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

Percentage Accurate: 99.7% → 99.7%

Time: 6.4s

Alternatives: 13

Speedup: 1.0×

• 20.8% 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, 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. Final simplification 99.9%

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

Alternative 2: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{-6} \lor \neg \left(z \leq 4.9 \cdot 10^{-15}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.3e-6) (not (<= z 4.9e-15))) (* 6.0 (* (- y x) z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.3e-6) || !(z <= 4.9e-15)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-7.3d-6)) .or. (.not. (z <= 4.9d-15))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.3e-6) || !(z <= 4.9e-15)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.3e-6) or not (z <= 4.9e-15):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.3e-6) || !(z <= 4.9e-15))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.3e-6) || ~((z <= 4.9e-15)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.3e-6], N[Not[LessEqual[z, 4.9e-15]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.30000000000000041e-6 or 4.8999999999999999e-15 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 96.5%

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

      1. +-commutative 96.5%

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

      2. metadata-eval 96.5%

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

      3. cancel-sign-sub-inv 96.5%

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

      4. *-commutative 96.5%

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

      5. associate-*l* 96.5%

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

      6. *-commutative 96.5%

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

      7. associate-*l* 96.5%

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

      8. distribute-lft-out-- 99.8%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.5%

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

   if -7.30000000000000041e-6 < z < 4.8999999999999999e-15

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 75.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{-6} \lor \neg \left(z \leq 4.9 \cdot 10^{-15}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-8}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.25e-8)
   (* 6.0 (* (- y x) z))
   (if (<= z 7e-21) x (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.25e-8) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 7e-21) {
		tmp = x;
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.25d-8)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 7d-21) then
        tmp = x
    else
        tmp = z * ((y - x) * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.25e-8) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 7e-21) {
		tmp = x;
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.25e-8:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 7e-21:
		tmp = x
	else:
		tmp = z * ((y - x) * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.25e-8)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 7e-21)
		tmp = x;
	else
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.25e-8)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 7e-21)
		tmp = x;
	else
		tmp = z * ((y - x) * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.25e-8], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-21], x, N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2499999999999999e-8

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 96.8%

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

      1. +-commutative 96.8%

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

      2. metadata-eval 96.8%

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

      3. cancel-sign-sub-inv 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-*l* 96.8%

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

      6. *-commutative 96.8%

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

      7. associate-*l* 96.8%

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

      8. distribute-lft-out-- 99.7%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.3%

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

   if -1.2499999999999999e-8 < z < 7.0000000000000007e-21

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 75.4%

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

   if 7.0000000000000007e-21 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 96.0%

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

      1. +-commutative 96.0%

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

      2. metadata-eval 96.0%

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

      3. cancel-sign-sub-inv 96.0%

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

      4. *-commutative 96.0%

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

      5. associate-*l* 96.2%

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

      6. *-commutative 96.2%

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

      7. associate-*l* 96.2%

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

      8. distribute-lft-out-- 99.9%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l* 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-8}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]

Alternative 4: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-8}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.2e-8)
   (* 6.0 (* (- y x) z))
   (if (<= z 7e-11) x (* (- y x) (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2e-8) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 7e-11) {
		tmp = x;
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.2d-8)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 7d-11) then
        tmp = x
    else
        tmp = (y - x) * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2e-8) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 7e-11) {
		tmp = x;
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.2e-8:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 7e-11:
		tmp = x
	else:
		tmp = (y - x) * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.2e-8)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 7e-11)
		tmp = x;
	else
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.2e-8)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 7e-11)
		tmp = x;
	else
		tmp = (y - x) * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.2e-8], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-11], x, N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999999e-8

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 96.8%

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

      1. +-commutative 96.8%

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

      2. metadata-eval 96.8%

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

      3. cancel-sign-sub-inv 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-*l* 96.8%

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

      6. *-commutative 96.8%

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

      7. associate-*l* 96.8%

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

      8. distribute-lft-out-- 99.7%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.3%

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

   if -1.19999999999999999e-8 < z < 7.00000000000000038e-11

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 75.4%

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

   if 7.00000000000000038e-11 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 96.0%

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

      1. +-commutative 96.0%

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

      2. metadata-eval 96.0%

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

      3. cancel-sign-sub-inv 96.0%

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

      4. *-commutative 96.0%

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

      5. associate-*l* 96.2%

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

      6. *-commutative 96.2%

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

      7. associate-*l* 96.2%

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

      8. distribute-lft-out-- 99.9%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-8}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 5: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-5}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-11}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.2e-5)
   (* 6.0 (* (- y x) z))
   (if (<= z 5.7e-11) (+ x (* -6.0 (* x z))) (* (- y x) (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e-5) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 5.7e-11) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.2d-5)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 5.7d-11) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = (y - x) * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e-5) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 5.7e-11) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.2e-5:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 5.7e-11:
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = (y - x) * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.2e-5)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 5.7e-11)
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.2e-5)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 5.7e-11)
		tmp = x + (-6.0 * (x * z));
	else
		tmp = (y - x) * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.2e-5], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e-11], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999986e-5

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 96.8%

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

      1. +-commutative 96.8%

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

      2. metadata-eval 96.8%

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

      3. cancel-sign-sub-inv 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-*l* 96.8%

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

      6. *-commutative 96.8%

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

      7. associate-*l* 96.8%

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

      8. distribute-lft-out-- 99.7%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.3%

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

   if -3.19999999999999986e-5 < z < 5.6999999999999997e-11

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 75.8%

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

   if 5.6999999999999997e-11 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 96.0%

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

      1. +-commutative 96.0%

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

      2. metadata-eval 96.0%

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

      3. cancel-sign-sub-inv 96.0%

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

      4. *-commutative 96.0%

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

      5. associate-*l* 96.2%

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

      6. *-commutative 96.2%

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

      7. associate-*l* 96.2%

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

      8. distribute-lft-out-- 99.9%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-5}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-11}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 6: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-9}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1850.0)
   (* 6.0 (* (- y x) z))
   (if (<= z 8.5e-9) (+ x (* 6.0 (* y z))) (* (- y x) (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1850.0) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 8.5e-9) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1850.0d0)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 8.5d-9) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = (y - x) * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1850.0) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 8.5e-9) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1850.0:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 8.5e-9:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = (y - x) * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1850.0)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 8.5e-9)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1850.0)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 8.5e-9)
		tmp = x + (6.0 * (y * z));
	else
		tmp = (y - x) * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1850.0], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-9], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1850

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 96.8%

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

      1. +-commutative 96.8%

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

      2. metadata-eval 96.8%

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

      3. cancel-sign-sub-inv 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-*l* 96.8%

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

      6. *-commutative 96.8%

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

      7. associate-*l* 96.7%

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

      8. distribute-lft-out-- 99.7%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.3%

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

   if -1850 < z < 8.5e-9

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 99.5%

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

   if 8.5e-9 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 96.0%

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

      1. +-commutative 96.0%

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

      2. metadata-eval 96.0%

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

      3. cancel-sign-sub-inv 96.0%

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

      4. *-commutative 96.0%

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

      5. associate-*l* 96.2%

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

      6. *-commutative 96.2%

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

      7. associate-*l* 96.2%

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

      8. distribute-lft-out-- 99.9%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-9}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 7: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-9}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1850.0)
   (* 6.0 (* (- y x) z))
   (if (<= z 8.5e-9) (+ x (* z (* y 6.0))) (* (- y x) (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1850.0) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 8.5e-9) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1850.0d0)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 8.5d-9) then
        tmp = x + (z * (y * 6.0d0))
    else
        tmp = (y - x) * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1850.0) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 8.5e-9) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1850.0:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 8.5e-9:
		tmp = x + (z * (y * 6.0))
	else:
		tmp = (y - x) * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1850.0)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 8.5e-9)
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	else
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1850.0)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 8.5e-9)
		tmp = x + (z * (y * 6.0));
	else
		tmp = (y - x) * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1850.0], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-9], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1850

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 96.8%

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

      1. +-commutative 96.8%

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

      2. metadata-eval 96.8%

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

      3. cancel-sign-sub-inv 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-*l* 96.8%

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

      6. *-commutative 96.8%

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

      7. associate-*l* 96.7%

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

      8. distribute-lft-out-- 99.7%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.3%

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

   if -1850 < z < 8.5e-9

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 99.6%

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

   if 8.5e-9 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 96.0%

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

      1. +-commutative 96.0%

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

      2. metadata-eval 96.0%

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

      3. cancel-sign-sub-inv 96.0%

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

      4. *-commutative 96.0%

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

      5. associate-*l* 96.2%

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

      6. *-commutative 96.2%

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

      7. associate-*l* 96.2%

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

      8. distribute-lft-out-- 99.9%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-9}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 8: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1850 \lor \neg \left(z \leq 5.6 \cdot 10^{+15}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1850.0) (not (<= z 5.6e+15))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1850.0) || !(z <= 5.6e+15)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1850.0d0)) .or. (.not. (z <= 5.6d+15))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1850.0) || !(z <= 5.6e+15)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1850.0) or not (z <= 5.6e+15):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1850.0) || !(z <= 5.6e+15))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1850.0) || ~((z <= 5.6e+15)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1850.0], N[Not[LessEqual[z, 5.6e+15]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1850 or 5.6e15 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 96.4%

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

      1. +-commutative 96.4%

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

      2. metadata-eval 96.4%

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

      3. cancel-sign-sub-inv 96.4%

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

      4. *-commutative 96.4%

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

      5. associate-*l* 96.4%

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

      6. *-commutative 96.4%

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

      7. associate-*l* 96.4%

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

      8. distribute-lft-out-- 99.8%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.5%

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

   6. Taylor expanded in y around 0 53.8%

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

   if -1850 < z < 5.6e15

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 73.4%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1850 \lor \neg \left(z \leq 5.6 \cdot 10^{+15}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1850.0) (* -6.0 (* x z)) (if (<= z 2.05e-16) x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1850.0) {
		tmp = -6.0 * (x * z);
	} else if (z <= 2.05e-16) {
		tmp = x;
	} else {
		tmp = 6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1850.0d0)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= 2.05d-16) then
        tmp = x
    else
        tmp = 6.0d0 * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1850.0) {
		tmp = -6.0 * (x * z);
	} else if (z <= 2.05e-16) {
		tmp = x;
	} else {
		tmp = 6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1850.0:
		tmp = -6.0 * (x * z)
	elif z <= 2.05e-16:
		tmp = x
	else:
		tmp = 6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1850.0)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= 2.05e-16)
		tmp = x;
	else
		tmp = Float64(6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1850.0)
		tmp = -6.0 * (x * z);
	elseif (z <= 2.05e-16)
		tmp = x;
	else
		tmp = 6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1850.0], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-16], x, N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1850

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 96.8%

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

      1. +-commutative 96.8%

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

      2. metadata-eval 96.8%

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

      3. cancel-sign-sub-inv 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-*l* 96.8%

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

      6. *-commutative 96.8%

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

      7. associate-*l* 96.7%

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

      8. distribute-lft-out-- 99.7%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.3%

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

   6. Taylor expanded in y around 0 57.6%

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

   if -1850 < z < 2.05000000000000003e-16

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 74.9%

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

   if 2.05000000000000003e-16 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 96.0%

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

      1. +-commutative 96.0%

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

      2. metadata-eval 96.0%

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

      3. cancel-sign-sub-inv 96.0%

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

      4. *-commutative 96.0%

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

      5. associate-*l* 96.2%

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

      6. *-commutative 96.2%

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

      7. associate-*l* 96.2%

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

      8. distribute-lft-out-- 99.9%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in y around inf 62.1%

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

      1. *-commutative 62.1%

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

   8. Simplified 62.1%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 10: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1850.0) (* -6.0 (* x z)) (if (<= z 2.9e-11) x (* y (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1850.0) {
		tmp = -6.0 * (x * z);
	} else if (z <= 2.9e-11) {
		tmp = x;
	} else {
		tmp = y * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1850.0d0)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= 2.9d-11) then
        tmp = x
    else
        tmp = y * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1850.0) {
		tmp = -6.0 * (x * z);
	} else if (z <= 2.9e-11) {
		tmp = x;
	} else {
		tmp = y * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1850.0:
		tmp = -6.0 * (x * z)
	elif z <= 2.9e-11:
		tmp = x
	else:
		tmp = y * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1850.0)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= 2.9e-11)
		tmp = x;
	else
		tmp = Float64(y * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1850.0)
		tmp = -6.0 * (x * z);
	elseif (z <= 2.9e-11)
		tmp = x;
	else
		tmp = y * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1850.0], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-11], x, N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1850

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 96.8%

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

      1. +-commutative 96.8%

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

      2. metadata-eval 96.8%

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

      3. cancel-sign-sub-inv 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-*l* 96.8%

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

      6. *-commutative 96.8%

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

      7. associate-*l* 96.7%

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

      8. distribute-lft-out-- 99.7%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.3%

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

   6. Taylor expanded in y around 0 57.6%

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

   if -1850 < z < 2.9e-11

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 74.9%

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

   if 2.9e-11 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 96.0%

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

      1. +-commutative 96.0%

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

      2. metadata-eval 96.0%

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

      3. cancel-sign-sub-inv 96.0%

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

      4. *-commutative 96.0%

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

      5. associate-*l* 96.2%

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

      6. *-commutative 96.2%

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

      7. associate-*l* 96.2%

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

      8. distribute-lft-out-- 99.9%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in y around inf 62.1%

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

      1. *-commutative 62.1%

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

      2. *-commutative 62.1%

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

      3. *-commutative 62.1%

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

      4. associate-*r* 62.3%

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

   8. Simplified 62.3%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 11: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1850.0) (* z (* x -6.0)) (if (<= z 1.55e-11) x (* y (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1850.0) {
		tmp = z * (x * -6.0);
	} else if (z <= 1.55e-11) {
		tmp = x;
	} else {
		tmp = y * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1850.0d0)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= 1.55d-11) then
        tmp = x
    else
        tmp = y * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1850.0) {
		tmp = z * (x * -6.0);
	} else if (z <= 1.55e-11) {
		tmp = x;
	} else {
		tmp = y * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1850.0:
		tmp = z * (x * -6.0)
	elif z <= 1.55e-11:
		tmp = x
	else:
		tmp = y * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1850.0)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= 1.55e-11)
		tmp = x;
	else
		tmp = Float64(y * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1850.0)
		tmp = z * (x * -6.0);
	elseif (z <= 1.55e-11)
		tmp = x;
	else
		tmp = y * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1850.0], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-11], x, N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1850

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 96.8%

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

      1. +-commutative 96.8%

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

      2. metadata-eval 96.8%

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

      3. cancel-sign-sub-inv 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-*l* 96.8%

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

      6. *-commutative 96.8%

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

      7. associate-*l* 96.7%

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

      8. distribute-lft-out-- 99.7%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.3%

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

      1. associate-*r* 99.3%

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

      2. *-commutative 99.3%

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

      3. associate-*l* 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in y around 0 57.6%

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

      1. *-commutative 57.6%

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

   10. Simplified 57.6%

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

   if -1850 < z < 1.55000000000000014e-11

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 74.9%

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

   if 1.55000000000000014e-11 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 96.0%

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

      1. +-commutative 96.0%

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

      2. metadata-eval 96.0%

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

      3. cancel-sign-sub-inv 96.0%

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

      4. *-commutative 96.0%

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

      5. associate-*l* 96.2%

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

      6. *-commutative 96.2%

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

      7. associate-*l* 96.2%

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

      8. distribute-lft-out-- 99.9%

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

      9. associate-*r* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in y around inf 62.1%

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

      1. *-commutative 62.1%

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

      2. *-commutative 62.1%

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

      3. *-commutative 62.1%

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

      4. associate-*r* 62.3%

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

   8. Simplified 62.3%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 12: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 98.3%

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

   1. +-commutative 98.3%

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

   2. metadata-eval 98.3%

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

   3. cancel-sign-sub-inv 98.3%

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

   4. *-commutative 98.3%

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

   5. associate-*l* 98.3%

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

   6. *-commutative 98.3%

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

   7. associate-*l* 98.3%

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

   8. distribute-lft-out-- 99.9%

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

   9. associate-*r* 99.8%

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

4. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 13: 36.3% 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. Taylor expanded in z around 0 41.1%

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

3. Final simplification 41.1%

   \[\leadsto x \]

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 2023318 
(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)))