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

Percentage Accurate: 97.8% → 100.0%

Time: 5.1s

Alternatives: 8

Speedup: 1.3×

• 21.6% 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 98.4%

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

   1. *-commutative 98.4%

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

   2. distribute-lft-out-- 98.4%

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

   3. *-rgt-identity 98.4%

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

   4. cancel-sign-sub-inv 98.4%

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

   5. +-commutative 98.4%

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

   6. +-commutative 98.4%

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

   7. associate-+l+ 98.4%

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

   8. +-commutative 98.4%

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

   9. *-commutative 98.4%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. 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, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -3.05 \cdot 10^{+255}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.38 \cdot 10^{+150}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+86}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -240:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-130}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-42}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+73} \lor \neg \left(x \leq 9 \cdot 10^{+185}\right) \land x \leq 3.3 \cdot 10^{+252}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -3.05e+255)
     (* x z)
     (if (<= x -1.38e+150)
       t_0
       (if (<= x -9e+86)
         (* x z)
         (if (<= x -1.25e+52)
           t_0
           (if (<= x -240.0)
             (* x z)
             (if (<= x 8e-130)
               y
               (if (<= x 3.8e-64)
                 (* x z)
                 (if (<= x 4.8e-42)
                   y
                   (if (or (<= x 3.9e+73)
                           (and (not (<= x 9e+185)) (<= x 3.3e+252)))
                     (* x z)
                     t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -3.05e+255) {
		tmp = x * z;
	} else if (x <= -1.38e+150) {
		tmp = t_0;
	} else if (x <= -9e+86) {
		tmp = x * z;
	} else if (x <= -1.25e+52) {
		tmp = t_0;
	} else if (x <= -240.0) {
		tmp = x * z;
	} else if (x <= 8e-130) {
		tmp = y;
	} else if (x <= 3.8e-64) {
		tmp = x * z;
	} else if (x <= 4.8e-42) {
		tmp = y;
	} else if ((x <= 3.9e+73) || (!(x <= 9e+185) && (x <= 3.3e+252))) {
		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 = x * -y
    if (x <= (-3.05d+255)) then
        tmp = x * z
    else if (x <= (-1.38d+150)) then
        tmp = t_0
    else if (x <= (-9d+86)) then
        tmp = x * z
    else if (x <= (-1.25d+52)) then
        tmp = t_0
    else if (x <= (-240.0d0)) then
        tmp = x * z
    else if (x <= 8d-130) then
        tmp = y
    else if (x <= 3.8d-64) then
        tmp = x * z
    else if (x <= 4.8d-42) then
        tmp = y
    else if ((x <= 3.9d+73) .or. (.not. (x <= 9d+185)) .and. (x <= 3.3d+252)) 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 = x * -y;
	double tmp;
	if (x <= -3.05e+255) {
		tmp = x * z;
	} else if (x <= -1.38e+150) {
		tmp = t_0;
	} else if (x <= -9e+86) {
		tmp = x * z;
	} else if (x <= -1.25e+52) {
		tmp = t_0;
	} else if (x <= -240.0) {
		tmp = x * z;
	} else if (x <= 8e-130) {
		tmp = y;
	} else if (x <= 3.8e-64) {
		tmp = x * z;
	} else if (x <= 4.8e-42) {
		tmp = y;
	} else if ((x <= 3.9e+73) || (!(x <= 9e+185) && (x <= 3.3e+252))) {
		tmp = x * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if x <= -3.05e+255:
		tmp = x * z
	elif x <= -1.38e+150:
		tmp = t_0
	elif x <= -9e+86:
		tmp = x * z
	elif x <= -1.25e+52:
		tmp = t_0
	elif x <= -240.0:
		tmp = x * z
	elif x <= 8e-130:
		tmp = y
	elif x <= 3.8e-64:
		tmp = x * z
	elif x <= 4.8e-42:
		tmp = y
	elif (x <= 3.9e+73) or (not (x <= 9e+185) and (x <= 3.3e+252)):
		tmp = x * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (x <= -3.05e+255)
		tmp = Float64(x * z);
	elseif (x <= -1.38e+150)
		tmp = t_0;
	elseif (x <= -9e+86)
		tmp = Float64(x * z);
	elseif (x <= -1.25e+52)
		tmp = t_0;
	elseif (x <= -240.0)
		tmp = Float64(x * z);
	elseif (x <= 8e-130)
		tmp = y;
	elseif (x <= 3.8e-64)
		tmp = Float64(x * z);
	elseif (x <= 4.8e-42)
		tmp = y;
	elseif ((x <= 3.9e+73) || (!(x <= 9e+185) && (x <= 3.3e+252)))
		tmp = Float64(x * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -y;
	tmp = 0.0;
	if (x <= -3.05e+255)
		tmp = x * z;
	elseif (x <= -1.38e+150)
		tmp = t_0;
	elseif (x <= -9e+86)
		tmp = x * z;
	elseif (x <= -1.25e+52)
		tmp = t_0;
	elseif (x <= -240.0)
		tmp = x * z;
	elseif (x <= 8e-130)
		tmp = y;
	elseif (x <= 3.8e-64)
		tmp = x * z;
	elseif (x <= 4.8e-42)
		tmp = y;
	elseif ((x <= 3.9e+73) || (~((x <= 9e+185)) && (x <= 3.3e+252)))
		tmp = x * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[x, -3.05e+255], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.38e+150], t$95$0, If[LessEqual[x, -9e+86], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.25e+52], t$95$0, If[LessEqual[x, -240.0], N[(x * z), $MachinePrecision], If[LessEqual[x, 8e-130], y, If[LessEqual[x, 3.8e-64], N[(x * z), $MachinePrecision], If[LessEqual[x, 4.8e-42], y, If[Or[LessEqual[x, 3.9e+73], And[N[Not[LessEqual[x, 9e+185]], $MachinePrecision], LessEqual[x, 3.3e+252]]], N[(x * z), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.04999999999999998e255 or -1.3800000000000001e150 < x < -8.99999999999999986e86 or -1.25e52 < x < -240 or 8.0000000000000007e-130 < x < 3.8000000000000002e-64 or 4.80000000000000005e-42 < x < 3.9000000000000001e73 or 9.0000000000000004e185 < x < 3.3000000000000001e252

   1. Initial program 95.6%

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

   2. Taylor expanded in y around 0 72.0%

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

   if -3.04999999999999998e255 < x < -1.3800000000000001e150 or -8.99999999999999986e86 < x < -1.25e52 or 3.9000000000000001e73 < x < 9.0000000000000004e185 or 3.3000000000000001e252 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. distribute-rgt-neg-out 76.2%

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

   7. Simplified 76.2%

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

   if -240 < x < 8.0000000000000007e-130 or 3.8000000000000002e-64 < x < 4.80000000000000005e-42

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.1%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+255}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.38 \cdot 10^{+150}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+86}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -240:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-130}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-42}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+73} \lor \neg \left(x \leq 9 \cdot 10^{+185}\right) \land x \leq 3.3 \cdot 10^{+252}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 82.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -0.03:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-130}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-42}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= x -0.03)
     t_0
     (if (<= x 5.3e-130)
       y
       (if (<= x 1.15e-62) (* x z) (if (<= x 7e-42) y t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -0.03) {
		tmp = t_0;
	} else if (x <= 5.3e-130) {
		tmp = y;
	} else if (x <= 1.15e-62) {
		tmp = x * z;
	} else if (x <= 7e-42) {
		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 <= (-0.03d0)) then
        tmp = t_0
    else if (x <= 5.3d-130) then
        tmp = y
    else if (x <= 1.15d-62) then
        tmp = x * z
    else if (x <= 7d-42) 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 <= -0.03) {
		tmp = t_0;
	} else if (x <= 5.3e-130) {
		tmp = y;
	} else if (x <= 1.15e-62) {
		tmp = x * z;
	} else if (x <= 7e-42) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z - y)
	tmp = 0
	if x <= -0.03:
		tmp = t_0
	elif x <= 5.3e-130:
		tmp = y
	elif x <= 1.15e-62:
		tmp = x * z
	elif x <= 7e-42:
		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 <= -0.03)
		tmp = t_0;
	elseif (x <= 5.3e-130)
		tmp = y;
	elseif (x <= 1.15e-62)
		tmp = Float64(x * z);
	elseif (x <= 7e-42)
		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 <= -0.03)
		tmp = t_0;
	elseif (x <= 5.3e-130)
		tmp = y;
	elseif (x <= 1.15e-62)
		tmp = x * z;
	elseif (x <= 7e-42)
		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, -0.03], t$95$0, If[LessEqual[x, 5.3e-130], y, If[LessEqual[x, 1.15e-62], N[(x * z), $MachinePrecision], If[LessEqual[x, 7e-42], y, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.029999999999999999 or 7.0000000000000004e-42 < x

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf 96.2%

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

      1. mul-1-neg 96.2%

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

      2. sub-neg 96.2%

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

   4. Simplified 96.2%

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

   if -0.029999999999999999 < x < 5.3000000000000004e-130 or 1.15e-62 < x < 7.0000000000000004e-42

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.7%

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

   if 5.3000000000000004e-130 < x < 1.15e-62

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 81.4%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.03:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-130}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-42}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 4: 59.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -240 \lor \neg \left(x \leq 8 \cdot 10^{-130}\right) \land \left(x \leq 5.6 \cdot 10^{-64} \lor \neg \left(x \leq 7.5 \cdot 10^{-42}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -240.0)
         (and (not (<= x 8e-130)) (or (<= x 5.6e-64) (not (<= x 7.5e-42)))))
   (* x z)
   y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -240.0) || (!(x <= 8e-130) && ((x <= 5.6e-64) || !(x <= 7.5e-42)))) {
		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 <= (-240.0d0)) .or. (.not. (x <= 8d-130)) .and. (x <= 5.6d-64) .or. (.not. (x <= 7.5d-42))) 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 <= -240.0) || (!(x <= 8e-130) && ((x <= 5.6e-64) || !(x <= 7.5e-42)))) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -240.0) or (not (x <= 8e-130) and ((x <= 5.6e-64) or not (x <= 7.5e-42))):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -240.0) || (!(x <= 8e-130) && ((x <= 5.6e-64) || !(x <= 7.5e-42))))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -240.0) || (~((x <= 8e-130)) && ((x <= 5.6e-64) || ~((x <= 7.5e-42)))))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -240.0], And[N[Not[LessEqual[x, 8e-130]], $MachinePrecision], Or[LessEqual[x, 5.6e-64], N[Not[LessEqual[x, 7.5e-42]], $MachinePrecision]]]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -240 or 8.0000000000000007e-130 < x < 5.60000000000000008e-64 or 7.49999999999999972e-42 < x

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 56.0%

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

   if -240 < x < 8.0000000000000007e-130 or 5.60000000000000008e-64 < x < 7.49999999999999972e-42

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.1%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -240 \lor \neg \left(x \leq 8 \cdot 10^{-130}\right) \land \left(x \leq 5.6 \cdot 10^{-64} \lor \neg \left(x \leq 7.5 \cdot 10^{-42}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+77} \lor \neg \left(y \leq 72000000000000\right):\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.9e+77) (not (<= y 72000000000000.0)))
   (* y (- 1.0 x))
   (* x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e+77) || !(y <= 72000000000000.0)) {
		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 <= (-1.9d+77)) .or. (.not. (y <= 72000000000000.0d0))) 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 <= -1.9e+77) || !(y <= 72000000000000.0)) {
		tmp = y * (1.0 - x);
	} else {
		tmp = x * (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.9e+77) or not (y <= 72000000000000.0):
		tmp = y * (1.0 - x)
	else:
		tmp = x * (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.9e+77) || !(y <= 72000000000000.0))
		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 <= -1.9e+77) || ~((y <= 72000000000000.0)))
		tmp = y * (1.0 - x);
	else
		tmp = x * (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.9e+77], N[Not[LessEqual[y, 72000000000000.0]], $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 < -1.9000000000000001e77 or 7.2e13 < y

   1. Initial program 96.7%

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

   2. Taylor expanded in y around inf 91.9%

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

   if -1.9000000000000001e77 < y < 7.2e13

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. sub-neg 80.5%

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

   4. Simplified 80.5%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+77} \lor \neg \left(y \leq 72000000000000\right):\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 6: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 2.4 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 2.4e-10))) (* x (- z y)) (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 2.4e-10)) {
		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 <= 2.4d-10))) 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 <= 2.4e-10)) {
		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 <= 2.4e-10):
		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 <= 2.4e-10))
		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 <= 2.4e-10)))
		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, 2.4e-10]], $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 2.4e-10 < x

   1. Initial program 97.0%

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

   2. Taylor expanded in x around inf 98.2%

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

      1. mul-1-neg 98.2%

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

      2. sub-neg 98.2%

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

   4. Simplified 98.2%

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

   if -1 < x < 2.4e-10

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-out-- 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. +-commutative 100.0%

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

      9. *-commutative 100.0%

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

      10. distribute-rgt-out 100.0%

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

      11. fma-def 100.0%

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

      12. +-commutative 100.0%

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

      13. 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. Step-by-step derivation

      1. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in z around inf 98.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 2.4 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]

Alternative 7: 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 98.4%

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

   1. *-commutative 98.4%

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

   2. distribute-lft-out-- 98.4%

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

   3. *-rgt-identity 98.4%

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

   4. cancel-sign-sub-inv 98.4%

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

   5. +-commutative 98.4%

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

   6. +-commutative 98.4%

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

   7. associate-+l+ 98.4%

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

   8. +-commutative 98.4%

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

   9. *-commutative 98.4%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. 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. Step-by-step derivation

   1. fma-udef 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 8: 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 98.4%

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

2. Taylor expanded in x around 0 34.2%

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

3. Final simplification 34.2%

   \[\leadsto y \]

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 2023313 
(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)))