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

Percentage Accurate: 98.0% → 100.0%

Time: 5.0s

Alternatives: 6

Speedup: 0.5×

• 20.6% 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: 98.0% 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

1. Initial program 96.1%

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

   1. sub-neg 96.1%

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

   2. +-commutative 96.1%

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

   3. distribute-rgt1-in 96.1%

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

   4. associate-+l+ 96.1%

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

   5. +-commutative 96.1%

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

   6. *-commutative 96.1%

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

   7. neg-mul-1 96.1%

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

   8. associate-*r* 96.1%

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

   9. *-commutative 96.1%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

       \[\leadsto \mathsf{fma}\left(x, z + \color{blue}{\left(-y\right)}, y\right) \]

   15. unsub-neg 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - x\right) + x \cdot z\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y (- 1.0 x)) (* x z))))
   (if (<= t_0 2e+290) t_0 (* x (- z y)))))

C

double code(double x, double y, double z) {
	double t_0 = (y * (1.0 - x)) + (x * z);
	double tmp;
	if (t_0 <= 2e+290) {
		tmp = t_0;
	} else {
		tmp = x * (z - 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) :: t_0
    real(8) :: tmp
    t_0 = (y * (1.0d0 - x)) + (x * z)
    if (t_0 <= 2d+290) then
        tmp = t_0
    else
        tmp = x * (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * (1.0 - x)) + (x * z);
	double tmp;
	if (t_0 <= 2e+290) {
		tmp = t_0;
	} else {
		tmp = x * (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * (1.0 - x)) + (x * z)
	tmp = 0
	if t_0 <= 2e+290:
		tmp = t_0
	else:
		tmp = x * (z - y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) + Float64(x * z))
	tmp = 0.0
	if (t_0 <= 2e+290)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * (1.0 - x)) + (x * z);
	tmp = 0.0;
	if (t_0 <= 2e+290)
		tmp = t_0;
	else
		tmp = x * (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 2e+290], t$95$0, N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (-.f64 1 x) y) (*.f64 x z)) < 2.00000000000000012e290

   1. Initial program 100.0%

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

   if 2.00000000000000012e290 < (+.f64 (*.f64 (-.f64 1 x) y) (*.f64 x z))

   1. Initial program 72.2%

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

   2. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{\left(z + -1 \cdot y\right) \cdot x} \]
   3. Step-by-step derivation

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(1 - x\right) + x \cdot z \leq 2 \cdot 10^{+290}:\\ \;\;\;\;y \cdot \left(1 - x\right) + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 3: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-33} \lor \neg \left(x \leq 1.36 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e-33) (not (<= x 1.36e-19))) (* x (- z y)) (* y (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e-33) || !(x <= 1.36e-19)) {
		tmp = x * (z - y);
	} 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 ((x <= (-3.8d-33)) .or. (.not. (x <= 1.36d-19))) then
        tmp = x * (z - y)
    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 ((x <= -3.8e-33) || !(x <= 1.36e-19)) {
		tmp = x * (z - y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e-33) or not (x <= 1.36e-19):
		tmp = x * (z - y)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e-33) || !(x <= 1.36e-19))
		tmp = Float64(x * Float64(z - y));
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.8e-33) || ~((x <= 1.36e-19)))
		tmp = x * (z - y);
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e-33], N[Not[LessEqual[x, 1.36e-19]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.79999999999999994e-33 or 1.3599999999999999e-19 < x

   1. Initial program 92.5%

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

   2. Taylor expanded in x around inf 97.5%

      \[\leadsto \color{blue}{\left(z + -1 \cdot y\right) \cdot x} \]
   3. Step-by-step derivation

      1. mul-1-neg 97.5%

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

      2. unsub-neg 97.5%

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

   4. Simplified 97.5%

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

   if -3.79999999999999994e-33 < x < 1.3599999999999999e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.9%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-33} \lor \neg \left(x \leq 1.36 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 4: 75.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.1e+62) (* x z) (if (<= z 3.1e+50) (* y (- 1.0 x)) (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e+62) {
		tmp = x * z;
	} else if (z <= 3.1e+50) {
		tmp = y * (1.0 - x);
	} else {
		tmp = 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 (z <= (-4.1d+62)) then
        tmp = x * z
    else if (z <= 3.1d+50) then
        tmp = y * (1.0d0 - x)
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e+62) {
		tmp = x * z;
	} else if (z <= 3.1e+50) {
		tmp = y * (1.0 - x);
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.1e+62:
		tmp = x * z
	elif z <= 3.1e+50:
		tmp = y * (1.0 - x)
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.1e+62)
		tmp = Float64(x * z);
	elseif (z <= 3.1e+50)
		tmp = Float64(y * Float64(1.0 - x));
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.1e+62)
		tmp = x * z;
	elseif (z <= 3.1e+50)
		tmp = y * (1.0 - x);
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.1e+62], N[(x * z), $MachinePrecision], If[LessEqual[z, 3.1e+50], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.09999999999999984e62 or 3.10000000000000003e50 < z

   1. Initial program 90.8%

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

   2. Taylor expanded in y around 0 76.2%

      \[\leadsto \color{blue}{z \cdot x} \]

   if -4.09999999999999984e62 < z < 3.10000000000000003e50

   1. Initial program 99.4%

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

   2. Taylor expanded in y around inf 83.3%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 5: 61.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-33}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-21}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.7e-33) (* x z) (if (<= x 2.75e-21) y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.7e-33) {
		tmp = x * z;
	} else if (x <= 2.75e-21) {
		tmp = y;
	} else {
		tmp = 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 <= (-2.7d-33)) then
        tmp = x * z
    else if (x <= 2.75d-21) then
        tmp = y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.7e-33) {
		tmp = x * z;
	} else if (x <= 2.75e-21) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.7e-33:
		tmp = x * z
	elif x <= 2.75e-21:
		tmp = y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.7e-33)
		tmp = Float64(x * z);
	elseif (x <= 2.75e-21)
		tmp = y;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.7e-33)
		tmp = x * z;
	elseif (x <= 2.75e-21)
		tmp = y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.7e-33], N[(x * z), $MachinePrecision], If[LessEqual[x, 2.75e-21], y, N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7000000000000001e-33 or 2.74999999999999989e-21 < x

   1. Initial program 92.5%

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

   2. Taylor expanded in y around 0 57.9%

      \[\leadsto \color{blue}{z \cdot x} \]

   if -2.7000000000000001e-33 < x < 2.74999999999999989e-21

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.9%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-33}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-21}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 6: 36.1% 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

1. Initial program 96.1%

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

2. Taylor expanded in x around 0 40.1%

   \[\leadsto \color{blue}{y} \]

3. Final simplification 40.1%

   \[\leadsto y \]

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 2023278 
(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)))