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

Percentage Accurate: 98.0% → 100.0%

Time: 7.3s

Alternatives: 8

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: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - x\right) \cdot y + x \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* (- 1.0 x) y) (* x z)))

C

double code(double x, double y, double z) {
	return ((1.0 - x) * y) + (x * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((1.0d0 - x) * y) + (x * z)
end function

Java

public static double code(double x, double y, double z) {
	return ((1.0 - x) * y) + (x * z);
}

Python

def code(x, y, z):
	return ((1.0 - x) * y) + (x * z)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(1.0 - x) * y) + Float64(x * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((1.0 - x) * y) + (x * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. +-commutative 98.4%

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

   2. *-commutative 98.4%

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

   3. distribute-lft-out-- 98.4%

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

   4. *-rgt-identity 98.4%

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

   5. cancel-sign-sub-inv 98.4%

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

   6. +-commutative 98.4%

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

   7. associate-+r+ 98.4%

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

   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 99.9%

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

   11. fma-define 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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 58.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+218}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+180}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+136}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+44}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-37} \lor \neg \left(x \leq -9.5 \cdot 10^{-71} \lor \neg \left(x \leq -8.5 \cdot 10^{-96}\right) \land \left(x \leq -7.5 \cdot 10^{-120} \lor \neg \left(x \leq -1.55 \cdot 10^{-178}\right) \land x \leq 4.1 \cdot 10^{-7}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -1.35e+218)
     (* x z)
     (if (<= x -1e+180)
       t_0
       (if (<= x -4.2e+136)
         (* x z)
         (if (<= x -3.2e+44)
           t_0
           (if (or (<= x -3.2e-37)
                   (not
                    (or (<= x -9.5e-71)
                        (and (not (<= x -8.5e-96))
                             (or (<= x -7.5e-120)
                                 (and (not (<= x -1.55e-178))
                                      (<= x 4.1e-7)))))))
             (* x z)
             y)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -1.35e+218) {
		tmp = x * z;
	} else if (x <= -1e+180) {
		tmp = t_0;
	} else if (x <= -4.2e+136) {
		tmp = x * z;
	} else if (x <= -3.2e+44) {
		tmp = t_0;
	} else if ((x <= -3.2e-37) || !((x <= -9.5e-71) || (!(x <= -8.5e-96) && ((x <= -7.5e-120) || (!(x <= -1.55e-178) && (x <= 4.1e-7)))))) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x * -y
    if (x <= (-1.35d+218)) then
        tmp = x * z
    else if (x <= (-1d+180)) then
        tmp = t_0
    else if (x <= (-4.2d+136)) then
        tmp = x * z
    else if (x <= (-3.2d+44)) then
        tmp = t_0
    else if ((x <= (-3.2d-37)) .or. (.not. (x <= (-9.5d-71)) .or. (.not. (x <= (-8.5d-96))) .and. (x <= (-7.5d-120)) .or. (.not. (x <= (-1.55d-178))) .and. (x <= 4.1d-7))) 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 t_0 = x * -y;
	double tmp;
	if (x <= -1.35e+218) {
		tmp = x * z;
	} else if (x <= -1e+180) {
		tmp = t_0;
	} else if (x <= -4.2e+136) {
		tmp = x * z;
	} else if (x <= -3.2e+44) {
		tmp = t_0;
	} else if ((x <= -3.2e-37) || !((x <= -9.5e-71) || (!(x <= -8.5e-96) && ((x <= -7.5e-120) || (!(x <= -1.55e-178) && (x <= 4.1e-7)))))) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if x <= -1.35e+218:
		tmp = x * z
	elif x <= -1e+180:
		tmp = t_0
	elif x <= -4.2e+136:
		tmp = x * z
	elif x <= -3.2e+44:
		tmp = t_0
	elif (x <= -3.2e-37) or not ((x <= -9.5e-71) or (not (x <= -8.5e-96) and ((x <= -7.5e-120) or (not (x <= -1.55e-178) and (x <= 4.1e-7))))):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (x <= -1.35e+218)
		tmp = Float64(x * z);
	elseif (x <= -1e+180)
		tmp = t_0;
	elseif (x <= -4.2e+136)
		tmp = Float64(x * z);
	elseif (x <= -3.2e+44)
		tmp = t_0;
	elseif ((x <= -3.2e-37) || !((x <= -9.5e-71) || (!(x <= -8.5e-96) && ((x <= -7.5e-120) || (!(x <= -1.55e-178) && (x <= 4.1e-7))))))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -y;
	tmp = 0.0;
	if (x <= -1.35e+218)
		tmp = x * z;
	elseif (x <= -1e+180)
		tmp = t_0;
	elseif (x <= -4.2e+136)
		tmp = x * z;
	elseif (x <= -3.2e+44)
		tmp = t_0;
	elseif ((x <= -3.2e-37) || ~(((x <= -9.5e-71) || (~((x <= -8.5e-96)) && ((x <= -7.5e-120) || (~((x <= -1.55e-178)) && (x <= 4.1e-7)))))))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[x, -1.35e+218], N[(x * z), $MachinePrecision], If[LessEqual[x, -1e+180], t$95$0, If[LessEqual[x, -4.2e+136], N[(x * z), $MachinePrecision], If[LessEqual[x, -3.2e+44], t$95$0, If[Or[LessEqual[x, -3.2e-37], N[Not[Or[LessEqual[x, -9.5e-71], And[N[Not[LessEqual[x, -8.5e-96]], $MachinePrecision], Or[LessEqual[x, -7.5e-120], And[N[Not[LessEqual[x, -1.55e-178]], $MachinePrecision], LessEqual[x, 4.1e-7]]]]]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35000000000000006e218 or -1e180 < x < -4.1999999999999998e136 or -3.20000000000000004e44 < x < -3.1999999999999999e-37 or -9.4999999999999994e-71 < x < -8.49999999999999983e-96 or -7.5000000000000004e-120 < x < -1.55e-178 or 4.0999999999999999e-7 < x

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0 64.5%

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

   if -1.35000000000000006e218 < x < -1e180 or -4.1999999999999998e136 < x < -3.20000000000000004e44

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf 100.0%

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

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 68.4%

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

      1. associate-*r* 68.4%

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

      2. neg-mul-1 68.4%

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

      3. *-commutative 68.4%

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

   8. Simplified 68.4%

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

   if -3.1999999999999999e-37 < x < -9.4999999999999994e-71 or -8.49999999999999983e-96 < x < -7.5000000000000004e-120 or -1.55e-178 < x < 4.0999999999999999e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+218}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+180}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+136}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-37} \lor \neg \left(x \leq -9.5 \cdot 10^{-71} \lor \neg \left(x \leq -8.5 \cdot 10^{-96}\right) \land \left(x \leq -7.5 \cdot 10^{-120} \lor \neg \left(x \leq -1.55 \cdot 10^{-178}\right) \land x \leq 4.1 \cdot 10^{-7}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{-38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-71}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-97}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-120}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-178} \lor \neg \left(x \leq 6.6 \cdot 10^{-7}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= x -6.6e-38)
     t_0
     (if (<= x -4.6e-71)
       y
       (if (<= x -7.2e-97)
         (* x z)
         (if (<= x -7.5e-120)
           y
           (if (or (<= x -1.55e-178) (not (<= x 6.6e-7)))
             t_0
             (* y (- 1.0 x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -6.6e-38) {
		tmp = t_0;
	} else if (x <= -4.6e-71) {
		tmp = y;
	} else if (x <= -7.2e-97) {
		tmp = x * z;
	} else if (x <= -7.5e-120) {
		tmp = y;
	} else if ((x <= -1.55e-178) || !(x <= 6.6e-7)) {
		tmp = t_0;
	} else {
		tmp = y * (1.0 - x);
	}
	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 <= (-6.6d-38)) then
        tmp = t_0
    else if (x <= (-4.6d-71)) then
        tmp = y
    else if (x <= (-7.2d-97)) then
        tmp = x * z
    else if (x <= (-7.5d-120)) then
        tmp = y
    else if ((x <= (-1.55d-178)) .or. (.not. (x <= 6.6d-7))) then
        tmp = t_0
    else
        tmp = y * (1.0d0 - x)
    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 <= -6.6e-38) {
		tmp = t_0;
	} else if (x <= -4.6e-71) {
		tmp = y;
	} else if (x <= -7.2e-97) {
		tmp = x * z;
	} else if (x <= -7.5e-120) {
		tmp = y;
	} else if ((x <= -1.55e-178) || !(x <= 6.6e-7)) {
		tmp = t_0;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z - y)
	tmp = 0
	if x <= -6.6e-38:
		tmp = t_0
	elif x <= -4.6e-71:
		tmp = y
	elif x <= -7.2e-97:
		tmp = x * z
	elif x <= -7.5e-120:
		tmp = y
	elif (x <= -1.55e-178) or not (x <= 6.6e-7):
		tmp = t_0
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z - y))
	tmp = 0.0
	if (x <= -6.6e-38)
		tmp = t_0;
	elseif (x <= -4.6e-71)
		tmp = y;
	elseif (x <= -7.2e-97)
		tmp = Float64(x * z);
	elseif (x <= -7.5e-120)
		tmp = y;
	elseif ((x <= -1.55e-178) || !(x <= 6.6e-7))
		tmp = t_0;
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z - y);
	tmp = 0.0;
	if (x <= -6.6e-38)
		tmp = t_0;
	elseif (x <= -4.6e-71)
		tmp = y;
	elseif (x <= -7.2e-97)
		tmp = x * z;
	elseif (x <= -7.5e-120)
		tmp = y;
	elseif ((x <= -1.55e-178) || ~((x <= 6.6e-7)))
		tmp = t_0;
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.6e-38], t$95$0, If[LessEqual[x, -4.6e-71], y, If[LessEqual[x, -7.2e-97], N[(x * z), $MachinePrecision], If[LessEqual[x, -7.5e-120], y, If[Or[LessEqual[x, -1.55e-178], N[Not[LessEqual[x, 6.6e-7]], $MachinePrecision]], t$95$0, N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.6000000000000005e-38 or -7.5000000000000004e-120 < x < -1.55e-178 or 6.6000000000000003e-7 < x

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf 93.7%

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

      1. mul-1-neg 93.7%

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

      2. sub-neg 93.7%

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

   5. Simplified 93.7%

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

   if -6.6000000000000005e-38 < x < -4.5999999999999997e-71 or -7.19999999999999995e-97 < x < -7.5000000000000004e-120

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   if -4.5999999999999997e-71 < x < -7.19999999999999995e-97

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   if -1.55e-178 < x < 6.6000000000000003e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.9%

      \[\leadsto \color{blue}{y \cdot \left(1 - x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-71}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-97}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-120}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-178} \lor \neg \left(x \leq 6.6 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-38} \lor \neg \left(x \leq -3.5 \cdot 10^{-71}\right) \land \left(x \leq -1.55 \cdot 10^{-178} \lor \neg \left(x \leq 4.1 \cdot 10^{-7}\right)\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.4e-38)
         (and (not (<= x -3.5e-71))
              (or (<= x -1.55e-178) (not (<= x 4.1e-7)))))
   (* x (- z y))
   y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.4e-38) || (!(x <= -3.5e-71) && ((x <= -1.55e-178) || !(x <= 4.1e-7)))) {
		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 <= (-3.4d-38)) .or. (.not. (x <= (-3.5d-71))) .and. (x <= (-1.55d-178)) .or. (.not. (x <= 4.1d-7))) 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 <= -3.4e-38) || (!(x <= -3.5e-71) && ((x <= -1.55e-178) || !(x <= 4.1e-7)))) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.4e-38) or (not (x <= -3.5e-71) and ((x <= -1.55e-178) or not (x <= 4.1e-7))):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.4e-38) || (!(x <= -3.5e-71) && ((x <= -1.55e-178) || !(x <= 4.1e-7))))
		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 <= -3.4e-38) || (~((x <= -3.5e-71)) && ((x <= -1.55e-178) || ~((x <= 4.1e-7)))))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.4e-38], And[N[Not[LessEqual[x, -3.5e-71]], $MachinePrecision], Or[LessEqual[x, -1.55e-178], N[Not[LessEqual[x, 4.1e-7]], $MachinePrecision]]]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -3.4000000000000002e-38 or -3.4999999999999999e-71 < x < -1.55e-178 or 4.0999999999999999e-7 < x

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf 91.3%

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

      1. mul-1-neg 91.3%

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

      2. sub-neg 91.3%

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

   5. Simplified 91.3%

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

   if -3.4000000000000002e-38 < x < -3.4999999999999999e-71 or -1.55e-178 < x < 4.0999999999999999e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-38} \lor \neg \left(x \leq -3.5 \cdot 10^{-71}\right) \land \left(x \leq -1.55 \cdot 10^{-178} \lor \neg \left(x \leq 4.1 \cdot 10^{-7}\right)\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-40} \lor \neg \left(x \leq -5.9 \cdot 10^{-71}\right) \land \left(x \leq -1.55 \cdot 10^{-178} \lor \neg \left(x \leq 4.1 \cdot 10^{-7}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e-40)
         (and (not (<= x -5.9e-71))
              (or (<= x -1.55e-178) (not (<= x 4.1e-7)))))
   (* x z)
   y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e-40) || (!(x <= -5.9e-71) && ((x <= -1.55e-178) || !(x <= 4.1e-7)))) {
		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 <= (-7d-40)) .or. (.not. (x <= (-5.9d-71))) .and. (x <= (-1.55d-178)) .or. (.not. (x <= 4.1d-7))) 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 <= -7e-40) || (!(x <= -5.9e-71) && ((x <= -1.55e-178) || !(x <= 4.1e-7)))) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e-40) or (not (x <= -5.9e-71) and ((x <= -1.55e-178) or not (x <= 4.1e-7))):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e-40) || (!(x <= -5.9e-71) && ((x <= -1.55e-178) || !(x <= 4.1e-7))))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7e-40) || (~((x <= -5.9e-71)) && ((x <= -1.55e-178) || ~((x <= 4.1e-7)))))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e-40], And[N[Not[LessEqual[x, -5.9e-71]], $MachinePrecision], Or[LessEqual[x, -1.55e-178], N[Not[LessEqual[x, 4.1e-7]], $MachinePrecision]]]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -7.0000000000000003e-40 or -5.90000000000000002e-71 < x < -1.55e-178 or 4.0999999999999999e-7 < x

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 55.3%

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

   if -7.0000000000000003e-40 < x < -5.90000000000000002e-71 or -1.55e-178 < x < 4.0999999999999999e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.1%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-40} \lor \neg \left(x \leq -5.9 \cdot 10^{-71}\right) \land \left(x \leq -1.55 \cdot 10^{-178} \lor \neg \left(x \leq 4.1 \cdot 10^{-7}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -33000000000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -33000000000.0) (not (<= x 1.0))) (* x (- z y)) (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -33000000000.0) || !(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 <= (-33000000000.0d0)) .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 <= -33000000000.0) || !(x <= 1.0)) {
		tmp = x * (z - y);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -33000000000.0) 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 <= -33000000000.0) || !(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 <= -33000000000.0) || ~((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, -33000000000.0], 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 < -3.3e10 or 1 < x

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 98.6%

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

      1. mul-1-neg 98.6%

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

      2. sub-neg 98.6%

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

   5. Simplified 98.6%

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

   if -3.3e10 < x < 1

   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-rgt-out-- 100.0%

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

      3. *-lft-identity 100.0%

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

      4. associate-+l- 100.0%

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

      5. 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 97.8%

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

      1. neg-mul-1 97.8%

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

      2. distribute-rgt-neg-in 97.8%

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

   7. Simplified 97.8%

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

      1. sub-neg 97.8%

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

      2. +-commutative 97.8%

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

      3. distribute-rgt-neg-out 97.8%

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

      4. remove-double-neg 97.8%

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

   9. Applied egg-rr 97.8%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -33000000000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 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-rgt-out-- 98.4%

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

   3. *-lft-identity 98.4%

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

   4. associate-+l- 98.4%

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

   5. distribute-lft-out-- 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 8: 35.5% 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. Add Preprocessing

3. Taylor expanded in x around 0 34.3%

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

4. Final simplification 34.3%

   \[\leadsto y \]
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 2024115 
(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)))