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

Percentage Accurate: 97.7% → 100.0%

Time: 5.3s

Alternatives: 7

Speedup: 1.3×

• 21.4% 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, 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 96.5%

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

   1. remove-double-neg 96.5%

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

   2. distribute-rgt-neg-out 96.5%

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

   3. neg-sub0 96.5%

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

   4. neg-sub0 96.5%

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

   5. *-commutative 96.5%

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

   6. distribute-lft-neg-in 96.5%

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

   7. remove-double-neg 96.5%

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

   8. distribute-rgt-out-- 96.5%

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

   9. *-lft-identity 96.5%

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

   10. associate-+l- 96.5%

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

   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: 60.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -4.7 \cdot 10^{+282}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+219}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+192}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+122}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -600:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-24}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+66}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= x -4.7e+282)
     (* x z)
     (if (<= x -4.8e+219)
       t_0
       (if (<= x -2.8e+192)
         (* x z)
         (if (<= x -4e+122)
           t_0
           (if (<= x -7.5e+84)
             (* x z)
             (if (<= x -600.0)
               t_0
               (if (<= x 5.7e-24) y (if (<= x 5e+66) (* x z) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (x <= -4.7e+282) {
		tmp = x * z;
	} else if (x <= -4.8e+219) {
		tmp = t_0;
	} else if (x <= -2.8e+192) {
		tmp = x * z;
	} else if (x <= -4e+122) {
		tmp = t_0;
	} else if (x <= -7.5e+84) {
		tmp = x * z;
	} else if (x <= -600.0) {
		tmp = t_0;
	} else if (x <= 5.7e-24) {
		tmp = y;
	} else if (x <= 5e+66) {
		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 <= (-4.7d+282)) then
        tmp = x * z
    else if (x <= (-4.8d+219)) then
        tmp = t_0
    else if (x <= (-2.8d+192)) then
        tmp = x * z
    else if (x <= (-4d+122)) then
        tmp = t_0
    else if (x <= (-7.5d+84)) then
        tmp = x * z
    else if (x <= (-600.0d0)) then
        tmp = t_0
    else if (x <= 5.7d-24) then
        tmp = y
    else if (x <= 5d+66) 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 <= -4.7e+282) {
		tmp = x * z;
	} else if (x <= -4.8e+219) {
		tmp = t_0;
	} else if (x <= -2.8e+192) {
		tmp = x * z;
	} else if (x <= -4e+122) {
		tmp = t_0;
	} else if (x <= -7.5e+84) {
		tmp = x * z;
	} else if (x <= -600.0) {
		tmp = t_0;
	} else if (x <= 5.7e-24) {
		tmp = y;
	} else if (x <= 5e+66) {
		tmp = x * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if x <= -4.7e+282:
		tmp = x * z
	elif x <= -4.8e+219:
		tmp = t_0
	elif x <= -2.8e+192:
		tmp = x * z
	elif x <= -4e+122:
		tmp = t_0
	elif x <= -7.5e+84:
		tmp = x * z
	elif x <= -600.0:
		tmp = t_0
	elif x <= 5.7e-24:
		tmp = y
	elif x <= 5e+66:
		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 <= -4.7e+282)
		tmp = Float64(x * z);
	elseif (x <= -4.8e+219)
		tmp = t_0;
	elseif (x <= -2.8e+192)
		tmp = Float64(x * z);
	elseif (x <= -4e+122)
		tmp = t_0;
	elseif (x <= -7.5e+84)
		tmp = Float64(x * z);
	elseif (x <= -600.0)
		tmp = t_0;
	elseif (x <= 5.7e-24)
		tmp = y;
	elseif (x <= 5e+66)
		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 <= -4.7e+282)
		tmp = x * z;
	elseif (x <= -4.8e+219)
		tmp = t_0;
	elseif (x <= -2.8e+192)
		tmp = x * z;
	elseif (x <= -4e+122)
		tmp = t_0;
	elseif (x <= -7.5e+84)
		tmp = x * z;
	elseif (x <= -600.0)
		tmp = t_0;
	elseif (x <= 5.7e-24)
		tmp = y;
	elseif (x <= 5e+66)
		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, -4.7e+282], N[(x * z), $MachinePrecision], If[LessEqual[x, -4.8e+219], t$95$0, If[LessEqual[x, -2.8e+192], N[(x * z), $MachinePrecision], If[LessEqual[x, -4e+122], t$95$0, If[LessEqual[x, -7.5e+84], N[(x * z), $MachinePrecision], If[LessEqual[x, -600.0], t$95$0, If[LessEqual[x, 5.7e-24], y, If[LessEqual[x, 5e+66], N[(x * z), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.70000000000000035e282 or -4.8000000000000001e219 < x < -2.79999999999999976e192 or -4.00000000000000006e122 < x < -7.5000000000000001e84 or 5.70000000000000002e-24 < x < 4.99999999999999991e66

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0 86.5%

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

   if -4.70000000000000035e282 < x < -4.8000000000000001e219 or -2.79999999999999976e192 < x < -4.00000000000000006e122 or -7.5000000000000001e84 < x < -600 or 4.99999999999999991e66 < x

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. sub-neg 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. distribute-rgt-neg-out 71.9%

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

   8. Simplified 71.9%

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

   if -600 < x < 5.70000000000000002e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 72.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+282}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+219}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+192}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -600:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-24}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+66}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-19} \lor \neg \left(x \leq -6.2 \cdot 10^{-145}\right) \land \left(x \leq -5.8 \cdot 10^{-187} \lor \neg \left(x \leq 5.8 \cdot 10^{-24}\right)\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.7e-19)
         (and (not (<= x -6.2e-145))
              (or (<= x -5.8e-187) (not (<= x 5.8e-24)))))
   (* x (- z y))
   y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.7e-19) || (!(x <= -6.2e-145) && ((x <= -5.8e-187) || !(x <= 5.8e-24)))) {
		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 <= (-3.7d-19)) .or. (.not. (x <= (-6.2d-145))) .and. (x <= (-5.8d-187)) .or. (.not. (x <= 5.8d-24))) 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 <= -3.7e-19) || (!(x <= -6.2e-145) && ((x <= -5.8e-187) || !(x <= 5.8e-24)))) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.7e-19) or (not (x <= -6.2e-145) and ((x <= -5.8e-187) or not (x <= 5.8e-24))):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.7e-19) || (!(x <= -6.2e-145) && ((x <= -5.8e-187) || !(x <= 5.8e-24))))
		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 <= -3.7e-19) || (~((x <= -6.2e-145)) && ((x <= -5.8e-187) || ~((x <= 5.8e-24)))))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.7e-19], And[N[Not[LessEqual[x, -6.2e-145]], $MachinePrecision], Or[LessEqual[x, -5.8e-187], N[Not[LessEqual[x, 5.8e-24]], $MachinePrecision]]]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -3.70000000000000005e-19 or -6.20000000000000001e-145 < x < -5.79999999999999977e-187 or 5.7999999999999997e-24 < x

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 96.5%

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

      1. mul-1-neg 96.5%

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

      2. sub-neg 96.5%

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

   5. Simplified 96.5%

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

   if -3.70000000000000005e-19 < x < -6.20000000000000001e-145 or -5.79999999999999977e-187 < x < 5.7999999999999997e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.2%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-19} \lor \neg \left(x \leq -6.2 \cdot 10^{-145}\right) \land \left(x \leq -5.8 \cdot 10^{-187} \lor \neg \left(x \leq 5.8 \cdot 10^{-24}\right)\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -0.38:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-187} \lor \neg \left(x \leq 9.2 \cdot 10^{-25}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= x -0.38)
     t_0
     (if (<= x -5.8e-145)
       (* y (- 1.0 x))
       (if (or (<= x -5.8e-187) (not (<= x 9.2e-25))) t_0 y)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -0.38) {
		tmp = t_0;
	} else if (x <= -5.8e-145) {
		tmp = y * (1.0 - x);
	} else if ((x <= -5.8e-187) || !(x <= 9.2e-25)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * (z - y)
    if (x <= (-0.38d0)) then
        tmp = t_0
    else if (x <= (-5.8d-145)) then
        tmp = y * (1.0d0 - x)
    else if ((x <= (-5.8d-187)) .or. (.not. (x <= 9.2d-25))) then
        tmp = t_0
    else
        tmp = y
    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 <= -0.38) {
		tmp = t_0;
	} else if (x <= -5.8e-145) {
		tmp = y * (1.0 - x);
	} else if ((x <= -5.8e-187) || !(x <= 9.2e-25)) {
		tmp = t_0;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z - y)
	tmp = 0
	if x <= -0.38:
		tmp = t_0
	elif x <= -5.8e-145:
		tmp = y * (1.0 - x)
	elif (x <= -5.8e-187) or not (x <= 9.2e-25):
		tmp = t_0
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z - y))
	tmp = 0.0
	if (x <= -0.38)
		tmp = t_0;
	elseif (x <= -5.8e-145)
		tmp = Float64(y * Float64(1.0 - x));
	elseif ((x <= -5.8e-187) || !(x <= 9.2e-25))
		tmp = t_0;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z - y);
	tmp = 0.0;
	if (x <= -0.38)
		tmp = t_0;
	elseif (x <= -5.8e-145)
		tmp = y * (1.0 - x);
	elseif ((x <= -5.8e-187) || ~((x <= 9.2e-25)))
		tmp = t_0;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.38], t$95$0, If[LessEqual[x, -5.8e-145], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5.8e-187], N[Not[LessEqual[x, 9.2e-25]], $MachinePrecision]], t$95$0, y]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.38 or -5.79999999999999968e-145 < x < -5.79999999999999977e-187 or 9.1999999999999997e-25 < x

   1. Initial program 93.4%

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

   3. Taylor expanded in x around inf 98.4%

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

      1. mul-1-neg 98.4%

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

      2. sub-neg 98.4%

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

   5. Simplified 98.4%

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

   if -0.38 < x < -5.79999999999999968e-145

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 73.5%

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

   if -5.79999999999999977e-187 < x < 9.1999999999999997e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.1%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.38:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-187} \lor \neg \left(x \leq 9.2 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-19} \lor \neg \left(x \leq -5.8 \cdot 10^{-145}\right) \land \left(x \leq -5.8 \cdot 10^{-187} \lor \neg \left(x \leq 5.8 \cdot 10^{-24}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.1e-19)
         (and (not (<= x -5.8e-145))
              (or (<= x -5.8e-187) (not (<= x 5.8e-24)))))
   (* x z)
   y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.1e-19) || (!(x <= -5.8e-145) && ((x <= -5.8e-187) || !(x <= 5.8e-24)))) {
		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 <= (-4.1d-19)) .or. (.not. (x <= (-5.8d-145))) .and. (x <= (-5.8d-187)) .or. (.not. (x <= 5.8d-24))) 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 <= -4.1e-19) || (!(x <= -5.8e-145) && ((x <= -5.8e-187) || !(x <= 5.8e-24)))) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.1e-19) or (not (x <= -5.8e-145) and ((x <= -5.8e-187) or not (x <= 5.8e-24))):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.1e-19) || (!(x <= -5.8e-145) && ((x <= -5.8e-187) || !(x <= 5.8e-24))))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.1e-19) || (~((x <= -5.8e-145)) && ((x <= -5.8e-187) || ~((x <= 5.8e-24)))))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.1e-19], And[N[Not[LessEqual[x, -5.8e-145]], $MachinePrecision], Or[LessEqual[x, -5.8e-187], N[Not[LessEqual[x, 5.8e-24]], $MachinePrecision]]]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -4.09999999999999985e-19 or -5.79999999999999968e-145 < x < -5.79999999999999977e-187 or 5.7999999999999997e-24 < x

   1. Initial program 93.6%

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

   3. Taylor expanded in y around 0 52.3%

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

   if -4.09999999999999985e-19 < x < -5.79999999999999968e-145 or -5.79999999999999977e-187 < x < 5.7999999999999997e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.2%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-19} \lor \neg \left(x \leq -5.8 \cdot 10^{-145}\right) \land \left(x \leq -5.8 \cdot 10^{-187} \lor \neg \left(x \leq 5.8 \cdot 10^{-24}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -600 \lor \neg \left(x \leq 5.8 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -600.0) (not (<= x 5.8e-24))) (* x (- z y)) (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -600.0) || !(x <= 5.8e-24)) {
		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 <= (-600.0d0)) .or. (.not. (x <= 5.8d-24))) 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 <= -600.0) || !(x <= 5.8e-24)) {
		tmp = x * (z - y);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -600.0) or not (x <= 5.8e-24):
		tmp = x * (z - y)
	else:
		tmp = y + (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -600.0) || !(x <= 5.8e-24))
		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 <= -600.0) || ~((x <= 5.8e-24)))
		tmp = x * (z - y);
	else
		tmp = y + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -600.0], N[Not[LessEqual[x, 5.8e-24]], $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 < -600 or 5.7999999999999997e-24 < x

   1. Initial program 92.9%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 -600 < x < 5.7999999999999997e-24

   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 99.1%

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

      1. neg-mul-1 99.1%

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

      2. *-commutative 99.1%

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

      3. distribute-rgt-neg-in 99.1%

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

   7. Simplified 99.1%

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

      1. sub-neg 99.1%

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

      2. +-commutative 99.1%

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

      3. distribute-rgt-neg-out 99.1%

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

      4. remove-double-neg 99.1%

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

   9. Applied egg-rr 99.1%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -600 \lor \neg \left(x \leq 5.8 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]
5. 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

1. Initial program 96.5%

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

3. Taylor expanded in x around 0 38.4%

   \[\leadsto \color{blue}{y} \]
4. 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 2024092 
(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)))