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

Percentage Accurate: 99.7% → 99.8%

Time: 8.3s

Alternatives: 13

Speedup: 1.0×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. +-commutative 99.4%

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

   2. associate-*l* 99.8%

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

   3. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+248}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+82} \lor \neg \left(z \leq 5.6 \cdot 10^{+233}\right) \land z \leq 1.55 \cdot 10^{+264}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* y z))))
   (if (<= z -5.2e+248)
     t_0
     (if (<= z -6e+190)
       t_1
       (if (<= z -1.6e+63)
         t_0
         (if (<= z -4.3e-65)
           t_1
           (if (<= z 1.12e-175)
             x
             (if (<= z 1.05e-123)
               t_1
               (if (<= z 5.2e-18)
                 x
                 (if (or (<= z 4.2e+82)
                         (and (not (<= z 5.6e+233)) (<= z 1.55e+264)))
                   t_1
                   t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -5.2e+248) {
		tmp = t_0;
	} else if (z <= -6e+190) {
		tmp = t_1;
	} else if (z <= -1.6e+63) {
		tmp = t_0;
	} else if (z <= -4.3e-65) {
		tmp = t_1;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 1.05e-123) {
		tmp = t_1;
	} else if (z <= 5.2e-18) {
		tmp = x;
	} else if ((z <= 4.2e+82) || (!(z <= 5.6e+233) && (z <= 1.55e+264))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (x * z)
    t_1 = 6.0d0 * (y * z)
    if (z <= (-5.2d+248)) then
        tmp = t_0
    else if (z <= (-6d+190)) then
        tmp = t_1
    else if (z <= (-1.6d+63)) then
        tmp = t_0
    else if (z <= (-4.3d-65)) then
        tmp = t_1
    else if (z <= 1.12d-175) then
        tmp = x
    else if (z <= 1.05d-123) then
        tmp = t_1
    else if (z <= 5.2d-18) then
        tmp = x
    else if ((z <= 4.2d+82) .or. (.not. (z <= 5.6d+233)) .and. (z <= 1.55d+264)) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -5.2e+248) {
		tmp = t_0;
	} else if (z <= -6e+190) {
		tmp = t_1;
	} else if (z <= -1.6e+63) {
		tmp = t_0;
	} else if (z <= -4.3e-65) {
		tmp = t_1;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 1.05e-123) {
		tmp = t_1;
	} else if (z <= 5.2e-18) {
		tmp = x;
	} else if ((z <= 4.2e+82) || (!(z <= 5.6e+233) && (z <= 1.55e+264))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -5.2e+248:
		tmp = t_0
	elif z <= -6e+190:
		tmp = t_1
	elif z <= -1.6e+63:
		tmp = t_0
	elif z <= -4.3e-65:
		tmp = t_1
	elif z <= 1.12e-175:
		tmp = x
	elif z <= 1.05e-123:
		tmp = t_1
	elif z <= 5.2e-18:
		tmp = x
	elif (z <= 4.2e+82) or (not (z <= 5.6e+233) and (z <= 1.55e+264)):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -5.2e+248)
		tmp = t_0;
	elseif (z <= -6e+190)
		tmp = t_1;
	elseif (z <= -1.6e+63)
		tmp = t_0;
	elseif (z <= -4.3e-65)
		tmp = t_1;
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 1.05e-123)
		tmp = t_1;
	elseif (z <= 5.2e-18)
		tmp = x;
	elseif ((z <= 4.2e+82) || (!(z <= 5.6e+233) && (z <= 1.55e+264)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -5.2e+248)
		tmp = t_0;
	elseif (z <= -6e+190)
		tmp = t_1;
	elseif (z <= -1.6e+63)
		tmp = t_0;
	elseif (z <= -4.3e-65)
		tmp = t_1;
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 1.05e-123)
		tmp = t_1;
	elseif (z <= 5.2e-18)
		tmp = x;
	elseif ((z <= 4.2e+82) || (~((z <= 5.6e+233)) && (z <= 1.55e+264)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+248], t$95$0, If[LessEqual[z, -6e+190], t$95$1, If[LessEqual[z, -1.6e+63], t$95$0, If[LessEqual[z, -4.3e-65], t$95$1, If[LessEqual[z, 1.12e-175], x, If[LessEqual[z, 1.05e-123], t$95$1, If[LessEqual[z, 5.2e-18], x, If[Or[LessEqual[z, 4.2e+82], And[N[Not[LessEqual[z, 5.6e+233]], $MachinePrecision], LessEqual[z, 1.55e+264]]], t$95$1, t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.20000000000000019e248 or -5.99999999999999964e190 < z < -1.60000000000000006e63 or 4.2e82 < z < 5.60000000000000021e233 or 1.54999999999999991e264 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in y around 0 71.8%

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

   if -5.20000000000000019e248 < z < -5.99999999999999964e190 or -1.60000000000000006e63 < z < -4.30000000000000024e-65 or 1.1200000000000001e-175 < z < 1.05e-123 or 5.2000000000000001e-18 < z < 4.2e82 or 5.60000000000000021e233 < z < 1.54999999999999991e264

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 84.1%

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

   4. Taylor expanded in y around inf 68.3%

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

      1. *-commutative 68.3%

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

   6. Simplified 68.3%

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

   if -4.30000000000000024e-65 < z < 1.1200000000000001e-175 or 1.05e-123 < z < 5.2000000000000001e-18

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.4%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+248}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+190}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+63}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-65}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-123}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+82} \lor \neg \left(z \leq 5.6 \cdot 10^{+233}\right) \land z \leq 1.55 \cdot 10^{+264}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot -6\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+254}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+84} \lor \neg \left(z \leq 2.55 \cdot 10^{+237}\right) \land z \leq 9.6 \cdot 10^{+262}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x -6.0))) (t_1 (* 6.0 (* y z))))
   (if (<= z -3.5e+254)
     t_0
     (if (<= z -3.3e+190)
       t_1
       (if (<= z -1.35e+71)
         t_0
         (if (<= z -5e-65)
           t_1
           (if (<= z 1.12e-175)
             x
             (if (<= z 1.05e-123)
               t_1
               (if (<= z 8.5e-19)
                 x
                 (if (or (<= z 1.38e+84)
                         (and (not (<= z 2.55e+237)) (<= z 9.6e+262)))
                   t_1
                   t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -3.5e+254) {
		tmp = t_0;
	} else if (z <= -3.3e+190) {
		tmp = t_1;
	} else if (z <= -1.35e+71) {
		tmp = t_0;
	} else if (z <= -5e-65) {
		tmp = t_1;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 1.05e-123) {
		tmp = t_1;
	} else if (z <= 8.5e-19) {
		tmp = x;
	} else if ((z <= 1.38e+84) || (!(z <= 2.55e+237) && (z <= 9.6e+262))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * (x * (-6.0d0))
    t_1 = 6.0d0 * (y * z)
    if (z <= (-3.5d+254)) then
        tmp = t_0
    else if (z <= (-3.3d+190)) then
        tmp = t_1
    else if (z <= (-1.35d+71)) then
        tmp = t_0
    else if (z <= (-5d-65)) then
        tmp = t_1
    else if (z <= 1.12d-175) then
        tmp = x
    else if (z <= 1.05d-123) then
        tmp = t_1
    else if (z <= 8.5d-19) then
        tmp = x
    else if ((z <= 1.38d+84) .or. (.not. (z <= 2.55d+237)) .and. (z <= 9.6d+262)) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -3.5e+254) {
		tmp = t_0;
	} else if (z <= -3.3e+190) {
		tmp = t_1;
	} else if (z <= -1.35e+71) {
		tmp = t_0;
	} else if (z <= -5e-65) {
		tmp = t_1;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 1.05e-123) {
		tmp = t_1;
	} else if (z <= 8.5e-19) {
		tmp = x;
	} else if ((z <= 1.38e+84) || (!(z <= 2.55e+237) && (z <= 9.6e+262))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * -6.0)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -3.5e+254:
		tmp = t_0
	elif z <= -3.3e+190:
		tmp = t_1
	elif z <= -1.35e+71:
		tmp = t_0
	elif z <= -5e-65:
		tmp = t_1
	elif z <= 1.12e-175:
		tmp = x
	elif z <= 1.05e-123:
		tmp = t_1
	elif z <= 8.5e-19:
		tmp = x
	elif (z <= 1.38e+84) or (not (z <= 2.55e+237) and (z <= 9.6e+262)):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * -6.0))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -3.5e+254)
		tmp = t_0;
	elseif (z <= -3.3e+190)
		tmp = t_1;
	elseif (z <= -1.35e+71)
		tmp = t_0;
	elseif (z <= -5e-65)
		tmp = t_1;
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 1.05e-123)
		tmp = t_1;
	elseif (z <= 8.5e-19)
		tmp = x;
	elseif ((z <= 1.38e+84) || (!(z <= 2.55e+237) && (z <= 9.6e+262)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * -6.0);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -3.5e+254)
		tmp = t_0;
	elseif (z <= -3.3e+190)
		tmp = t_1;
	elseif (z <= -1.35e+71)
		tmp = t_0;
	elseif (z <= -5e-65)
		tmp = t_1;
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 1.05e-123)
		tmp = t_1;
	elseif (z <= 8.5e-19)
		tmp = x;
	elseif ((z <= 1.38e+84) || (~((z <= 2.55e+237)) && (z <= 9.6e+262)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+254], t$95$0, If[LessEqual[z, -3.3e+190], t$95$1, If[LessEqual[z, -1.35e+71], t$95$0, If[LessEqual[z, -5e-65], t$95$1, If[LessEqual[z, 1.12e-175], x, If[LessEqual[z, 1.05e-123], t$95$1, If[LessEqual[z, 8.5e-19], x, If[Or[LessEqual[z, 1.38e+84], And[N[Not[LessEqual[z, 2.55e+237]], $MachinePrecision], LessEqual[z, 9.6e+262]]], t$95$1, t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.50000000000000017e254 or -3.3e190 < z < -1.34999999999999998e71 or 1.38e84 < z < 2.54999999999999989e237 or 9.59999999999999932e262 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in y around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. associate-*r* 72.0%

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

      3. *-commutative 72.0%

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

   6. Simplified 72.0%

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

   if -3.50000000000000017e254 < z < -3.3e190 or -1.34999999999999998e71 < z < -4.99999999999999983e-65 or 1.1200000000000001e-175 < z < 1.05e-123 or 8.50000000000000003e-19 < z < 1.38e84 or 2.54999999999999989e237 < z < 9.59999999999999932e262

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 84.1%

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

   4. Taylor expanded in y around inf 68.3%

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

      1. *-commutative 68.3%

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

   6. Simplified 68.3%

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

   if -4.99999999999999983e-65 < z < 1.1200000000000001e-175 or 1.05e-123 < z < 8.50000000000000003e-19

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.4%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+254}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+190}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-65}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-123}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+84} \lor \neg \left(z \leq 2.55 \cdot 10^{+237}\right) \land z \leq 9.6 \cdot 10^{+262}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \end{array} \]

Alternative 4: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot -6\right)\\ t_1 := z \cdot \left(y \cdot 6\right)\\ t_2 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+252}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+231} \lor \neg \left(z \leq 5.4 \cdot 10^{+261}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x -6.0))) (t_1 (* z (* y 6.0))) (t_2 (* 6.0 (* y z))))
   (if (<= z -1.6e+252)
     t_0
     (if (<= z -1.4e+190)
       t_1
       (if (<= z -8.5e+66)
         t_0
         (if (<= z -4.3e-65)
           t_1
           (if (<= z 1.12e-175)
             x
             (if (<= z 6.2e-122)
               t_2
               (if (<= z 5.6e-20)
                 x
                 (if (<= z 4.2e+82)
                   t_2
                   (if (or (<= z 2.1e+231) (not (<= z 5.4e+261)))
                     t_0
                     t_1)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * -6.0);
	double t_1 = z * (y * 6.0);
	double t_2 = 6.0 * (y * z);
	double tmp;
	if (z <= -1.6e+252) {
		tmp = t_0;
	} else if (z <= -1.4e+190) {
		tmp = t_1;
	} else if (z <= -8.5e+66) {
		tmp = t_0;
	} else if (z <= -4.3e-65) {
		tmp = t_1;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 6.2e-122) {
		tmp = t_2;
	} else if (z <= 5.6e-20) {
		tmp = x;
	} else if (z <= 4.2e+82) {
		tmp = t_2;
	} else if ((z <= 2.1e+231) || !(z <= 5.4e+261)) {
		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) :: t_2
    real(8) :: tmp
    t_0 = z * (x * (-6.0d0))
    t_1 = z * (y * 6.0d0)
    t_2 = 6.0d0 * (y * z)
    if (z <= (-1.6d+252)) then
        tmp = t_0
    else if (z <= (-1.4d+190)) then
        tmp = t_1
    else if (z <= (-8.5d+66)) then
        tmp = t_0
    else if (z <= (-4.3d-65)) then
        tmp = t_1
    else if (z <= 1.12d-175) then
        tmp = x
    else if (z <= 6.2d-122) then
        tmp = t_2
    else if (z <= 5.6d-20) then
        tmp = x
    else if (z <= 4.2d+82) then
        tmp = t_2
    else if ((z <= 2.1d+231) .or. (.not. (z <= 5.4d+261))) 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 = z * (x * -6.0);
	double t_1 = z * (y * 6.0);
	double t_2 = 6.0 * (y * z);
	double tmp;
	if (z <= -1.6e+252) {
		tmp = t_0;
	} else if (z <= -1.4e+190) {
		tmp = t_1;
	} else if (z <= -8.5e+66) {
		tmp = t_0;
	} else if (z <= -4.3e-65) {
		tmp = t_1;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 6.2e-122) {
		tmp = t_2;
	} else if (z <= 5.6e-20) {
		tmp = x;
	} else if (z <= 4.2e+82) {
		tmp = t_2;
	} else if ((z <= 2.1e+231) || !(z <= 5.4e+261)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * -6.0)
	t_1 = z * (y * 6.0)
	t_2 = 6.0 * (y * z)
	tmp = 0
	if z <= -1.6e+252:
		tmp = t_0
	elif z <= -1.4e+190:
		tmp = t_1
	elif z <= -8.5e+66:
		tmp = t_0
	elif z <= -4.3e-65:
		tmp = t_1
	elif z <= 1.12e-175:
		tmp = x
	elif z <= 6.2e-122:
		tmp = t_2
	elif z <= 5.6e-20:
		tmp = x
	elif z <= 4.2e+82:
		tmp = t_2
	elif (z <= 2.1e+231) or not (z <= 5.4e+261):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * -6.0))
	t_1 = Float64(z * Float64(y * 6.0))
	t_2 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.6e+252)
		tmp = t_0;
	elseif (z <= -1.4e+190)
		tmp = t_1;
	elseif (z <= -8.5e+66)
		tmp = t_0;
	elseif (z <= -4.3e-65)
		tmp = t_1;
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 6.2e-122)
		tmp = t_2;
	elseif (z <= 5.6e-20)
		tmp = x;
	elseif (z <= 4.2e+82)
		tmp = t_2;
	elseif ((z <= 2.1e+231) || !(z <= 5.4e+261))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * -6.0);
	t_1 = z * (y * 6.0);
	t_2 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.6e+252)
		tmp = t_0;
	elseif (z <= -1.4e+190)
		tmp = t_1;
	elseif (z <= -8.5e+66)
		tmp = t_0;
	elseif (z <= -4.3e-65)
		tmp = t_1;
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 6.2e-122)
		tmp = t_2;
	elseif (z <= 5.6e-20)
		tmp = x;
	elseif (z <= 4.2e+82)
		tmp = t_2;
	elseif ((z <= 2.1e+231) || ~((z <= 5.4e+261)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+252], t$95$0, If[LessEqual[z, -1.4e+190], t$95$1, If[LessEqual[z, -8.5e+66], t$95$0, If[LessEqual[z, -4.3e-65], t$95$1, If[LessEqual[z, 1.12e-175], x, If[LessEqual[z, 6.2e-122], t$95$2, If[LessEqual[z, 5.6e-20], x, If[LessEqual[z, 4.2e+82], t$95$2, If[Or[LessEqual[z, 2.1e+231], N[Not[LessEqual[z, 5.4e+261]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6000000000000001e252 or -1.39999999999999998e190 < z < -8.5000000000000004e66 or 4.2e82 < z < 2.09999999999999984e231 or 5.40000000000000005e261 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in y around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. associate-*r* 72.0%

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

      3. *-commutative 72.0%

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

   6. Simplified 72.0%

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

   if -1.6000000000000001e252 < z < -1.39999999999999998e190 or -8.5000000000000004e66 < z < -4.30000000000000024e-65 or 2.09999999999999984e231 < z < 5.40000000000000005e261

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 87.6%

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

   4. Taylor expanded in y around inf 68.7%

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

      1. associate-*r* 68.8%

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

      2. *-commutative 68.8%

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

   6. Simplified 68.8%

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

   if -4.30000000000000024e-65 < z < 1.1200000000000001e-175 or 6.1999999999999997e-122 < z < 5.6000000000000005e-20

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.4%

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

   if 1.1200000000000001e-175 < z < 6.1999999999999997e-122 or 5.6000000000000005e-20 < z < 4.2e82

   1. Initial program 96.8%

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

   2. Taylor expanded in z around 0 99.5%

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

   3. Taylor expanded in z around inf 79.4%

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

   4. Taylor expanded in y around inf 67.9%

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

      1. *-commutative 67.9%

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

   6. Simplified 67.9%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+252}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+190}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-65}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-122}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+82}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+231} \lor \neg \left(z \leq 5.4 \cdot 10^{+261}\right):\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]

Alternative 5: 59.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := z \cdot \left(x \cdot -6\right)\\ t_2 := z \cdot \left(y \cdot 6\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+255}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-123}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+233} \lor \neg \left(z \leq 10^{+262}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* z (* x -6.0))) (t_2 (* z (* y 6.0))))
   (if (<= z -6.5e+255)
     (* x (* z -6.0))
     (if (<= z -3e+193)
       t_2
       (if (<= z -1.56e+63)
         t_1
         (if (<= z -5e-65)
           t_2
           (if (<= z 1.12e-175)
             x
             (if (<= z 2.8e-123)
               t_0
               (if (<= z 7.2e-20)
                 x
                 (if (<= z 1.9e+84)
                   t_0
                   (if (or (<= z 6.8e+233) (not (<= z 1e+262)))
                     t_1
                     t_2)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = z * (x * -6.0);
	double t_2 = z * (y * 6.0);
	double tmp;
	if (z <= -6.5e+255) {
		tmp = x * (z * -6.0);
	} else if (z <= -3e+193) {
		tmp = t_2;
	} else if (z <= -1.56e+63) {
		tmp = t_1;
	} else if (z <= -5e-65) {
		tmp = t_2;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 2.8e-123) {
		tmp = t_0;
	} else if (z <= 7.2e-20) {
		tmp = x;
	} else if (z <= 1.9e+84) {
		tmp = t_0;
	} else if ((z <= 6.8e+233) || !(z <= 1e+262)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    t_1 = z * (x * (-6.0d0))
    t_2 = z * (y * 6.0d0)
    if (z <= (-6.5d+255)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= (-3d+193)) then
        tmp = t_2
    else if (z <= (-1.56d+63)) then
        tmp = t_1
    else if (z <= (-5d-65)) then
        tmp = t_2
    else if (z <= 1.12d-175) then
        tmp = x
    else if (z <= 2.8d-123) then
        tmp = t_0
    else if (z <= 7.2d-20) then
        tmp = x
    else if (z <= 1.9d+84) then
        tmp = t_0
    else if ((z <= 6.8d+233) .or. (.not. (z <= 1d+262))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = z * (x * -6.0);
	double t_2 = z * (y * 6.0);
	double tmp;
	if (z <= -6.5e+255) {
		tmp = x * (z * -6.0);
	} else if (z <= -3e+193) {
		tmp = t_2;
	} else if (z <= -1.56e+63) {
		tmp = t_1;
	} else if (z <= -5e-65) {
		tmp = t_2;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 2.8e-123) {
		tmp = t_0;
	} else if (z <= 7.2e-20) {
		tmp = x;
	} else if (z <= 1.9e+84) {
		tmp = t_0;
	} else if ((z <= 6.8e+233) || !(z <= 1e+262)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = z * (x * -6.0)
	t_2 = z * (y * 6.0)
	tmp = 0
	if z <= -6.5e+255:
		tmp = x * (z * -6.0)
	elif z <= -3e+193:
		tmp = t_2
	elif z <= -1.56e+63:
		tmp = t_1
	elif z <= -5e-65:
		tmp = t_2
	elif z <= 1.12e-175:
		tmp = x
	elif z <= 2.8e-123:
		tmp = t_0
	elif z <= 7.2e-20:
		tmp = x
	elif z <= 1.9e+84:
		tmp = t_0
	elif (z <= 6.8e+233) or not (z <= 1e+262):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(z * Float64(x * -6.0))
	t_2 = Float64(z * Float64(y * 6.0))
	tmp = 0.0
	if (z <= -6.5e+255)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= -3e+193)
		tmp = t_2;
	elseif (z <= -1.56e+63)
		tmp = t_1;
	elseif (z <= -5e-65)
		tmp = t_2;
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 2.8e-123)
		tmp = t_0;
	elseif (z <= 7.2e-20)
		tmp = x;
	elseif (z <= 1.9e+84)
		tmp = t_0;
	elseif ((z <= 6.8e+233) || !(z <= 1e+262))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = z * (x * -6.0);
	t_2 = z * (y * 6.0);
	tmp = 0.0;
	if (z <= -6.5e+255)
		tmp = x * (z * -6.0);
	elseif (z <= -3e+193)
		tmp = t_2;
	elseif (z <= -1.56e+63)
		tmp = t_1;
	elseif (z <= -5e-65)
		tmp = t_2;
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 2.8e-123)
		tmp = t_0;
	elseif (z <= 7.2e-20)
		tmp = x;
	elseif (z <= 1.9e+84)
		tmp = t_0;
	elseif ((z <= 6.8e+233) || ~((z <= 1e+262)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+255], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e+193], t$95$2, If[LessEqual[z, -1.56e+63], t$95$1, If[LessEqual[z, -5e-65], t$95$2, If[LessEqual[z, 1.12e-175], x, If[LessEqual[z, 2.8e-123], t$95$0, If[LessEqual[z, 7.2e-20], x, If[LessEqual[z, 1.9e+84], t$95$0, If[Or[LessEqual[z, 6.8e+233], N[Not[LessEqual[z, 1e+262]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.50000000000000003e255

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 87.4%

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

   3. Taylor expanded in z around inf 87.4%

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

   if -6.50000000000000003e255 < z < -3e193 or -1.56e63 < z < -4.99999999999999983e-65 or 6.80000000000000044e233 < z < 1e262

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 87.6%

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

   4. Taylor expanded in y around inf 68.7%

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

      1. associate-*r* 68.8%

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

      2. *-commutative 68.8%

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

   6. Simplified 68.8%

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

   if -3e193 < z < -1.56e63 or 1.9e84 < z < 6.80000000000000044e233 or 1e262 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in y around 0 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-*r* 68.5%

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

      3. *-commutative 68.5%

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

   6. Simplified 68.5%

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

   if -4.99999999999999983e-65 < z < 1.1200000000000001e-175 or 2.7999999999999999e-123 < z < 7.19999999999999948e-20

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.4%

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

   if 1.1200000000000001e-175 < z < 2.7999999999999999e-123 or 7.19999999999999948e-20 < z < 1.9e84

   1. Initial program 96.8%

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

   2. Taylor expanded in z around 0 99.5%

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

   3. Taylor expanded in z around inf 79.4%

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

   4. Taylor expanded in y around inf 67.9%

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

      1. *-commutative 67.9%

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

   6. Simplified 67.9%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+255}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+193}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-65}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-123}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+84}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+233} \lor \neg \left(z \leq 10^{+262}\right):\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]

Alternative 6: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-123}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* (- y x) z))))
   (if (<= z -3.7e-65)
     t_0
     (if (<= z 1.12e-175)
       x
       (if (<= z 1.05e-123) (* 6.0 (* y z)) (if (<= z 3.6e-18) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * ((y - x) * z);
	double tmp;
	if (z <= -3.7e-65) {
		tmp = t_0;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 1.05e-123) {
		tmp = 6.0 * (y * z);
	} else if (z <= 3.6e-18) {
		tmp = 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 * ((y - x) * z)
    if (z <= (-3.7d-65)) then
        tmp = t_0
    else if (z <= 1.12d-175) then
        tmp = x
    else if (z <= 1.05d-123) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 3.6d-18) then
        tmp = 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 * ((y - x) * z);
	double tmp;
	if (z <= -3.7e-65) {
		tmp = t_0;
	} else if (z <= 1.12e-175) {
		tmp = x;
	} else if (z <= 1.05e-123) {
		tmp = 6.0 * (y * z);
	} else if (z <= 3.6e-18) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * ((y - x) * z)
	tmp = 0
	if z <= -3.7e-65:
		tmp = t_0
	elif z <= 1.12e-175:
		tmp = x
	elif z <= 1.05e-123:
		tmp = 6.0 * (y * z)
	elif z <= 3.6e-18:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -3.7e-65)
		tmp = t_0;
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 1.05e-123)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 3.6e-18)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -3.7e-65)
		tmp = t_0;
	elseif (z <= 1.12e-175)
		tmp = x;
	elseif (z <= 1.05e-123)
		tmp = 6.0 * (y * z);
	elseif (z <= 3.6e-18)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e-65], t$95$0, If[LessEqual[z, 1.12e-175], x, If[LessEqual[z, 1.05e-123], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-18], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7e-65 or 3.6000000000000001e-18 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 95.0%

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

   if -3.7e-65 < z < 1.1200000000000001e-175 or 1.05e-123 < z < 3.6000000000000001e-18

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.4%

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

   if 1.1200000000000001e-175 < z < 1.05e-123

   1. Initial program 94.4%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 67.6%

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

   4. Taylor expanded in y around inf 67.9%

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

      1. *-commutative 67.9%

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

   6. Simplified 67.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-65}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-123}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 7: 80.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+59} \lor \neg \left(x \leq 1.1 \cdot 10^{+75}\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.4e+59) (not (<= x 1.1e+75)))
   (* x (+ 1.0 (* z -6.0)))
   (* 6.0 (* (- y x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e+59) || !(x <= 1.1e+75)) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.4d+59)) .or. (.not. (x <= 1.1d+75))) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    else
        tmp = 6.0d0 * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e+59) || !(x <= 1.1e+75)) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.4e+59) or not (x <= 1.1e+75):
		tmp = x * (1.0 + (z * -6.0))
	else:
		tmp = 6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4e+59) || !(x <= 1.1e+75))
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	else
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.4e+59) || ~((x <= 1.1e+75)))
		tmp = x * (1.0 + (z * -6.0));
	else
		tmp = 6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.4e+59], N[Not[LessEqual[x, 1.1e+75]], $MachinePrecision]], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999e59 or 1.10000000000000006e75 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 95.0%

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

   if -1.3999999999999999e59 < x < 1.10000000000000006e75

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 81.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+59} \lor \neg \left(x \leq 1.1 \cdot 10^{+75}\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 8: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 0.00086\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.17) (not (<= z 0.00086)))
   (* 6.0 (* (- y x) z))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 0.00086)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.17d0)) .or. (.not. (z <= 0.00086d0))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x + (6.0d0 * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 0.00086)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.17) or not (z <= 0.00086):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.17) || !(z <= 0.00086))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.17) || ~((z <= 0.00086)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.17], N[Not[LessEqual[z, 0.00086]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.170000000000000012 or 8.59999999999999979e-4 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 99.2%

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

   if -0.170000000000000012 < z < 8.59999999999999979e-4

   1. Initial program 99.0%

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

   2. Taylor expanded in y around inf 98.7%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 0.00086\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 9: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.18 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.18) (not (<= z 0.165)))
   (* 6.0 (* (- y x) z))
   (+ x (* y (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.18) || !(z <= 0.165)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.18d0)) .or. (.not. (z <= 0.165d0))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x + (y * (6.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.18) || !(z <= 0.165)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.18) or not (z <= 0.165):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.18) || !(z <= 0.165))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.18) || ~((z <= 0.165)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.18], N[Not[LessEqual[z, 0.165]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.17999999999999999 or 0.165000000000000008 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 99.2%

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

   if -0.17999999999999999 < z < 0.165000000000000008

   1. Initial program 99.0%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. flip-- 48.4%

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

      4. associate-*r/ 48.3%

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

   3. Applied egg-rr 48.3%

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

      1. associate-/l* 48.3%

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

      2. *-commutative 48.3%

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

      3. associate-/l* 48.3%

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

      4. difference-of-squares 48.4%

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

      5. associate-/r* 99.8%

         \[\leadsto x + \frac{z}{\frac{\color{blue}{\frac{\frac{y + x}{y + x}}{y - x}}}{6}} \]

      6. *-inverses 99.8%

         \[\leadsto x + \frac{z}{\frac{\frac{\color{blue}{1}}{y - x}}{6}} \]

   5. Simplified 99.8%

      \[\leadsto x + \color{blue}{\frac{z}{\frac{\frac{1}{y - x}}{6}}} \]

   6. Taylor expanded in y around inf 98.6%

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

      1. associate-*r* 97.9%

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

      2. *-commutative 97.9%

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

      3. associate-*r* 98.7%

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

   8. Simplified 98.7%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.18 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 10: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0205 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.0205) (not (<= z 0.165))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0205) || !(z <= 0.165)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.0205d0)) .or. (.not. (z <= 0.165d0))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0205) || !(z <= 0.165)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.0205) or not (z <= 0.165):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.0205) || !(z <= 0.165))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.0205) || ~((z <= 0.165)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.0205], N[Not[LessEqual[z, 0.165]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.0205000000000000009 or 0.165000000000000008 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 99.2%

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

   4. Taylor expanded in y around 0 55.8%

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

   if -0.0205000000000000009 < z < 0.165000000000000008

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 64.0%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0205 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

2. Final simplification 99.4%

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

Alternative 12: 99.8% accurate, 1.0× speedup

Math

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

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(y - x) * Float64(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[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

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

   1. associate-*l* 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 13: 36.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.4%

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

2. Taylor expanded in z around 0 32.1%

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

3. Final simplification 32.1%

   \[\leadsto x \]

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023182 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

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

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