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

Percentage Accurate: 97.6% → 100.0%

Time: 4.3s

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: 97.6% 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: 58.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{+219}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+74}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-79}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-141}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-216}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-42}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+49} \lor \neg \left(x \leq 1.35 \cdot 10^{+248}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -4.4e+219)
     t_0
     (if (<= x -2.8e+74)
       (* x z)
       (if (<= x -2.7e+26)
         t_0
         (if (<= x -1.5e-79)
           (* x z)
           (if (<= x -1.1e-141)
             y
             (if (<= x -2.8e-216)
               (* x z)
               (if (<= x 9.5e-42)
                 y
                 (if (or (<= x 1.45e+49) (not (<= x 1.35e+248)))
                   (* x z)
                   t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -4.4e+219) {
		tmp = t_0;
	} else if (x <= -2.8e+74) {
		tmp = x * z;
	} else if (x <= -2.7e+26) {
		tmp = t_0;
	} else if (x <= -1.5e-79) {
		tmp = x * z;
	} else if (x <= -1.1e-141) {
		tmp = y;
	} else if (x <= -2.8e-216) {
		tmp = x * z;
	} else if (x <= 9.5e-42) {
		tmp = y;
	} else if ((x <= 1.45e+49) || !(x <= 1.35e+248)) {
		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 <= (-4.4d+219)) then
        tmp = t_0
    else if (x <= (-2.8d+74)) then
        tmp = x * z
    else if (x <= (-2.7d+26)) then
        tmp = t_0
    else if (x <= (-1.5d-79)) then
        tmp = x * z
    else if (x <= (-1.1d-141)) then
        tmp = y
    else if (x <= (-2.8d-216)) then
        tmp = x * z
    else if (x <= 9.5d-42) then
        tmp = y
    else if ((x <= 1.45d+49) .or. (.not. (x <= 1.35d+248))) 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 <= -4.4e+219) {
		tmp = t_0;
	} else if (x <= -2.8e+74) {
		tmp = x * z;
	} else if (x <= -2.7e+26) {
		tmp = t_0;
	} else if (x <= -1.5e-79) {
		tmp = x * z;
	} else if (x <= -1.1e-141) {
		tmp = y;
	} else if (x <= -2.8e-216) {
		tmp = x * z;
	} else if (x <= 9.5e-42) {
		tmp = y;
	} else if ((x <= 1.45e+49) || !(x <= 1.35e+248)) {
		tmp = x * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if x <= -4.4e+219:
		tmp = t_0
	elif x <= -2.8e+74:
		tmp = x * z
	elif x <= -2.7e+26:
		tmp = t_0
	elif x <= -1.5e-79:
		tmp = x * z
	elif x <= -1.1e-141:
		tmp = y
	elif x <= -2.8e-216:
		tmp = x * z
	elif x <= 9.5e-42:
		tmp = y
	elif (x <= 1.45e+49) or not (x <= 1.35e+248):
		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 <= -4.4e+219)
		tmp = t_0;
	elseif (x <= -2.8e+74)
		tmp = Float64(x * z);
	elseif (x <= -2.7e+26)
		tmp = t_0;
	elseif (x <= -1.5e-79)
		tmp = Float64(x * z);
	elseif (x <= -1.1e-141)
		tmp = y;
	elseif (x <= -2.8e-216)
		tmp = Float64(x * z);
	elseif (x <= 9.5e-42)
		tmp = y;
	elseif ((x <= 1.45e+49) || !(x <= 1.35e+248))
		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 <= -4.4e+219)
		tmp = t_0;
	elseif (x <= -2.8e+74)
		tmp = x * z;
	elseif (x <= -2.7e+26)
		tmp = t_0;
	elseif (x <= -1.5e-79)
		tmp = x * z;
	elseif (x <= -1.1e-141)
		tmp = y;
	elseif (x <= -2.8e-216)
		tmp = x * z;
	elseif (x <= 9.5e-42)
		tmp = y;
	elseif ((x <= 1.45e+49) || ~((x <= 1.35e+248)))
		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, -4.4e+219], t$95$0, If[LessEqual[x, -2.8e+74], N[(x * z), $MachinePrecision], If[LessEqual[x, -2.7e+26], t$95$0, If[LessEqual[x, -1.5e-79], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.1e-141], y, If[LessEqual[x, -2.8e-216], N[(x * z), $MachinePrecision], If[LessEqual[x, 9.5e-42], y, If[Or[LessEqual[x, 1.45e+49], N[Not[LessEqual[x, 1.35e+248]], $MachinePrecision]], N[(x * z), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

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

Alternative 3: 81.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{-94} \lor \neg \left(x \leq -4.8 \cdot 10^{-141}\right) \land \left(x \leq -2.8 \cdot 10^{-216} \lor \neg \left(x \leq 6.4 \cdot 10^{-18}\right)\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.08e-94)
         (and (not (<= x -4.8e-141))
              (or (<= x -2.8e-216) (not (<= x 6.4e-18)))))
   (* x (- z y))
   y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.08e-94) || (!(x <= -4.8e-141) && ((x <= -2.8e-216) || !(x <= 6.4e-18)))) {
		tmp = x * (z - y);
	} 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 <= (-1.08d-94)) .or. (.not. (x <= (-4.8d-141))) .and. (x <= (-2.8d-216)) .or. (.not. (x <= 6.4d-18))) then
        tmp = x * (z - y)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.08e-94) || (!(x <= -4.8e-141) && ((x <= -2.8e-216) || !(x <= 6.4e-18)))) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.08e-94) or (not (x <= -4.8e-141) and ((x <= -2.8e-216) or not (x <= 6.4e-18))):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.08e-94) || (!(x <= -4.8e-141) && ((x <= -2.8e-216) || !(x <= 6.4e-18))))
		tmp = Float64(x * Float64(z - y));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.08e-94) || (~((x <= -4.8e-141)) && ((x <= -2.8e-216) || ~((x <= 6.4e-18)))))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.08e-94], And[N[Not[LessEqual[x, -4.8e-141]], $MachinePrecision], Or[LessEqual[x, -2.8e-216], N[Not[LessEqual[x, 6.4e-18]], $MachinePrecision]]]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

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

Alternative 4: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-79} \lor \neg \left(x \leq -1.1 \cdot 10^{-141}\right) \land \left(x \leq -1.5 \cdot 10^{-216} \lor \neg \left(x \leq 2.9 \cdot 10^{-42}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.5e-79)
         (and (not (<= x -1.1e-141))
              (or (<= x -1.5e-216) (not (<= x 2.9e-42)))))
   (* x z)
   y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-79) || (!(x <= -1.1e-141) && ((x <= -1.5e-216) || !(x <= 2.9e-42)))) {
		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 <= (-8.5d-79)) .or. (.not. (x <= (-1.1d-141))) .and. (x <= (-1.5d-216)) .or. (.not. (x <= 2.9d-42))) 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 <= -8.5e-79) || (!(x <= -1.1e-141) && ((x <= -1.5e-216) || !(x <= 2.9e-42)))) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.5e-79) or (not (x <= -1.1e-141) and ((x <= -1.5e-216) or not (x <= 2.9e-42))):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.5e-79) || (!(x <= -1.1e-141) && ((x <= -1.5e-216) || !(x <= 2.9e-42))))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.5e-79) || (~((x <= -1.1e-141)) && ((x <= -1.5e-216) || ~((x <= 2.9e-42)))))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e-79], And[N[Not[LessEqual[x, -1.1e-141]], $MachinePrecision], Or[LessEqual[x, -1.5e-216], N[Not[LessEqual[x, 2.9e-42]], $MachinePrecision]]]], N[(x * z), $MachinePrecision], y]

Derivation

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

Alternative 5: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+24} \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.4e+24) (not (<= x 1.0))) (* x (- z y)) (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.4e+24) || !(x <= 1.0)) {
		tmp = x * (z - y);
	} 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 ((x <= (-3.4d+24)) .or. (.not. (x <= 1.0d0))) then
        tmp = x * (z - y)
    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 ((x <= -3.4e+24) || !(x <= 1.0)) {
		tmp = x * (z - y);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.4e+24) or not (x <= 1.0):
		tmp = x * (z - y)
	else:
		tmp = y + (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.4e+24) || !(x <= 1.0))
		tmp = Float64(x * Float64(z - y));
	else
		tmp = Float64(y + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.4e+24) || ~((x <= 1.0)))
		tmp = x * (z - y);
	else
		tmp = y + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.4e+24], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * z), $MachinePrecision]), $MachinePrecision]]

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: 36.7% 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 2024003 
(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)))