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

Percentage Accurate: 97.8% → 100.0%

Time: 6.5s

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: 97.8% 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 98.8%

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

   1. sub-neg 98.8%

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

   2. +-commutative 98.8%

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

   3. distribute-rgt1-in 98.8%

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

   4. associate-+l+ 98.8%

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

   5. +-commutative 98.8%

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

   6. *-commutative 98.8%

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

   7. neg-mul-1 98.8%

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

   8. associate-*r* 98.8%

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

   9. *-commutative 98.8%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

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

   15. 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. Final simplification 100.0%

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

Alternative 2: 59.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -7.4 \cdot 10^{+113}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-131}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 10^{+37}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+233}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -7.4e+113)
     (* x z)
     (if (<= x -3.5e+68)
       t_0
       (if (<= x -7.2e-131)
         (* x z)
         (if (<= x 1.6e-25)
           y
           (if (<= x 1e+37) (* x z) (if (<= x 5e+233) t_0 (* x z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -7.4e+113) {
		tmp = x * z;
	} else if (x <= -3.5e+68) {
		tmp = t_0;
	} else if (x <= -7.2e-131) {
		tmp = x * z;
	} else if (x <= 1.6e-25) {
		tmp = y;
	} else if (x <= 1e+37) {
		tmp = x * z;
	} else if (x <= 5e+233) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * -y
    if (x <= (-7.4d+113)) then
        tmp = x * z
    else if (x <= (-3.5d+68)) then
        tmp = t_0
    else if (x <= (-7.2d-131)) then
        tmp = x * z
    else if (x <= 1.6d-25) then
        tmp = y
    else if (x <= 1d+37) then
        tmp = x * z
    else if (x <= 5d+233) then
        tmp = t_0
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -7.4e+113) {
		tmp = x * z;
	} else if (x <= -3.5e+68) {
		tmp = t_0;
	} else if (x <= -7.2e-131) {
		tmp = x * z;
	} else if (x <= 1.6e-25) {
		tmp = y;
	} else if (x <= 1e+37) {
		tmp = x * z;
	} else if (x <= 5e+233) {
		tmp = t_0;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if x <= -7.4e+113:
		tmp = x * z
	elif x <= -3.5e+68:
		tmp = t_0
	elif x <= -7.2e-131:
		tmp = x * z
	elif x <= 1.6e-25:
		tmp = y
	elif x <= 1e+37:
		tmp = x * z
	elif x <= 5e+233:
		tmp = t_0
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (x <= -7.4e+113)
		tmp = Float64(x * z);
	elseif (x <= -3.5e+68)
		tmp = t_0;
	elseif (x <= -7.2e-131)
		tmp = Float64(x * z);
	elseif (x <= 1.6e-25)
		tmp = y;
	elseif (x <= 1e+37)
		tmp = Float64(x * z);
	elseif (x <= 5e+233)
		tmp = t_0;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -y;
	tmp = 0.0;
	if (x <= -7.4e+113)
		tmp = x * z;
	elseif (x <= -3.5e+68)
		tmp = t_0;
	elseif (x <= -7.2e-131)
		tmp = x * z;
	elseif (x <= 1.6e-25)
		tmp = y;
	elseif (x <= 1e+37)
		tmp = x * z;
	elseif (x <= 5e+233)
		tmp = t_0;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[x, -7.4e+113], N[(x * z), $MachinePrecision], If[LessEqual[x, -3.5e+68], t$95$0, If[LessEqual[x, -7.2e-131], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.6e-25], y, If[LessEqual[x, 1e+37], N[(x * z), $MachinePrecision], If[LessEqual[x, 5e+233], t$95$0, N[(x * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.3999999999999996e113 or -3.49999999999999977e68 < x < -7.1999999999999999e-131 or 1.6000000000000001e-25 < x < 9.99999999999999954e36 or 5.00000000000000009e233 < x

   1. Initial program 98.2%

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

   2. Taylor expanded in y around 0 70.8%

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

   if -7.3999999999999996e113 < x < -3.49999999999999977e68 or 9.99999999999999954e36 < x < 5.00000000000000009e233

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. +-commutative 98.3%

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

      3. distribute-rgt1-in 98.3%

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

      4. associate-+l+ 98.3%

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

      5. +-commutative 98.3%

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

      6. *-commutative 98.3%

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

      7. neg-mul-1 98.3%

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

      8. associate-*r* 98.3%

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

      9. *-commutative 98.3%

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

      10. distribute-rgt-out 100.0%

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

      11. fma-def 100.0%

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

      12. +-commutative 100.0%

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

      13. *-commutative 100.0%

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

      14. neg-mul-1 100.0%

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

      15. 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. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in z around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. distribute-rgt-neg-in 70.2%

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

   7. Simplified 70.2%

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

   if -7.1999999999999999e-131 < x < 1.6000000000000001e-25

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.5%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+113}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-131}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 10^{+37}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+233}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3: 82.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-131} \lor \neg \left(x \leq 1.65 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.2e-131) (not (<= x 1.65e-25))) (* x (- z y)) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.2e-131) || !(x <= 1.65e-25)) {
		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 <= (-7.2d-131)) .or. (.not. (x <= 1.65d-25))) 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 <= -7.2e-131) || !(x <= 1.65e-25)) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.2e-131) or not (x <= 1.65e-25):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.2e-131) || !(x <= 1.65e-25))
		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 <= -7.2e-131) || ~((x <= 1.65e-25)))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.2e-131], N[Not[LessEqual[x, 1.65e-25]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -7.1999999999999999e-131 or 1.6499999999999999e-25 < x

   1. Initial program 98.2%

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

      1. sub-neg 98.2%

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

      2. +-commutative 98.2%

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

      3. distribute-rgt1-in 98.2%

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

      4. associate-+l+ 98.2%

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

      5. +-commutative 98.2%

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

      6. *-commutative 98.2%

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

      7. neg-mul-1 98.2%

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

      8. associate-*r* 98.2%

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

      9. *-commutative 98.2%

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

      10. distribute-rgt-out 100.0%

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

      11. fma-def 100.0%

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

      12. +-commutative 100.0%

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

      13. *-commutative 100.0%

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

      14. neg-mul-1 100.0%

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

      15. 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. Taylor expanded in x around inf 92.3%

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

   if -7.1999999999999999e-131 < x < 1.6499999999999999e-25

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.5%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-131} \lor \neg \left(x \leq 1.65 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4: 98.8% accurate, 1.0× 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 97.8%

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

      1. sub-neg 97.8%

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

      2. +-commutative 97.8%

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

      3. distribute-rgt1-in 97.8%

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

      4. associate-+l+ 97.8%

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

      5. +-commutative 97.8%

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

      6. *-commutative 97.8%

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

      7. neg-mul-1 97.8%

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

      8. associate-*r* 97.8%

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

      9. *-commutative 97.8%

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

      10. distribute-rgt-out 100.0%

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

      11. fma-def 100.0%

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

      12. +-commutative 100.0%

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

      13. *-commutative 100.0%

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

      14. neg-mul-1 100.0%

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

      15. 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. Taylor expanded in x around inf 98.3%

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

   if -1 < x < 1

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-rgt1-in 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. *-commutative 100.0%

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

      7. neg-mul-1 100.0%

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

      8. associate-*r* 100.0%

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

      9. *-commutative 100.0%

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

      10. distribute-rgt-out 100.0%

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

      11. fma-def 100.0%

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

      12. +-commutative 100.0%

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

      13. *-commutative 100.0%

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

      14. neg-mul-1 100.0%

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

      15. 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. Taylor expanded in x around 0 100.0%

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

   5. Taylor expanded in z around inf 98.9%

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

4. Final simplification 98.6%

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

Alternative 5: 59.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-131}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.2e-131) (* x z) (if (<= x 1.55e-25) y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-131) {
		tmp = x * z;
	} else if (x <= 1.55e-25) {
		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 (x <= (-7.2d-131)) then
        tmp = x * z
    else if (x <= 1.55d-25) 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 (x <= -7.2e-131) {
		tmp = x * z;
	} else if (x <= 1.55e-25) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.2e-131:
		tmp = x * z
	elif x <= 1.55e-25:
		tmp = y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.2e-131)
		tmp = Float64(x * z);
	elseif (x <= 1.55e-25)
		tmp = y;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.2e-131)
		tmp = x * z;
	elseif (x <= 1.55e-25)
		tmp = y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.2e-131], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.55e-25], y, N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.1999999999999999e-131 or 1.54999999999999997e-25 < x

   1. Initial program 98.2%

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

   2. Taylor expanded in y around 0 56.9%

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

   if -7.1999999999999999e-131 < x < 1.54999999999999997e-25

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.5%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-131}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

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 98.8%

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

   1. sub-neg 98.8%

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

   2. +-commutative 98.8%

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

   3. distribute-rgt1-in 98.8%

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

   4. associate-+l+ 98.8%

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

   5. +-commutative 98.8%

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

   6. *-commutative 98.8%

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

   7. neg-mul-1 98.8%

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

   8. associate-*r* 98.8%

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

   9. *-commutative 98.8%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

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

   15. 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. Taylor expanded in x around 0 100.0%

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

5. Final simplification 100.0%

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

Alternative 7: 37.0% 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 98.8%

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

2. Taylor expanded in x around 0 29.6%

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

3. Final simplification 29.6%

   \[\leadsto y \]

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 2023252 
(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)))