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

Percentage Accurate: 98.1% → 100.0%

Time: 4.5s

Alternatives: 6

Speedup: 1.3×

• 20.7% 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: 98.1% 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. remove-double-neg 98.0%

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

   2. distribute-rgt-neg-out 98.0%

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

   3. neg-sub0 98.0%

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

   4. neg-sub0 98.0%

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

   5. *-commutative 98.0%

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

   6. distribute-lft-neg-in 98.0%

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

   7. remove-double-neg 98.0%

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

   8. distribute-rgt-out-- 98.0%

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

   9. *-lft-identity 98.0%

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

   10. associate-+l- 98.0%

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

   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. Final simplification 100.0%

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

Alternative 2: 83.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-38} \lor \neg \left(x \leq -5.3 \cdot 10^{-140}\right) \land \left(x \leq -3.15 \cdot 10^{-155} \lor \neg \left(x \leq 3.1 \cdot 10^{-35}\right)\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.6e-38)
         (and (not (<= x -5.3e-140))
              (or (<= x -3.15e-155) (not (<= x 3.1e-35)))))
   (* x (- z y))
   y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.6e-38) || (!(x <= -5.3e-140) && ((x <= -3.15e-155) || !(x <= 3.1e-35)))) {
		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 <= (-4.6d-38)) .or. (.not. (x <= (-5.3d-140))) .and. (x <= (-3.15d-155)) .or. (.not. (x <= 3.1d-35))) 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 <= -4.6e-38) || (!(x <= -5.3e-140) && ((x <= -3.15e-155) || !(x <= 3.1e-35)))) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.6e-38) or (not (x <= -5.3e-140) and ((x <= -3.15e-155) or not (x <= 3.1e-35))):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.6e-38) || (!(x <= -5.3e-140) && ((x <= -3.15e-155) || !(x <= 3.1e-35))))
		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 <= -4.6e-38) || (~((x <= -5.3e-140)) && ((x <= -3.15e-155) || ~((x <= 3.1e-35)))))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.6e-38], And[N[Not[LessEqual[x, -5.3e-140]], $MachinePrecision], Or[LessEqual[x, -3.15e-155], N[Not[LessEqual[x, 3.1e-35]], $MachinePrecision]]]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -4.60000000000000003e-38 or -5.29999999999999984e-140 < x < -3.14999999999999985e-155 or 3.10000000000000012e-35 < x

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf 95.8%

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

      1. mul-1-neg 95.8%

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

      2. sub-neg 95.8%

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

   4. Simplified 95.8%

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

   if -4.60000000000000003e-38 < x < -5.29999999999999984e-140 or -3.14999999999999985e-155 < x < 3.10000000000000012e-35

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-38} \lor \neg \left(x \leq -5.3 \cdot 10^{-140}\right) \land \left(x \leq -3.15 \cdot 10^{-155} \lor \neg \left(x \leq 3.1 \cdot 10^{-35}\right)\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3: 61.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-35} \lor \neg \left(x \leq -5.3 \cdot 10^{-140}\right) \land \left(x \leq -3.15 \cdot 10^{-155} \lor \neg \left(x \leq 9.6 \cdot 10^{-37}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.05e-35)
         (and (not (<= x -5.3e-140))
              (or (<= x -3.15e-155) (not (<= x 9.6e-37)))))
   (* x z)
   y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e-35) || (!(x <= -5.3e-140) && ((x <= -3.15e-155) || !(x <= 9.6e-37)))) {
		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 <= (-1.05d-35)) .or. (.not. (x <= (-5.3d-140))) .and. (x <= (-3.15d-155)) .or. (.not. (x <= 9.6d-37))) 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 <= -1.05e-35) || (!(x <= -5.3e-140) && ((x <= -3.15e-155) || !(x <= 9.6e-37)))) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.05e-35) or (not (x <= -5.3e-140) and ((x <= -3.15e-155) or not (x <= 9.6e-37))):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.05e-35) || (!(x <= -5.3e-140) && ((x <= -3.15e-155) || !(x <= 9.6e-37))))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.05e-35) || (~((x <= -5.3e-140)) && ((x <= -3.15e-155) || ~((x <= 9.6e-37)))))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.05e-35], And[N[Not[LessEqual[x, -5.3e-140]], $MachinePrecision], Or[LessEqual[x, -3.15e-155], N[Not[LessEqual[x, 9.6e-37]], $MachinePrecision]]]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e-35 or -5.29999999999999984e-140 < x < -3.14999999999999985e-155 or 9.59999999999999963e-37 < x

   1. Initial program 96.6%

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

   2. Taylor expanded in y around 0 59.1%

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

   if -1.05e-35 < x < -5.29999999999999984e-140 or -3.14999999999999985e-155 < x < 9.59999999999999963e-37

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.5%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-35} \lor \neg \left(x \leq -5.3 \cdot 10^{-140}\right) \land \left(x \leq -3.15 \cdot 10^{-155} \lor \neg \left(x \leq 9.6 \cdot 10^{-37}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4: 54.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-41}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-237}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 6400000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.5e-41)
   (* x z)
   (if (<= z -8.8e-237) (* x (- y)) (if (<= z 6400000.0) y (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e-41) {
		tmp = x * z;
	} else if (z <= -8.8e-237) {
		tmp = x * -y;
	} else if (z <= 6400000.0) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-8.5d-41)) then
        tmp = x * z
    else if (z <= (-8.8d-237)) then
        tmp = x * -y
    else if (z <= 6400000.0d0) then
        tmp = y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e-41) {
		tmp = x * z;
	} else if (z <= -8.8e-237) {
		tmp = x * -y;
	} else if (z <= 6400000.0) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.5e-41:
		tmp = x * z
	elif z <= -8.8e-237:
		tmp = x * -y
	elif z <= 6400000.0:
		tmp = y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.5e-41)
		tmp = Float64(x * z);
	elseif (z <= -8.8e-237)
		tmp = Float64(x * Float64(-y));
	elseif (z <= 6400000.0)
		tmp = y;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.5e-41)
		tmp = x * z;
	elseif (z <= -8.8e-237)
		tmp = x * -y;
	elseif (z <= 6400000.0)
		tmp = y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.5e-41], N[(x * z), $MachinePrecision], If[LessEqual[z, -8.8e-237], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, 6400000.0], y, N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999996e-41 or 6.4e6 < z

   1. Initial program 96.5%

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

   2. Taylor expanded in y around 0 70.0%

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

   if -8.4999999999999996e-41 < z < -8.79999999999999992e-237

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.7%

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

      1. mul-1-neg 79.7%

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

      2. sub-neg 79.7%

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

   4. Simplified 79.7%

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

   5. Taylor expanded in z around 0 62.5%

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

      1. associate-*r* 62.5%

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

      2. mul-1-neg 62.5%

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

   7. Simplified 62.5%

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

   if -8.79999999999999992e-237 < z < 6.4e6

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 58.3%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-41}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-237}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 6400000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 5: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+25} \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.6e+25) (not (<= x 1.0))) (* x (- z y)) (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.6e+25) || !(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 <= (-1.6d+25)) .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 <= -1.6e+25) || !(x <= 1.0)) {
		tmp = x * (z - y);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.6e+25) 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 <= -1.6e+25) || !(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 <= -1.6e+25) || ~((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, -1.6e+25], 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 < -1.6e25 or 1 < x

   1. Initial program 96.0%

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

   2. Taylor expanded in x around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. sub-neg 99.5%

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

   4. Simplified 99.5%

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

   if -1.6e25 < 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. Taylor expanded in y around 0 98.0%

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

      1. associate-*r* 98.0%

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

      2. neg-mul-1 98.0%

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

   6. Simplified 98.0%

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

      1. cancel-sign-sub 98.0%

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

      2. +-commutative 98.0%

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

   8. Applied egg-rr 98.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+25} \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]

Alternative 6: 37.2% 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. Taylor expanded in x around 0 34.5%

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

3. Final simplification 34.5%

   \[\leadsto y \]

Developer target: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023332 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (- y (* x (- y z)))

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