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

Percentage Accurate: 96.1% → 99.7%

Time: 12.2s

Alternatives: 6

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: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := -y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 10^{+141}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 (<= (* y z) (- INFINITY))
     t_0
     (if (<= (* y z) 1e+141) (* x (- 1.0 (* y z))) 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 ((y * z) <= -((double) INFINITY)) {
		tmp = t_0;
	} else if ((y * z) <= 1e+141) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

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 ((y * z) <= -Double.POSITIVE_INFINITY) {
		tmp = t_0;
	} else if ((y * z) <= 1e+141) {
		tmp = x * (1.0 - (y * z));
	} 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 (y * z) <= -math.inf:
		tmp = t_0
	elif (y * z) <= 1e+141:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(-Float64(y * Float64(x * z)))
	tmp = 0.0
	if (Float64(y * z) <= Float64(-Inf))
		tmp = t_0;
	elseif (Float64(y * z) <= 1e+141)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	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 ((y * z) <= -Inf)
		tmp = t_0;
	elseif ((y * z) <= 1e+141)
		tmp = x * (1.0 - (y * z));
	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[(y * z), $MachinePrecision], (-Infinity)], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 1e+141], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -inf.0 or 1.00000000000000002e141 < (*.f64 y z)

   1. Initial program 84.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 98.3

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

   5. Simplified 98.3%

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

   if -inf.0 < (*.f64 y z) < 1.00000000000000002e141

   1. Initial program 99.8%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;-y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \cdot z \leq 10^{+141}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := -y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq -10:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 (<= (* y z) (- INFINITY))
     t_0
     (if (<= (* y z) -10.0) (* (* y z) (- x)) (if (<= (* y z) 0.5) 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 ((y * z) <= -((double) INFINITY)) {
		tmp = t_0;
	} else if ((y * z) <= -10.0) {
		tmp = (y * z) * -x;
	} else if ((y * z) <= 0.5) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

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 ((y * z) <= -Double.POSITIVE_INFINITY) {
		tmp = t_0;
	} else if ((y * z) <= -10.0) {
		tmp = (y * z) * -x;
	} else if ((y * z) <= 0.5) {
		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 (y * z) <= -math.inf:
		tmp = t_0
	elif (y * z) <= -10.0:
		tmp = (y * z) * -x
	elif (y * z) <= 0.5:
		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(y * Float64(x * z)))
	tmp = 0.0
	if (Float64(y * z) <= Float64(-Inf))
		tmp = t_0;
	elseif (Float64(y * z) <= -10.0)
		tmp = Float64(Float64(y * z) * Float64(-x));
	elseif (Float64(y * z) <= 0.5)
		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 ((y * z) <= -Inf)
		tmp = t_0;
	elseif ((y * z) <= -10.0)
		tmp = (y * z) * -x;
	elseif ((y * z) <= 0.5)
		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[(y * z), $MachinePrecision], (-Infinity)], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], -10.0], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.5], x, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -inf.0 or 0.5 < (*.f64 y z)

   1. Initial program 89.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 90.9

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

   5. Simplified 90.9%

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

   if -inf.0 < (*.f64 y z) < -10

   1. Initial program 99.5%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 94.4

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

   5. Simplified 94.4%

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

   if -10 < (*.f64 y z) < 0.5

   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 97.4%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;-y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \cdot z \leq -10:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -10:\\ \;\;\;\;\left(y \cdot \left(-x\right)\right) \cdot z\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -10.0)
   (* (* y (- x)) z)
   (if (<= (* y z) 0.5) x (- (* y (* x z))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -10.0) {
		tmp = (y * -x) * z;
	} else if ((y * z) <= 0.5) {
		tmp = x;
	} else {
		tmp = -(y * (x * z));
	}
	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) :: tmp
    if ((y * z) <= (-10.0d0)) then
        tmp = (y * -x) * z
    else if ((y * z) <= 0.5d0) then
        tmp = x
    else
        tmp = -(y * (x * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -10.0) {
		tmp = (y * -x) * z;
	} else if ((y * z) <= 0.5) {
		tmp = x;
	} else {
		tmp = -(y * (x * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -10.0:
		tmp = (y * -x) * z
	elif (y * z) <= 0.5:
		tmp = x
	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(y * z) <= -10.0)
		tmp = Float64(Float64(y * Float64(-x)) * z);
	elseif (Float64(y * z) <= 0.5)
		tmp = x;
	else
		tmp = Float64(-Float64(y * Float64(x * 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 ((y * z) <= -10.0)
		tmp = (y * -x) * z;
	elseif ((y * z) <= 0.5)
		tmp = x;
	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[(y * z), $MachinePrecision], -10.0], N[(N[(y * (-x)), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.5], x, (-N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -10

   1. Initial program 92.5%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 88.9

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

   5. Simplified 88.9%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(-z\right)\right)} \]
   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 87.5

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

   7. Applied egg-rr 87.5%

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

   if -10 < (*.f64 y z) < 0.5

   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 97.4%

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

   if 0.5 < (*.f64 y z)

   1. Initial program 92.8%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 88.4

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

   5. Simplified 88.4%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -10:\\ \;\;\;\;\left(y \cdot \left(-x\right)\right) \cdot z\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{if}\;y \cdot z \leq -10:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 z) (- x))))
   (if (<= (* y z) -10.0) t_0 (if (<= (* y z) 0.5) x t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = (y * z) * -x;
	double tmp;
	if ((y * z) <= -10.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.5) {
		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 * z) * -x
    if ((y * z) <= (-10.0d0)) then
        tmp = t_0
    else if ((y * z) <= 0.5d0) 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 * z) * -x;
	double tmp;
	if ((y * z) <= -10.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.5) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = (y * z) * -x
	tmp = 0
	if (y * z) <= -10.0:
		tmp = t_0
	elif (y * z) <= 0.5:
		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(y * z) * Float64(-x))
	tmp = 0.0
	if (Float64(y * z) <= -10.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 0.5)
		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 * z) * -x;
	tmp = 0.0;
	if ((y * z) <= -10.0)
		tmp = t_0;
	elseif ((y * z) <= 0.5)
		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[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -10.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 0.5], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -10 or 0.5 < (*.f64 y z)

   1. Initial program 92.7%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 90.0

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

   5. Simplified 90.0%

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

   if -10 < (*.f64 y z) < 0.5

   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 97.4%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -10:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 20000000000:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(-x\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x 20000000000.0) (fma (* y (- x)) z x) (* x (- 1.0 (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 20000000000.0) {
		tmp = fma((y * -x), z, x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (x <= 20000000000.0)
		tmp = fma(Float64(y * Float64(-x)), z, x);
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	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, 20000000000.0], N[(N[(y * (-x)), $MachinePrecision] * z + x), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2e10

   1. Initial program 94.7%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. distribute-lft-neg-in N/A

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

      5. associate-*r* N/A

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

      6. *-rgt-identity N/A

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

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

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

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

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

      9. neg-lowering-neg.f64 95.7

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

   4. Applied egg-rr 95.7%

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

   if 2e10 < x

   1. Initial program 99.8%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 20000000000:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(-x\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.0% 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 96.1%

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

3. Taylor expanded in y around 0

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

5. Simplified 47.8%

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

Reproduce

herbie shell --seed 2024198 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))