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

Percentage Accurate: 98.3% → 100.0%

Time: 5.7s

Alternatives: 7

Speedup: 1.3×

• 20.0% 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: 98.3% 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 98.0%

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

   1. *-commutative 98.0%

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

   2. distribute-rgt-out-- 98.0%

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

   3. *-lft-identity 98.0%

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

   4. associate-+l- 98.0%

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

   5. 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: 61.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -5 \cdot 10^{+191}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+113}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+80}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-51}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+143}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= x -5e+191)
     (* x z)
     (if (<= x -1.9e+113)
       t_0
       (if (<= x -6.6e+80)
         (* x z)
         (if (<= x -2.45e+19)
           t_0
           (if (<= x -4.8e-51)
             (* x z)
             (if (<= x 3.2e-95) y (if (<= x 6.5e+143) (* x z) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (x <= -5e+191) {
		tmp = x * z;
	} else if (x <= -1.9e+113) {
		tmp = t_0;
	} else if (x <= -6.6e+80) {
		tmp = x * z;
	} else if (x <= -2.45e+19) {
		tmp = t_0;
	} else if (x <= -4.8e-51) {
		tmp = x * z;
	} else if (x <= 3.2e-95) {
		tmp = y;
	} else if (x <= 6.5e+143) {
		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 = y * -x
    if (x <= (-5d+191)) then
        tmp = x * z
    else if (x <= (-1.9d+113)) then
        tmp = t_0
    else if (x <= (-6.6d+80)) then
        tmp = x * z
    else if (x <= (-2.45d+19)) then
        tmp = t_0
    else if (x <= (-4.8d-51)) then
        tmp = x * z
    else if (x <= 3.2d-95) then
        tmp = y
    else if (x <= 6.5d+143) 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 = y * -x;
	double tmp;
	if (x <= -5e+191) {
		tmp = x * z;
	} else if (x <= -1.9e+113) {
		tmp = t_0;
	} else if (x <= -6.6e+80) {
		tmp = x * z;
	} else if (x <= -2.45e+19) {
		tmp = t_0;
	} else if (x <= -4.8e-51) {
		tmp = x * z;
	} else if (x <= 3.2e-95) {
		tmp = y;
	} else if (x <= 6.5e+143) {
		tmp = x * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if x <= -5e+191:
		tmp = x * z
	elif x <= -1.9e+113:
		tmp = t_0
	elif x <= -6.6e+80:
		tmp = x * z
	elif x <= -2.45e+19:
		tmp = t_0
	elif x <= -4.8e-51:
		tmp = x * z
	elif x <= 3.2e-95:
		tmp = y
	elif x <= 6.5e+143:
		tmp = x * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (x <= -5e+191)
		tmp = Float64(x * z);
	elseif (x <= -1.9e+113)
		tmp = t_0;
	elseif (x <= -6.6e+80)
		tmp = Float64(x * z);
	elseif (x <= -2.45e+19)
		tmp = t_0;
	elseif (x <= -4.8e-51)
		tmp = Float64(x * z);
	elseif (x <= 3.2e-95)
		tmp = y;
	elseif (x <= 6.5e+143)
		tmp = Float64(x * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -x;
	tmp = 0.0;
	if (x <= -5e+191)
		tmp = x * z;
	elseif (x <= -1.9e+113)
		tmp = t_0;
	elseif (x <= -6.6e+80)
		tmp = x * z;
	elseif (x <= -2.45e+19)
		tmp = t_0;
	elseif (x <= -4.8e-51)
		tmp = x * z;
	elseif (x <= 3.2e-95)
		tmp = y;
	elseif (x <= 6.5e+143)
		tmp = x * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[x, -5e+191], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.9e+113], t$95$0, If[LessEqual[x, -6.6e+80], N[(x * z), $MachinePrecision], If[LessEqual[x, -2.45e+19], t$95$0, If[LessEqual[x, -4.8e-51], N[(x * z), $MachinePrecision], If[LessEqual[x, 3.2e-95], y, If[LessEqual[x, 6.5e+143], N[(x * z), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.0000000000000002e191 or -1.9000000000000002e113 < x < -6.59999999999999982e80 or -2.45e19 < x < -4.8e-51 or 3.1999999999999997e-95 < x < 6.4999999999999997e143

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 62.2%

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

   if -5.0000000000000002e191 < x < -1.9000000000000002e113 or -6.59999999999999982e80 < x < -2.45e19 or 6.4999999999999997e143 < x

   1. Initial program 95.2%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 78.1%

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

      1. mul-1-neg 78.1%

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

      2. distribute-rgt-neg-out 78.1%

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

   8. Simplified 78.1%

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

   if -4.8e-51 < x < 3.1999999999999997e-95

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+191}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+80}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-51}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+143}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-59} \lor \neg \left(x \leq 4.7 \cdot 10^{-91}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2e-59) (not (<= x 4.7e-91))) (* x (- z y)) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e-59) || !(x <= 4.7e-91)) {
		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 <= (-2d-59)) .or. (.not. (x <= 4.7d-91))) 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 <= -2e-59) || !(x <= 4.7e-91)) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2e-59) or not (x <= 4.7e-91):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2e-59) || !(x <= 4.7e-91))
		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 <= -2e-59) || ~((x <= 4.7e-91)))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2e-59], N[Not[LessEqual[x, 4.7e-91]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -2.0000000000000001e-59 or 4.70000000000000006e-91 < x

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. sub-neg 91.7%

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

   5. Simplified 91.7%

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

   if -2.0000000000000001e-59 < x < 4.70000000000000006e-91

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.7%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-59} \lor \neg \left(x \leq 4.7 \cdot 10^{-91}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-23} \lor \neg \left(y \leq 6 \cdot 10^{+74}\right):\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.55e-23) (not (<= y 6e+74))) (* y (- 1.0 x)) (* x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.55e-23) || !(y <= 6e+74)) {
		tmp = y * (1.0 - x);
	} 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) :: tmp
    if ((y <= (-2.55d-23)) .or. (.not. (y <= 6d+74))) then
        tmp = y * (1.0d0 - x)
    else
        tmp = x * (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.55e-23) || !(y <= 6e+74)) {
		tmp = y * (1.0 - x);
	} else {
		tmp = x * (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.55e-23) or not (y <= 6e+74):
		tmp = y * (1.0 - x)
	else:
		tmp = x * (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.55e-23) || !(y <= 6e+74))
		tmp = Float64(y * Float64(1.0 - x));
	else
		tmp = Float64(x * Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.55e-23) || ~((y <= 6e+74)))
		tmp = y * (1.0 - x);
	else
		tmp = x * (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.55e-23], N[Not[LessEqual[y, 6e+74]], $MachinePrecision]], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.55000000000000005e-23 or 6e74 < y

   1. Initial program 95.9%

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

   3. Taylor expanded in y around inf 88.2%

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

   if -2.55000000000000005e-23 < y < 6e74

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. sub-neg 86.2%

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

   5. Simplified 86.2%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-23} \lor \neg \left(y \leq 6 \cdot 10^{+74}\right):\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.55e-23)
   (* y (- 1.0 x))
   (if (<= y 2.25e+74) (* x (- z y)) (- y (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.55e-23) {
		tmp = y * (1.0 - x);
	} else if (y <= 2.25e+74) {
		tmp = x * (z - y);
	} else {
		tmp = y - (y * 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 (y <= (-2.55d-23)) then
        tmp = y * (1.0d0 - x)
    else if (y <= 2.25d+74) then
        tmp = x * (z - y)
    else
        tmp = y - (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.55e-23) {
		tmp = y * (1.0 - x);
	} else if (y <= 2.25e+74) {
		tmp = x * (z - y);
	} else {
		tmp = y - (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.55e-23:
		tmp = y * (1.0 - x)
	elif y <= 2.25e+74:
		tmp = x * (z - y)
	else:
		tmp = y - (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.55e-23)
		tmp = Float64(y * Float64(1.0 - x));
	elseif (y <= 2.25e+74)
		tmp = Float64(x * Float64(z - y));
	else
		tmp = Float64(y - Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.55e-23)
		tmp = y * (1.0 - x);
	elseif (y <= 2.25e+74)
		tmp = x * (z - y);
	else
		tmp = y - (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.55e-23], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+74], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.55000000000000005e-23

   1. Initial program 97.2%

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

   3. Taylor expanded in y around inf 87.9%

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

   if -2.55000000000000005e-23 < y < 2.25e74

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. sub-neg 86.2%

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

   5. Simplified 86.2%

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

   if 2.25e74 < y

   1. Initial program 94.1%

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

      1. *-commutative 94.1%

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

      2. distribute-rgt-out-- 94.1%

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

      3. *-lft-identity 94.1%

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

      4. associate-+l- 94.1%

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

      5. 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 inf 88.7%

      \[\leadsto y - \color{blue}{x \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 88.7%

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

   7. Simplified 88.7%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-50} \lor \neg \left(x \leq 3.8 \cdot 10^{-93}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.8e-50) (not (<= x 3.8e-93))) (* x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.8e-50) || !(x <= 3.8e-93)) {
		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 <= (-1.8d-50)) .or. (.not. (x <= 3.8d-93))) 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 <= -1.8e-50) || !(x <= 3.8e-93)) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.8e-50) or not (x <= 3.8e-93):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.8e-50) || !(x <= 3.8e-93))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.8e-50) || ~((x <= 3.8e-93)))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.8e-50], N[Not[LessEqual[x, 3.8e-93]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -1.7999999999999999e-50 or 3.7999999999999999e-93 < x

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 50.3%

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

   if -1.7999999999999999e-50 < x < 3.7999999999999999e-93

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.1%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-50} \lor \neg \left(x \leq 3.8 \cdot 10^{-93}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.4% 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 98.0%

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

3. Taylor expanded in x around 0 31.6%

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

4. Final simplification 31.6%

   \[\leadsto y \]
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 2024109 
(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)))