.8%

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

      15. associate-+r+ 62.8%

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

      16. metadata-eval 62.8%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. associate-*r* 62.8%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      18. metadata-eval 62.8%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

   7. Simplified 62.8%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   8. Taylor expanded in z around inf 62.2%

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

      1. associate-*r* 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-*r* 62.4%

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

      4. *-commutative 62.4%

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

   10. Simplified 62.4%

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

Alternative 7: 99.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (- y x) (* 6.0 (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	return x + ((y - x) * (6.0 * (0.6666666666666666 - 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 * (0.6666666666666666d0 - z)))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * (6.0 * (0.6666666666666666 - z)));
}

Python

def code(x, y, z):
	return x + ((y - x) * (6.0 * (0.6666666666666666 - z)))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * Float64(6.0 * Float64(0.6666666666666666 - z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * (6.0 * (0.6666666666666666 - z)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(6.0 * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

   2. associate-*l* 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

   3. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

   4. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \left(\color{blue}{0.6666666666666666} - z\right), x\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. fma-undefine 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + x} \]

6. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + x} \]

7. Final simplification 99.8%

   \[\leadsto x + \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) \]
8. Add Preprocessing

Alternative 8: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (- 0.6666666666666666 z) (* (- y x) 6.0))))

C

double code(double x, double y, double z) {
	return x + ((0.6666666666666666 - 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 + ((0.6666666666666666d0 - z) * ((y - x) * 6.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((0.6666666666666666 - z) * ((y - x) * 6.0));
}

Python

def code(x, y, z):
	return x + ((0.6666666666666666 - z) * ((y - x) * 6.0))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(0.6666666666666666 - z) * Float64(Float64(y - x) * 6.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((0.6666666666666666 - z) * ((y - x) * 6.0));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(0.6666666666666666 - z), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Final simplification 99.5%

   \[\leadsto x + \left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right) \]
6. Add Preprocessing

Alternative 9: 51.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(-3 + z \cdot 6\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (+ -3.0 (* z 6.0))))

C

double code(double x, double y, double z) {
	return x * (-3.0 + (z * 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 * ((-3.0d0) + (z * 6.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x * (-3.0 + (z * 6.0));
}

Python

def code(x, y, z):
	return x * (-3.0 + (z * 6.0))

Julia

function code(x, y, z)
	return Float64(x * Float64(-3.0 + Float64(z * 6.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (-3.0 + (z * 6.0));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

   2. associate-*l* 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

   3. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

   4. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \left(\color{blue}{0.6666666666666666} - z\right), x\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 56.5%

   \[\leadsto \color{blue}{x + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)} \]
6. Step-by-step derivation

   1. *-lft-identity 56.5%

      \[\leadsto \color{blue}{1 \cdot x} + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right) \]

   2. *-commutative 56.5%

      \[\leadsto 1 \cdot x + -6 \cdot \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot x\right)} \]

   3. associate-*r* 56.7%

      \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x} \]

   4. sub-neg 56.7%

      \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

   5. distribute-rgt-in 56.7%

      \[\leadsto 1 \cdot x + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)} \cdot x \]

   6. metadata-eval 56.7%

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

   7. neg-mul-1 56.7%

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

   8. associate-*r* 56.7%

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

   9. *-commutative 56.7%

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

   10. metadata-eval 56.7%

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

   11. distribute-lft-in 56.7%

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

   12. distribute-rgt-in 56.7%

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

   13. distribute-lft-in 56.7%

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

   14. metadata-eval 56.7%

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

   15. associate-+r+ 56.7%

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

   16. metadata-eval 56.7%

       \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

   17. associate-*r* 56.7%

       \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

   18. metadata-eval 56.7%

       \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

7. Simplified 56.7%

   \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

8. Final simplification 56.7%

   \[\leadsto x \cdot \left(-3 + z \cdot 6\right) \]
9. Add Preprocessing

Alternative 10: 26.1% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

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 * (-3.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * -3.0;
}

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

   2. associate-*l* 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

   3. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

   4. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \left(\color{blue}{0.6666666666666666} - z\right), x\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 56.5%

   \[\leadsto \color{blue}{x + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)} \]
6. Step-by-step derivation

   1. *-lft-identity 56.5%

      \[\leadsto \color{blue}{1 \cdot x} + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right) \]

   2. *-commutative 56.5%

      \[\leadsto 1 \cdot x + -6 \cdot \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot x\right)} \]

   3. associate-*r* 56.7%

      \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x} \]

   4. sub-neg 56.7%

      \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

   5. distribute-rgt-in 56.7%

      \[\leadsto 1 \cdot x + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)} \cdot x \]

   6. metadata-eval 56.7%

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

   7. neg-mul-1 56.7%

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

   8. associate-*r* 56.7%

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

   9. *-commutative 56.7%

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

   10. metadata-eval 56.7%

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

   11. distribute-lft-in 56.7%

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

   12. distribute-rgt-in 56.7%

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

   13. distribute-lft-in 56.7%

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

   14. metadata-eval 56.7%

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

   15. associate-+r+ 56.7%

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

   16. metadata-eval 56.7%

       \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

   17. associate-*r* 56.7%

       \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

   18. metadata-eval 56.7%

       \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

7. Simplified 56.7%

   \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

8. Taylor expanded in z around 0 26.8%

   \[\leadsto \color{blue}{-3 \cdot x} \]
9. Step-by-step derivation

   1. *-commutative 26.8%

      \[\leadsto \color{blue}{x \cdot -3} \]

10. Simplified 26.8%

    \[\leadsto \color{blue}{x \cdot -3} \]
11. Add Preprocessing

Alternative 11: 2.6% accurate, 13.0× 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%

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

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 56.6%

   \[\leadsto x + \color{blue}{\left(-6 \cdot x\right)} \cdot \left(0.6666666666666666 - z\right) \]

6. Taylor expanded in z around inf 31.1%

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

   1. neg-mul-1 31.1%

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

8. Simplified 31.1%

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

9. Taylor expanded in z around 0 2.6%

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

Reproduce

herbie shell --seed 2024131 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))