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

Percentage Accurate: 98.1% → 100.0%

Time: 5.7s

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 98.8%

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

   1. remove-double-neg 98.8%

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

   2. distribute-rgt-neg-out 98.8%

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

   3. neg-sub0 98.8%

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

   4. neg-sub0 98.8%

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

   5. *-commutative 98.8%

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

   6. distribute-lft-neg-in 98.8%

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

   7. remove-double-neg 98.8%

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

   8. distribute-rgt-out-- 98.8%

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

   9. *-lft-identity 98.8%

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

   10. associate-+l- 98.8%

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

   11. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 61.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+226}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+119}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-14}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-91}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 10^{-62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -7.5e+226)
     (* x z)
     (if (<= x -1.15e+119)
       t_0
       (if (<= x -1.15e-14)
         (* x z)
         (if (<= x 7e-91)
           y
           (if (<= x 1e-62) (* x z) (if (<= x 1.0) y t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -7.5e+226) {
		tmp = x * z;
	} else if (x <= -1.15e+119) {
		tmp = t_0;
	} else if (x <= -1.15e-14) {
		tmp = x * z;
	} else if (x <= 7e-91) {
		tmp = y;
	} else if (x <= 1e-62) {
		tmp = x * z;
	} else if (x <= 1.0) {
		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 * -y
    if (x <= (-7.5d+226)) then
        tmp = x * z
    else if (x <= (-1.15d+119)) then
        tmp = t_0
    else if (x <= (-1.15d-14)) then
        tmp = x * z
    else if (x <= 7d-91) then
        tmp = y
    else if (x <= 1d-62) then
        tmp = x * z
    else if (x <= 1.0d0) 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 * -y;
	double tmp;
	if (x <= -7.5e+226) {
		tmp = x * z;
	} else if (x <= -1.15e+119) {
		tmp = t_0;
	} else if (x <= -1.15e-14) {
		tmp = x * z;
	} else if (x <= 7e-91) {
		tmp = y;
	} else if (x <= 1e-62) {
		tmp = x * z;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if x <= -7.5e+226:
		tmp = x * z
	elif x <= -1.15e+119:
		tmp = t_0
	elif x <= -1.15e-14:
		tmp = x * z
	elif x <= 7e-91:
		tmp = y
	elif x <= 1e-62:
		tmp = x * z
	elif x <= 1.0:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (x <= -7.5e+226)
		tmp = Float64(x * z);
	elseif (x <= -1.15e+119)
		tmp = t_0;
	elseif (x <= -1.15e-14)
		tmp = Float64(x * z);
	elseif (x <= 7e-91)
		tmp = y;
	elseif (x <= 1e-62)
		tmp = Float64(x * z);
	elseif (x <= 1.0)
		tmp = y;
	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 <= -7.5e+226)
		tmp = x * z;
	elseif (x <= -1.15e+119)
		tmp = t_0;
	elseif (x <= -1.15e-14)
		tmp = x * z;
	elseif (x <= 7e-91)
		tmp = y;
	elseif (x <= 1e-62)
		tmp = x * z;
	elseif (x <= 1.0)
		tmp = y;
	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, -7.5e+226], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.15e+119], t$95$0, If[LessEqual[x, -1.15e-14], N[(x * z), $MachinePrecision], If[LessEqual[x, 7e-91], y, If[LessEqual[x, 1e-62], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.0], y, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.49999999999999964e226 or -1.15e119 < x < -1.14999999999999999e-14 or 6.9999999999999997e-91 < x < 1e-62

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 72.6%

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

   if -7.49999999999999964e226 < x < -1.15e119 or 1 < x

   1. Initial program 97.8%

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

   3. Taylor expanded in x around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. sub-neg 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in z around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. distribute-rgt-neg-out 58.2%

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

   8. Simplified 58.2%

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

   if -1.14999999999999999e-14 < x < 6.9999999999999997e-91 or 1e-62 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.3%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+226}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-14}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-91}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 10^{-62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-38} \lor \neg \left(x \leq 8.6 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.35e-38) (not (<= x 8.6e-85))) (* x (- z y)) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.35e-38) || !(x <= 8.6e-85)) {
		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 <= (-1.35d-38)) .or. (.not. (x <= 8.6d-85))) 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 <= -1.35e-38) || !(x <= 8.6e-85)) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.35e-38) or not (x <= 8.6e-85):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.35e-38) || !(x <= 8.6e-85))
		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 <= -1.35e-38) || ~((x <= 8.6e-85)))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.35e-38], N[Not[LessEqual[x, 8.6e-85]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -1.35000000000000003e-38 or 8.59999999999999998e-85 < x

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. sub-neg 94.1%

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

   5. Simplified 94.1%

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

   if -1.35000000000000003e-38 < x < 8.59999999999999998e-85

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.6%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-38} \lor \neg \left(x \leq 8.6 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1150000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1150000.0) (not (<= x 1.0))) (* x (- z y)) (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1150000.0) || !(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 <= (-1150000.0d0)) .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 <= -1150000.0) || !(x <= 1.0)) {
		tmp = x * (z - y);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1150000.0) 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 <= -1150000.0) || !(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 <= -1150000.0) || ~((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, -1150000.0], 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 < -1.15e6 or 1 < x

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. sub-neg 98.9%

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

   5. Simplified 98.9%

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

   if -1.15e6 < 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 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-out 99.8%

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

   7. Simplified 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. distribute-rgt-neg-out 99.8%

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

      4. remove-double-neg 99.8%

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

   9. Applied egg-rr 99.8%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1150000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-16} \lor \neg \left(x \leq 7.8 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45e-16) (not (<= x 7.8e-85))) (* x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45e-16) || !(x <= 7.8e-85)) {
		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 <= (-1.45d-16)) .or. (.not. (x <= 7.8d-85))) 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 <= -1.45e-16) || !(x <= 7.8e-85)) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.45e-16) or not (x <= 7.8e-85):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.45e-16) || !(x <= 7.8e-85))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.45e-16) || ~((x <= 7.8e-85)))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.45e-16], N[Not[LessEqual[x, 7.8e-85]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -1.4499999999999999e-16 or 7.79999999999999977e-85 < x

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 53.1%

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

   if -1.4499999999999999e-16 < x < 7.79999999999999977e-85

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-16} \lor \neg \left(x \leq 7.8 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.8% 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. Add Preprocessing

3. Taylor expanded in x around 0 34.6%

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

4. Final simplification 34.6%

   \[\leadsto y \]
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 2024047 
(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)))