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

Percentage Accurate: 99.7% → 99.8%

Time: 8.2s

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, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 61.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot -6\right)\\ t_1 := z \cdot \left(6 \cdot y\right)\\ t_2 := y \cdot \left(6 \cdot z\right)\\ t_3 := x \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+237}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+197}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+149}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7.1 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-54}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+149}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x -6.0)))
        (t_1 (* z (* 6.0 y)))
        (t_2 (* y (* 6.0 z)))
        (t_3 (* x (* z -6.0))))
   (if (<= z -1.7e+237)
     t_2
     (if (<= z -2.25e+197)
       t_3
       (if (<= z -4.4e+169)
         t_1
         (if (<= z -1.75e+149)
           (* -6.0 (* x z))
           (if (<= z -7.1e+93)
             t_2
             (if (<= z -3.5e+14)
               t_0
               (if (<= z -4.1e-54)
                 (* 6.0 (* z y))
                 (if (<= z 1.6e-39)
                   x
                   (if (<= z 1.14e+114)
                     t_2
                     (if (<= z 7.8e+149)
                       t_0
                       (if (<= z 1.55e+185) t_1 t_3)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * -6.0);
	double t_1 = z * (6.0 * y);
	double t_2 = y * (6.0 * z);
	double t_3 = x * (z * -6.0);
	double tmp;
	if (z <= -1.7e+237) {
		tmp = t_2;
	} else if (z <= -2.25e+197) {
		tmp = t_3;
	} else if (z <= -4.4e+169) {
		tmp = t_1;
	} else if (z <= -1.75e+149) {
		tmp = -6.0 * (x * z);
	} else if (z <= -7.1e+93) {
		tmp = t_2;
	} else if (z <= -3.5e+14) {
		tmp = t_0;
	} else if (z <= -4.1e-54) {
		tmp = 6.0 * (z * y);
	} else if (z <= 1.6e-39) {
		tmp = x;
	} else if (z <= 1.14e+114) {
		tmp = t_2;
	} else if (z <= 7.8e+149) {
		tmp = t_0;
	} else if (z <= 1.55e+185) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = z * (x * (-6.0d0))
    t_1 = z * (6.0d0 * y)
    t_2 = y * (6.0d0 * z)
    t_3 = x * (z * (-6.0d0))
    if (z <= (-1.7d+237)) then
        tmp = t_2
    else if (z <= (-2.25d+197)) then
        tmp = t_3
    else if (z <= (-4.4d+169)) then
        tmp = t_1
    else if (z <= (-1.75d+149)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= (-7.1d+93)) then
        tmp = t_2
    else if (z <= (-3.5d+14)) then
        tmp = t_0
    else if (z <= (-4.1d-54)) then
        tmp = 6.0d0 * (z * y)
    else if (z <= 1.6d-39) then
        tmp = x
    else if (z <= 1.14d+114) then
        tmp = t_2
    else if (z <= 7.8d+149) then
        tmp = t_0
    else if (z <= 1.55d+185) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * -6.0);
	double t_1 = z * (6.0 * y);
	double t_2 = y * (6.0 * z);
	double t_3 = x * (z * -6.0);
	double tmp;
	if (z <= -1.7e+237) {
		tmp = t_2;
	} else if (z <= -2.25e+197) {
		tmp = t_3;
	} else if (z <= -4.4e+169) {
		tmp = t_1;
	} else if (z <= -1.75e+149) {
		tmp = -6.0 * (x * z);
	} else if (z <= -7.1e+93) {
		tmp = t_2;
	} else if (z <= -3.5e+14) {
		tmp = t_0;
	} else if (z <= -4.1e-54) {
		tmp = 6.0 * (z * y);
	} else if (z <= 1.6e-39) {
		tmp = x;
	} else if (z <= 1.14e+114) {
		tmp = t_2;
	} else if (z <= 7.8e+149) {
		tmp = t_0;
	} else if (z <= 1.55e+185) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * -6.0)
	t_1 = z * (6.0 * y)
	t_2 = y * (6.0 * z)
	t_3 = x * (z * -6.0)
	tmp = 0
	if z <= -1.7e+237:
		tmp = t_2
	elif z <= -2.25e+197:
		tmp = t_3
	elif z <= -4.4e+169:
		tmp = t_1
	elif z <= -1.75e+149:
		tmp = -6.0 * (x * z)
	elif z <= -7.1e+93:
		tmp = t_2
	elif z <= -3.5e+14:
		tmp = t_0
	elif z <= -4.1e-54:
		tmp = 6.0 * (z * y)
	elif z <= 1.6e-39:
		tmp = x
	elif z <= 1.14e+114:
		tmp = t_2
	elif z <= 7.8e+149:
		tmp = t_0
	elif z <= 1.55e+185:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * -6.0))
	t_1 = Float64(z * Float64(6.0 * y))
	t_2 = Float64(y * Float64(6.0 * z))
	t_3 = Float64(x * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -1.7e+237)
		tmp = t_2;
	elseif (z <= -2.25e+197)
		tmp = t_3;
	elseif (z <= -4.4e+169)
		tmp = t_1;
	elseif (z <= -1.75e+149)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= -7.1e+93)
		tmp = t_2;
	elseif (z <= -3.5e+14)
		tmp = t_0;
	elseif (z <= -4.1e-54)
		tmp = Float64(6.0 * Float64(z * y));
	elseif (z <= 1.6e-39)
		tmp = x;
	elseif (z <= 1.14e+114)
		tmp = t_2;
	elseif (z <= 7.8e+149)
		tmp = t_0;
	elseif (z <= 1.55e+185)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * -6.0);
	t_1 = z * (6.0 * y);
	t_2 = y * (6.0 * z);
	t_3 = x * (z * -6.0);
	tmp = 0.0;
	if (z <= -1.7e+237)
		tmp = t_2;
	elseif (z <= -2.25e+197)
		tmp = t_3;
	elseif (z <= -4.4e+169)
		tmp = t_1;
	elseif (z <= -1.75e+149)
		tmp = -6.0 * (x * z);
	elseif (z <= -7.1e+93)
		tmp = t_2;
	elseif (z <= -3.5e+14)
		tmp = t_0;
	elseif (z <= -4.1e-54)
		tmp = 6.0 * (z * y);
	elseif (z <= 1.6e-39)
		tmp = x;
	elseif (z <= 1.14e+114)
		tmp = t_2;
	elseif (z <= 7.8e+149)
		tmp = t_0;
	elseif (z <= 1.55e+185)
		tmp = t_1;
	else
		tmp = t_3;
	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[(6.0 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+237], t$95$2, If[LessEqual[z, -2.25e+197], t$95$3, If[LessEqual[z, -4.4e+169], t$95$1, If[LessEqual[z, -1.75e+149], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.1e+93], t$95$2, If[LessEqual[z, -3.5e+14], t$95$0, If[LessEqual[z, -4.1e-54], N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-39], x, If[LessEqual[z, 1.14e+114], t$95$2, If[LessEqual[z, 7.8e+149], t$95$0, If[LessEqual[z, 1.55e+185], t$95$1, t$95$3]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.7000000000000002e237 or -1.75000000000000006e149 < z < -7.1000000000000004e93 or 1.5999999999999999e-39 < z < 1.14e114

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in z around inf 87.4%

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

   5. Taylor expanded in y around inf 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-*r* 66.5%

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

   7. Simplified 66.5%

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

   if -1.7000000000000002e237 < z < -2.2500000000000001e197 or 1.55e185 < z

   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 64.7%

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

   4. Taylor expanded in z around inf 64.7%

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

   if -2.2500000000000001e197 < z < -4.4e169 or 7.7999999999999998e149 < z < 1.55e185

   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 99.7%

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

   4. Taylor expanded in z around inf 99.7%

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

   5. Taylor expanded in y around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. metadata-eval 99.7%

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

      4. cancel-sign-sub-inv 99.7%

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

      5. associate-*l* 99.7%

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

      6. unsub-neg 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-*l* 99.6%

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

      9. distribute-rgt-neg-out 99.6%

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

      10. distribute-lft-out 99.6%

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

      11. sub-neg 99.6%

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

      12. *-commutative 99.6%

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

      13. associate-*r* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around inf 88.0%

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

   if -4.4e169 < z < -1.75000000000000006e149

   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 99.8%

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

   4. Taylor expanded in z around inf 99.8%

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

   5. Taylor expanded in y around 0 99.8%

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

   if -7.1000000000000004e93 < z < -3.5e14 or 1.14e114 < z < 7.7999999999999998e149

   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 99.8%

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

   4. Taylor expanded in z around inf 99.8%

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

   5. Taylor expanded in y around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-*r* 71.9%

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

      3. *-commutative 71.9%

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

      4. associate-*r* 72.0%

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

   7. Simplified 72.0%

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

   if -3.5e14 < z < -4.1000000000000001e-54

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in z around inf 80.5%

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

   5. Taylor expanded in y around inf 79.1%

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

      1. *-commutative 79.1%

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

   7. Simplified 79.1%

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

   if -4.1000000000000001e-54 < z < 1.5999999999999999e-39

   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 77.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 7 regimes into one program.

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+237}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+169}:\\ \;\;\;\;z \cdot \left(6 \cdot y\right)\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+149}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7.1 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-54}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+149}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+185}:\\ \;\;\;\;z \cdot \left(6 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot y\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+237}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+103}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+23} \lor \neg \left(z \leq 3.8 \cdot 10^{+148}\right) \land z \leq 2.2 \cdot 10^{+184}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z y))) (t_1 (* -6.0 (* x z))))
   (if (<= z -1.7e+237)
     t_0
     (if (<= z -4.2e+148)
       t_1
       (if (<= z -1.05e+103)
         t_0
         (if (<= z -1.62e+14)
           t_1
           (if (<= z -4.1e-54)
             t_0
             (if (<= z 6.3e-40)
               x
               (if (or (<= z 5e+23)
                       (and (not (<= z 3.8e+148)) (<= z 2.2e+184)))
                 t_0
                 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -1.7e+237) {
		tmp = t_0;
	} else if (z <= -4.2e+148) {
		tmp = t_1;
	} else if (z <= -1.05e+103) {
		tmp = t_0;
	} else if (z <= -1.62e+14) {
		tmp = t_1;
	} else if (z <= -4.1e-54) {
		tmp = t_0;
	} else if (z <= 6.3e-40) {
		tmp = x;
	} else if ((z <= 5e+23) || (!(z <= 3.8e+148) && (z <= 2.2e+184))) {
		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 * y)
    t_1 = (-6.0d0) * (x * z)
    if (z <= (-1.7d+237)) then
        tmp = t_0
    else if (z <= (-4.2d+148)) then
        tmp = t_1
    else if (z <= (-1.05d+103)) then
        tmp = t_0
    else if (z <= (-1.62d+14)) then
        tmp = t_1
    else if (z <= (-4.1d-54)) then
        tmp = t_0
    else if (z <= 6.3d-40) then
        tmp = x
    else if ((z <= 5d+23) .or. (.not. (z <= 3.8d+148)) .and. (z <= 2.2d+184)) 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 * y);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -1.7e+237) {
		tmp = t_0;
	} else if (z <= -4.2e+148) {
		tmp = t_1;
	} else if (z <= -1.05e+103) {
		tmp = t_0;
	} else if (z <= -1.62e+14) {
		tmp = t_1;
	} else if (z <= -4.1e-54) {
		tmp = t_0;
	} else if (z <= 6.3e-40) {
		tmp = x;
	} else if ((z <= 5e+23) || (!(z <= 3.8e+148) && (z <= 2.2e+184))) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (z * y)
	t_1 = -6.0 * (x * z)
	tmp = 0
	if z <= -1.7e+237:
		tmp = t_0
	elif z <= -4.2e+148:
		tmp = t_1
	elif z <= -1.05e+103:
		tmp = t_0
	elif z <= -1.62e+14:
		tmp = t_1
	elif z <= -4.1e-54:
		tmp = t_0
	elif z <= 6.3e-40:
		tmp = x
	elif (z <= 5e+23) or (not (z <= 3.8e+148) and (z <= 2.2e+184)):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * y))
	t_1 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1.7e+237)
		tmp = t_0;
	elseif (z <= -4.2e+148)
		tmp = t_1;
	elseif (z <= -1.05e+103)
		tmp = t_0;
	elseif (z <= -1.62e+14)
		tmp = t_1;
	elseif (z <= -4.1e-54)
		tmp = t_0;
	elseif (z <= 6.3e-40)
		tmp = x;
	elseif ((z <= 5e+23) || (!(z <= 3.8e+148) && (z <= 2.2e+184)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (z * y);
	t_1 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1.7e+237)
		tmp = t_0;
	elseif (z <= -4.2e+148)
		tmp = t_1;
	elseif (z <= -1.05e+103)
		tmp = t_0;
	elseif (z <= -1.62e+14)
		tmp = t_1;
	elseif (z <= -4.1e-54)
		tmp = t_0;
	elseif (z <= 6.3e-40)
		tmp = x;
	elseif ((z <= 5e+23) || (~((z <= 3.8e+148)) && (z <= 2.2e+184)))
		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 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+237], t$95$0, If[LessEqual[z, -4.2e+148], t$95$1, If[LessEqual[z, -1.05e+103], t$95$0, If[LessEqual[z, -1.62e+14], t$95$1, If[LessEqual[z, -4.1e-54], t$95$0, If[LessEqual[z, 6.3e-40], x, If[Or[LessEqual[z, 5e+23], And[N[Not[LessEqual[z, 3.8e+148]], $MachinePrecision], LessEqual[z, 2.2e+184]]], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7000000000000002e237 or -4.19999999999999998e148 < z < -1.0500000000000001e103 or -1.62e14 < z < -4.1000000000000001e-54 or 6.3000000000000001e-40 < z < 4.9999999999999999e23 or 3.7999999999999998e148 < z < 2.2e184

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in z around inf 86.4%

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

   5. Taylor expanded in y around inf 74.3%

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

      1. *-commutative 74.3%

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

   7. Simplified 74.3%

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

   if -1.7000000000000002e237 < z < -4.19999999999999998e148 or -1.0500000000000001e103 < z < -1.62e14 or 4.9999999999999999e23 < z < 3.7999999999999998e148 or 2.2e184 < z

   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 99.8%

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

   4. Taylor expanded in z around inf 99.8%

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

   5. Taylor expanded in y around 0 64.5%

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

   if -4.1000000000000001e-54 < z < 6.3000000000000001e-40

   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 77.8%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+237}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+148}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+103}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{+14}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-54}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+23} \lor \neg \left(z \leq 3.8 \cdot 10^{+148}\right) \land z \leq 2.2 \cdot 10^{+184}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot y\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+237}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+98}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{+24}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+184}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z y))) (t_1 (* -6.0 (* x z))))
   (if (<= z -2.55e+237)
     t_0
     (if (<= z -1.45e+149)
       t_1
       (if (<= z -1e+98)
         t_0
         (if (<= z -6.4e+14)
           t_1
           (if (<= z -6.8e-54)
             t_0
             (if (<= z 1.55e-39)
               x
               (if (<= z 2.02e+24)
                 t_0
                 (if (<= z 3.8e+148)
                   t_1
                   (if (<= z 1.2e+184) t_0 (* x (* z -6.0)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -2.55e+237) {
		tmp = t_0;
	} else if (z <= -1.45e+149) {
		tmp = t_1;
	} else if (z <= -1e+98) {
		tmp = t_0;
	} else if (z <= -6.4e+14) {
		tmp = t_1;
	} else if (z <= -6.8e-54) {
		tmp = t_0;
	} else if (z <= 1.55e-39) {
		tmp = x;
	} else if (z <= 2.02e+24) {
		tmp = t_0;
	} else if (z <= 3.8e+148) {
		tmp = t_1;
	} else if (z <= 1.2e+184) {
		tmp = t_0;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (z * y)
    t_1 = (-6.0d0) * (x * z)
    if (z <= (-2.55d+237)) then
        tmp = t_0
    else if (z <= (-1.45d+149)) then
        tmp = t_1
    else if (z <= (-1d+98)) then
        tmp = t_0
    else if (z <= (-6.4d+14)) then
        tmp = t_1
    else if (z <= (-6.8d-54)) then
        tmp = t_0
    else if (z <= 1.55d-39) then
        tmp = x
    else if (z <= 2.02d+24) then
        tmp = t_0
    else if (z <= 3.8d+148) then
        tmp = t_1
    else if (z <= 1.2d+184) then
        tmp = t_0
    else
        tmp = x * (z * (-6.0d0))
    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 t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -2.55e+237) {
		tmp = t_0;
	} else if (z <= -1.45e+149) {
		tmp = t_1;
	} else if (z <= -1e+98) {
		tmp = t_0;
	} else if (z <= -6.4e+14) {
		tmp = t_1;
	} else if (z <= -6.8e-54) {
		tmp = t_0;
	} else if (z <= 1.55e-39) {
		tmp = x;
	} else if (z <= 2.02e+24) {
		tmp = t_0;
	} else if (z <= 3.8e+148) {
		tmp = t_1;
	} else if (z <= 1.2e+184) {
		tmp = t_0;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (z * y)
	t_1 = -6.0 * (x * z)
	tmp = 0
	if z <= -2.55e+237:
		tmp = t_0
	elif z <= -1.45e+149:
		tmp = t_1
	elif z <= -1e+98:
		tmp = t_0
	elif z <= -6.4e+14:
		tmp = t_1
	elif z <= -6.8e-54:
		tmp = t_0
	elif z <= 1.55e-39:
		tmp = x
	elif z <= 2.02e+24:
		tmp = t_0
	elif z <= 3.8e+148:
		tmp = t_1
	elif z <= 1.2e+184:
		tmp = t_0
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * y))
	t_1 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.55e+237)
		tmp = t_0;
	elseif (z <= -1.45e+149)
		tmp = t_1;
	elseif (z <= -1e+98)
		tmp = t_0;
	elseif (z <= -6.4e+14)
		tmp = t_1;
	elseif (z <= -6.8e-54)
		tmp = t_0;
	elseif (z <= 1.55e-39)
		tmp = x;
	elseif (z <= 2.02e+24)
		tmp = t_0;
	elseif (z <= 3.8e+148)
		tmp = t_1;
	elseif (z <= 1.2e+184)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (z * y);
	t_1 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.55e+237)
		tmp = t_0;
	elseif (z <= -1.45e+149)
		tmp = t_1;
	elseif (z <= -1e+98)
		tmp = t_0;
	elseif (z <= -6.4e+14)
		tmp = t_1;
	elseif (z <= -6.8e-54)
		tmp = t_0;
	elseif (z <= 1.55e-39)
		tmp = x;
	elseif (z <= 2.02e+24)
		tmp = t_0;
	elseif (z <= 3.8e+148)
		tmp = t_1;
	elseif (z <= 1.2e+184)
		tmp = t_0;
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e+237], t$95$0, If[LessEqual[z, -1.45e+149], t$95$1, If[LessEqual[z, -1e+98], t$95$0, If[LessEqual[z, -6.4e+14], t$95$1, If[LessEqual[z, -6.8e-54], t$95$0, If[LessEqual[z, 1.55e-39], x, If[LessEqual[z, 2.02e+24], t$95$0, If[LessEqual[z, 3.8e+148], t$95$1, If[LessEqual[z, 1.2e+184], t$95$0, N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.54999999999999989e237 or -1.4500000000000001e149 < z < -9.99999999999999998e97 or -6.4e14 < z < -6.79999999999999975e-54 or 1.54999999999999985e-39 < z < 2.0199999999999999e24 or 3.7999999999999998e148 < z < 1.19999999999999998e184

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in z around inf 86.4%

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

   5. Taylor expanded in y around inf 74.3%

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

      1. *-commutative 74.3%

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

   7. Simplified 74.3%

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

   if -2.54999999999999989e237 < z < -1.4500000000000001e149 or -9.99999999999999998e97 < z < -6.4e14 or 2.0199999999999999e24 < z < 3.7999999999999998e148

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in z around inf 99.7%

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

   5. Taylor expanded in y around 0 66.7%

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

   if -6.79999999999999975e-54 < z < 1.54999999999999985e-39

   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 77.8%

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

   if 1.19999999999999998e184 < z

   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 60.6%

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

   4. Taylor expanded in z around inf 60.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+237}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+149}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+98}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+14}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-54}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{+24}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+148}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+184}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(6 \cdot z\right)\\ t_1 := 6 \cdot \left(z \cdot y\right)\\ t_2 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+237}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.48 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+109}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+116}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+149}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* 6.0 z))) (t_1 (* 6.0 (* z y))) (t_2 (* -6.0 (* x z))))
   (if (<= z -2.2e+237)
     t_0
     (if (<= z -1.48e+150)
       t_2
       (if (<= z -6.6e+109)
         t_0
         (if (<= z -5.1e+14)
           t_2
           (if (<= z -2.9e-54)
             t_1
             (if (<= z 1.32e-39)
               x
               (if (<= z 2.6e+116)
                 t_0
                 (if (<= z 7.2e+149)
                   t_2
                   (if (<= z 3e+184) t_1 (* x (* z -6.0)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double t_1 = 6.0 * (z * y);
	double t_2 = -6.0 * (x * z);
	double tmp;
	if (z <= -2.2e+237) {
		tmp = t_0;
	} else if (z <= -1.48e+150) {
		tmp = t_2;
	} else if (z <= -6.6e+109) {
		tmp = t_0;
	} else if (z <= -5.1e+14) {
		tmp = t_2;
	} else if (z <= -2.9e-54) {
		tmp = t_1;
	} else if (z <= 1.32e-39) {
		tmp = x;
	} else if (z <= 2.6e+116) {
		tmp = t_0;
	} else if (z <= 7.2e+149) {
		tmp = t_2;
	} else if (z <= 3e+184) {
		tmp = t_1;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = y * (6.0d0 * z)
    t_1 = 6.0d0 * (z * y)
    t_2 = (-6.0d0) * (x * z)
    if (z <= (-2.2d+237)) then
        tmp = t_0
    else if (z <= (-1.48d+150)) then
        tmp = t_2
    else if (z <= (-6.6d+109)) then
        tmp = t_0
    else if (z <= (-5.1d+14)) then
        tmp = t_2
    else if (z <= (-2.9d-54)) then
        tmp = t_1
    else if (z <= 1.32d-39) then
        tmp = x
    else if (z <= 2.6d+116) then
        tmp = t_0
    else if (z <= 7.2d+149) then
        tmp = t_2
    else if (z <= 3d+184) then
        tmp = t_1
    else
        tmp = x * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double t_1 = 6.0 * (z * y);
	double t_2 = -6.0 * (x * z);
	double tmp;
	if (z <= -2.2e+237) {
		tmp = t_0;
	} else if (z <= -1.48e+150) {
		tmp = t_2;
	} else if (z <= -6.6e+109) {
		tmp = t_0;
	} else if (z <= -5.1e+14) {
		tmp = t_2;
	} else if (z <= -2.9e-54) {
		tmp = t_1;
	} else if (z <= 1.32e-39) {
		tmp = x;
	} else if (z <= 2.6e+116) {
		tmp = t_0;
	} else if (z <= 7.2e+149) {
		tmp = t_2;
	} else if (z <= 3e+184) {
		tmp = t_1;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (6.0 * z)
	t_1 = 6.0 * (z * y)
	t_2 = -6.0 * (x * z)
	tmp = 0
	if z <= -2.2e+237:
		tmp = t_0
	elif z <= -1.48e+150:
		tmp = t_2
	elif z <= -6.6e+109:
		tmp = t_0
	elif z <= -5.1e+14:
		tmp = t_2
	elif z <= -2.9e-54:
		tmp = t_1
	elif z <= 1.32e-39:
		tmp = x
	elif z <= 2.6e+116:
		tmp = t_0
	elif z <= 7.2e+149:
		tmp = t_2
	elif z <= 3e+184:
		tmp = t_1
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(6.0 * z))
	t_1 = Float64(6.0 * Float64(z * y))
	t_2 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.2e+237)
		tmp = t_0;
	elseif (z <= -1.48e+150)
		tmp = t_2;
	elseif (z <= -6.6e+109)
		tmp = t_0;
	elseif (z <= -5.1e+14)
		tmp = t_2;
	elseif (z <= -2.9e-54)
		tmp = t_1;
	elseif (z <= 1.32e-39)
		tmp = x;
	elseif (z <= 2.6e+116)
		tmp = t_0;
	elseif (z <= 7.2e+149)
		tmp = t_2;
	elseif (z <= 3e+184)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (6.0 * z);
	t_1 = 6.0 * (z * y);
	t_2 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.2e+237)
		tmp = t_0;
	elseif (z <= -1.48e+150)
		tmp = t_2;
	elseif (z <= -6.6e+109)
		tmp = t_0;
	elseif (z <= -5.1e+14)
		tmp = t_2;
	elseif (z <= -2.9e-54)
		tmp = t_1;
	elseif (z <= 1.32e-39)
		tmp = x;
	elseif (z <= 2.6e+116)
		tmp = t_0;
	elseif (z <= 7.2e+149)
		tmp = t_2;
	elseif (z <= 3e+184)
		tmp = t_1;
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+237], t$95$0, If[LessEqual[z, -1.48e+150], t$95$2, If[LessEqual[z, -6.6e+109], t$95$0, If[LessEqual[z, -5.1e+14], t$95$2, If[LessEqual[z, -2.9e-54], t$95$1, If[LessEqual[z, 1.32e-39], x, If[LessEqual[z, 2.6e+116], t$95$0, If[LessEqual[z, 7.2e+149], t$95$2, If[LessEqual[z, 3e+184], t$95$1, N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.2e237 or -1.47999999999999991e150 < z < -6.5999999999999998e109 or 1.31999999999999997e-39 < z < 2.59999999999999987e116

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in z around inf 87.4%

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

   5. Taylor expanded in y around inf 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-*r* 66.5%

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

   7. Simplified 66.5%

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

   if -2.2e237 < z < -1.47999999999999991e150 or -6.5999999999999998e109 < z < -5.1e14 or 2.59999999999999987e116 < z < 7.1999999999999999e149

   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 99.8%

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

   4. Taylor expanded in z around inf 99.8%

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

   5. Taylor expanded in y around 0 70.3%

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

   if -5.1e14 < z < -2.90000000000000015e-54 or 7.1999999999999999e149 < z < 2.99999999999999986e184

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in z around inf 90.1%

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

   5. Taylor expanded in y around inf 84.5%

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

      1. *-commutative 84.5%

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

   7. Simplified 84.5%

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

   if -2.90000000000000015e-54 < z < 1.31999999999999997e-39

   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 77.8%

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

   if 2.99999999999999986e184 < z

   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 60.6%

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

   4. Taylor expanded in z around inf 60.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+237}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.48 \cdot 10^{+150}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+109}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{+14}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-54}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+149}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+184}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(6 \cdot z\right)\\ t_1 := z \cdot \left(x \cdot -6\right)\\ t_2 := 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+237}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{+149}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+98}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+114}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+183}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* 6.0 z))) (t_1 (* z (* x -6.0))) (t_2 (* 6.0 (* z y))))
   (if (<= z -2.85e+237)
     t_0
     (if (<= z -2.95e+149)
       (* -6.0 (* x z))
       (if (<= z -3.3e+98)
         t_0
         (if (<= z -1.55e+14)
           t_1
           (if (<= z -4e-54)
             t_2
             (if (<= z 1.55e-39)
               x
               (if (<= z 2.3e+114)
                 t_0
                 (if (<= z 2.6e+149)
                   t_1
                   (if (<= z 1.45e+183) t_2 (* x (* z -6.0)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double t_1 = z * (x * -6.0);
	double t_2 = 6.0 * (z * y);
	double tmp;
	if (z <= -2.85e+237) {
		tmp = t_0;
	} else if (z <= -2.95e+149) {
		tmp = -6.0 * (x * z);
	} else if (z <= -3.3e+98) {
		tmp = t_0;
	} else if (z <= -1.55e+14) {
		tmp = t_1;
	} else if (z <= -4e-54) {
		tmp = t_2;
	} else if (z <= 1.55e-39) {
		tmp = x;
	} else if (z <= 2.3e+114) {
		tmp = t_0;
	} else if (z <= 2.6e+149) {
		tmp = t_1;
	} else if (z <= 1.45e+183) {
		tmp = t_2;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = y * (6.0d0 * z)
    t_1 = z * (x * (-6.0d0))
    t_2 = 6.0d0 * (z * y)
    if (z <= (-2.85d+237)) then
        tmp = t_0
    else if (z <= (-2.95d+149)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= (-3.3d+98)) then
        tmp = t_0
    else if (z <= (-1.55d+14)) then
        tmp = t_1
    else if (z <= (-4d-54)) then
        tmp = t_2
    else if (z <= 1.55d-39) then
        tmp = x
    else if (z <= 2.3d+114) then
        tmp = t_0
    else if (z <= 2.6d+149) then
        tmp = t_1
    else if (z <= 1.45d+183) then
        tmp = t_2
    else
        tmp = x * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double t_1 = z * (x * -6.0);
	double t_2 = 6.0 * (z * y);
	double tmp;
	if (z <= -2.85e+237) {
		tmp = t_0;
	} else if (z <= -2.95e+149) {
		tmp = -6.0 * (x * z);
	} else if (z <= -3.3e+98) {
		tmp = t_0;
	} else if (z <= -1.55e+14) {
		tmp = t_1;
	} else if (z <= -4e-54) {
		tmp = t_2;
	} else if (z <= 1.55e-39) {
		tmp = x;
	} else if (z <= 2.3e+114) {
		tmp = t_0;
	} else if (z <= 2.6e+149) {
		tmp = t_1;
	} else if (z <= 1.45e+183) {
		tmp = t_2;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (6.0 * z)
	t_1 = z * (x * -6.0)
	t_2 = 6.0 * (z * y)
	tmp = 0
	if z <= -2.85e+237:
		tmp = t_0
	elif z <= -2.95e+149:
		tmp = -6.0 * (x * z)
	elif z <= -3.3e+98:
		tmp = t_0
	elif z <= -1.55e+14:
		tmp = t_1
	elif z <= -4e-54:
		tmp = t_2
	elif z <= 1.55e-39:
		tmp = x
	elif z <= 2.3e+114:
		tmp = t_0
	elif z <= 2.6e+149:
		tmp = t_1
	elif z <= 1.45e+183:
		tmp = t_2
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(6.0 * z))
	t_1 = Float64(z * Float64(x * -6.0))
	t_2 = Float64(6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -2.85e+237)
		tmp = t_0;
	elseif (z <= -2.95e+149)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= -3.3e+98)
		tmp = t_0;
	elseif (z <= -1.55e+14)
		tmp = t_1;
	elseif (z <= -4e-54)
		tmp = t_2;
	elseif (z <= 1.55e-39)
		tmp = x;
	elseif (z <= 2.3e+114)
		tmp = t_0;
	elseif (z <= 2.6e+149)
		tmp = t_1;
	elseif (z <= 1.45e+183)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (6.0 * z);
	t_1 = z * (x * -6.0);
	t_2 = 6.0 * (z * y);
	tmp = 0.0;
	if (z <= -2.85e+237)
		tmp = t_0;
	elseif (z <= -2.95e+149)
		tmp = -6.0 * (x * z);
	elseif (z <= -3.3e+98)
		tmp = t_0;
	elseif (z <= -1.55e+14)
		tmp = t_1;
	elseif (z <= -4e-54)
		tmp = t_2;
	elseif (z <= 1.55e-39)
		tmp = x;
	elseif (z <= 2.3e+114)
		tmp = t_0;
	elseif (z <= 2.6e+149)
		tmp = t_1;
	elseif (z <= 1.45e+183)
		tmp = t_2;
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.85e+237], t$95$0, If[LessEqual[z, -2.95e+149], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e+98], t$95$0, If[LessEqual[z, -1.55e+14], t$95$1, If[LessEqual[z, -4e-54], t$95$2, If[LessEqual[z, 1.55e-39], x, If[LessEqual[z, 2.3e+114], t$95$0, If[LessEqual[z, 2.6e+149], t$95$1, If[LessEqual[z, 1.45e+183], t$95$2, N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.84999999999999997e237 or -2.9500000000000001e149 < z < -3.30000000000000028e98 or 1.54999999999999985e-39 < z < 2.3e114

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in z around inf 87.4%

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

   5. Taylor expanded in y around inf 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-*r* 66.5%

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

   7. Simplified 66.5%

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

   if -2.84999999999999997e237 < z < -2.9500000000000001e149

   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 99.7%

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

   4. Taylor expanded in z around inf 99.7%

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

   5. Taylor expanded in y around 0 68.6%

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

   if -3.30000000000000028e98 < z < -1.55e14 or 2.3e114 < z < 2.59999999999999979e149

   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 99.8%

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

   4. Taylor expanded in z around inf 99.8%

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

   5. Taylor expanded in y around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-*r* 71.9%

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

      3. *-commutative 71.9%

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

      4. associate-*r* 72.0%

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

   7. Simplified 72.0%

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

   if -1.55e14 < z < -4.0000000000000001e-54 or 2.59999999999999979e149 < z < 1.45e183

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in z around inf 90.1%

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

   5. Taylor expanded in y around inf 84.5%

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

      1. *-commutative 84.5%

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

   7. Simplified 84.5%

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

   if -4.0000000000000001e-54 < z < 1.54999999999999985e-39

   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 77.8%

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

   if 1.45e183 < z

   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 60.6%

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

   4. Taylor expanded in z around inf 60.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+237}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{+149}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-54}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+149}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+183}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + z \cdot \left(6 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{6}{\frac{1}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.6)
   (* 6.0 (* z (- y x)))
   (if (<= z 0.17) (+ x (* z (* 6.0 y))) (* z (/ 6.0 (/ 1.0 (- y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.6) {
		tmp = 6.0 * (z * (y - x));
	} else if (z <= 0.17) {
		tmp = x + (z * (6.0 * y));
	} else {
		tmp = z * (6.0 / (1.0 / (y - 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 <= (-6.6d0)) then
        tmp = 6.0d0 * (z * (y - x))
    else if (z <= 0.17d0) then
        tmp = x + (z * (6.0d0 * y))
    else
        tmp = z * (6.0d0 / (1.0d0 / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.6) {
		tmp = 6.0 * (z * (y - x));
	} else if (z <= 0.17) {
		tmp = x + (z * (6.0 * y));
	} else {
		tmp = z * (6.0 / (1.0 / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.6:
		tmp = 6.0 * (z * (y - x))
	elif z <= 0.17:
		tmp = x + (z * (6.0 * y))
	else:
		tmp = z * (6.0 / (1.0 / (y - x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.6)
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 0.17)
		tmp = Float64(x + Float64(z * Float64(6.0 * y)));
	else
		tmp = Float64(z * Float64(6.0 / Float64(1.0 / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.6)
		tmp = 6.0 * (z * (y - x));
	elseif (z <= 0.17)
		tmp = x + (z * (6.0 * y));
	else
		tmp = z * (6.0 / (1.0 / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.6], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], N[(x + N[(z * N[(6.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(6.0 / N[(1.0 / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5999999999999996

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.8%

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

   4. Taylor expanded in z around inf 99.8%

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

   if -6.5999999999999996 < 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 98.5%

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

   if 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 z around 0 99.7%

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

   4. Taylor expanded in z around inf 98.1%

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

   5. Taylor expanded in y around 0 95.0%

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

      1. +-commutative 95.0%

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

      2. *-commutative 95.0%

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

      3. metadata-eval 95.0%

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

      4. cancel-sign-sub-inv 95.0%

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

      5. associate-*l* 95.0%

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

      6. unsub-neg 95.0%

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

      7. *-commutative 95.0%

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

      8. associate-*l* 95.0%

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

      9. distribute-rgt-neg-out 95.0%

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

      10. distribute-lft-out 98.1%

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

      11. sub-neg 98.1%

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

      12. *-commutative 98.1%

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

      13. associate-*r* 98.0%

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

   7. Simplified 98.0%

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

      1. associate-*r* 98.1%

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

      2. flip-- 73.6%

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

      3. associate-*r/ 63.5%

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

      4. pow2 63.5%

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

      5. pow2 63.5%

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

   9. Applied egg-rr 63.5%

      \[\leadsto \color{blue}{\frac{\left(z \cdot 6\right) \cdot \left({y}^{2} - {x}^{2}\right)}{y + x}} \]
   10. Step-by-step derivation

       1. associate-/l* 73.6%

          \[\leadsto \color{blue}{\frac{z \cdot 6}{\frac{y + x}{{y}^{2} - {x}^{2}}}} \]

       2. *-commutative 73.6%

          \[\leadsto \frac{\color{blue}{6 \cdot z}}{\frac{y + x}{{y}^{2} - {x}^{2}}} \]

       3. associate-/l* 73.6%

          \[\leadsto \color{blue}{\frac{6}{\frac{\frac{y + x}{{y}^{2} - {x}^{2}}}{z}}} \]

       4. associate-/r/ 73.7%

          \[\leadsto \color{blue}{\frac{6}{\frac{y + x}{{y}^{2} - {x}^{2}}} \cdot z} \]

       5. unpow2 73.7%

          \[\leadsto \frac{6}{\frac{y + x}{\color{blue}{y \cdot y} - {x}^{2}}} \cdot z \]

       6. unpow2 73.7%

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

       7. difference-of-squares 76.8%

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

       8. associate-/r* 98.2%

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

       9. *-inverses 98.2%

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

   11. Simplified 98.2%

       \[\leadsto \color{blue}{\frac{6}{\frac{1}{y - x}} \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + z \cdot \left(6 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{6}{\frac{1}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-54} \lor \neg \left(z \leq 1.5 \cdot 10^{-39}\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.5e-54) (not (<= z 1.5e-39))) (* 6.0 (* z (- y x))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.5e-54) || !(z <= 1.5e-39)) {
		tmp = 6.0 * (z * (y - 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 <= (-6.5d-54)) .or. (.not. (z <= 1.5d-39))) then
        tmp = 6.0d0 * (z * (y - 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 <= -6.5e-54) || !(z <= 1.5e-39)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.5e-54) or not (z <= 1.5e-39):
		tmp = 6.0 * (z * (y - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.5e-54) || !(z <= 1.5e-39))
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.5e-54) || ~((z <= 1.5e-39)))
		tmp = 6.0 * (z * (y - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.5e-54], N[Not[LessEqual[z, 1.5e-39]], $MachinePrecision]], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.49999999999999991e-54 or 1.50000000000000014e-39 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.8%

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

   4. Taylor expanded in z around inf 93.9%

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

   if -6.49999999999999991e-54 < z < 1.50000000000000014e-39

   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 77.8%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-54} \lor \neg \left(z \leq 1.5 \cdot 10^{-39}\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-54} \lor \neg \left(z \leq 550\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.6e-54) (not (<= z 550.0)))
   (* 6.0 (* z (- y x)))
   (* x (+ 1.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.6e-54) || !(z <= 550.0)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x * (1.0 + (z * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.6d-54)) .or. (.not. (z <= 550.0d0))) then
        tmp = 6.0d0 * (z * (y - x))
    else
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.6e-54) || !(z <= 550.0)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x * (1.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.6e-54) or not (z <= 550.0):
		tmp = 6.0 * (z * (y - x))
	else:
		tmp = x * (1.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.6e-54) || !(z <= 550.0))
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.6e-54) || ~((z <= 550.0)))
		tmp = 6.0 * (z * (y - x));
	else
		tmp = x * (1.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.6e-54], N[Not[LessEqual[z, 550.0]], $MachinePrecision]], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.59999999999999976e-54 or 550 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.8%

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

   4. Taylor expanded in z around inf 98.1%

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

   if -3.59999999999999976e-54 < z < 550

   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 74.9%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-54} \lor \neg \left(z \leq 550\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+14} \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.05e+14) (not (<= z 0.17)))
   (* 6.0 (* z (- y x)))
   (+ x (* 6.0 (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05e+14) || !(z <= 0.17)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x + (6.0 * (z * 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 <= (-1.05d+14)) .or. (.not. (z <= 0.17d0))) then
        tmp = 6.0d0 * (z * (y - x))
    else
        tmp = x + (6.0d0 * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05e+14) || !(z <= 0.17)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x + (6.0 * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.05e+14) or not (z <= 0.17):
		tmp = 6.0 * (z * (y - x))
	else:
		tmp = x + (6.0 * (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.05e+14) || !(z <= 0.17))
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	else
		tmp = Float64(x + Float64(6.0 * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.05e+14) || ~((z <= 0.17)))
		tmp = 6.0 * (z * (y - x));
	else
		tmp = x + (6.0 * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.05e+14], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e14 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 z around 0 99.8%

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

   4. Taylor expanded in z around inf 98.9%

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

   if -1.05e14 < 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 98.5%

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

      1. *-commutative 98.5%

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

   5. Simplified 98.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+14} \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.6) (not (<= z 0.17)))
   (* 6.0 (* z (- y x)))
   (+ x (* z (* 6.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.6) || !(z <= 0.17)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x + (z * (6.0 * 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 <= (-6.6d0)) .or. (.not. (z <= 0.17d0))) then
        tmp = 6.0d0 * (z * (y - x))
    else
        tmp = x + (z * (6.0d0 * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.6) || !(z <= 0.17)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x + (z * (6.0 * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.6) or not (z <= 0.17):
		tmp = 6.0 * (z * (y - x))
	else:
		tmp = x + (z * (6.0 * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.6) || !(z <= 0.17))
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	else
		tmp = Float64(x + Float64(z * Float64(6.0 * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.6) || ~((z <= 0.17)))
		tmp = 6.0 * (z * (y - x));
	else
		tmp = x + (z * (6.0 * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.6], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(6.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5999999999999996 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 z around 0 99.7%

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

   4. Taylor expanded in z around inf 98.9%

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

   if -6.5999999999999996 < 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 98.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-9} \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.6e-9) (not (<= z 0.17))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.6e-9) || !(z <= 0.17)) {
		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 <= (-6.6d-9)) .or. (.not. (z <= 0.17d0))) 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 <= -6.6e-9) || !(z <= 0.17)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.6e-9) or not (z <= 0.17):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.6e-9) || !(z <= 0.17))
		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 <= -6.6e-9) || ~((z <= 0.17)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.6e-9], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.60000000000000037e-9 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 z around 0 99.8%

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

   4. Taylor expanded in z around inf 99.0%

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

   5. Taylor expanded in y around 0 48.4%

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

   if -6.60000000000000037e-9 < 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 71.9%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-9} \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.5% 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 35.8%

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

4. Final simplification 35.8%

   \[\leadsto x \]
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 2024031 
(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)))