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

Percentage Accurate: 96.0% → 97.8%

Time: 1.1s

Alternatives: 7

Speedup: 0.5×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

\[\mathsf{TRUE}\left(\right)\]

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: 96.0% 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: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t\_0 \leq 4 \cdot 10^{+261}:\\ \;\;\;\;x \cdot \left(1 - t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;1 - \left(x \cdot \left(1 - y\right)\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= t_0 4e+261) (* x (- 1.0 t_0)) (- 1.0 (* (* x (- 1.0 y)) z)))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= 4e+261) {
		tmp = x * (1.0 - t_0);
	} else {
		tmp = 1.0 - ((x * (1.0 - 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) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 - y) * z
    if (t_0 <= 4d+261) then
        tmp = x * (1.0d0 - t_0)
    else
        tmp = 1.0d0 - ((x * (1.0d0 - y)) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= 4e+261) {
		tmp = x * (1.0 - t_0);
	} else {
		tmp = 1.0 - ((x * (1.0 - y)) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * z
	tmp = 0
	if t_0 <= 4e+261:
		tmp = x * (1.0 - t_0)
	else:
		tmp = 1.0 - ((x * (1.0 - y)) * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_0 <= 4e+261)
		tmp = Float64(x * Float64(1.0 - t_0));
	else
		tmp = Float64(1.0 - Float64(Float64(x * Float64(1.0 - y)) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	tmp = 0.0;
	if (t_0 <= 4e+261)
		tmp = x * (1.0 - t_0);
	else
		tmp = 1.0 - ((x * (1.0 - y)) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, 4e+261], N[(x * N[(1.0 - t$95$0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 3.9999999999999997e261

   1. Initial program 99.1%

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

   if 3.9999999999999997e261 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 68.7%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 31.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 - 1 \cdot z \]

   8. Applied rewrites 97.0%

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

Alternative 2: 71.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \left(1 - y\right) \cdot z\\ t_1 := x \cdot \left(1 - y\right)\\ t_2 := 1 - t\_1 \cdot z\\ \mathbf{if}\;t\_0 \leq -2000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* (- 1.0 y) z)))
        (t_1 (* x (- 1.0 y)))
        (t_2 (- 1.0 (* t_1 z))))
   (if (<= t_0 -2000.0) t_2 (if (<= t_0 2e+21) t_1 t_2))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - ((1.0 - y) * z);
	double t_1 = x * (1.0 - y);
	double t_2 = 1.0 - (t_1 * z);
	double tmp;
	if (t_0 <= -2000.0) {
		tmp = t_2;
	} else if (t_0 <= 2e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 - ((1.0d0 - y) * z)
    t_1 = x * (1.0d0 - y)
    t_2 = 1.0d0 - (t_1 * z)
    if (t_0 <= (-2000.0d0)) then
        tmp = t_2
    else if (t_0 <= 2d+21) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - ((1.0 - y) * z);
	double t_1 = x * (1.0 - y);
	double t_2 = 1.0 - (t_1 * z);
	double tmp;
	if (t_0 <= -2000.0) {
		tmp = t_2;
	} else if (t_0 <= 2e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - ((1.0 - y) * z)
	t_1 = x * (1.0 - y)
	t_2 = 1.0 - (t_1 * z)
	tmp = 0
	if t_0 <= -2000.0:
		tmp = t_2
	elif t_0 <= 2e+21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(Float64(1.0 - y) * z))
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(1.0 - Float64(t_1 * z))
	tmp = 0.0
	if (t_0 <= -2000.0)
		tmp = t_2;
	elseif (t_0 <= 2e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - ((1.0 - y) * z);
	t_1 = x * (1.0 - y);
	t_2 = 1.0 - (t_1 * z);
	tmp = 0.0;
	if (t_0 <= -2000.0)
		tmp = t_2;
	elseif (t_0 <= 2e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(t$95$1 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2000.0], t$95$2, If[LessEqual[t$95$0, 2e+21], t$95$1, t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)) < -2e3 or 2e21 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z))

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 11.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 - 1 \cdot z \]

   8. Applied rewrites 75.9%

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

   if -2e3 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)) < 2e21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 60.9%

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

Alternative 3: 34.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+227}:\\ \;\;\;\;1 - \left(1 - y\right) \cdot z\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-10}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1 - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 y))))
   (if (<= z -2.5e+227)
     (- 1.0 (* (- 1.0 y) z))
     (if (<= z 9.5e-10) t_0 (- 1.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - y);
	double tmp;
	if (z <= -2.5e+227) {
		tmp = 1.0 - ((1.0 - y) * z);
	} else if (z <= 9.5e-10) {
		tmp = t_0;
	} else {
		tmp = 1.0 - 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 - y)
    if (z <= (-2.5d+227)) then
        tmp = 1.0d0 - ((1.0d0 - y) * z)
    else if (z <= 9.5d-10) then
        tmp = t_0
    else
        tmp = 1.0d0 - 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 - y);
	double tmp;
	if (z <= -2.5e+227) {
		tmp = 1.0 - ((1.0 - y) * z);
	} else if (z <= 9.5e-10) {
		tmp = t_0;
	} else {
		tmp = 1.0 - t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - y)
	tmp = 0
	if z <= -2.5e+227:
		tmp = 1.0 - ((1.0 - y) * z)
	elif z <= 9.5e-10:
		tmp = t_0
	else:
		tmp = 1.0 - t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -2.5e+227)
		tmp = Float64(1.0 - Float64(Float64(1.0 - y) * z));
	elseif (z <= 9.5e-10)
		tmp = t_0;
	else
		tmp = Float64(1.0 - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -2.5e+227)
		tmp = 1.0 - ((1.0 - y) * z);
	elseif (z <= 9.5e-10)
		tmp = t_0;
	else
		tmp = 1.0 - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+227], N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-10], t$95$0, N[(1.0 - t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4999999999999998e227

   1. Initial program 86.5%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 34.9%

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

   if -2.4999999999999998e227 < z < 9.50000000000000028e-10

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 43.1%

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

   if 9.50000000000000028e-10 < z

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 10.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 - 1 \cdot z \]

   8. Applied rewrites 75.4%

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

   9. Taylor expanded in y around 0

      \[\leadsto 1 - z \]

   11. Applied rewrites 17.5%

       \[\leadsto 1 - x \cdot \color{blue}{\left(1 - y\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 34.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq 9.5 \cdot 10^{-10}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1 - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 y)))) (if (<= z 9.5e-10) t_0 (- 1.0 t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - y);
	double tmp;
	if (z <= 9.5e-10) {
		tmp = t_0;
	} else {
		tmp = 1.0 - 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 - y)
    if (z <= 9.5d-10) then
        tmp = t_0
    else
        tmp = 1.0d0 - 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 - y);
	double tmp;
	if (z <= 9.5e-10) {
		tmp = t_0;
	} else {
		tmp = 1.0 - t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - y)
	tmp = 0
	if z <= 9.5e-10:
		tmp = t_0
	else:
		tmp = 1.0 - t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= 9.5e-10)
		tmp = t_0;
	else
		tmp = Float64(1.0 - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= 9.5e-10)
		tmp = t_0;
	else
		tmp = 1.0 - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 9.5e-10], t$95$0, N[(1.0 - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 9.50000000000000028e-10

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 39.7%

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

   if 9.50000000000000028e-10 < z

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 10.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 - 1 \cdot z \]

   8. Applied rewrites 75.4%

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

   9. Taylor expanded in y around 0

      \[\leadsto 1 - z \]

   11. Applied rewrites 17.5%

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

Alternative 5: 33.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.0) {
		tmp = x * (1.0 - y);
	} else {
		tmp = (1.0 - 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 <= 1.0d0) then
        tmp = x * (1.0d0 - y)
    else
        tmp = (1.0d0 - y) * z
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.0:
		tmp = x * (1.0 - y)
	else:
		tmp = (1.0 - y) * z
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < 1

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 39.2%

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

   if 1 < z

   1. Initial program 92.7%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 10.3%

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

Alternative 6: 7.3% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.9%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 7.2%

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

Alternative 7: 3.3% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ 1 - y \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 - y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.9%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 7.2%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 3.4%

   \[\leadsto \color{blue}{1 - y} \]
9. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.3× 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 2024321 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64
  :pre (TRUE)

  :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))))