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

Percentage Accurate: 99.7% → 99.8%

Time: 9.4s

Alternatives: 12

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 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 99.9%

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

   1. associate-*l* 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 60.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+241}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+71}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3700:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+216}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* -6.0 (* x z))))
   (if (<= z -4.9e+241)
     t_0
     (if (<= z -1.3e+130)
       t_1
       (if (<= z -1.55e+71)
         t_0
         (if (<= z -3700.0)
           t_1
           (if (<= z 0.065) x (if (<= z 2.1e+216) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -4.9e+241) {
		tmp = t_0;
	} else if (z <= -1.3e+130) {
		tmp = t_1;
	} else if (z <= -1.55e+71) {
		tmp = t_0;
	} else if (z <= -3700.0) {
		tmp = t_1;
	} else if (z <= 0.065) {
		tmp = x;
	} else if (z <= 2.1e+216) {
		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 * (y * z)
    t_1 = (-6.0d0) * (x * z)
    if (z <= (-4.9d+241)) then
        tmp = t_0
    else if (z <= (-1.3d+130)) then
        tmp = t_1
    else if (z <= (-1.55d+71)) then
        tmp = t_0
    else if (z <= (-3700.0d0)) then
        tmp = t_1
    else if (z <= 0.065d0) then
        tmp = x
    else if (z <= 2.1d+216) 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 * (y * z);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -4.9e+241) {
		tmp = t_0;
	} else if (z <= -1.3e+130) {
		tmp = t_1;
	} else if (z <= -1.55e+71) {
		tmp = t_0;
	} else if (z <= -3700.0) {
		tmp = t_1;
	} else if (z <= 0.065) {
		tmp = x;
	} else if (z <= 2.1e+216) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = -6.0 * (x * z)
	tmp = 0
	if z <= -4.9e+241:
		tmp = t_0
	elif z <= -1.3e+130:
		tmp = t_1
	elif z <= -1.55e+71:
		tmp = t_0
	elif z <= -3700.0:
		tmp = t_1
	elif z <= 0.065:
		tmp = x
	elif z <= 2.1e+216:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -4.9e+241)
		tmp = t_0;
	elseif (z <= -1.3e+130)
		tmp = t_1;
	elseif (z <= -1.55e+71)
		tmp = t_0;
	elseif (z <= -3700.0)
		tmp = t_1;
	elseif (z <= 0.065)
		tmp = x;
	elseif (z <= 2.1e+216)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -4.9e+241)
		tmp = t_0;
	elseif (z <= -1.3e+130)
		tmp = t_1;
	elseif (z <= -1.55e+71)
		tmp = t_0;
	elseif (z <= -3700.0)
		tmp = t_1;
	elseif (z <= 0.065)
		tmp = x;
	elseif (z <= 2.1e+216)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.9e+241], t$95$0, If[LessEqual[z, -1.3e+130], t$95$1, If[LessEqual[z, -1.55e+71], t$95$0, If[LessEqual[z, -3700.0], t$95$1, If[LessEqual[z, 0.065], x, If[LessEqual[z, 2.1e+216], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.89999999999999972e241 or -1.2999999999999999e130 < z < -1.55000000000000009e71 or 0.065000000000000002 < z < 2.10000000000000001e216

   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 0 94.7%

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

   4. Taylor expanded in y around inf 64.4%

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

      1. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   if -4.89999999999999972e241 < z < -1.2999999999999999e130 or -1.55000000000000009e71 < z < -3700 or 2.10000000000000001e216 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-define 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sub-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 97.1%

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

   6. Taylor expanded in x around inf 65.8%

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

   if -3700 < z < 0.065000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+241}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+130}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+71}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3700:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+216}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+241}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+130}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+70}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3700:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+215}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* x (* z -6.0))))
   (if (<= z -3.1e+241)
     t_0
     (if (<= z -1.1e+130)
       (* -6.0 (* x z))
       (if (<= z -1.26e+70)
         t_0
         (if (<= z -3700.0)
           t_1
           (if (<= z 0.065) x (if (<= z 4.5e+215) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = x * (z * -6.0);
	double tmp;
	if (z <= -3.1e+241) {
		tmp = t_0;
	} else if (z <= -1.1e+130) {
		tmp = -6.0 * (x * z);
	} else if (z <= -1.26e+70) {
		tmp = t_0;
	} else if (z <= -3700.0) {
		tmp = t_1;
	} else if (z <= 0.065) {
		tmp = x;
	} else if (z <= 4.5e+215) {
		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 * (y * z)
    t_1 = x * (z * (-6.0d0))
    if (z <= (-3.1d+241)) then
        tmp = t_0
    else if (z <= (-1.1d+130)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= (-1.26d+70)) then
        tmp = t_0
    else if (z <= (-3700.0d0)) then
        tmp = t_1
    else if (z <= 0.065d0) then
        tmp = x
    else if (z <= 4.5d+215) 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 * (y * z);
	double t_1 = x * (z * -6.0);
	double tmp;
	if (z <= -3.1e+241) {
		tmp = t_0;
	} else if (z <= -1.1e+130) {
		tmp = -6.0 * (x * z);
	} else if (z <= -1.26e+70) {
		tmp = t_0;
	} else if (z <= -3700.0) {
		tmp = t_1;
	} else if (z <= 0.065) {
		tmp = x;
	} else if (z <= 4.5e+215) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = x * (z * -6.0)
	tmp = 0
	if z <= -3.1e+241:
		tmp = t_0
	elif z <= -1.1e+130:
		tmp = -6.0 * (x * z)
	elif z <= -1.26e+70:
		tmp = t_0
	elif z <= -3700.0:
		tmp = t_1
	elif z <= 0.065:
		tmp = x
	elif z <= 4.5e+215:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(x * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -3.1e+241)
		tmp = t_0;
	elseif (z <= -1.1e+130)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= -1.26e+70)
		tmp = t_0;
	elseif (z <= -3700.0)
		tmp = t_1;
	elseif (z <= 0.065)
		tmp = x;
	elseif (z <= 4.5e+215)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = x * (z * -6.0);
	tmp = 0.0;
	if (z <= -3.1e+241)
		tmp = t_0;
	elseif (z <= -1.1e+130)
		tmp = -6.0 * (x * z);
	elseif (z <= -1.26e+70)
		tmp = t_0;
	elseif (z <= -3700.0)
		tmp = t_1;
	elseif (z <= 0.065)
		tmp = x;
	elseif (z <= 4.5e+215)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+241], t$95$0, If[LessEqual[z, -1.1e+130], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.26e+70], t$95$0, If[LessEqual[z, -3700.0], t$95$1, If[LessEqual[z, 0.065], x, If[LessEqual[z, 4.5e+215], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1000000000000001e241 or -1.09999999999999997e130 < z < -1.26000000000000001e70 or 0.065000000000000002 < z < 4.5000000000000002e215

   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 0 94.7%

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

   4. Taylor expanded in y around inf 64.4%

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

      1. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   if -3.1000000000000001e241 < z < -1.09999999999999997e130

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. fma-define 99.9%

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

      4. remove-double-neg 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sub-neg 99.9%

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

      8. distribute-neg-in 99.9%

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

      9. remove-double-neg 99.9%

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

      10. +-commutative 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.9%

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

   6. Taylor expanded in x around inf 70.7%

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

   if -1.26000000000000001e70 < z < -3700 or 4.5000000000000002e215 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 94.5%

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

   4. Taylor expanded in z around inf 95.4%

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

      1. metadata-eval 95.4%

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

      2. associate-*r* 95.4%

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

      3. neg-mul-1 95.4%

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

      4. distribute-lft-in 95.5%

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

      5. sub-neg 95.5%

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

      6. associate-*r* 95.6%

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

      7. *-commutative 95.6%

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

   6. Simplified 95.6%

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

   7. Taylor expanded in x around inf 62.9%

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

      1. associate-*r* 62.9%

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

      2. *-commutative 62.9%

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

   9. Simplified 62.9%

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

   10. Taylor expanded in z around 0 62.9%

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

       1. *-commutative 62.9%

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

       2. associate-*l* 63.0%

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

   12. Simplified 63.0%

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

   if -3700 < z < 0.065000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+241}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+130}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+70}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3700:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+215}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+242}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+130}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+70}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3700:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+219}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* x (* z -6.0))))
   (if (<= z -3.5e+242)
     t_0
     (if (<= z -3.3e+130)
       (* z (* x -6.0))
       (if (<= z -9e+70)
         t_0
         (if (<= z -3700.0)
           t_1
           (if (<= z 0.065) x (if (<= z 9e+219) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = x * (z * -6.0);
	double tmp;
	if (z <= -3.5e+242) {
		tmp = t_0;
	} else if (z <= -3.3e+130) {
		tmp = z * (x * -6.0);
	} else if (z <= -9e+70) {
		tmp = t_0;
	} else if (z <= -3700.0) {
		tmp = t_1;
	} else if (z <= 0.065) {
		tmp = x;
	} else if (z <= 9e+219) {
		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 * (y * z)
    t_1 = x * (z * (-6.0d0))
    if (z <= (-3.5d+242)) then
        tmp = t_0
    else if (z <= (-3.3d+130)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= (-9d+70)) then
        tmp = t_0
    else if (z <= (-3700.0d0)) then
        tmp = t_1
    else if (z <= 0.065d0) then
        tmp = x
    else if (z <= 9d+219) 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 * (y * z);
	double t_1 = x * (z * -6.0);
	double tmp;
	if (z <= -3.5e+242) {
		tmp = t_0;
	} else if (z <= -3.3e+130) {
		tmp = z * (x * -6.0);
	} else if (z <= -9e+70) {
		tmp = t_0;
	} else if (z <= -3700.0) {
		tmp = t_1;
	} else if (z <= 0.065) {
		tmp = x;
	} else if (z <= 9e+219) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = x * (z * -6.0)
	tmp = 0
	if z <= -3.5e+242:
		tmp = t_0
	elif z <= -3.3e+130:
		tmp = z * (x * -6.0)
	elif z <= -9e+70:
		tmp = t_0
	elif z <= -3700.0:
		tmp = t_1
	elif z <= 0.065:
		tmp = x
	elif z <= 9e+219:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(x * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -3.5e+242)
		tmp = t_0;
	elseif (z <= -3.3e+130)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= -9e+70)
		tmp = t_0;
	elseif (z <= -3700.0)
		tmp = t_1;
	elseif (z <= 0.065)
		tmp = x;
	elseif (z <= 9e+219)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = x * (z * -6.0);
	tmp = 0.0;
	if (z <= -3.5e+242)
		tmp = t_0;
	elseif (z <= -3.3e+130)
		tmp = z * (x * -6.0);
	elseif (z <= -9e+70)
		tmp = t_0;
	elseif (z <= -3700.0)
		tmp = t_1;
	elseif (z <= 0.065)
		tmp = x;
	elseif (z <= 9e+219)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+242], t$95$0, If[LessEqual[z, -3.3e+130], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e+70], t$95$0, If[LessEqual[z, -3700.0], t$95$1, If[LessEqual[z, 0.065], x, If[LessEqual[z, 9e+219], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4999999999999999e242 or -3.3e130 < z < -8.9999999999999999e70 or 0.065000000000000002 < z < 9.00000000000000047e219

   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 0 94.7%

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

   4. Taylor expanded in y around inf 64.4%

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

      1. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   if -3.4999999999999999e242 < z < -3.3e130

   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 0 99.7%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. metadata-eval 99.9%

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

      2. associate-*r* 99.9%

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

      3. neg-mul-1 99.9%

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

      4. distribute-lft-in 99.9%

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

      5. sub-neg 99.9%

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

      6. associate-*r* 99.9%

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

      7. *-commutative 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in x around inf 70.7%

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

      1. associate-*r* 70.7%

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

      2. *-commutative 70.7%

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

   9. Simplified 70.7%

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

   if -8.9999999999999999e70 < z < -3700 or 9.00000000000000047e219 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 94.5%

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

   4. Taylor expanded in z around inf 95.4%

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

      1. metadata-eval 95.4%

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

      2. associate-*r* 95.4%

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

      3. neg-mul-1 95.4%

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

      4. distribute-lft-in 95.5%

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

      5. sub-neg 95.5%

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

      6. associate-*r* 95.6%

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

      7. *-commutative 95.6%

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

   6. Simplified 95.6%

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

   7. Taylor expanded in x around inf 62.9%

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

      1. associate-*r* 62.9%

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

      2. *-commutative 62.9%

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

   9. Simplified 62.9%

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

   10. Taylor expanded in z around 0 62.9%

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

       1. *-commutative 62.9%

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

       2. associate-*l* 63.0%

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

   12. Simplified 63.0%

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

   if -3700 < z < 0.065000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+242}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+130}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+70}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3700:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+219}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+242}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+130}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+71}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3700:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+216}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* x (* z -6.0))))
   (if (<= z -1.7e+242)
     t_0
     (if (<= z -1.06e+130)
       (* z (* x -6.0))
       (if (<= z -1.06e+71)
         t_0
         (if (<= z -3700.0)
           t_1
           (if (<= z 0.065) x (if (<= z 1.2e+216) (* z (* y 6.0)) t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = x * (z * -6.0);
	double tmp;
	if (z <= -1.7e+242) {
		tmp = t_0;
	} else if (z <= -1.06e+130) {
		tmp = z * (x * -6.0);
	} else if (z <= -1.06e+71) {
		tmp = t_0;
	} else if (z <= -3700.0) {
		tmp = t_1;
	} else if (z <= 0.065) {
		tmp = x;
	} else if (z <= 1.2e+216) {
		tmp = z * (y * 6.0);
	} 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 * (y * z)
    t_1 = x * (z * (-6.0d0))
    if (z <= (-1.7d+242)) then
        tmp = t_0
    else if (z <= (-1.06d+130)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= (-1.06d+71)) then
        tmp = t_0
    else if (z <= (-3700.0d0)) then
        tmp = t_1
    else if (z <= 0.065d0) then
        tmp = x
    else if (z <= 1.2d+216) then
        tmp = z * (y * 6.0d0)
    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 * (y * z);
	double t_1 = x * (z * -6.0);
	double tmp;
	if (z <= -1.7e+242) {
		tmp = t_0;
	} else if (z <= -1.06e+130) {
		tmp = z * (x * -6.0);
	} else if (z <= -1.06e+71) {
		tmp = t_0;
	} else if (z <= -3700.0) {
		tmp = t_1;
	} else if (z <= 0.065) {
		tmp = x;
	} else if (z <= 1.2e+216) {
		tmp = z * (y * 6.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = x * (z * -6.0)
	tmp = 0
	if z <= -1.7e+242:
		tmp = t_0
	elif z <= -1.06e+130:
		tmp = z * (x * -6.0)
	elif z <= -1.06e+71:
		tmp = t_0
	elif z <= -3700.0:
		tmp = t_1
	elif z <= 0.065:
		tmp = x
	elif z <= 1.2e+216:
		tmp = z * (y * 6.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(x * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -1.7e+242)
		tmp = t_0;
	elseif (z <= -1.06e+130)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= -1.06e+71)
		tmp = t_0;
	elseif (z <= -3700.0)
		tmp = t_1;
	elseif (z <= 0.065)
		tmp = x;
	elseif (z <= 1.2e+216)
		tmp = Float64(z * Float64(y * 6.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = x * (z * -6.0);
	tmp = 0.0;
	if (z <= -1.7e+242)
		tmp = t_0;
	elseif (z <= -1.06e+130)
		tmp = z * (x * -6.0);
	elseif (z <= -1.06e+71)
		tmp = t_0;
	elseif (z <= -3700.0)
		tmp = t_1;
	elseif (z <= 0.065)
		tmp = x;
	elseif (z <= 1.2e+216)
		tmp = z * (y * 6.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+242], t$95$0, If[LessEqual[z, -1.06e+130], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.06e+71], t$95$0, If[LessEqual[z, -3700.0], t$95$1, If[LessEqual[z, 0.065], x, If[LessEqual[z, 1.2e+216], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.69999999999999991e242 or -1.06e130 < z < -1.06e71

   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 0 93.9%

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

   4. Taylor expanded in y around inf 70.4%

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

      1. *-commutative 70.4%

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

   6. Simplified 70.4%

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

   if -1.69999999999999991e242 < z < -1.06e130

   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 0 99.7%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. metadata-eval 99.9%

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

      2. associate-*r* 99.9%

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

      3. neg-mul-1 99.9%

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

      4. distribute-lft-in 99.9%

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

      5. sub-neg 99.9%

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

      6. associate-*r* 99.9%

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

      7. *-commutative 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in x around inf 70.7%

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

      1. associate-*r* 70.7%

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

      2. *-commutative 70.7%

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

   9. Simplified 70.7%

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

   if -1.06e71 < z < -3700 or 1.2e216 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 94.5%

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

   4. Taylor expanded in z around inf 95.4%

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

      1. metadata-eval 95.4%

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

      2. associate-*r* 95.4%

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

      3. neg-mul-1 95.4%

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

      4. distribute-lft-in 95.5%

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

      5. sub-neg 95.5%

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

      6. associate-*r* 95.6%

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

      7. *-commutative 95.6%

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

   6. Simplified 95.6%

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

   7. Taylor expanded in x around inf 62.9%

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

      1. associate-*r* 62.9%

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

      2. *-commutative 62.9%

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

   9. Simplified 62.9%

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

   10. Taylor expanded in z around 0 62.9%

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

       1. *-commutative 62.9%

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

       2. associate-*l* 63.0%

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

   12. Simplified 63.0%

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

   if -3700 < z < 0.065000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.5%

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

   if 0.065000000000000002 < z < 1.2e216

   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 0 95.3%

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

   4. Taylor expanded in y around inf 59.9%

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

      1. associate-*r* 60.1%

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

      2. *-commutative 60.1%

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

   6. Simplified 60.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+242}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+130}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+71}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3700:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+216}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-14} \lor \neg \left(z \leq 0.065\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.4e-14) (not (<= z 0.065))) (* -6.0 (* z (- x y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.4e-14) || !(z <= 0.065)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.4d-14)) .or. (.not. (z <= 0.065d0))) then
        tmp = (-6.0d0) * (z * (x - y))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.4e-14) || !(z <= 0.065)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.4e-14) or not (z <= 0.065):
		tmp = -6.0 * (z * (x - y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.4e-14) || !(z <= 0.065))
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.4e-14) || ~((z <= 0.065)))
		tmp = -6.0 * (z * (x - y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.4e-14], N[Not[LessEqual[z, 0.065]], $MachinePrecision]], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.40000000000000003e-14 or 0.065000000000000002 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-define 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sub-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 98.1%

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

   if -3.40000000000000003e-14 < z < 0.065000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 80.9%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-14} \lor \neg \left(z \leq 0.065\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-11} \lor \neg \left(z \leq 0.065\right):\\ \;\;\;\;\left(z \cdot -6\right) \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.5e-11) (not (<= z 0.065))) (* (* z -6.0) (- x y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.5e-11) || !(z <= 0.065)) {
		tmp = (z * -6.0) * (x - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-9.5d-11)) .or. (.not. (z <= 0.065d0))) then
        tmp = (z * (-6.0d0)) * (x - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.5e-11) || !(z <= 0.065)) {
		tmp = (z * -6.0) * (x - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.5e-11) or not (z <= 0.065):
		tmp = (z * -6.0) * (x - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.5e-11) || !(z <= 0.065))
		tmp = Float64(Float64(z * -6.0) * Float64(x - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9.5e-11) || ~((z <= 0.065)))
		tmp = (z * -6.0) * (x - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.5e-11], N[Not[LessEqual[z, 0.065]], $MachinePrecision]], N[(N[(z * -6.0), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.49999999999999951e-11 or 0.065000000000000002 < 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 0 95.5%

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

   4. Taylor expanded in z around inf 98.2%

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

      1. metadata-eval 98.2%

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

      2. associate-*r* 98.2%

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

      3. neg-mul-1 98.2%

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

      4. distribute-lft-in 98.2%

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

      5. sub-neg 98.2%

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

      6. associate-*r* 98.3%

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

      7. *-commutative 98.3%

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

   6. Simplified 98.3%

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

   if -9.49999999999999951e-11 < z < 0.065000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 80.9%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-11} \lor \neg \left(z \leq 0.065\right):\\ \;\;\;\;\left(z \cdot -6\right) \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-12} \lor \neg \left(z \leq 70\right):\\ \;\;\;\;\left(z \cdot -6\right) \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6e-12) (not (<= z 70.0)))
   (* (* z -6.0) (- x y))
   (+ x (* x (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e-12) || !(z <= 70.0)) {
		tmp = (z * -6.0) * (x - y);
	} else {
		tmp = x + (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) :: tmp
    if ((z <= (-6d-12)) .or. (.not. (z <= 70.0d0))) then
        tmp = (z * (-6.0d0)) * (x - y)
    else
        tmp = x + (x * (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e-12) || !(z <= 70.0)) {
		tmp = (z * -6.0) * (x - y);
	} else {
		tmp = x + (x * (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6e-12) or not (z <= 70.0):
		tmp = (z * -6.0) * (x - y)
	else:
		tmp = x + (x * (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6e-12) || !(z <= 70.0))
		tmp = Float64(Float64(z * -6.0) * Float64(x - y));
	else
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6e-12) || ~((z <= 70.0)))
		tmp = (z * -6.0) * (x - y);
	else
		tmp = x + (x * (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6e-12], N[Not[LessEqual[z, 70.0]], $MachinePrecision]], N[(N[(z * -6.0), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000003e-12 or 70 < 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 0 95.5%

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

   4. Taylor expanded in z around inf 98.2%

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

      1. metadata-eval 98.2%

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

      2. associate-*r* 98.2%

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

      3. neg-mul-1 98.2%

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

      4. distribute-lft-in 98.2%

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

      5. sub-neg 98.2%

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

      6. associate-*r* 98.3%

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

      7. *-commutative 98.3%

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

   6. Simplified 98.3%

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

   if -6.0000000000000003e-12 < z < 70

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.6%

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

      1. associate-*r* 82.6%

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

      2. *-commutative 82.6%

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

      3. associate-*r* 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-12} \lor \neg \left(z \leq 70\right):\\ \;\;\;\;\left(z \cdot -6\right) \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.8% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 0.17)))
   (* (* z -6.0) (- x y))
   (+ x (* y (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.17)) {
		tmp = (z * -6.0) * (x - y);
	} 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 <= (-0.165d0)) .or. (.not. (z <= 0.17d0))) then
        tmp = (z * (-6.0d0)) * (x - y)
    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 <= -0.165) || !(z <= 0.17)) {
		tmp = (z * -6.0) * (x - y);
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 0.17):
		tmp = (z * -6.0) * (x - y)
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 0.17))
		tmp = Float64(Float64(z * -6.0) * Float64(x - y));
	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 <= -0.165) || ~((z <= 0.17)))
		tmp = (z * -6.0) * (x - y);
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(N[(z * -6.0), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 0.170000000000000012 < 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 0 95.5%

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

   4. Taylor expanded in z around inf 98.2%

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

      1. metadata-eval 98.2%

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

      2. associate-*r* 98.2%

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

      3. neg-mul-1 98.2%

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

      4. distribute-lft-in 98.2%

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

      5. sub-neg 98.2%

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

      6. associate-*r* 98.3%

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

      7. *-commutative 98.3%

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

   6. Simplified 98.3%

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

   if -0.165000000000000008 < z < 0.170000000000000012

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 98.3%

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

   4. Taylor expanded in y around 0 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-*l* 98.3%

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

   6. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 10: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3700 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3700.0) (not (<= z 0.17))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3700.0) || !(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 <= (-3700.0d0)) .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 <= -3700.0) || !(z <= 0.17)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3700.0) 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 <= -3700.0) || !(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 <= -3700.0) || ~((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, -3700.0], 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 < -3700 or 0.170000000000000012 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-define 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sub-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 98.6%

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

   6. Taylor expanded in x around inf 51.7%

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

   if -3700 < z < 0.170000000000000012

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.5%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3700 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

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 99.9%

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

3. Final simplification 99.9%

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

Alternative 12: 36.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around 0 37.7%

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

4. Final simplification 37.7%

   \[\leadsto x \]
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 2024040 
(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)))