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

Percentage Accurate: 96.1% → 99.4%

Time: 10.1s

Alternatives: 5

Speedup: 0.4×

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: 96.1% 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: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot y \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(1 - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* z y) (- INFINITY))
   (* z (* x (- y)))
   (if (<= (* z y) 5e+119) (* x (- 1.0 (* z y))) (* y (* x (- z))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z * y) <= -((double) INFINITY)) {
		tmp = z * (x * -y);
	} else if ((z * y) <= 5e+119) {
		tmp = x * (1.0 - (z * y));
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z * y) <= -Double.POSITIVE_INFINITY) {
		tmp = z * (x * -y);
	} else if ((z * y) <= 5e+119) {
		tmp = x * (1.0 - (z * y));
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z * y) <= -math.inf:
		tmp = z * (x * -y)
	elif (z * y) <= 5e+119:
		tmp = x * (1.0 - (z * y))
	else:
		tmp = y * (x * -z)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(z * y) <= Float64(-Inf))
		tmp = Float64(z * Float64(x * Float64(-y)));
	elseif (Float64(z * y) <= 5e+119)
		tmp = Float64(x * Float64(1.0 - Float64(z * y)));
	else
		tmp = Float64(y * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * y) <= -Inf)
		tmp = z * (x * -y);
	elseif ((z * y) <= 5e+119)
		tmp = x * (1.0 - (z * y));
	else
		tmp = y * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(z * y), $MachinePrecision], (-Infinity)], N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * y), $MachinePrecision], 5e+119], N[(x * N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -inf.0

   1. Initial program 63.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-lowering-neg.f64 63.6

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

   5. Simplified 63.6%

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

      1. distribute-rgt-neg-out N/A

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

      2. distribute-lft-neg-in N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. neg-lowering-neg.f64 99.9

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

   7. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 y z) < 4.9999999999999999e119

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   if 4.9999999999999999e119 < (*.f64 y z)

   1. Initial program 89.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. neg-lowering-neg.f64 95.5

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

   5. Simplified 95.5%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(1 - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{if}\;z \cdot y \leq -4000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \cdot y \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x (- z)))))
   (if (<= (* z y) -4000.0) t_0 (if (<= (* z y) 1e-9) x t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = y * (x * -z);
	double tmp;
	if ((z * y) <= -4000.0) {
		tmp = t_0;
	} else if ((z * y) <= 1e-9) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 ((z * y) <= (-4000.0d0)) then
        tmp = t_0
    else if ((z * y) <= 1d-9) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = y * (x * -z);
	double tmp;
	if ((z * y) <= -4000.0) {
		tmp = t_0;
	} else if ((z * y) <= 1e-9) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = y * (x * -z)
	tmp = 0
	if (z * y) <= -4000.0:
		tmp = t_0
	elif (z * y) <= 1e-9:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(y * Float64(x * Float64(-z)))
	tmp = 0.0
	if (Float64(z * y) <= -4000.0)
		tmp = t_0;
	elseif (Float64(z * y) <= 1e-9)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = y * (x * -z);
	tmp = 0.0;
	if ((z * y) <= -4000.0)
		tmp = t_0;
	elseif ((z * y) <= 1e-9)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * y), $MachinePrecision], -4000.0], t$95$0, If[LessEqual[N[(z * y), $MachinePrecision], 1e-9], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -4e3 or 1.00000000000000006e-9 < (*.f64 y z)

   1. Initial program 90.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. neg-lowering-neg.f64 91.7

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

   5. Simplified 91.7%

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

   if -4e3 < (*.f64 y z) < 1.00000000000000006e-9

   1. Initial program 100.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 97.5%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -4000:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \cdot y \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := -x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \cdot y \leq -4000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \cdot y \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (* z y)))))
   (if (<= (* z y) -4000.0) t_0 (if (<= (* z y) 1e-9) x t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = -(x * (z * y));
	double tmp;
	if ((z * y) <= -4000.0) {
		tmp = t_0;
	} else if ((z * y) <= 1e-9) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 * (z * y))
    if ((z * y) <= (-4000.0d0)) then
        tmp = t_0
    else if ((z * y) <= 1d-9) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = -(x * (z * y));
	double tmp;
	if ((z * y) <= -4000.0) {
		tmp = t_0;
	} else if ((z * y) <= 1e-9) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = -(x * (z * y))
	tmp = 0
	if (z * y) <= -4000.0:
		tmp = t_0
	elif (z * y) <= 1e-9:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(-Float64(x * Float64(z * y)))
	tmp = 0.0
	if (Float64(z * y) <= -4000.0)
		tmp = t_0;
	elseif (Float64(z * y) <= 1e-9)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = -(x * (z * y));
	tmp = 0.0;
	if ((z * y) <= -4000.0)
		tmp = t_0;
	elseif ((z * y) <= 1e-9)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = (-N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[N[(z * y), $MachinePrecision], -4000.0], t$95$0, If[LessEqual[N[(z * y), $MachinePrecision], 1e-9], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -4e3 or 1.00000000000000006e-9 < (*.f64 y z)

   1. Initial program 90.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-lowering-neg.f64 88.1

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

   5. Simplified 88.1%

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

   if -4e3 < (*.f64 y z) < 1.00000000000000006e-9

   1. Initial program 100.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 97.5%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -4000:\\ \;\;\;\;-x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \cdot y \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 100:\\ \;\;\;\;\mathsf{fma}\left(x \cdot \left(-z\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x 100.0) (fma (* x (- z)) y x) (* x (- 1.0 (* z y)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 100.0) {
		tmp = fma((x * -z), y, x);
	} else {
		tmp = x * (1.0 - (z * y));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (x <= 100.0)
		tmp = fma(Float64(x * Float64(-z)), y, x);
	else
		tmp = Float64(x * Float64(1.0 - Float64(z * y)));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[x, 100.0], N[(N[(x * (-z)), $MachinePrecision] * y + x), $MachinePrecision], N[(x * N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 100

   1. Initial program 93.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*r* N/A

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

      7. *-rgt-identity N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. neg-lowering-neg.f64 94.9

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

   4. Applied egg-rr 94.9%

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

   if 100 < x

   1. Initial program 100.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 100:\\ \;\;\;\;\mathsf{fma}\left(x \cdot \left(-z\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.2% accurate, 14.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ x \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 x)

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return x
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := x

Derivation

1. Initial program 94.8%

   \[x \cdot \left(1 - y \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 45.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024205 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))