Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I

Percentage Accurate: 95.6% → 97.6%

Time: 3.1s

Alternatives: 5

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (y * 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 * (1.0d0 - (y * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Python

def code(x, y, z):
	return x * (1.0 - (y * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(y * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (y * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (y * 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 * (1.0d0 - (y * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Python

def code(x, y, z):
	return x * (1.0 - (y * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(y * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (y * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - y \cdot z\right)\\ \mathbf{if}\;t_0 \leq 10^{+306}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* y z)))))
   (if (<= t_0 1e+306) t_0 (* y (* x (- z))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= 1e+306) {
		tmp = t_0;
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 - (y * z))
    if (t_0 <= 1d+306) then
        tmp = t_0
    else
        tmp = y * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= 1e+306) {
		tmp = t_0;
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - (y * z))
	tmp = 0
	if t_0 <= 1e+306:
		tmp = t_0
	else:
		tmp = y * (x * -z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(y * z)))
	tmp = 0.0
	if (t_0 <= 1e+306)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - (y * z));
	tmp = 0.0;
	if (t_0 <= 1e+306)
		tmp = t_0;
	else
		tmp = y * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 1e+306], t$95$0, N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 y z))) < 1.00000000000000002e306

   1. Initial program 99.0%

      \[x \cdot \left(1 - y \cdot z\right) \]

   if 1.00000000000000002e306 < (*.f64 x (-.f64 1 (*.f64 y z)))

   1. Initial program 84.8%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 84.8%

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

      1. mul-1-neg 84.8%

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

      2. associate-*r* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-*r* 100.0%

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

      6. distribute-rgt-neg-out 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - y \cdot z\right) \leq 10^{+306}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 2: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+56} \lor \neg \left(y \leq -1.65 \cdot 10^{-15}\right) \land \left(y \leq -3.7 \cdot 10^{-28} \lor \neg \left(y \leq 1.95 \cdot 10^{-62}\right)\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8e+56)
         (and (not (<= y -1.65e-15))
              (or (<= y -3.7e-28) (not (<= y 1.95e-62)))))
   (* z (* y (- x)))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8e+56) || (!(y <= -1.65e-15) && ((y <= -3.7e-28) || !(y <= 1.95e-62)))) {
		tmp = 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 ((y <= (-8d+56)) .or. (.not. (y <= (-1.65d-15))) .and. (y <= (-3.7d-28)) .or. (.not. (y <= 1.95d-62))) then
        tmp = 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 ((y <= -8e+56) || (!(y <= -1.65e-15) && ((y <= -3.7e-28) || !(y <= 1.95e-62)))) {
		tmp = z * (y * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8e+56) or (not (y <= -1.65e-15) and ((y <= -3.7e-28) or not (y <= 1.95e-62))):
		tmp = z * (y * -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8e+56) || (!(y <= -1.65e-15) && ((y <= -3.7e-28) || !(y <= 1.95e-62))))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8e+56) || (~((y <= -1.65e-15)) && ((y <= -3.7e-28) || ~((y <= 1.95e-62)))))
		tmp = z * (y * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8e+56], And[N[Not[LessEqual[y, -1.65e-15]], $MachinePrecision], Or[LessEqual[y, -3.7e-28], N[Not[LessEqual[y, 1.95e-62]], $MachinePrecision]]]], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.00000000000000074e56 or -1.65e-15 < y < -3.7000000000000002e-28 or 1.9500000000000002e-62 < y

   1. Initial program 94.9%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 71.2%

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

      1. mul-1-neg 71.2%

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

      2. associate-*r* 69.3%

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

   4. Simplified 69.3%

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

   if -8.00000000000000074e56 < y < -1.65e-15 or -3.7000000000000002e-28 < y < 1.9500000000000002e-62

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around 0 78.1%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+56} \lor \neg \left(y \leq -1.65 \cdot 10^{-15}\right) \land \left(y \leq -3.7 \cdot 10^{-28} \lor \neg \left(y \leq 1.95 \cdot 10^{-62}\right)\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 70.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+58}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y (- z)))))
   (if (<= y -4.6e+58)
     t_0
     (if (<= y -8.5e-15)
       x
       (if (<= y -1.45e-29) t_0 (if (<= y 3.4e-62) x (* z (* y (- x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * -z);
	double tmp;
	if (y <= -4.6e+58) {
		tmp = t_0;
	} else if (y <= -8.5e-15) {
		tmp = x;
	} else if (y <= -1.45e-29) {
		tmp = t_0;
	} else if (y <= 3.4e-62) {
		tmp = x;
	} else {
		tmp = z * (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) :: t_0
    real(8) :: tmp
    t_0 = x * (y * -z)
    if (y <= (-4.6d+58)) then
        tmp = t_0
    else if (y <= (-8.5d-15)) then
        tmp = x
    else if (y <= (-1.45d-29)) then
        tmp = t_0
    else if (y <= 3.4d-62) then
        tmp = x
    else
        tmp = z * (y * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y * -z);
	double tmp;
	if (y <= -4.6e+58) {
		tmp = t_0;
	} else if (y <= -8.5e-15) {
		tmp = x;
	} else if (y <= -1.45e-29) {
		tmp = t_0;
	} else if (y <= 3.4e-62) {
		tmp = x;
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * -z)
	tmp = 0
	if y <= -4.6e+58:
		tmp = t_0
	elif y <= -8.5e-15:
		tmp = x
	elif y <= -1.45e-29:
		tmp = t_0
	elif y <= 3.4e-62:
		tmp = x
	else:
		tmp = z * (y * -x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * Float64(-z)))
	tmp = 0.0
	if (y <= -4.6e+58)
		tmp = t_0;
	elseif (y <= -8.5e-15)
		tmp = x;
	elseif (y <= -1.45e-29)
		tmp = t_0;
	elseif (y <= 3.4e-62)
		tmp = x;
	else
		tmp = Float64(z * Float64(y * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y * -z);
	tmp = 0.0;
	if (y <= -4.6e+58)
		tmp = t_0;
	elseif (y <= -8.5e-15)
		tmp = x;
	elseif (y <= -1.45e-29)
		tmp = t_0;
	elseif (y <= 3.4e-62)
		tmp = x;
	else
		tmp = z * (y * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+58], t$95$0, If[LessEqual[y, -8.5e-15], x, If[LessEqual[y, -1.45e-29], t$95$0, If[LessEqual[y, 3.4e-62], x, N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.60000000000000005e58 or -8.50000000000000007e-15 < y < -1.45000000000000012e-29

   1. Initial program 96.1%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-rgt-neg-in 82.5%

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

      3. distribute-rgt-neg-out 82.5%

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

   4. Simplified 82.5%

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

   if -4.60000000000000005e58 < y < -8.50000000000000007e-15 or -1.45000000000000012e-29 < y < 3.39999999999999988e-62

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around 0 78.1%

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

   if 3.39999999999999988e-62 < y

   1. Initial program 94.2%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. associate-*r* 64.3%

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

   4. Simplified 64.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 4: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.22 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x (- z)))))
   (if (<= y -4.4e+57)
     t_0
     (if (<= y -2.22e-13)
       x
       (if (<= y -6.2e-28) (* x (* y (- z))) (if (<= y 3.4e-62) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * -z);
	double tmp;
	if (y <= -4.4e+57) {
		tmp = t_0;
	} else if (y <= -2.22e-13) {
		tmp = x;
	} else if (y <= -6.2e-28) {
		tmp = x * (y * -z);
	} else if (y <= 3.4e-62) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x * -z)
    if (y <= (-4.4d+57)) then
        tmp = t_0
    else if (y <= (-2.22d-13)) then
        tmp = x
    else if (y <= (-6.2d-28)) then
        tmp = x * (y * -z)
    else if (y <= 3.4d-62) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x * -z);
	double tmp;
	if (y <= -4.4e+57) {
		tmp = t_0;
	} else if (y <= -2.22e-13) {
		tmp = x;
	} else if (y <= -6.2e-28) {
		tmp = x * (y * -z);
	} else if (y <= 3.4e-62) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * -z)
	tmp = 0
	if y <= -4.4e+57:
		tmp = t_0
	elif y <= -2.22e-13:
		tmp = x
	elif y <= -6.2e-28:
		tmp = x * (y * -z)
	elif y <= 3.4e-62:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * Float64(-z)))
	tmp = 0.0
	if (y <= -4.4e+57)
		tmp = t_0;
	elseif (y <= -2.22e-13)
		tmp = x;
	elseif (y <= -6.2e-28)
		tmp = Float64(x * Float64(y * Float64(-z)));
	elseif (y <= 3.4e-62)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * -z);
	tmp = 0.0;
	if (y <= -4.4e+57)
		tmp = t_0;
	elseif (y <= -2.22e-13)
		tmp = x;
	elseif (y <= -6.2e-28)
		tmp = x * (y * -z);
	elseif (y <= 3.4e-62)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+57], t$95$0, If[LessEqual[y, -2.22e-13], x, If[LessEqual[y, -6.2e-28], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-62], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4000000000000001e57 or 3.39999999999999988e-62 < y

   1. Initial program 94.9%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-*r* 69.2%

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

      3. distribute-rgt-neg-in 69.2%

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

      4. *-commutative 69.2%

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

      5. associate-*r* 72.0%

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

      6. distribute-rgt-neg-out 72.0%

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

   4. Simplified 72.0%

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

   if -4.4000000000000001e57 < y < -2.21999999999999988e-13 or -6.19999999999999984e-28 < y < 3.39999999999999988e-62

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around 0 78.7%

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

   if -2.21999999999999988e-13 < y < -6.19999999999999984e-28

   1. Initial program 100.0%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 85.1%

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

      1. mul-1-neg 85.1%

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

      2. distribute-rgt-neg-in 85.1%

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

      3. distribute-rgt-neg-out 85.1%

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

   4. Simplified 85.1%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq -2.22 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 5: 50.1% accurate, 7.0× 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 97.3%

   \[x \cdot \left(1 - y \cdot z\right) \]

2. Taylor expanded in y around 0 50.5%

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

3. Final simplification 50.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023311 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))