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

Percentage Accurate: 96.2% → 99.9%

Time: 1.6s

Alternatives: 7

Speedup: 0.5×

• 79.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (* 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)
use fmin_fmax_functions
    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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	x * ((1) - (((1) - y) * z))
END code

Initial Program: 96.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (* 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)
use fmin_fmax_functions
    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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	x * ((1) - (((1) - y) * z))
END code

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\mathsf{copysign}\left(1, x\right) \cdot \begin{array}{l} \mathbf{if}\;\left|x\right| \leq 3.790276828303043 \cdot 10^{-54}:\\ \;\;\;\;\mathsf{fma}\left(z, \left(y - 1\right) \cdot \left|x\right|, \left|x\right|\right)\\ \mathbf{else}:\\ \;\;\;\;\left|x\right| \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (*
 (copysign 1.0 x)
 (if (<= (fabs x) 3.790276828303043e-54)
   (fma z (* (- y 1.0) (fabs x)) (fabs x))
   (* (fabs x) (- 1.0 (* (- 1.0 y) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (fabs(x) <= 3.790276828303043e-54) {
		tmp = fma(z, ((y - 1.0) * fabs(x)), fabs(x));
	} else {
		tmp = fabs(x) * (1.0 - ((1.0 - y) * z));
	}
	return copysign(1.0, x) * tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (abs(x) <= 3.790276828303043e-54)
		tmp = fma(z, Float64(Float64(y - 1.0) * abs(x)), abs(x));
	else
		tmp = Float64(abs(x) * Float64(1.0 - Float64(Float64(1.0 - y) * z)));
	end
	return Float64(copysign(1.0, x) * tmp)
end

Wolfram

code[x_, y_, z_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[x], $MachinePrecision], 3.790276828303043e-54], N[(z * N[(N[(y - 1.0), $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] + N[Abs[x], $MachinePrecision]), $MachinePrecision], N[(N[Abs[x], $MachinePrecision] * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 3.790276828303043e-54

   1. Initial program 96.2%

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

   3. Applied rewrites 96.2%

      \[\leadsto \mathsf{fma}\left(z, \left(y - 1\right) \cdot x, x\right) \]

   if 3.790276828303043e-54 < x

   1. Initial program 96.2%

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

Alternative 2: 99.8% accurate, 0.5× speedup

Math

\[\mathsf{copysign}\left(1, x\right) \cdot \begin{array}{l} \mathbf{if}\;\left|x\right| \leq 3.3832657300342604 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(z, \left(y - 1\right) \cdot \left|x\right|, \left|x\right|\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left|x\right|, y - 1, \left|x\right|\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (*
 (copysign 1.0 x)
 (if (<= (fabs x) 3.3832657300342604e-87)
   (fma z (* (- y 1.0) (fabs x)) (fabs x))
   (fma (* z (fabs x)) (- y 1.0) (fabs x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (fabs(x) <= 3.3832657300342604e-87) {
		tmp = fma(z, ((y - 1.0) * fabs(x)), fabs(x));
	} else {
		tmp = fma((z * fabs(x)), (y - 1.0), fabs(x));
	}
	return copysign(1.0, x) * tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (abs(x) <= 3.3832657300342604e-87)
		tmp = fma(z, Float64(Float64(y - 1.0) * abs(x)), abs(x));
	else
		tmp = fma(Float64(z * abs(x)), Float64(y - 1.0), abs(x));
	end
	return Float64(copysign(1.0, x) * tmp)
end

Wolfram

code[x_, y_, z_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[x], $MachinePrecision], 3.3832657300342604e-87], N[(z * N[(N[(y - 1.0), $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] + N[Abs[x], $MachinePrecision]), $MachinePrecision], N[(N[(z * N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[(y - 1.0), $MachinePrecision] + N[Abs[x], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 3.3832657300342604e-87

   1. Initial program 96.2%

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

   3. Applied rewrites 96.2%

      \[\leadsto \mathsf{fma}\left(z, \left(y - 1\right) \cdot x, x\right) \]

   if 3.3832657300342604e-87 < x

   1. Initial program 96.2%

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

   3. Applied rewrites 97.8%

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

Alternative 3: 96.2% accurate, 1.1× speedup

Math

\[\mathsf{fma}\left(z, \left(y - 1\right) \cdot x, x\right) \]

FPCore

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

C

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

Julia

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(z * ((y - (1)) * x)) + x
END code

Derivation

1. Initial program 96.2%

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

3. Applied rewrites 96.2%

   \[\leadsto \mathsf{fma}\left(z, \left(y - 1\right) \cdot x, x\right) \]
4. Add Preprocessing

Alternative 4: 95.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{fma}\left(z, x \cdot y, x\right)\\ \mathbf{if}\;1 - y \leq -5000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - y \leq 1.02:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (fma z (* x y) x)))
  (if (<= (- 1.0 y) -5000000.0)
    t_0
    (if (<= (- 1.0 y) 1.02) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(z, (x * y), x);
	double tmp;
	if ((1.0 - y) <= -5000000.0) {
		tmp = t_0;
	} else if ((1.0 - y) <= 1.02) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(z, Float64(x * y), x)
	tmp = 0.0
	if (Float64(1.0 - y) <= -5000000.0)
		tmp = t_0;
	elseif (Float64(1.0 - y) <= 1.02)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[N[(1.0 - y), $MachinePrecision], -5000000.0], t$95$0, If[LessEqual[N[(1.0 - y), $MachinePrecision], 1.02], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = ((z * (x * y)) + x) IN
		LET tmp_1 = IF (((1) - y) <= (1020000000000000017763568394002504646778106689453125e-51)) THEN (x * ((1) - z)) ELSE t_0 ENDIF IN
		LET tmp = IF (((1) - y) <= (-5e6)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -5e6 or 1.02 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 96.2%

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

   3. Applied rewrites 96.2%

      \[\leadsto \mathsf{fma}\left(z, \left(y - 1\right) \cdot x, x\right) \]

   4. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(z, x \cdot y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 72.1%

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

   if -5e6 < (-.f64 #s(literal 1 binary64) y) < 1.02

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0

      \[\leadsto x \cdot \left(1 - z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 66.0%

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

Alternative 5: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -2.7021837473509395 \cdot 10^{+34}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 8862164.475566508:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* x (* y z))))
  (if (<= y -2.7021837473509395e+34)
    t_0
    (if (<= y 8862164.475566508) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if (y <= -2.7021837473509395e+34) {
		tmp = t_0;
	} else if (y <= 8862164.475566508) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y * z)
    if (y <= (-2.7021837473509395d+34)) then
        tmp = t_0
    else if (y <= 8862164.475566508d0) then
        tmp = x * (1.0d0 - z)
    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 * (y * z);
	double tmp;
	if (y <= -2.7021837473509395e+34) {
		tmp = t_0;
	} else if (y <= 8862164.475566508) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * z)
	tmp = 0
	if y <= -2.7021837473509395e+34:
		tmp = t_0
	elif y <= 8862164.475566508:
		tmp = x * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -2.7021837473509395e+34)
		tmp = t_0;
	elseif (y <= 8862164.475566508)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y * z);
	tmp = 0.0;
	if (y <= -2.7021837473509395e+34)
		tmp = t_0;
	elseif (y <= 8862164.475566508)
		tmp = x * (1.0 - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7021837473509395e+34], t$95$0, If[LessEqual[y, 8862164.475566508], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (x * (y * z)) IN
		LET tmp_1 = IF (y <= (886216447556650824844837188720703125e-29)) THEN (x * ((1) - z)) ELSE t_0 ENDIF IN
		LET tmp = IF (y <= (-27021837473509394603557797526241280)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -2.7021837473509395e34 or 8862164.4755665082 < y

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf

      \[\leadsto x \cdot \left(y \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 35.8%

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

   if -2.7021837473509395e34 < y < 8862164.4755665082

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0

      \[\leadsto x \cdot \left(1 - z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 66.0%

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

Alternative 6: 66.0% accurate, 1.8× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (* 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)
use fmin_fmax_functions
    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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	x * ((1) - z)
END code

Derivation

1. Initial program 96.2%

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

2. Taylor expanded in y around 0

   \[\leadsto x \cdot \left(1 - z\right) \]
3. Step-by-step derivation

4. Applied rewrites 66.0%

   \[\leadsto x \cdot \left(1 - z\right) \]
5. Add Preprocessing

Alternative 7: 38.8% accurate, 3.0× speedup

Math

\[x \cdot 1 \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (* x 1.0))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	x * (1)
END code

Derivation

1. Initial program 96.2%

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

2. Taylor expanded in y around inf

   \[\leadsto x \cdot \left(y \cdot z\right) \]
3. Step-by-step derivation

4. Applied rewrites 35.8%

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

5. Taylor expanded in z around 0

   \[\leadsto x \cdot 1 \]
6. Step-by-step derivation

7. Applied rewrites 38.8%

   \[\leadsto x \cdot 1 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64
  (* x (- 1.0 (* (- 1.0 y) z))))