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

Percentage Accurate: 98.0% → 100.0%

Time: 5.8s

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: 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 99.6%

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

   1. *-commutative 99.6%

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

   2. distribute-lft-out-- 99.6%

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

   3. *-rgt-identity 99.6%

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

   4. cancel-sign-sub-inv 99.6%

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

   5. associate-+l+ 99.6%

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

   6. +-commutative 99.6%

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

   7. *-commutative 99.6%

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

   8. distribute-rgt-out 100.0%

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

   9. fma-define 100.0%

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

   10. +-commutative 100.0%

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

   11. 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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 83.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{-56}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-179}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-151}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= x -8e-56)
     t_0
     (if (<= x 8e-179)
       y
       (if (<= x 2.65e-151) (* x z) (if (<= x 1.55e-53) y t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -8e-56) {
		tmp = t_0;
	} else if (x <= 8e-179) {
		tmp = y;
	} else if (x <= 2.65e-151) {
		tmp = x * z;
	} else if (x <= 1.55e-53) {
		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 <= (-8d-56)) then
        tmp = t_0
    else if (x <= 8d-179) then
        tmp = y
    else if (x <= 2.65d-151) then
        tmp = x * z
    else if (x <= 1.55d-53) 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 <= -8e-56) {
		tmp = t_0;
	} else if (x <= 8e-179) {
		tmp = y;
	} else if (x <= 2.65e-151) {
		tmp = x * z;
	} else if (x <= 1.55e-53) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z - y)
	tmp = 0
	if x <= -8e-56:
		tmp = t_0
	elif x <= 8e-179:
		tmp = y
	elif x <= 2.65e-151:
		tmp = x * z
	elif x <= 1.55e-53:
		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 <= -8e-56)
		tmp = t_0;
	elseif (x <= 8e-179)
		tmp = y;
	elseif (x <= 2.65e-151)
		tmp = Float64(x * z);
	elseif (x <= 1.55e-53)
		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 <= -8e-56)
		tmp = t_0;
	elseif (x <= 8e-179)
		tmp = y;
	elseif (x <= 2.65e-151)
		tmp = x * z;
	elseif (x <= 1.55e-53)
		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, -8e-56], t$95$0, If[LessEqual[x, 8e-179], y, If[LessEqual[x, 2.65e-151], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.55e-53], y, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.0000000000000003e-56 or 1.55000000000000008e-53 < x

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 89.3%

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

      1. mul-1-neg 89.3%

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

      2. sub-neg 89.3%

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

   5. Simplified 89.3%

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

   if -8.0000000000000003e-56 < x < 8.0000000000000002e-179 or 2.64999999999999989e-151 < x < 1.55000000000000008e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.9%

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

   if 8.0000000000000002e-179 < x < 2.64999999999999989e-151

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-179}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-151}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+44} \lor \neg \left(y \leq 5.5 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.9e+44) (not (<= y 5.5e+29))) (* y (- 1.0 x)) (* x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.9e+44) || !(y <= 5.5e+29)) {
		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 <= (-5.9d+44)) .or. (.not. (y <= 5.5d+29))) 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 <= -5.9e+44) || !(y <= 5.5e+29)) {
		tmp = y * (1.0 - x);
	} else {
		tmp = x * (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.9e+44) or not (y <= 5.5e+29):
		tmp = y * (1.0 - x)
	else:
		tmp = x * (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.9e+44) || !(y <= 5.5e+29))
		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 <= -5.9e+44) || ~((y <= 5.5e+29)))
		tmp = y * (1.0 - x);
	else
		tmp = x * (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.9e+44], N[Not[LessEqual[y, 5.5e+29]], $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 < -5.89999999999999965e44 or 5.5e29 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.5%

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

   if -5.89999999999999965e44 < y < 5.5e29

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. sub-neg 78.4%

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

   5. Simplified 78.4%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+44} \lor \neg \left(y \leq 5.5 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = x * (z - y);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = x * (z - y)
    else
        tmp = y + (x * z)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $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 or 1 < x

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf 97.7%

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

      1. mul-1-neg 97.7%

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

      2. sub-neg 97.7%

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

   5. Simplified 97.7%

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

   if -1 < x < 1

   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 99.2%

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

      1. neg-mul-1 99.2%

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

      2. distribute-rgt-neg-in 99.2%

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

   7. Simplified 99.2%

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

      1. *-commutative 99.2%

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

      2. cancel-sign-sub 99.2%

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

      3. *-commutative 99.2%

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

      4. +-commutative 99.2%

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

   9. Applied egg-rr 99.2%

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

4. Final simplification 98.5%

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

Alternative 5: 54.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+44}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+139}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+44) y (if (<= y 6.5e+139) (* x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+44) {
		tmp = y;
	} else if (y <= 6.5e+139) {
		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 (y <= (-2.7d+44)) then
        tmp = y
    else if (y <= 6.5d+139) 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 (y <= -2.7e+44) {
		tmp = y;
	} else if (y <= 6.5e+139) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+44:
		tmp = y
	elif y <= 6.5e+139:
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+44)
		tmp = y;
	elseif (y <= 6.5e+139)
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.7e+44)
		tmp = y;
	elseif (y <= 6.5e+139)
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+44], y, If[LessEqual[y, 6.5e+139], N[(x * z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e44 or 6.5000000000000003e139 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 66.6%

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

   if -2.7e44 < y < 6.5000000000000003e139

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 62.7%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+44}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+139}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ y + x \cdot \left(z - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ y (* x (- z y))))

C

double code(double x, double y, double z) {
	return y + (x * (z - y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y + (x * (z - y))
end function

Java

public static double code(double x, double y, double z) {
	return y + (x * (z - y));
}

Python

def code(x, y, z):
	return y + (x * (z - y))

Julia

function code(x, y, z)
	return Float64(y + Float64(x * Float64(z - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = y + (x * (z - y));
end

Wolfram

code[x_, y_, z_] := N[(y + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

   1. remove-double-neg 99.6%

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

   2. distribute-rgt-neg-out 99.6%

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

   3. neg-sub0 99.6%

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

   4. neg-sub0 99.6%

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

   5. *-commutative 99.6%

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

   6. distribute-lft-neg-in 99.6%

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

   7. remove-double-neg 99.6%

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

   8. distribute-rgt-out-- 99.6%

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

   9. *-lft-identity 99.6%

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

   10. associate-+l- 99.6%

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

   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 7: 36.0% 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 99.6%

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

3. Taylor expanded in x around 0 38.1%

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

4. Final simplification 38.1%

   \[\leadsto y \]
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 2024080 
(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)))