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

Percentage Accurate: 97.8% → 100.0%

Time: 4.4s

Alternatives: 8

Speedup: 1.3×

• 21.7% 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: 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 97.3%

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

   1. *-commutative 97.3%

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

   2. distribute-lft-out-- 97.3%

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

   3. *-rgt-identity 97.3%

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

   4. cancel-sign-sub-inv 97.3%

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

   5. +-commutative 97.3%

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

   6. +-commutative 97.3%

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

   7. associate-+l+ 97.3%

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

   8. +-commutative 97.3%

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

   9. *-commutative 97.3%

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

   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: 62.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+140}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{-26}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-39}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+72} \lor \neg \left(x \leq 2.4 \cdot 10^{+173}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= x -1e+140)
     t_0
     (if (<= x -1.16e-26)
       (* x z)
       (if (<= x 3.6e-39)
         y
         (if (or (<= x 6.5e+72) (not (<= x 2.4e+173))) (* x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (x <= -1e+140) {
		tmp = t_0;
	} else if (x <= -1.16e-26) {
		tmp = x * z;
	} else if (x <= 3.6e-39) {
		tmp = y;
	} else if ((x <= 6.5e+72) || !(x <= 2.4e+173)) {
		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 = y * -x
    if (x <= (-1d+140)) then
        tmp = t_0
    else if (x <= (-1.16d-26)) then
        tmp = x * z
    else if (x <= 3.6d-39) then
        tmp = y
    else if ((x <= 6.5d+72) .or. (.not. (x <= 2.4d+173))) 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 = y * -x;
	double tmp;
	if (x <= -1e+140) {
		tmp = t_0;
	} else if (x <= -1.16e-26) {
		tmp = x * z;
	} else if (x <= 3.6e-39) {
		tmp = y;
	} else if ((x <= 6.5e+72) || !(x <= 2.4e+173)) {
		tmp = x * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if x <= -1e+140:
		tmp = t_0
	elif x <= -1.16e-26:
		tmp = x * z
	elif x <= 3.6e-39:
		tmp = y
	elif (x <= 6.5e+72) or not (x <= 2.4e+173):
		tmp = x * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (x <= -1e+140)
		tmp = t_0;
	elseif (x <= -1.16e-26)
		tmp = Float64(x * z);
	elseif (x <= 3.6e-39)
		tmp = y;
	elseif ((x <= 6.5e+72) || !(x <= 2.4e+173))
		tmp = Float64(x * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -x;
	tmp = 0.0;
	if (x <= -1e+140)
		tmp = t_0;
	elseif (x <= -1.16e-26)
		tmp = x * z;
	elseif (x <= 3.6e-39)
		tmp = y;
	elseif ((x <= 6.5e+72) || ~((x <= 2.4e+173)))
		tmp = x * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[x, -1e+140], t$95$0, If[LessEqual[x, -1.16e-26], N[(x * z), $MachinePrecision], If[LessEqual[x, 3.6e-39], y, If[Or[LessEqual[x, 6.5e+72], N[Not[LessEqual[x, 2.4e+173]], $MachinePrecision]], N[(x * z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.00000000000000006e140 or 6.5000000000000001e72 < x < 2.3999999999999999e173

   1. Initial program 92.9%

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

   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. unsub-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 69.4%

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

      1. associate-*r* 69.4%

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

      2. mul-1-neg 69.4%

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

   7. Simplified 69.4%

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

   if -1.00000000000000006e140 < x < -1.16000000000000002e-26 or 3.6000000000000001e-39 < x < 6.5000000000000001e72 or 2.3999999999999999e173 < x

   1. Initial program 96.5%

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

   2. Taylor expanded in y around 0 71.3%

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

   if -1.16000000000000002e-26 < x < 3.6000000000000001e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.4%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{-26}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-39}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+72} \lor \neg \left(x \leq 2.4 \cdot 10^{+173}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-28} \lor \neg \left(x \leq 3.1 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.2e-28) (not (<= x 3.1e-38))) (* x (- z y)) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e-28) || !(x <= 3.1e-38)) {
		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 <= (-5.2d-28)) .or. (.not. (x <= 3.1d-38))) 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 <= -5.2e-28) || !(x <= 3.1e-38)) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.2e-28) or not (x <= 3.1e-38):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.2e-28) || !(x <= 3.1e-38))
		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 <= -5.2e-28) || ~((x <= 3.1e-38)))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.2e-28], N[Not[LessEqual[x, 3.1e-38]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -5.2e-28 or 3.09999999999999983e-38 < x

   1. Initial program 95.0%

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

   2. Taylor expanded in x around inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. unsub-neg 98.8%

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

   4. Simplified 98.8%

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

   if -5.2e-28 < x < 3.09999999999999983e-38

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-28} \lor \neg \left(x \leq 3.1 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-21} \lor \neg \left(x \leq 2.25 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.05e-21) (not (<= x 2.25e-38)))
   (* x (- z y))
   (* y (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.05e-21) || !(x <= 2.25e-38)) {
		tmp = x * (z - y);
	} 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) :: tmp
    if ((x <= (-2.05d-21)) .or. (.not. (x <= 2.25d-38))) then
        tmp = x * (z - y)
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.05e-21) || !(x <= 2.25e-38)) {
		tmp = x * (z - y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.05e-21) or not (x <= 2.25e-38):
		tmp = x * (z - y)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.05e-21) || !(x <= 2.25e-38))
		tmp = Float64(x * Float64(z - y));
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.05e-21) || ~((x <= 2.25e-38)))
		tmp = x * (z - y);
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.05e-21], N[Not[LessEqual[x, 2.25e-38]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.04999999999999997e-21 or 2.25000000000000004e-38 < x

   1. Initial program 95.0%

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

   2. Taylor expanded in x around inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. unsub-neg 98.8%

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

   4. Simplified 98.8%

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

   if -2.04999999999999997e-21 < x < 2.25000000000000004e-38

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 72.4%

      \[\leadsto \color{blue}{y \cdot \left(1 - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-21} \lor \neg \left(x \leq 2.25 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 97.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1.25 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.25e-37))) (* x (- z y)) (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.25e-37)) {
		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 <= 1.25d-37))) 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 <= 1.25e-37)) {
		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 <= 1.25e-37):
		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 <= 1.25e-37))
		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 <= 1.25e-37)))
		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, 1.25e-37]], $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 1.2499999999999999e-37 < x

   1. Initial program 94.8%

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

   2. Taylor expanded in x around inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

   4. Simplified 99.4%

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

   if -1 < x < 1.2499999999999999e-37

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

   6. Taylor expanded in z around inf 99.6%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1.25 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]

Alternative 6: 62.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-33} \lor \neg \left(x \leq 4.7 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.36e-33) (not (<= x 4.7e-39))) (* x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.36e-33) || !(x <= 4.7e-39)) {
		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 <= (-1.36d-33)) .or. (.not. (x <= 4.7d-39))) 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 <= -1.36e-33) || !(x <= 4.7e-39)) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.36e-33) or not (x <= 4.7e-39):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.36e-33) || !(x <= 4.7e-39))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.36e-33) || ~((x <= 4.7e-39)))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.36e-33], N[Not[LessEqual[x, 4.7e-39]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -1.36e-33 or 4.7000000000000002e-39 < x

   1. Initial program 95.0%

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

   2. Taylor expanded in y around 0 57.0%

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

   if -1.36e-33 < x < 4.7000000000000002e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.4%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-33} \lor \neg \left(x \leq 4.7 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

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 97.3%

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

2. Taylor expanded in x around 0 100.0%

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

   1. mul-1-neg 100.0%

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

4. Simplified 100.0%

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

5. Taylor expanded in x around 0 100.0%

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

6. Final simplification 100.0%

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

Alternative 8: 36.7% 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 97.3%

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

2. Taylor expanded in x around 0 34.4%

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

3. Final simplification 34.4%

   \[\leadsto y \]

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 2023305 
(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)))