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

Percentage Accurate: 99.8% → 99.8%

Time: 10.1s

Alternatives: 15

Speedup: 1.0×

• 21.1% 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: 99.8% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. *-commutative 99.8%

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

   3. fma-define 99.8%

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

   4. remove-double-neg 99.8%

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

   5. distribute-lft-neg-in 99.8%

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

   6. distribute-rgt-neg-in 99.8%

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

   7. sub-neg 99.8%

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

   8. distribute-neg-in 99.8%

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

   9. remove-double-neg 99.8%

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

   10. +-commutative 99.8%

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

   11. sub-neg 99.8%

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

   12. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 60.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot x\right)\\ t_1 := 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+214}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+44}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.235 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+58} \lor \neg \left(z \leq 8.2 \cdot 10^{+148}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z x))) (t_1 (* 6.0 (* z y))))
   (if (<= z -1.2e+214)
     t_0
     (if (<= z -3.8e+108)
       t_1
       (if (<= z -5.5e+44)
         t_0
         (if (<= z -1.235e-89)
           t_1
           (if (<= z 0.17)
             x
             (if (or (<= z 6e+58) (not (<= z 8.2e+148))) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * x);
	double t_1 = 6.0 * (z * y);
	double tmp;
	if (z <= -1.2e+214) {
		tmp = t_0;
	} else if (z <= -3.8e+108) {
		tmp = t_1;
	} else if (z <= -5.5e+44) {
		tmp = t_0;
	} else if (z <= -1.235e-89) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 6e+58) || !(z <= 8.2e+148)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) * (z * x)
    t_1 = 6.0d0 * (z * y)
    if (z <= (-1.2d+214)) then
        tmp = t_0
    else if (z <= (-3.8d+108)) then
        tmp = t_1
    else if (z <= (-5.5d+44)) then
        tmp = t_0
    else if (z <= (-1.235d-89)) then
        tmp = t_1
    else if (z <= 0.17d0) then
        tmp = x
    else if ((z <= 6d+58) .or. (.not. (z <= 8.2d+148))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * x);
	double t_1 = 6.0 * (z * y);
	double tmp;
	if (z <= -1.2e+214) {
		tmp = t_0;
	} else if (z <= -3.8e+108) {
		tmp = t_1;
	} else if (z <= -5.5e+44) {
		tmp = t_0;
	} else if (z <= -1.235e-89) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 6e+58) || !(z <= 8.2e+148)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * x)
	t_1 = 6.0 * (z * y)
	tmp = 0
	if z <= -1.2e+214:
		tmp = t_0
	elif z <= -3.8e+108:
		tmp = t_1
	elif z <= -5.5e+44:
		tmp = t_0
	elif z <= -1.235e-89:
		tmp = t_1
	elif z <= 0.17:
		tmp = x
	elif (z <= 6e+58) or not (z <= 8.2e+148):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * x))
	t_1 = Float64(6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -1.2e+214)
		tmp = t_0;
	elseif (z <= -3.8e+108)
		tmp = t_1;
	elseif (z <= -5.5e+44)
		tmp = t_0;
	elseif (z <= -1.235e-89)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 6e+58) || !(z <= 8.2e+148))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * x);
	t_1 = 6.0 * (z * y);
	tmp = 0.0;
	if (z <= -1.2e+214)
		tmp = t_0;
	elseif (z <= -3.8e+108)
		tmp = t_1;
	elseif (z <= -5.5e+44)
		tmp = t_0;
	elseif (z <= -1.235e-89)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 6e+58) || ~((z <= 8.2e+148)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+214], t$95$0, If[LessEqual[z, -3.8e+108], t$95$1, If[LessEqual[z, -5.5e+44], t$95$0, If[LessEqual[z, -1.235e-89], t$95$1, If[LessEqual[z, 0.17], x, If[Or[LessEqual[z, 6e+58], N[Not[LessEqual[z, 8.2e+148]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e214 or -3.80000000000000008e108 < z < -5.5000000000000001e44 or 0.170000000000000012 < z < 6.0000000000000005e58 or 8.1999999999999996e148 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 72.5%

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

      1. +-commutative 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in z around inf 69.2%

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

   if -1.2e214 < z < -3.80000000000000008e108 or -5.5000000000000001e44 < z < -1.235e-89 or 6.0000000000000005e58 < z < 8.1999999999999996e148

   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* 99.6%

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

      5. fma-define 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 65.1%

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

      1. *-commutative 65.1%

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

   7. Simplified 65.1%

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

   if -1.235e-89 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+214}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+108}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+44}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -1.235 \cdot 10^{-89}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+58} \lor \neg \left(z \leq 8.2 \cdot 10^{+148}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot x\right)\\ t_1 := 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+213}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.235 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+56} \lor \neg \left(z \leq 8.4 \cdot 10^{+148}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z x))) (t_1 (* 6.0 (* z y))))
   (if (<= z -6.5e+213)
     t_0
     (if (<= z -5.5e+142)
       t_1
       (if (<= z -4.6e+44)
         (* x (* z -6.0))
         (if (<= z -1.235e-89)
           t_1
           (if (<= z 0.17)
             x
             (if (or (<= z 3.2e+56) (not (<= z 8.4e+148))) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * x);
	double t_1 = 6.0 * (z * y);
	double tmp;
	if (z <= -6.5e+213) {
		tmp = t_0;
	} else if (z <= -5.5e+142) {
		tmp = t_1;
	} else if (z <= -4.6e+44) {
		tmp = x * (z * -6.0);
	} else if (z <= -1.235e-89) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 3.2e+56) || !(z <= 8.4e+148)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) * (z * x)
    t_1 = 6.0d0 * (z * y)
    if (z <= (-6.5d+213)) then
        tmp = t_0
    else if (z <= (-5.5d+142)) then
        tmp = t_1
    else if (z <= (-4.6d+44)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= (-1.235d-89)) then
        tmp = t_1
    else if (z <= 0.17d0) then
        tmp = x
    else if ((z <= 3.2d+56) .or. (.not. (z <= 8.4d+148))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * x);
	double t_1 = 6.0 * (z * y);
	double tmp;
	if (z <= -6.5e+213) {
		tmp = t_0;
	} else if (z <= -5.5e+142) {
		tmp = t_1;
	} else if (z <= -4.6e+44) {
		tmp = x * (z * -6.0);
	} else if (z <= -1.235e-89) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 3.2e+56) || !(z <= 8.4e+148)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * x)
	t_1 = 6.0 * (z * y)
	tmp = 0
	if z <= -6.5e+213:
		tmp = t_0
	elif z <= -5.5e+142:
		tmp = t_1
	elif z <= -4.6e+44:
		tmp = x * (z * -6.0)
	elif z <= -1.235e-89:
		tmp = t_1
	elif z <= 0.17:
		tmp = x
	elif (z <= 3.2e+56) or not (z <= 8.4e+148):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * x))
	t_1 = Float64(6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -6.5e+213)
		tmp = t_0;
	elseif (z <= -5.5e+142)
		tmp = t_1;
	elseif (z <= -4.6e+44)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= -1.235e-89)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 3.2e+56) || !(z <= 8.4e+148))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * x);
	t_1 = 6.0 * (z * y);
	tmp = 0.0;
	if (z <= -6.5e+213)
		tmp = t_0;
	elseif (z <= -5.5e+142)
		tmp = t_1;
	elseif (z <= -4.6e+44)
		tmp = x * (z * -6.0);
	elseif (z <= -1.235e-89)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 3.2e+56) || ~((z <= 8.4e+148)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+213], t$95$0, If[LessEqual[z, -5.5e+142], t$95$1, If[LessEqual[z, -4.6e+44], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.235e-89], t$95$1, If[LessEqual[z, 0.17], x, If[Or[LessEqual[z, 3.2e+56], N[Not[LessEqual[z, 8.4e+148]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.49999999999999982e213 or 0.170000000000000012 < z < 3.20000000000000003e56 or 8.39999999999999996e148 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 72.2%

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

      1. +-commutative 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in z around inf 68.4%

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

   if -6.49999999999999982e213 < z < -5.50000000000000035e142 or -4.60000000000000009e44 < z < -1.235e-89 or 3.20000000000000003e56 < z < 8.39999999999999996e148

   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* 99.6%

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

      5. fma-define 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in y around inf 65.9%

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

      1. *-commutative 65.9%

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

   7. Simplified 65.9%

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

   if -5.50000000000000035e142 < z < -4.60000000000000009e44

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 67.8%

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

      1. +-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in z around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*r* 67.8%

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

      3. *-commutative 67.8%

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

   8. Simplified 67.8%

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

   if -1.235e-89 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+213}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+142}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.235 \cdot 10^{-89}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+56} \lor \neg \left(z \leq 8.4 \cdot 10^{+148}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot x\right)\\ t_1 := 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+214}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.235 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+57} \lor \neg \left(z \leq 2.9 \cdot 10^{+149}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z x))) (t_1 (* 6.0 (* z y))))
   (if (<= z -3.4e+214)
     t_0
     (if (<= z -9.4e+142)
       t_1
       (if (<= z -1.2e+45)
         (* x (* z -6.0))
         (if (<= z -1.235e-89)
           (* y (* z 6.0))
           (if (<= z 0.17)
             x
             (if (or (<= z 8.5e+57) (not (<= z 2.9e+149))) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * x);
	double t_1 = 6.0 * (z * y);
	double tmp;
	if (z <= -3.4e+214) {
		tmp = t_0;
	} else if (z <= -9.4e+142) {
		tmp = t_1;
	} else if (z <= -1.2e+45) {
		tmp = x * (z * -6.0);
	} else if (z <= -1.235e-89) {
		tmp = y * (z * 6.0);
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 8.5e+57) || !(z <= 2.9e+149)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) * (z * x)
    t_1 = 6.0d0 * (z * y)
    if (z <= (-3.4d+214)) then
        tmp = t_0
    else if (z <= (-9.4d+142)) then
        tmp = t_1
    else if (z <= (-1.2d+45)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= (-1.235d-89)) then
        tmp = y * (z * 6.0d0)
    else if (z <= 0.17d0) then
        tmp = x
    else if ((z <= 8.5d+57) .or. (.not. (z <= 2.9d+149))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * x);
	double t_1 = 6.0 * (z * y);
	double tmp;
	if (z <= -3.4e+214) {
		tmp = t_0;
	} else if (z <= -9.4e+142) {
		tmp = t_1;
	} else if (z <= -1.2e+45) {
		tmp = x * (z * -6.0);
	} else if (z <= -1.235e-89) {
		tmp = y * (z * 6.0);
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 8.5e+57) || !(z <= 2.9e+149)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * x)
	t_1 = 6.0 * (z * y)
	tmp = 0
	if z <= -3.4e+214:
		tmp = t_0
	elif z <= -9.4e+142:
		tmp = t_1
	elif z <= -1.2e+45:
		tmp = x * (z * -6.0)
	elif z <= -1.235e-89:
		tmp = y * (z * 6.0)
	elif z <= 0.17:
		tmp = x
	elif (z <= 8.5e+57) or not (z <= 2.9e+149):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * x))
	t_1 = Float64(6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -3.4e+214)
		tmp = t_0;
	elseif (z <= -9.4e+142)
		tmp = t_1;
	elseif (z <= -1.2e+45)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= -1.235e-89)
		tmp = Float64(y * Float64(z * 6.0));
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 8.5e+57) || !(z <= 2.9e+149))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * x);
	t_1 = 6.0 * (z * y);
	tmp = 0.0;
	if (z <= -3.4e+214)
		tmp = t_0;
	elseif (z <= -9.4e+142)
		tmp = t_1;
	elseif (z <= -1.2e+45)
		tmp = x * (z * -6.0);
	elseif (z <= -1.235e-89)
		tmp = y * (z * 6.0);
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 8.5e+57) || ~((z <= 2.9e+149)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+214], t$95$0, If[LessEqual[z, -9.4e+142], t$95$1, If[LessEqual[z, -1.2e+45], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.235e-89], N[(y * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], x, If[Or[LessEqual[z, 8.5e+57], N[Not[LessEqual[z, 2.9e+149]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.3999999999999998e214 or 0.170000000000000012 < z < 8.5000000000000001e57 or 2.9000000000000002e149 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 72.2%

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

      1. +-commutative 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in z around inf 68.4%

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

   if -3.3999999999999998e214 < z < -9.4e142 or 8.5000000000000001e57 < z < 2.9000000000000002e149

   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* 99.7%

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

      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* 99.7%

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

      5. fma-define 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 69.1%

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

      1. *-commutative 69.1%

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

   7. Simplified 69.1%

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

   if -9.4e142 < z < -1.19999999999999995e45

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 67.8%

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

      1. +-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in z around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*r* 67.8%

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

      3. *-commutative 67.8%

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

   8. Simplified 67.8%

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

   if -1.19999999999999995e45 < z < -1.235e-89

   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* 99.4%

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

      5. fma-define 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in y around inf 81.8%

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

      1. *-commutative 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in z around inf 60.7%

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

      1. associate-*r* 61.1%

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

      2. *-commutative 61.1%

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

      3. associate-*r* 61.0%

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

   10. Simplified 61.0%

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

   if -1.235e-89 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.3%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+214}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{+142}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.235 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+57} \lor \neg \left(z \leq 2.9 \cdot 10^{+149}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot x\right)\\ t_1 := 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+216}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.235 \cdot 10^{-89}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+55} \lor \neg \left(z \leq 7 \cdot 10^{+149}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z x))) (t_1 (* 6.0 (* z y))))
   (if (<= z -1.75e+216)
     t_0
     (if (<= z -5.2e+143)
       t_1
       (if (<= z -5.5e+44)
         (* x (* z -6.0))
         (if (<= z -1.235e-89)
           (* z (* y 6.0))
           (if (<= z 0.17)
             x
             (if (or (<= z 2.15e+55) (not (<= z 7e+149))) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * x);
	double t_1 = 6.0 * (z * y);
	double tmp;
	if (z <= -1.75e+216) {
		tmp = t_0;
	} else if (z <= -5.2e+143) {
		tmp = t_1;
	} else if (z <= -5.5e+44) {
		tmp = x * (z * -6.0);
	} else if (z <= -1.235e-89) {
		tmp = z * (y * 6.0);
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 2.15e+55) || !(z <= 7e+149)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) * (z * x)
    t_1 = 6.0d0 * (z * y)
    if (z <= (-1.75d+216)) then
        tmp = t_0
    else if (z <= (-5.2d+143)) then
        tmp = t_1
    else if (z <= (-5.5d+44)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= (-1.235d-89)) then
        tmp = z * (y * 6.0d0)
    else if (z <= 0.17d0) then
        tmp = x
    else if ((z <= 2.15d+55) .or. (.not. (z <= 7d+149))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * x);
	double t_1 = 6.0 * (z * y);
	double tmp;
	if (z <= -1.75e+216) {
		tmp = t_0;
	} else if (z <= -5.2e+143) {
		tmp = t_1;
	} else if (z <= -5.5e+44) {
		tmp = x * (z * -6.0);
	} else if (z <= -1.235e-89) {
		tmp = z * (y * 6.0);
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 2.15e+55) || !(z <= 7e+149)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * x)
	t_1 = 6.0 * (z * y)
	tmp = 0
	if z <= -1.75e+216:
		tmp = t_0
	elif z <= -5.2e+143:
		tmp = t_1
	elif z <= -5.5e+44:
		tmp = x * (z * -6.0)
	elif z <= -1.235e-89:
		tmp = z * (y * 6.0)
	elif z <= 0.17:
		tmp = x
	elif (z <= 2.15e+55) or not (z <= 7e+149):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * x))
	t_1 = Float64(6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -1.75e+216)
		tmp = t_0;
	elseif (z <= -5.2e+143)
		tmp = t_1;
	elseif (z <= -5.5e+44)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= -1.235e-89)
		tmp = Float64(z * Float64(y * 6.0));
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 2.15e+55) || !(z <= 7e+149))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * x);
	t_1 = 6.0 * (z * y);
	tmp = 0.0;
	if (z <= -1.75e+216)
		tmp = t_0;
	elseif (z <= -5.2e+143)
		tmp = t_1;
	elseif (z <= -5.5e+44)
		tmp = x * (z * -6.0);
	elseif (z <= -1.235e-89)
		tmp = z * (y * 6.0);
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 2.15e+55) || ~((z <= 7e+149)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+216], t$95$0, If[LessEqual[z, -5.2e+143], t$95$1, If[LessEqual[z, -5.5e+44], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.235e-89], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], x, If[Or[LessEqual[z, 2.15e+55], N[Not[LessEqual[z, 7e+149]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.74999999999999996e216 or 0.170000000000000012 < z < 2.1499999999999999e55 or 7.00000000000000023e149 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 72.2%

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

      1. +-commutative 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in z around inf 68.4%

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

   if -1.74999999999999996e216 < z < -5.1999999999999998e143 or 2.1499999999999999e55 < z < 7.00000000000000023e149

   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* 99.7%

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

      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* 99.7%

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

      5. fma-define 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 69.1%

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

      1. *-commutative 69.1%

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

   7. Simplified 69.1%

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

   if -5.1999999999999998e143 < z < -5.5000000000000001e44

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 67.8%

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

      1. +-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in z around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*r* 67.8%

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

      3. *-commutative 67.8%

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

   8. Simplified 67.8%

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

   if -5.5000000000000001e44 < z < -1.235e-89

   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* 99.4%

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

      5. fma-define 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in y around inf 60.7%

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

      1. associate-*r* 61.1%

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

      2. *-commutative 61.1%

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

   7. Simplified 61.1%

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

   if -1.235e-89 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.3%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+216}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+143}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.235 \cdot 10^{-89}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+55} \lor \neg \left(z \leq 7 \cdot 10^{+149}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+214}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+141}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.235 \cdot 10^{-89}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+59} \lor \neg \left(z \leq 1.1 \cdot 10^{+150}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z y))))
   (if (<= z -5e+214)
     (* z (* x -6.0))
     (if (<= z -3.6e+141)
       t_0
       (if (<= z -1e+45)
         (* x (* z -6.0))
         (if (<= z -1.235e-89)
           (* z (* y 6.0))
           (if (<= z 0.17)
             x
             (if (or (<= z 1.8e+59) (not (<= z 1.1e+150)))
               (* -6.0 (* z x))
               t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double tmp;
	if (z <= -5e+214) {
		tmp = z * (x * -6.0);
	} else if (z <= -3.6e+141) {
		tmp = t_0;
	} else if (z <= -1e+45) {
		tmp = x * (z * -6.0);
	} else if (z <= -1.235e-89) {
		tmp = z * (y * 6.0);
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 1.8e+59) || !(z <= 1.1e+150)) {
		tmp = -6.0 * (z * x);
	} 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) :: tmp
    t_0 = 6.0d0 * (z * y)
    if (z <= (-5d+214)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= (-3.6d+141)) then
        tmp = t_0
    else if (z <= (-1d+45)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= (-1.235d-89)) then
        tmp = z * (y * 6.0d0)
    else if (z <= 0.17d0) then
        tmp = x
    else if ((z <= 1.8d+59) .or. (.not. (z <= 1.1d+150))) then
        tmp = (-6.0d0) * (z * x)
    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 * (z * y);
	double tmp;
	if (z <= -5e+214) {
		tmp = z * (x * -6.0);
	} else if (z <= -3.6e+141) {
		tmp = t_0;
	} else if (z <= -1e+45) {
		tmp = x * (z * -6.0);
	} else if (z <= -1.235e-89) {
		tmp = z * (y * 6.0);
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 1.8e+59) || !(z <= 1.1e+150)) {
		tmp = -6.0 * (z * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (z * y)
	tmp = 0
	if z <= -5e+214:
		tmp = z * (x * -6.0)
	elif z <= -3.6e+141:
		tmp = t_0
	elif z <= -1e+45:
		tmp = x * (z * -6.0)
	elif z <= -1.235e-89:
		tmp = z * (y * 6.0)
	elif z <= 0.17:
		tmp = x
	elif (z <= 1.8e+59) or not (z <= 1.1e+150):
		tmp = -6.0 * (z * x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -5e+214)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= -3.6e+141)
		tmp = t_0;
	elseif (z <= -1e+45)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= -1.235e-89)
		tmp = Float64(z * Float64(y * 6.0));
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 1.8e+59) || !(z <= 1.1e+150))
		tmp = Float64(-6.0 * Float64(z * x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (z * y);
	tmp = 0.0;
	if (z <= -5e+214)
		tmp = z * (x * -6.0);
	elseif (z <= -3.6e+141)
		tmp = t_0;
	elseif (z <= -1e+45)
		tmp = x * (z * -6.0);
	elseif (z <= -1.235e-89)
		tmp = z * (y * 6.0);
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 1.8e+59) || ~((z <= 1.1e+150)))
		tmp = -6.0 * (z * x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+214], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e+141], t$95$0, If[LessEqual[z, -1e+45], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.235e-89], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], x, If[Or[LessEqual[z, 1.8e+59], N[Not[LessEqual[z, 1.1e+150]], $MachinePrecision]], N[(-6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.99999999999999953e214

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.2%

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

      1. +-commutative 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in z around inf 80.2%

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

      1. associate-*r* 80.3%

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

      2. *-commutative 80.3%

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

   8. Simplified 80.3%

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

   if -4.99999999999999953e214 < z < -3.6000000000000001e141 or 1.7999999999999999e59 < z < 1.1e150

   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* 99.7%

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

      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* 99.7%

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

      5. fma-define 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 69.1%

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

      1. *-commutative 69.1%

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

   7. Simplified 69.1%

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

   if -3.6000000000000001e141 < z < -9.9999999999999993e44

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 67.8%

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

      1. +-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in z around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*r* 67.8%

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

      3. *-commutative 67.8%

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

   8. Simplified 67.8%

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

   if -9.9999999999999993e44 < z < -1.235e-89

   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* 99.4%

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

      5. fma-define 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in y around inf 60.7%

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

      1. associate-*r* 61.1%

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

      2. *-commutative 61.1%

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

   7. Simplified 61.1%

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

   if -1.235e-89 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.3%

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

   if 0.170000000000000012 < z < 1.7999999999999999e59 or 1.1e150 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 68.2%

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

      1. +-commutative 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in z around inf 62.4%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+214}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+141}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.235 \cdot 10^{-89}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+59} \lor \neg \left(z \leq 1.1 \cdot 10^{+150}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot x}{z}\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+176}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{+111}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-14} \lor \neg \left(x \leq 3.25 \cdot 10^{-18}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z x) z)))
   (if (<= x -1.2e+176)
     t_0
     (if (<= x -4.1e+111)
       (* -6.0 (* z x))
       (if (or (<= x -1.05e-14) (not (<= x 3.25e-18))) t_0 (* z (* y 6.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * x) / z;
	double tmp;
	if (x <= -1.2e+176) {
		tmp = t_0;
	} else if (x <= -4.1e+111) {
		tmp = -6.0 * (z * x);
	} else if ((x <= -1.05e-14) || !(x <= 3.25e-18)) {
		tmp = t_0;
	} else {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = (z * x) / z
    if (x <= (-1.2d+176)) then
        tmp = t_0
    else if (x <= (-4.1d+111)) then
        tmp = (-6.0d0) * (z * x)
    else if ((x <= (-1.05d-14)) .or. (.not. (x <= 3.25d-18))) then
        tmp = t_0
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * x) / z;
	double tmp;
	if (x <= -1.2e+176) {
		tmp = t_0;
	} else if (x <= -4.1e+111) {
		tmp = -6.0 * (z * x);
	} else if ((x <= -1.05e-14) || !(x <= 3.25e-18)) {
		tmp = t_0;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * x) / z
	tmp = 0
	if x <= -1.2e+176:
		tmp = t_0
	elif x <= -4.1e+111:
		tmp = -6.0 * (z * x)
	elif (x <= -1.05e-14) or not (x <= 3.25e-18):
		tmp = t_0
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * x) / z)
	tmp = 0.0
	if (x <= -1.2e+176)
		tmp = t_0;
	elseif (x <= -4.1e+111)
		tmp = Float64(-6.0 * Float64(z * x));
	elseif ((x <= -1.05e-14) || !(x <= 3.25e-18))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * x) / z;
	tmp = 0.0;
	if (x <= -1.2e+176)
		tmp = t_0;
	elseif (x <= -4.1e+111)
		tmp = -6.0 * (z * x);
	elseif ((x <= -1.05e-14) || ~((x <= 3.25e-18)))
		tmp = t_0;
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -1.2e+176], t$95$0, If[LessEqual[x, -4.1e+111], N[(-6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.05e-14], N[Not[LessEqual[x, 3.25e-18]], $MachinePrecision]], t$95$0, N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2000000000000001e176 or -4.09999999999999986e111 < x < -1.0499999999999999e-14 or 3.25000000000000004e-18 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 79.8%

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

   4. Taylor expanded in z around 0 29.7%

      \[\leadsto z \cdot \color{blue}{\frac{x}{z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 64.2%

         \[\leadsto \color{blue}{\frac{z \cdot x}{z}} \]

   6. Applied egg-rr 64.2%

      \[\leadsto \color{blue}{\frac{z \cdot x}{z}} \]

   if -1.2000000000000001e176 < x < -4.09999999999999986e111

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 81.2%

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

      1. +-commutative 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in z around inf 50.8%

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

   if -1.0499999999999999e-14 < x < 3.25000000000000004e-18

   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* 99.7%

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

      5. fma-define 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 68.8%

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

      1. associate-*r* 68.8%

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

      2. *-commutative 68.8%

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

   7. Simplified 68.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+176}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{+111}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-14} \lor \neg \left(x \leq 3.25 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.235 \cdot 10^{-89} \lor \neg \left(z \leq 6.4 \cdot 10^{-6}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.235e-89) (not (<= z 6.4e-6))) (* -6.0 (* z (- x y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.235e-89) || !(z <= 6.4e-6)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.235d-89)) .or. (.not. (z <= 6.4d-6))) then
        tmp = (-6.0d0) * (z * (x - y))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.235e-89) || !(z <= 6.4e-6)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.235e-89) or not (z <= 6.4e-6):
		tmp = -6.0 * (z * (x - y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.235e-89) || !(z <= 6.4e-6))
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.235e-89) || ~((z <= 6.4e-6)))
		tmp = -6.0 * (z * (x - y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.235e-89], N[Not[LessEqual[z, 6.4e-6]], $MachinePrecision]], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.235e-89 or 6.3999999999999997e-6 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-define 99.7%

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

      4. remove-double-neg 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. +-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 92.8%

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

   if -1.235e-89 < z < 6.3999999999999997e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 73.2%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.235 \cdot 10^{-89} \lor \neg \left(z \leq 6.4 \cdot 10^{-6}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.235 \cdot 10^{-89} \lor \neg \left(z \leq 12000000000000\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.235e-89) (not (<= z 12000000000000.0)))
   (* -6.0 (* z (- x y)))
   (* x (+ (* z -6.0) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.235e-89) || !(z <= 12000000000000.0)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.235d-89)) .or. (.not. (z <= 12000000000000.0d0))) then
        tmp = (-6.0d0) * (z * (x - y))
    else
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.235e-89) || !(z <= 12000000000000.0)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.235e-89) or not (z <= 12000000000000.0):
		tmp = -6.0 * (z * (x - y))
	else:
		tmp = x * ((z * -6.0) + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.235e-89) || !(z <= 12000000000000.0))
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	else
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.235e-89) || ~((z <= 12000000000000.0)))
		tmp = -6.0 * (z * (x - y));
	else
		tmp = x * ((z * -6.0) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.235e-89], N[Not[LessEqual[z, 12000000000000.0]], $MachinePrecision]], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.235e-89 or 1.2e13 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-define 99.7%

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

      4. remove-double-neg 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. +-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 94.9%

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

   if -1.235e-89 < z < 1.2e13

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 75.5%

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

      1. +-commutative 75.5%

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

   5. Simplified 75.5%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.235 \cdot 10^{-89} \lor \neg \left(z \leq 12000000000000\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.235 \cdot 10^{-89}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 12000000000000:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.235e-89)
   (* (- y x) (* z 6.0))
   (if (<= z 12000000000000.0)
     (* x (+ (* z -6.0) 1.0))
     (* -6.0 (* z (- x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.235e-89) {
		tmp = (y - x) * (z * 6.0);
	} else if (z <= 12000000000000.0) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = -6.0 * (z * (x - y));
	}
	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 <= (-1.235d-89)) then
        tmp = (y - x) * (z * 6.0d0)
    else if (z <= 12000000000000.0d0) then
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    else
        tmp = (-6.0d0) * (z * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.235e-89) {
		tmp = (y - x) * (z * 6.0);
	} else if (z <= 12000000000000.0) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = -6.0 * (z * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.235e-89:
		tmp = (y - x) * (z * 6.0)
	elif z <= 12000000000000.0:
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = -6.0 * (z * (x - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.235e-89)
		tmp = Float64(Float64(y - x) * Float64(z * 6.0));
	elseif (z <= 12000000000000.0)
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	else
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.235e-89)
		tmp = (y - x) * (z * 6.0);
	elseif (z <= 12000000000000.0)
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = -6.0 * (z * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.235e-89], N[(N[(y - x), $MachinePrecision] * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 12000000000000.0], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.235e-89

   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* 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.7%

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

      5. fma-define 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf 90.9%

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

      1. associate-*r* 91.0%

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

      2. *-commutative 91.0%

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

      3. *-commutative 91.0%

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

   7. Simplified 91.0%

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

   if -1.235e-89 < z < 1.2e13

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 75.5%

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

      1. +-commutative 75.5%

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

   5. Simplified 75.5%

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

   if 1.2e13 < z

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. fma-define 99.6%

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

      4. remove-double-neg 99.6%

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

      5. distribute-lft-neg-in 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. sub-neg 99.6%

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

      8. distribute-neg-in 99.6%

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

      9. remove-double-neg 99.6%

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

      10. +-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 99.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.235 \cdot 10^{-89}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 12000000000000:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + y \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.165)
   (* (- y x) (* z 6.0))
   (if (<= z 0.17) (+ x (* y (* z 6.0))) (* -6.0 (* z (- x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = (y - x) * (z * 6.0);
	} else if (z <= 0.17) {
		tmp = x + (y * (z * 6.0));
	} else {
		tmp = -6.0 * (z * (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.165d0)) then
        tmp = (y - x) * (z * 6.0d0)
    else if (z <= 0.17d0) then
        tmp = x + (y * (z * 6.0d0))
    else
        tmp = (-6.0d0) * (z * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = (y - x) * (z * 6.0);
	} else if (z <= 0.17) {
		tmp = x + (y * (z * 6.0));
	} else {
		tmp = -6.0 * (z * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.165:
		tmp = (y - x) * (z * 6.0)
	elif z <= 0.17:
		tmp = x + (y * (z * 6.0))
	else:
		tmp = -6.0 * (z * (x - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.165)
		tmp = Float64(Float64(y - x) * Float64(z * 6.0));
	elseif (z <= 0.17)
		tmp = Float64(x + Float64(y * Float64(z * 6.0)));
	else
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.165)
		tmp = (y - x) * (z * 6.0);
	elseif (z <= 0.17)
		tmp = x + (y * (z * 6.0));
	else
		tmp = -6.0 * (z * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.165], N[(N[(y - x), $MachinePrecision] * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], N[(x + N[(y * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.165000000000000008

   1. Initial program 99.7%

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

      1. associate-*r* 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.8%

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

      5. fma-define 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 96.5%

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

      1. associate-*r* 96.6%

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

      2. *-commutative 96.6%

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

      3. *-commutative 96.6%

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

   7. Simplified 96.6%

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

   if -0.165000000000000008 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 98.1%

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

      1. *-commutative 98.1%

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

      2. associate-*r* 98.1%

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

   5. Simplified 98.1%

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

   if 0.170000000000000012 < z

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. fma-define 99.6%

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

      4. remove-double-neg 99.6%

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

      5. distribute-lft-neg-in 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. sub-neg 99.6%

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

      8. distribute-neg-in 99.6%

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

      9. remove-double-neg 99.6%

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

      10. +-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 96.2%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + y \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.14:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.14)
   (* (- y x) (* z 6.0))
   (if (<= z 0.17) (+ x (* z (* y 6.0))) (* -6.0 (* z (- x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.14) {
		tmp = (y - x) * (z * 6.0);
	} else if (z <= 0.17) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = -6.0 * (z * (x - y));
	}
	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 <= (-0.14d0)) then
        tmp = (y - x) * (z * 6.0d0)
    else if (z <= 0.17d0) then
        tmp = x + (z * (y * 6.0d0))
    else
        tmp = (-6.0d0) * (z * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.14) {
		tmp = (y - x) * (z * 6.0);
	} else if (z <= 0.17) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = -6.0 * (z * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.14:
		tmp = (y - x) * (z * 6.0)
	elif z <= 0.17:
		tmp = x + (z * (y * 6.0))
	else:
		tmp = -6.0 * (z * (x - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.14)
		tmp = Float64(Float64(y - x) * Float64(z * 6.0));
	elseif (z <= 0.17)
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	else
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.14)
		tmp = (y - x) * (z * 6.0);
	elseif (z <= 0.17)
		tmp = x + (z * (y * 6.0));
	else
		tmp = -6.0 * (z * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.14], N[(N[(y - x), $MachinePrecision] * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.14000000000000001

   1. Initial program 99.7%

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

      1. associate-*r* 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.8%

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

      5. fma-define 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 96.5%

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

      1. associate-*r* 96.6%

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

      2. *-commutative 96.6%

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

      3. *-commutative 96.6%

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

   7. Simplified 96.6%

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

   if -0.14000000000000001 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 98.2%

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

   if 0.170000000000000012 < z

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. fma-define 99.6%

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

      4. remove-double-neg 99.6%

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

      5. distribute-lft-neg-in 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. sub-neg 99.6%

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

      8. distribute-neg-in 99.6%

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

      9. remove-double-neg 99.6%

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

      10. +-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 96.2%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.14:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0025 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.0025) (not (<= z 0.17))) (* -6.0 (* z x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0025) || !(z <= 0.17)) {
		tmp = -6.0 * (z * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.0025d0)) .or. (.not. (z <= 0.17d0))) then
        tmp = (-6.0d0) * (z * x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0025) || !(z <= 0.17)) {
		tmp = -6.0 * (z * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.0025) or not (z <= 0.17):
		tmp = -6.0 * (z * x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.0025) || !(z <= 0.17))
		tmp = Float64(-6.0 * Float64(z * x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.0025) || ~((z <= 0.17)))
		tmp = -6.0 * (z * x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.0025], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(-6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.00250000000000000005 or 0.170000000000000012 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 58.7%

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

      1. +-commutative 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in z around inf 55.3%

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

   if -0.00250000000000000005 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 68.0%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0025 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 15: 36.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around 0 36.1%

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

4. Final simplification 36.1%

   \[\leadsto x \]
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 2024059 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (- x (* (* 6.0 z) (- x y)))

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