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

Percentage Accurate: 97.7% → 100.0%

Time: 4.0s

Alternatives: 7

Speedup: 1.3×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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: 97.7% 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: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-19}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-11}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+17} \lor \neg \left(x \leq 2.3 \cdot 10^{+52} \lor \neg \left(x \leq 2 \cdot 10^{+208}\right) \land x \leq 4.5 \cdot 10^{+284}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -2.8e+16)
     t_0
     (if (<= x -1.1e-19)
       (* x z)
       (if (<= x 1.95e-11)
         y
         (if (or (<= x 7.5e+17)
                 (not
                  (or (<= x 2.3e+52)
                      (and (not (<= x 2e+208)) (<= x 4.5e+284)))))
           (* x z)
           t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -2.8e+16) {
		tmp = t_0;
	} else if (x <= -1.1e-19) {
		tmp = x * z;
	} else if (x <= 1.95e-11) {
		tmp = y;
	} else if ((x <= 7.5e+17) || !((x <= 2.3e+52) || (!(x <= 2e+208) && (x <= 4.5e+284)))) {
		tmp = x * z;
	} 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 * -y
    if (x <= (-2.8d+16)) then
        tmp = t_0
    else if (x <= (-1.1d-19)) then
        tmp = x * z
    else if (x <= 1.95d-11) then
        tmp = y
    else if ((x <= 7.5d+17) .or. (.not. (x <= 2.3d+52) .or. (.not. (x <= 2d+208)) .and. (x <= 4.5d+284))) then
        tmp = x * 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;
	double tmp;
	if (x <= -2.8e+16) {
		tmp = t_0;
	} else if (x <= -1.1e-19) {
		tmp = x * z;
	} else if (x <= 1.95e-11) {
		tmp = y;
	} else if ((x <= 7.5e+17) || !((x <= 2.3e+52) || (!(x <= 2e+208) && (x <= 4.5e+284)))) {
		tmp = x * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if x <= -2.8e+16:
		tmp = t_0
	elif x <= -1.1e-19:
		tmp = x * z
	elif x <= 1.95e-11:
		tmp = y
	elif (x <= 7.5e+17) or not ((x <= 2.3e+52) or (not (x <= 2e+208) and (x <= 4.5e+284))):
		tmp = x * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (x <= -2.8e+16)
		tmp = t_0;
	elseif (x <= -1.1e-19)
		tmp = Float64(x * z);
	elseif (x <= 1.95e-11)
		tmp = y;
	elseif ((x <= 7.5e+17) || !((x <= 2.3e+52) || (!(x <= 2e+208) && (x <= 4.5e+284))))
		tmp = Float64(x * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -y;
	tmp = 0.0;
	if (x <= -2.8e+16)
		tmp = t_0;
	elseif (x <= -1.1e-19)
		tmp = x * z;
	elseif (x <= 1.95e-11)
		tmp = y;
	elseif ((x <= 7.5e+17) || ~(((x <= 2.3e+52) || (~((x <= 2e+208)) && (x <= 4.5e+284)))))
		tmp = x * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[x, -2.8e+16], t$95$0, If[LessEqual[x, -1.1e-19], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.95e-11], y, If[Or[LessEqual[x, 7.5e+17], N[Not[Or[LessEqual[x, 2.3e+52], And[N[Not[LessEqual[x, 2e+208]], $MachinePrecision], LessEqual[x, 4.5e+284]]]], $MachinePrecision]], N[(x * z), $MachinePrecision], t$95$0]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+76} \lor \neg \left(z \leq 11000000000\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e+76) (not (<= z 11000000000.0))) (* x z) (* y (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+76) || !(z <= 11000000000.0)) {
		tmp = x * z;
	} else {
		tmp = y * (1.0 - 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 <= (-1.8d+76)) .or. (.not. (z <= 11000000000.0d0))) then
        tmp = x * z
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+76) || !(z <= 11000000000.0)) {
		tmp = x * z;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e+76) or not (z <= 11000000000.0):
		tmp = x * z
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.8e+76) || !(z <= 11000000000.0))
		tmp = Float64(x * z);
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.8e+76) || ~((z <= 11000000000.0)))
		tmp = x * z;
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e+76], N[Not[LessEqual[z, 11000000000.0]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-24} \lor \neg \left(y \leq 1.4 \cdot 10^{+46}\right):\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.8e-24) (not (<= y 1.4e+46))) (* y (- 1.0 x)) (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e-24) || !(y <= 1.4e+46)) {
		tmp = y * (1.0 - x);
	} else {
		tmp = y + (x * 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 <= (-5.8d-24)) .or. (.not. (y <= 1.4d+46))) then
        tmp = y * (1.0d0 - x)
    else
        tmp = y + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e-24) || !(y <= 1.4e+46)) {
		tmp = y * (1.0 - x);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.8e-24) or not (y <= 1.4e+46):
		tmp = y * (1.0 - x)
	else:
		tmp = y + (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.8e-24) || !(y <= 1.4e+46))
		tmp = Float64(y * Float64(1.0 - x));
	else
		tmp = Float64(y + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.8e-24) || ~((y <= 1.4e+46)))
		tmp = y * (1.0 - x);
	else
		tmp = y + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.8e-24], N[Not[LessEqual[y, 1.4e+46]], $MachinePrecision]], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 61.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-21} \lor \neg \left(x \leq 2.4 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.16e-21) (not (<= x 2.4e-12))) (* x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.16e-21) || !(x <= 2.4e-12)) {
		tmp = x * z;
	} else {
		tmp = 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 ((x <= (-1.16d-21)) .or. (.not. (x <= 2.4d-12))) then
        tmp = x * z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.16e-21) || !(x <= 2.4e-12)) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.16e-21) or not (x <= 2.4e-12):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.16e-21) || !(x <= 2.4e-12))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.16e-21) || ~((x <= 2.4e-12)))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.16e-21], N[Not[LessEqual[x, 2.4e-12]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 36.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z)
	return y
end

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 100.0% accurate, 1.3× 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 2023350 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (- y (* x (- y z)))

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