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

Percentage Accurate: 96.2% → 98.5%

Time: 7.3s

Alternatives: 9

Speedup: 0.5×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e+14) (not (<= z 1.0)))
   (* (* x z) (+ y -1.0))
   (+ x (* x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+14) || !(z <= 1.0)) {
		tmp = (x * z) * (y + -1.0);
	} else {
		tmp = x + (x * (y * 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 <= (-1d+14)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x * z) * (y + (-1.0d0))
    else
        tmp = x + (x * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+14) || !(z <= 1.0)) {
		tmp = (x * z) * (y + -1.0);
	} else {
		tmp = x + (x * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1e+14) or not (z <= 1.0):
		tmp = (x * z) * (y + -1.0)
	else:
		tmp = x + (x * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1e+14) || !(z <= 1.0))
		tmp = Float64(Float64(x * z) * Float64(y + -1.0));
	else
		tmp = Float64(x + Float64(x * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1e+14) || ~((z <= 1.0)))
		tmp = (x * z) * (y + -1.0);
	else
		tmp = x + (x * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1e+14], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e14 or 1 < z

   1. Initial program 91.1%

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

   3. Taylor expanded in z around inf 89.0%

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

      1. associate-*r* 97.9%

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

      2. *-commutative 97.9%

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

      3. sub-neg 97.9%

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

      4. metadata-eval 97.9%

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

   5. Simplified 97.9%

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

   if -1e14 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.4%

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

      1. neg-mul-1 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in y around 0 99.4%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+255}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 1.0 (* z (+ y -1.0))))))
   (if (<= t_0 -1e+255) (* (* x z) (+ y -1.0)) t_0)))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= -1e+255) {
		tmp = (x * z) * (y + -1.0);
	} 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 = x * (1.0d0 + (z * (y + (-1.0d0))))
    if (t_0 <= (-1d+255)) then
        tmp = (x * z) * (y + (-1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= -1e+255) {
		tmp = (x * z) * (y + -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 + (z * (y + -1.0)))
	tmp = 0
	if t_0 <= -1e+255:
		tmp = (x * z) * (y + -1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))))
	tmp = 0.0
	if (t_0 <= -1e+255)
		tmp = Float64(Float64(x * z) * Float64(y + -1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 + (z * (y + -1.0)));
	tmp = 0.0;
	if (t_0 <= -1e+255)
		tmp = (x * z) * (y + -1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+255], N[(N[(x * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z))) < -9.99999999999999988e254

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf 90.4%

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

      1. associate-*r* 95.2%

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

      2. *-commutative 95.2%

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

      3. sub-neg 95.2%

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

      4. metadata-eval 95.2%

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

   5. Simplified 95.2%

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

   if -9.99999999999999988e254 < (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)))

   1. Initial program 96.0%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right) \leq -1 \cdot 10^{+255}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-31} \lor \neg \left(z \leq 5.2 \cdot 10^{-55}\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e-31) (not (<= z 5.2e-55))) (* (* x z) (+ y -1.0)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e-31) || !(z <= 5.2e-55)) {
		tmp = (x * z) * (y + -1.0);
	} 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 <= (-2.4d-31)) .or. (.not. (z <= 5.2d-55))) then
        tmp = (x * z) * (y + (-1.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e-31) || !(z <= 5.2e-55)) {
		tmp = (x * z) * (y + -1.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.4e-31) or not (z <= 5.2e-55):
		tmp = (x * z) * (y + -1.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.4e-31) || !(z <= 5.2e-55))
		tmp = Float64(Float64(x * z) * Float64(y + -1.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.4e-31) || ~((z <= 5.2e-55)))
		tmp = (x * z) * (y + -1.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.4e-31], N[Not[LessEqual[z, 5.2e-55]], $MachinePrecision]], N[(N[(x * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e-31 or 5.1999999999999998e-55 < z

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf 86.3%

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

      1. associate-*r* 91.5%

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

      2. *-commutative 91.5%

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

      3. sub-neg 91.5%

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

      4. metadata-eval 91.5%

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

   5. Simplified 91.5%

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

   if -2.4e-31 < z < 5.1999999999999998e-55

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 82.5%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-31} \lor \neg \left(z \leq 5.2 \cdot 10^{-55}\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+110} \lor \neg \left(y \leq 3.8 \cdot 10^{+82}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.7e+110) (not (<= y 3.8e+82))) (* z (* x y)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.7e+110) || !(y <= 3.8e+82)) {
		tmp = z * (x * y);
	} else {
		tmp = x * (1.0 - 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 ((y <= (-1.7d+110)) .or. (.not. (y <= 3.8d+82))) then
        tmp = z * (x * y)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.7e+110) || !(y <= 3.8e+82)) {
		tmp = z * (x * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.7e+110) or not (y <= 3.8e+82):
		tmp = z * (x * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.7e+110) || !(y <= 3.8e+82))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.7e+110) || ~((y <= 3.8e+82)))
		tmp = z * (x * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.7e+110], N[Not[LessEqual[y, 3.8e+82]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7000000000000001e110 or 3.80000000000000033e82 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf 78.7%

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

      1. *-commutative 78.7%

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

      2. *-commutative 78.7%

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

      3. associate-*l* 81.7%

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

   5. Simplified 81.7%

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

   if -1.7000000000000001e110 < y < 3.80000000000000033e82

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 88.5%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+110} \lor \neg \left(y \leq 3.8 \cdot 10^{+82}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+112}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.2e+112)
   (* y (* x z))
   (if (<= y 2.7e+82) (* x (- 1.0 z)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.2e+112) {
		tmp = y * (x * z);
	} else if (y <= 2.7e+82) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.2d+112)) then
        tmp = y * (x * z)
    else if (y <= 2.7d+82) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.2e+112) {
		tmp = y * (x * z);
	} else if (y <= 2.7e+82) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.2e+112:
		tmp = y * (x * z)
	elif y <= 2.7e+82:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.2e+112)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 2.7e+82)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.2e+112)
		tmp = y * (x * z);
	elseif (y <= 2.7e+82)
		tmp = x * (1.0 - z);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.2e+112], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+82], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1999999999999999e112

   1. Initial program 85.6%

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

   3. Taylor expanded in z around inf 78.4%

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

      1. associate-*r* 84.5%

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

      2. *-commutative 84.5%

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

      3. sub-neg 84.5%

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

      4. metadata-eval 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in y around inf 84.5%

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

   if -2.1999999999999999e112 < y < 2.6999999999999999e82

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 88.5%

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

   if 2.6999999999999999e82 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. *-commutative 79.0%

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

      3. associate-*l* 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+112}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+14} \lor \neg \left(z \leq 3.1 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e+14) (not (<= z 3.1e-9))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+14) || !(z <= 3.1e-9)) {
		tmp = 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 <= (-1d+14)) .or. (.not. (z <= 3.1d-9))) then
        tmp = 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 <= -1e+14) || !(z <= 3.1e-9)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1e+14) or not (z <= 3.1e-9):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1e+14) || !(z <= 3.1e-9))
		tmp = Float64(x * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1e+14) || ~((z <= 3.1e-9)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1e+14], N[Not[LessEqual[z, 3.1e-9]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1e14 or 3.10000000000000005e-9 < z

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf 88.7%

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

      1. associate-*r* 97.5%

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

      2. *-commutative 97.5%

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

      3. sub-neg 97.5%

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

      4. metadata-eval 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in y around 0 53.4%

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

      1. mul-1-neg 53.4%

         \[\leadsto \color{blue}{-x \cdot z} \]

      2. distribute-rgt-neg-in 53.4%

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

   8. Simplified 53.4%

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

   if -1e14 < z < 3.10000000000000005e-9

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 73.6%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+14} \lor \neg \left(z \leq 3.1 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+131} \lor \neg \left(z \leq 2.3 \cdot 10^{+23}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.2e+131) (not (<= z 2.3e+23))) (* x z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.2e+131) || !(z <= 2.3e+23)) {
		tmp = 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 <= (-1.2d+131)) .or. (.not. (z <= 2.3d+23))) then
        tmp = 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 <= -1.2e+131) || !(z <= 2.3e+23)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.2e+131) or not (z <= 2.3e+23):
		tmp = x * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.2e+131) || !(z <= 2.3e+23))
		tmp = Float64(x * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.2e+131) || ~((z <= 2.3e+23)))
		tmp = x * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.2e+131], N[Not[LessEqual[z, 2.3e+23]], $MachinePrecision]], N[(x * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e131 or 2.3e23 < z

   1. Initial program 89.5%

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

   3. Taylor expanded in z around inf 89.5%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 53.3%

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

      1. mul-1-neg 53.3%

         \[\leadsto \color{blue}{-x \cdot z} \]

      2. distribute-rgt-neg-in 53.3%

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

   8. Simplified 53.3%

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

      1. neg-sub0 53.3%

         \[\leadsto x \cdot \color{blue}{\left(0 - z\right)} \]

      2. sub-neg 53.3%

         \[\leadsto x \cdot \color{blue}{\left(0 + \left(-z\right)\right)} \]

      3. add-sqr-sqrt 19.1%

         \[\leadsto x \cdot \left(0 + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}}\right) \]

      4. sqrt-unprod 24.6%

         \[\leadsto x \cdot \left(0 + \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}\right) \]

      5. sqr-neg 24.6%

         \[\leadsto x \cdot \left(0 + \sqrt{\color{blue}{z \cdot z}}\right) \]

      6. sqrt-unprod 8.7%

         \[\leadsto x \cdot \left(0 + \color{blue}{\sqrt{z} \cdot \sqrt{z}}\right) \]

      7. add-sqr-sqrt 15.9%

         \[\leadsto x \cdot \left(0 + \color{blue}{z}\right) \]

   10. Applied egg-rr 15.9%

       \[\leadsto x \cdot \color{blue}{\left(0 + z\right)} \]

   11. Taylor expanded in x around 0 15.9%

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

   if -1.2e131 < z < 2.3e23

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 61.8%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+131} \lor \neg \left(z \leq 2.3 \cdot 10^{+23}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.4% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.8%

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

3. Taylor expanded in y around 0 65.4%

   \[\leadsto x \cdot \left(1 - \color{blue}{z}\right) \]
4. Add Preprocessing

Alternative 9: 38.6% 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 95.8%

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

3. Taylor expanded in z around 0 40.9%

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

Developer Target 1: 99.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ t_1 := x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{if}\;t\_0 < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z))))
        (t_1 (+ x (* (- 1.0 y) (* (- z) x)))))
   (if (< t_0 -1.618195973607049e+50)
     t_1
     (if (< t_0 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} 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 = x * (1.0d0 - ((1.0d0 - y) * z))
    t_1 = x + ((1.0d0 - y) * (-z * x))
    if (t_0 < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (t_0 < 3.892237649663903d+134) then
        tmp = ((x * y) * z) - ((x * z) - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	t_1 = x + ((1.0 - y) * (-z * x))
	tmp = 0
	if t_0 < -1.618195973607049e+50:
		tmp = t_1
	elif t_0 < 3.892237649663903e+134:
		tmp = ((x * y) * z) - ((x * z) - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	t_1 = Float64(x + Float64(Float64(1.0 - y) * Float64(Float64(-z) * x)))
	tmp = 0.0
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = Float64(Float64(Float64(x * y) * z) - Float64(Float64(x * z) - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	t_1 = x + ((1.0 - y) * (-z * x));
	tmp = 0.0;
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = ((x * y) * z) - ((x * z) - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(N[(1.0 - y), $MachinePrecision] * N[((-z) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$0, -1.618195973607049e+50], t$95$1, If[Less[t$95$0, 3.892237649663903e+134], N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024180 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- 1 (* (- 1 y) z))) -161819597360704900000000000000000000000000000000000) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 389223764966390300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x))))))

  (* x (- 1.0 (* (- 1.0 y) z))))