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

Percentage Accurate: 99.7% → 99.8%

Time: 10.2s

Alternatives: 12

Speedup: 1.0×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-*r* 99.8%

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

   2. +-commutative 99.8%

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

   3. *-commutative 99.8%

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

   4. associate-*r* 99.8%

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

   5. fma-def 99.8%

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 60.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+129}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.166:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+228} \lor \neg \left(z \leq 1.32 \cdot 10^{+306}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* -6.0 (* x z))))
   (if (<= z -3.5e+129)
     t_0
     (if (<= z -8.5e+91)
       t_1
       (if (<= z -4.4e+69)
         t_0
         (if (<= z -1.25e+35)
           t_1
           (if (<= z -1.55e-24)
             t_0
             (if (<= z 0.166)
               x
               (if (or (<= z 1.45e+228) (not (<= z 1.32e+306)))
                 t_1
                 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -3.5e+129) {
		tmp = t_0;
	} else if (z <= -8.5e+91) {
		tmp = t_1;
	} else if (z <= -4.4e+69) {
		tmp = t_0;
	} else if (z <= -1.25e+35) {
		tmp = t_1;
	} else if (z <= -1.55e-24) {
		tmp = t_0;
	} else if (z <= 0.166) {
		tmp = x;
	} else if ((z <= 1.45e+228) || !(z <= 1.32e+306)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    t_1 = (-6.0d0) * (x * z)
    if (z <= (-3.5d+129)) then
        tmp = t_0
    else if (z <= (-8.5d+91)) then
        tmp = t_1
    else if (z <= (-4.4d+69)) then
        tmp = t_0
    else if (z <= (-1.25d+35)) then
        tmp = t_1
    else if (z <= (-1.55d-24)) then
        tmp = t_0
    else if (z <= 0.166d0) then
        tmp = x
    else if ((z <= 1.45d+228) .or. (.not. (z <= 1.32d+306))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -3.5e+129) {
		tmp = t_0;
	} else if (z <= -8.5e+91) {
		tmp = t_1;
	} else if (z <= -4.4e+69) {
		tmp = t_0;
	} else if (z <= -1.25e+35) {
		tmp = t_1;
	} else if (z <= -1.55e-24) {
		tmp = t_0;
	} else if (z <= 0.166) {
		tmp = x;
	} else if ((z <= 1.45e+228) || !(z <= 1.32e+306)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = -6.0 * (x * z)
	tmp = 0
	if z <= -3.5e+129:
		tmp = t_0
	elif z <= -8.5e+91:
		tmp = t_1
	elif z <= -4.4e+69:
		tmp = t_0
	elif z <= -1.25e+35:
		tmp = t_1
	elif z <= -1.55e-24:
		tmp = t_0
	elif z <= 0.166:
		tmp = x
	elif (z <= 1.45e+228) or not (z <= 1.32e+306):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -3.5e+129)
		tmp = t_0;
	elseif (z <= -8.5e+91)
		tmp = t_1;
	elseif (z <= -4.4e+69)
		tmp = t_0;
	elseif (z <= -1.25e+35)
		tmp = t_1;
	elseif (z <= -1.55e-24)
		tmp = t_0;
	elseif (z <= 0.166)
		tmp = x;
	elseif ((z <= 1.45e+228) || !(z <= 1.32e+306))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -3.5e+129)
		tmp = t_0;
	elseif (z <= -8.5e+91)
		tmp = t_1;
	elseif (z <= -4.4e+69)
		tmp = t_0;
	elseif (z <= -1.25e+35)
		tmp = t_1;
	elseif (z <= -1.55e-24)
		tmp = t_0;
	elseif (z <= 0.166)
		tmp = x;
	elseif ((z <= 1.45e+228) || ~((z <= 1.32e+306)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+129], t$95$0, If[LessEqual[z, -8.5e+91], t$95$1, If[LessEqual[z, -4.4e+69], t$95$0, If[LessEqual[z, -1.25e+35], t$95$1, If[LessEqual[z, -1.55e-24], t$95$0, If[LessEqual[z, 0.166], x, If[Or[LessEqual[z, 1.45e+228], N[Not[LessEqual[z, 1.32e+306]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999998e129 or -8.4999999999999995e91 < z < -4.4000000000000003e69 or -1.25000000000000005e35 < z < -1.55e-24 or 1.45000000000000001e228 < z < 1.32e306

   1. Initial program 99.8%

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

      1. associate-*r* 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 70.8%

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

      1. *-commutative 70.8%

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

   7. Simplified 70.8%

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

   if -3.4999999999999998e129 < z < -8.4999999999999995e91 or -4.4000000000000003e69 < z < -1.25000000000000005e35 or 0.166000000000000009 < z < 1.45000000000000001e228 or 1.32e306 < z

   1. Initial program 99.6%

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

      1. associate-*r* 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. 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* 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*l* 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around 0 65.2%

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

   if -1.55e-24 < z < 0.166000000000000009

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 73.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+129}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+91}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+69}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+35}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-24}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.166:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+228} \lor \neg \left(z \leq 1.32 \cdot 10^{+306}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot -6\right)\\ t_2 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+126}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{+67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.166:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+284}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* x (* z -6.0))) (t_2 (* -6.0 (* x z))))
   (if (<= z -1.55e+126)
     t_0
     (if (<= z -1.26e+85)
       t_2
       (if (<= z -9.4e+67)
         t_0
         (if (<= z -1.5e+37)
           t_1
           (if (<= z -1.36e-24)
             t_0
             (if (<= z 0.166)
               x
               (if (<= z 2.25e+226) t_1 (if (<= z 4.8e+284) t_0 t_2))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = x * (z * -6.0);
	double t_2 = -6.0 * (x * z);
	double tmp;
	if (z <= -1.55e+126) {
		tmp = t_0;
	} else if (z <= -1.26e+85) {
		tmp = t_2;
	} else if (z <= -9.4e+67) {
		tmp = t_0;
	} else if (z <= -1.5e+37) {
		tmp = t_1;
	} else if (z <= -1.36e-24) {
		tmp = t_0;
	} else if (z <= 0.166) {
		tmp = x;
	} else if (z <= 2.25e+226) {
		tmp = t_1;
	} else if (z <= 4.8e+284) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    t_1 = x * (z * (-6.0d0))
    t_2 = (-6.0d0) * (x * z)
    if (z <= (-1.55d+126)) then
        tmp = t_0
    else if (z <= (-1.26d+85)) then
        tmp = t_2
    else if (z <= (-9.4d+67)) then
        tmp = t_0
    else if (z <= (-1.5d+37)) then
        tmp = t_1
    else if (z <= (-1.36d-24)) then
        tmp = t_0
    else if (z <= 0.166d0) then
        tmp = x
    else if (z <= 2.25d+226) then
        tmp = t_1
    else if (z <= 4.8d+284) then
        tmp = t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = x * (z * -6.0);
	double t_2 = -6.0 * (x * z);
	double tmp;
	if (z <= -1.55e+126) {
		tmp = t_0;
	} else if (z <= -1.26e+85) {
		tmp = t_2;
	} else if (z <= -9.4e+67) {
		tmp = t_0;
	} else if (z <= -1.5e+37) {
		tmp = t_1;
	} else if (z <= -1.36e-24) {
		tmp = t_0;
	} else if (z <= 0.166) {
		tmp = x;
	} else if (z <= 2.25e+226) {
		tmp = t_1;
	} else if (z <= 4.8e+284) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = x * (z * -6.0)
	t_2 = -6.0 * (x * z)
	tmp = 0
	if z <= -1.55e+126:
		tmp = t_0
	elif z <= -1.26e+85:
		tmp = t_2
	elif z <= -9.4e+67:
		tmp = t_0
	elif z <= -1.5e+37:
		tmp = t_1
	elif z <= -1.36e-24:
		tmp = t_0
	elif z <= 0.166:
		tmp = x
	elif z <= 2.25e+226:
		tmp = t_1
	elif z <= 4.8e+284:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(x * Float64(z * -6.0))
	t_2 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1.55e+126)
		tmp = t_0;
	elseif (z <= -1.26e+85)
		tmp = t_2;
	elseif (z <= -9.4e+67)
		tmp = t_0;
	elseif (z <= -1.5e+37)
		tmp = t_1;
	elseif (z <= -1.36e-24)
		tmp = t_0;
	elseif (z <= 0.166)
		tmp = x;
	elseif (z <= 2.25e+226)
		tmp = t_1;
	elseif (z <= 4.8e+284)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = x * (z * -6.0);
	t_2 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1.55e+126)
		tmp = t_0;
	elseif (z <= -1.26e+85)
		tmp = t_2;
	elseif (z <= -9.4e+67)
		tmp = t_0;
	elseif (z <= -1.5e+37)
		tmp = t_1;
	elseif (z <= -1.36e-24)
		tmp = t_0;
	elseif (z <= 0.166)
		tmp = x;
	elseif (z <= 2.25e+226)
		tmp = t_1;
	elseif (z <= 4.8e+284)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+126], t$95$0, If[LessEqual[z, -1.26e+85], t$95$2, If[LessEqual[z, -9.4e+67], t$95$0, If[LessEqual[z, -1.5e+37], t$95$1, If[LessEqual[z, -1.36e-24], t$95$0, If[LessEqual[z, 0.166], x, If[LessEqual[z, 2.25e+226], t$95$1, If[LessEqual[z, 4.8e+284], t$95$0, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.55e126 or -1.26000000000000003e85 < z < -9.40000000000000035e67 or -1.50000000000000011e37 < z < -1.36000000000000001e-24 or 2.24999999999999995e226 < z < 4.8000000000000001e284

   1. Initial program 99.8%

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

      1. associate-*r* 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 70.8%

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

      1. *-commutative 70.8%

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

   7. Simplified 70.8%

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

   if -1.55e126 < z < -1.26000000000000003e85 or 4.8000000000000001e284 < z

   1. Initial program 100.0%

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

      1. associate-*r* 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 100.0%

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

      5. fma-def 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 100.0%

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

   if -9.40000000000000035e67 < z < -1.50000000000000011e37 or 0.166000000000000009 < z < 2.24999999999999995e226

   1. Initial program 99.5%

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

      1. associate-*r* 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. 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* 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*l* 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around 0 61.6%

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

      1. *-commutative 61.6%

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

      2. *-commutative 61.6%

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

      3. *-commutative 61.6%

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

      4. associate-*l* 61.6%

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

   10. Simplified 61.6%

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

   if -1.36000000000000001e-24 < z < 0.166000000000000009

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 73.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+126}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{+67}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-24}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.166:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+284}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot 6\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ t_2 := x \cdot \left(z \cdot -6\right)\\ t_3 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+86}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+64}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.166:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+302}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y 6.0)))
        (t_1 (* 6.0 (* y z)))
        (t_2 (* x (* z -6.0)))
        (t_3 (* -6.0 (* x z))))
   (if (<= z -2.6e+133)
     t_1
     (if (<= z -4.1e+86)
       t_3
       (if (<= z -9.5e+64)
         t_0
         (if (<= z -3.2e+35)
           t_2
           (if (<= z -1.1e-24)
             t_0
             (if (<= z 0.166)
               x
               (if (<= z 2.8e+231) t_2 (if (<= z 1.5e+302) t_1 t_3))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y * 6.0);
	double t_1 = 6.0 * (y * z);
	double t_2 = x * (z * -6.0);
	double t_3 = -6.0 * (x * z);
	double tmp;
	if (z <= -2.6e+133) {
		tmp = t_1;
	} else if (z <= -4.1e+86) {
		tmp = t_3;
	} else if (z <= -9.5e+64) {
		tmp = t_0;
	} else if (z <= -3.2e+35) {
		tmp = t_2;
	} else if (z <= -1.1e-24) {
		tmp = t_0;
	} else if (z <= 0.166) {
		tmp = x;
	} else if (z <= 2.8e+231) {
		tmp = t_2;
	} else if (z <= 1.5e+302) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = z * (y * 6.0d0)
    t_1 = 6.0d0 * (y * z)
    t_2 = x * (z * (-6.0d0))
    t_3 = (-6.0d0) * (x * z)
    if (z <= (-2.6d+133)) then
        tmp = t_1
    else if (z <= (-4.1d+86)) then
        tmp = t_3
    else if (z <= (-9.5d+64)) then
        tmp = t_0
    else if (z <= (-3.2d+35)) then
        tmp = t_2
    else if (z <= (-1.1d-24)) then
        tmp = t_0
    else if (z <= 0.166d0) then
        tmp = x
    else if (z <= 2.8d+231) then
        tmp = t_2
    else if (z <= 1.5d+302) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y * 6.0);
	double t_1 = 6.0 * (y * z);
	double t_2 = x * (z * -6.0);
	double t_3 = -6.0 * (x * z);
	double tmp;
	if (z <= -2.6e+133) {
		tmp = t_1;
	} else if (z <= -4.1e+86) {
		tmp = t_3;
	} else if (z <= -9.5e+64) {
		tmp = t_0;
	} else if (z <= -3.2e+35) {
		tmp = t_2;
	} else if (z <= -1.1e-24) {
		tmp = t_0;
	} else if (z <= 0.166) {
		tmp = x;
	} else if (z <= 2.8e+231) {
		tmp = t_2;
	} else if (z <= 1.5e+302) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y * 6.0)
	t_1 = 6.0 * (y * z)
	t_2 = x * (z * -6.0)
	t_3 = -6.0 * (x * z)
	tmp = 0
	if z <= -2.6e+133:
		tmp = t_1
	elif z <= -4.1e+86:
		tmp = t_3
	elif z <= -9.5e+64:
		tmp = t_0
	elif z <= -3.2e+35:
		tmp = t_2
	elif z <= -1.1e-24:
		tmp = t_0
	elif z <= 0.166:
		tmp = x
	elif z <= 2.8e+231:
		tmp = t_2
	elif z <= 1.5e+302:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y * 6.0))
	t_1 = Float64(6.0 * Float64(y * z))
	t_2 = Float64(x * Float64(z * -6.0))
	t_3 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.6e+133)
		tmp = t_1;
	elseif (z <= -4.1e+86)
		tmp = t_3;
	elseif (z <= -9.5e+64)
		tmp = t_0;
	elseif (z <= -3.2e+35)
		tmp = t_2;
	elseif (z <= -1.1e-24)
		tmp = t_0;
	elseif (z <= 0.166)
		tmp = x;
	elseif (z <= 2.8e+231)
		tmp = t_2;
	elseif (z <= 1.5e+302)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y * 6.0);
	t_1 = 6.0 * (y * z);
	t_2 = x * (z * -6.0);
	t_3 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.6e+133)
		tmp = t_1;
	elseif (z <= -4.1e+86)
		tmp = t_3;
	elseif (z <= -9.5e+64)
		tmp = t_0;
	elseif (z <= -3.2e+35)
		tmp = t_2;
	elseif (z <= -1.1e-24)
		tmp = t_0;
	elseif (z <= 0.166)
		tmp = x;
	elseif (z <= 2.8e+231)
		tmp = t_2;
	elseif (z <= 1.5e+302)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+133], t$95$1, If[LessEqual[z, -4.1e+86], t$95$3, If[LessEqual[z, -9.5e+64], t$95$0, If[LessEqual[z, -3.2e+35], t$95$2, If[LessEqual[z, -1.1e-24], t$95$0, If[LessEqual[z, 0.166], x, If[LessEqual[z, 2.8e+231], t$95$2, If[LessEqual[z, 1.5e+302], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.5999999999999998e133 or 2.8e231 < z < 1.4999999999999999e302

   1. Initial program 99.9%

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

      1. associate-*r* 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.9%

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

      5. fma-def 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf 67.1%

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

      1. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   if -2.5999999999999998e133 < z < -4.0999999999999999e86 or 1.4999999999999999e302 < z

   1. Initial program 100.0%

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

      1. associate-*r* 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 100.0%

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

      5. fma-def 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 100.0%

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

   if -4.0999999999999999e86 < z < -9.50000000000000028e64 or -3.19999999999999983e35 < z < -1.10000000000000001e-24

   1. Initial program 99.7%

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

      1. associate-*r* 99.5%

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

      2. +-commutative 99.5%

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

      3. *-commutative 99.5%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in y around inf 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-*r* 78.7%

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

      3. *-commutative 78.7%

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

      4. associate-*r* 78.9%

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

   7. Simplified 78.9%

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

   if -9.50000000000000028e64 < z < -3.19999999999999983e35 or 0.166000000000000009 < z < 2.8e231

   1. Initial program 99.5%

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

      1. associate-*r* 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. 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* 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*l* 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around 0 61.6%

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

      1. *-commutative 61.6%

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

      2. *-commutative 61.6%

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

      3. *-commutative 61.6%

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

      4. associate-*l* 61.6%

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

   10. Simplified 61.6%

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

   if -1.10000000000000001e-24 < z < 0.166000000000000009

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 73.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+133}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+86}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.166:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+231}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+302}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-25} \lor \neg \left(z \leq 1.3 \cdot 10^{-42}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.6e-25) (not (<= z 1.3e-42))) (* 6.0 (* (- y x) z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.6e-25) || !(z <= 1.3e-42)) {
		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 <= (-1.6d-25)) .or. (.not. (z <= 1.3d-42))) 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 <= -1.6e-25) || !(z <= 1.3e-42)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.6e-25) or not (z <= 1.3e-42):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.6e-25) || !(z <= 1.3e-42))
		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 <= -1.6e-25) || ~((z <= 1.3e-42)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.6e-25], N[Not[LessEqual[z, 1.3e-42]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.6000000000000001e-25 or 1.3e-42 < z

   1. Initial program 99.7%

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

      1. associate-*r* 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 94.9%

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

   if -1.6000000000000001e-25 < z < 1.3e-42

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 75.5%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-25} \lor \neg \left(z \leq 1.3 \cdot 10^{-42}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 0.166)))
   (* 6.0 (* (- y x) z))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.166)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.165d0)) .or. (.not. (z <= 0.166d0))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x + (6.0d0 * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.166)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 0.166):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 0.166))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.165) || ~((z <= 0.166)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 0.166]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 0.166000000000000009 < z

   1. Initial program 99.7%

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

      1. associate-*r* 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 99.2%

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

   if -0.165000000000000008 < z < 0.166000000000000009

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 98.3%

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

      1. *-commutative 98.3%

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

   5. Simplified 98.3%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.15 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.15) (not (<= z 0.166)))
   (* 6.0 (* (- y x) z))
   (+ x (* z (* y 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.15) || !(z <= 0.166)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.15d0)) .or. (.not. (z <= 0.166d0))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x + (z * (y * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.15) || !(z <= 0.166)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.15) or not (z <= 0.166):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x + (z * (y * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.15) || !(z <= 0.166))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.15) || ~((z <= 0.166)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x + (z * (y * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.15], N[Not[LessEqual[z, 0.166]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.149999999999999994 or 0.166000000000000009 < z

   1. Initial program 99.7%

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

      1. associate-*r* 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 99.2%

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

   if -0.149999999999999994 < z < 0.166000000000000009

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 98.3%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.15 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.12e-24)
   (* z (* (- y x) 6.0))
   (if (<= z 3.7e-32) x (* 6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.12e-24) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 3.7e-32) {
		tmp = x;
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.12d-24)) then
        tmp = z * ((y - x) * 6.0d0)
    else if (z <= 3.7d-32) then
        tmp = x
    else
        tmp = 6.0d0 * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.12e-24) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 3.7e-32) {
		tmp = x;
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.12e-24:
		tmp = z * ((y - x) * 6.0)
	elif z <= 3.7e-32:
		tmp = x
	else:
		tmp = 6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.12e-24)
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	elseif (z <= 3.7e-32)
		tmp = x;
	else
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.12e-24)
		tmp = z * ((y - x) * 6.0);
	elseif (z <= 3.7e-32)
		tmp = x;
	else
		tmp = 6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.12e-24], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-32], x, N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.11999999999999995e-24

   1. Initial program 99.8%

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

      1. associate-*r* 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 95.4%

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

      1. associate-*r* 95.4%

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

      2. *-commutative 95.4%

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

      3. associate-*l* 95.4%

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

   7. Simplified 95.4%

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

   if -1.11999999999999995e-24 < z < 3.7e-32

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 75.5%

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

   if 3.7e-32 < z

   1. Initial program 99.6%

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

      1. associate-*r* 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 94.5%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+15}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.5e-24)
   (* z (* (- y x) 6.0))
   (if (<= z 1.75e+15) (+ x (* -6.0 (* x z))) (* 6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e-24) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 1.75e+15) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.5d-24)) then
        tmp = z * ((y - x) * 6.0d0)
    else if (z <= 1.75d+15) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = 6.0d0 * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e-24) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 1.75e+15) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.5e-24:
		tmp = z * ((y - x) * 6.0)
	elif z <= 1.75e+15:
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = 6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.5e-24)
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	elseif (z <= 1.75e+15)
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.5e-24)
		tmp = z * ((y - x) * 6.0);
	elseif (z <= 1.75e+15)
		tmp = x + (-6.0 * (x * z));
	else
		tmp = 6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.5e-24], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+15], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.49999999999999998e-24

   1. Initial program 99.8%

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

      1. associate-*r* 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 95.4%

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

      1. associate-*r* 95.4%

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

      2. *-commutative 95.4%

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

      3. associate-*l* 95.4%

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

   7. Simplified 95.4%

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

   if -1.49999999999999998e-24 < z < 1.75e15

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 74.6%

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

   if 1.75e15 < z

   1. Initial program 99.6%

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

      1. associate-*r* 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+15}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 0.166))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.166)) {
		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 <= (-0.165d0)) .or. (.not. (z <= 0.166d0))) 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 <= -0.165) || !(z <= 0.166)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 0.166):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 0.166))
		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 <= -0.165) || ~((z <= 0.166)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 0.166]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 0.166000000000000009 < z

   1. Initial program 99.7%

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

      1. associate-*r* 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 99.2%

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

      1. associate-*r* 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*l* 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in y around 0 51.5%

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

   if -0.165000000000000008 < z < 0.166000000000000009

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 70.2%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 99.4%

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

3. Taylor expanded in z around 0 99.8%

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

4. Final simplification 99.8%

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

Alternative 12: 36.7% 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 99.4%

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

3. Taylor expanded in z around 0 39.0%

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

4. Final simplification 39.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024024 
(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)))