Diagrams.Color.HSV:lerp from diagrams-contrib-1.3.0.5

Percentage Accurate: 98.1% → 98.1%

Time: 975.0ms

Alternatives: 4

Speedup: 1.0×

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

Specification

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

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

Alternative 2: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - x\right) + x \cdot z\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+137}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+64}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- 1.0 x) (* x z))))
   (if (<= z -6.8e+137) t_0 (if (<= z 7.8e+64) (* (- 1.0 x) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - x) + (x * z);
	double tmp;
	if (z <= -6.8e+137) {
		tmp = t_0;
	} else if (z <= 7.8e+64) {
		tmp = (1.0 - x) * y;
	} 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 = (1.0d0 - x) + (x * z)
    if (z <= (-6.8d+137)) then
        tmp = t_0
    else if (z <= 7.8d+64) then
        tmp = (1.0d0 - x) * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - x) + (x * z);
	double tmp;
	if (z <= -6.8e+137) {
		tmp = t_0;
	} else if (z <= 7.8e+64) {
		tmp = (1.0 - x) * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - x) + (x * z)
	tmp = 0
	if z <= -6.8e+137:
		tmp = t_0
	elif z <= 7.8e+64:
		tmp = (1.0 - x) * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - x) + Float64(x * z))
	tmp = 0.0
	if (z <= -6.8e+137)
		tmp = t_0;
	elseif (z <= 7.8e+64)
		tmp = Float64(Float64(1.0 - x) * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - x) + (x * z);
	tmp = 0.0;
	if (z <= -6.8e+137)
		tmp = t_0;
	elseif (z <= 7.8e+64)
		tmp = (1.0 - x) * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - x), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+137], t$95$0, If[LessEqual[z, 7.8e+64], N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.79999999999999973e137 or 7.7999999999999996e64 < z

   1. Initial program 97.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 62.0%

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

   if -6.79999999999999973e137 < z < 7.7999999999999996e64

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 80.3%

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

Alternative 3: 62.6% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 65.6%

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

Alternative 4: 3.5% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 65.6%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 3.5%

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

Developer Target 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (- y (* x (- y z))))

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