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

Percentage Accurate: 97.9% → 100.0%

Time: 5.2s

Alternatives: 7

Speedup: 1.3×

• 21.3% 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: 97.9% 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, 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

1. Initial program 97.2%

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

   1. remove-double-neg 97.2%

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

   2. distribute-rgt-neg-out 97.2%

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

   3. neg-sub0 97.2%

      \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-y\right)\right)} + x \cdot z \]

   4. neg-sub0 97.2%

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

   5. *-commutative 97.2%

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

   6. distribute-lft-neg-in 97.2%

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

   7. remove-double-neg 97.2%

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

   8. distribute-rgt-out-- 97.2%

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

   9. *-lft-identity 97.2%

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

   10. associate-+l- 97.2%

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

   11. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 61.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-30}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-92}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-42}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+77} \lor \neg \left(x \leq 2.5 \cdot 10^{+237}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.02e-30)
   (* x z)
   (if (<= x 3.1e-92)
     y
     (if (<= x 2.15e-42)
       (* x z)
       (if (<= x 6.8e-16)
         y
         (if (or (<= x 1.08e+77) (not (<= x 2.5e+237)))
           (* x z)
           (* x (- y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.02e-30) {
		tmp = x * z;
	} else if (x <= 3.1e-92) {
		tmp = y;
	} else if (x <= 2.15e-42) {
		tmp = x * z;
	} else if (x <= 6.8e-16) {
		tmp = y;
	} else if ((x <= 1.08e+77) || !(x <= 2.5e+237)) {
		tmp = x * z;
	} else {
		tmp = x * -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 <= (-1.02d-30)) then
        tmp = x * z
    else if (x <= 3.1d-92) then
        tmp = y
    else if (x <= 2.15d-42) then
        tmp = x * z
    else if (x <= 6.8d-16) then
        tmp = y
    else if ((x <= 1.08d+77) .or. (.not. (x <= 2.5d+237))) then
        tmp = x * z
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.02e-30) {
		tmp = x * z;
	} else if (x <= 3.1e-92) {
		tmp = y;
	} else if (x <= 2.15e-42) {
		tmp = x * z;
	} else if (x <= 6.8e-16) {
		tmp = y;
	} else if ((x <= 1.08e+77) || !(x <= 2.5e+237)) {
		tmp = x * z;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.02e-30:
		tmp = x * z
	elif x <= 3.1e-92:
		tmp = y
	elif x <= 2.15e-42:
		tmp = x * z
	elif x <= 6.8e-16:
		tmp = y
	elif (x <= 1.08e+77) or not (x <= 2.5e+237):
		tmp = x * z
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.02e-30)
		tmp = Float64(x * z);
	elseif (x <= 3.1e-92)
		tmp = y;
	elseif (x <= 2.15e-42)
		tmp = Float64(x * z);
	elseif (x <= 6.8e-16)
		tmp = y;
	elseif ((x <= 1.08e+77) || !(x <= 2.5e+237))
		tmp = Float64(x * z);
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.02e-30)
		tmp = x * z;
	elseif (x <= 3.1e-92)
		tmp = y;
	elseif (x <= 2.15e-42)
		tmp = x * z;
	elseif (x <= 6.8e-16)
		tmp = y;
	elseif ((x <= 1.08e+77) || ~((x <= 2.5e+237)))
		tmp = x * z;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.02e-30], N[(x * z), $MachinePrecision], If[LessEqual[x, 3.1e-92], y, If[LessEqual[x, 2.15e-42], N[(x * z), $MachinePrecision], If[LessEqual[x, 6.8e-16], y, If[Or[LessEqual[x, 1.08e+77], N[Not[LessEqual[x, 2.5e+237]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0199999999999999e-30 or 3.1000000000000001e-92 < x < 2.1500000000000001e-42 or 6.8e-16 < x < 1.07999999999999996e77 or 2.5000000000000001e237 < x

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0 66.8%

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

   if -1.0199999999999999e-30 < x < 3.1000000000000001e-92 or 2.1500000000000001e-42 < x < 6.8e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.2%

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

   if 1.07999999999999996e77 < x < 2.5000000000000001e237

   1. Initial program 92.5%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. sub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 65.4%

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

      1. mul-1-neg 65.4%

         \[\leadsto \color{blue}{-x \cdot y} \]

      2. distribute-rgt-neg-out 65.4%

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

   8. Simplified 65.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-30}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-92}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-42}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+77} \lor \neg \left(x \leq 2.5 \cdot 10^{+237}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{-32}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-92}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-42}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= x -6.5e-32)
     t_0
     (if (<= x 3.1e-92)
       y
       (if (<= x 2.25e-42) (* x z) (if (<= x 9.6e-17) y t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -6.5e-32) {
		tmp = t_0;
	} else if (x <= 3.1e-92) {
		tmp = y;
	} else if (x <= 2.25e-42) {
		tmp = x * z;
	} else if (x <= 9.6e-17) {
		tmp = 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 = x * (z - y)
    if (x <= (-6.5d-32)) then
        tmp = t_0
    else if (x <= 3.1d-92) then
        tmp = y
    else if (x <= 2.25d-42) then
        tmp = x * z
    else if (x <= 9.6d-17) then
        tmp = 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 = x * (z - y);
	double tmp;
	if (x <= -6.5e-32) {
		tmp = t_0;
	} else if (x <= 3.1e-92) {
		tmp = y;
	} else if (x <= 2.25e-42) {
		tmp = x * z;
	} else if (x <= 9.6e-17) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z - y)
	tmp = 0
	if x <= -6.5e-32:
		tmp = t_0
	elif x <= 3.1e-92:
		tmp = y
	elif x <= 2.25e-42:
		tmp = x * z
	elif x <= 9.6e-17:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z - y))
	tmp = 0.0
	if (x <= -6.5e-32)
		tmp = t_0;
	elseif (x <= 3.1e-92)
		tmp = y;
	elseif (x <= 2.25e-42)
		tmp = Float64(x * z);
	elseif (x <= 9.6e-17)
		tmp = y;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z - y);
	tmp = 0.0;
	if (x <= -6.5e-32)
		tmp = t_0;
	elseif (x <= 3.1e-92)
		tmp = y;
	elseif (x <= 2.25e-42)
		tmp = x * z;
	elseif (x <= 9.6e-17)
		tmp = y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.5e-32], t$95$0, If[LessEqual[x, 3.1e-92], y, If[LessEqual[x, 2.25e-42], N[(x * z), $MachinePrecision], If[LessEqual[x, 9.6e-17], y, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.49999999999999988e-32 or 9.59999999999999945e-17 < x

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. sub-neg 97.9%

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

   5. Simplified 97.9%

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

   if -6.49999999999999988e-32 < x < 3.1000000000000001e-92 or 2.25e-42 < x < 9.59999999999999945e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.2%

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

   if 3.1000000000000001e-92 < x < 2.25e-42

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.0%

      \[\leadsto \color{blue}{x \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-92}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-42}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -1.82 \cdot 10^{-31}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-42}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= x -1.82e-31)
     t_0
     (if (<= x 3.1e-92)
       (* y (- 1.0 x))
       (if (<= x 2.25e-42) (* x z) (if (<= x 5.2e-16) y t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -1.82e-31) {
		tmp = t_0;
	} else if (x <= 3.1e-92) {
		tmp = y * (1.0 - x);
	} else if (x <= 2.25e-42) {
		tmp = x * z;
	} else if (x <= 5.2e-16) {
		tmp = 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 = x * (z - y)
    if (x <= (-1.82d-31)) then
        tmp = t_0
    else if (x <= 3.1d-92) then
        tmp = y * (1.0d0 - x)
    else if (x <= 2.25d-42) then
        tmp = x * z
    else if (x <= 5.2d-16) then
        tmp = 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 = x * (z - y);
	double tmp;
	if (x <= -1.82e-31) {
		tmp = t_0;
	} else if (x <= 3.1e-92) {
		tmp = y * (1.0 - x);
	} else if (x <= 2.25e-42) {
		tmp = x * z;
	} else if (x <= 5.2e-16) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z - y)
	tmp = 0
	if x <= -1.82e-31:
		tmp = t_0
	elif x <= 3.1e-92:
		tmp = y * (1.0 - x)
	elif x <= 2.25e-42:
		tmp = x * z
	elif x <= 5.2e-16:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z - y))
	tmp = 0.0
	if (x <= -1.82e-31)
		tmp = t_0;
	elseif (x <= 3.1e-92)
		tmp = Float64(y * Float64(1.0 - x));
	elseif (x <= 2.25e-42)
		tmp = Float64(x * z);
	elseif (x <= 5.2e-16)
		tmp = y;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z - y);
	tmp = 0.0;
	if (x <= -1.82e-31)
		tmp = t_0;
	elseif (x <= 3.1e-92)
		tmp = y * (1.0 - x);
	elseif (x <= 2.25e-42)
		tmp = x * z;
	elseif (x <= 5.2e-16)
		tmp = y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.82e-31], t$95$0, If[LessEqual[x, 3.1e-92], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.25e-42], N[(x * z), $MachinePrecision], If[LessEqual[x, 5.2e-16], y, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.8199999999999999e-31 or 5.1999999999999997e-16 < x

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. sub-neg 97.9%

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

   5. Simplified 97.9%

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

   if -1.8199999999999999e-31 < x < 3.1000000000000001e-92

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.1%

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

   if 3.1000000000000001e-92 < x < 2.25e-42

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.0%

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

   if 2.25e-42 < x < 5.1999999999999997e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 86.4%

      \[\leadsto \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.82 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-42}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-32} \lor \neg \left(x \leq 2.65 \cdot 10^{-92} \lor \neg \left(x \leq 2.6 \cdot 10^{-42}\right) \land x \leq 3.4 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.6e-32)
         (not (or (<= x 2.65e-92) (and (not (<= x 2.6e-42)) (<= x 3.4e-16)))))
   (* x z)
   y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.6e-32) || !((x <= 2.65e-92) || (!(x <= 2.6e-42) && (x <= 3.4e-16)))) {
		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 <= (-4.6d-32)) .or. (.not. (x <= 2.65d-92) .or. (.not. (x <= 2.6d-42)) .and. (x <= 3.4d-16))) 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 <= -4.6e-32) || !((x <= 2.65e-92) || (!(x <= 2.6e-42) && (x <= 3.4e-16)))) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.6e-32) or not ((x <= 2.65e-92) or (not (x <= 2.6e-42) and (x <= 3.4e-16))):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.6e-32) || !((x <= 2.65e-92) || (!(x <= 2.6e-42) && (x <= 3.4e-16))))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.6e-32) || ~(((x <= 2.65e-92) || (~((x <= 2.6e-42)) && (x <= 3.4e-16)))))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.6e-32], N[Not[Or[LessEqual[x, 2.65e-92], And[N[Not[LessEqual[x, 2.6e-42]], $MachinePrecision], LessEqual[x, 3.4e-16]]]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -4.6000000000000001e-32 or 2.65000000000000015e-92 < x < 2.6e-42 or 3.4e-16 < x

   1. Initial program 95.1%

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

   3. Taylor expanded in y around 0 59.3%

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

   if -4.6000000000000001e-32 < x < 2.65000000000000015e-92 or 2.6e-42 < x < 3.4e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.2%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-32} \lor \neg \left(x \leq 2.65 \cdot 10^{-92} \lor \neg \left(x \leq 2.6 \cdot 10^{-42}\right) \land x \leq 3.4 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -18000000000000 \lor \neg \left(x \leq 8.5 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -18000000000000.0) (not (<= x 8.5e-15)))
   (* x (- z y))
   (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -18000000000000.0) || !(x <= 8.5e-15)) {
		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 <= (-18000000000000.0d0)) .or. (.not. (x <= 8.5d-15))) 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 <= -18000000000000.0) || !(x <= 8.5e-15)) {
		tmp = x * (z - y);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -18000000000000.0) or not (x <= 8.5e-15):
		tmp = x * (z - y)
	else:
		tmp = y + (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -18000000000000.0) || !(x <= 8.5e-15))
		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 <= -18000000000000.0) || ~((x <= 8.5e-15)))
		tmp = x * (z - y);
	else
		tmp = y + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -18000000000000.0], N[Not[LessEqual[x, 8.5e-15]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8e13 or 8.50000000000000007e-15 < x

   1. Initial program 94.4%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. sub-neg 99.8%

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

   5. Simplified 99.8%

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

   if -1.8e13 < x < 8.50000000000000007e-15

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-rgt-neg-out 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-y\right)\right)} + x \cdot z \]

      4. neg-sub0 100.0%

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

      5. *-commutative 100.0%

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

      6. distribute-lft-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. *-lft-identity 100.0%

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

      10. associate-+l- 100.0%

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

      11. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.7%

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

      1. neg-mul-1 98.7%

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

      2. distribute-rgt-neg-in 98.7%

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

   7. Simplified 98.7%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -18000000000000 \lor \neg \left(x \leq 8.5 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]
5. 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

1. Initial program 97.2%

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

3. Taylor expanded in x around 0 39.8%

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

4. Final simplification 39.8%

   \[\leadsto y \]
5. 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 2024075 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

  :alt
  (- y (* x (- y z)))

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