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

Percentage Accurate: 98.0% → 100.0%

Time: 2.6s

Alternatives: 7

Speedup: 0.5×

• 20.9% 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 98.0%

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

   1. sub-neg 98.0%

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

   2. +-commutative 98.0%

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

   3. distribute-rgt1-in 98.0%

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

   4. associate-+l+ 98.0%

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

   5. +-commutative 98.0%

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

   6. *-commutative 98.0%

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

   7. neg-mul-1 98.0%

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

   8. associate-*r* 98.0%

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

   9. *-commutative 98.0%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

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

   15. unsub-neg 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - x\right) + x \cdot z\\ \mathbf{if}\;t_0 \leq 10^{+304}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y (- 1.0 x)) (* x z))))
   (if (<= t_0 1e+304) t_0 (* x (- z y)))))

C

double code(double x, double y, double z) {
	double t_0 = (y * (1.0 - x)) + (x * z);
	double tmp;
	if (t_0 <= 1e+304) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (y * (1.0d0 - x)) + (x * z)
    if (t_0 <= 1d+304) then
        tmp = t_0
    else
        tmp = x * (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * (1.0 - x)) + (x * z);
	double tmp;
	if (t_0 <= 1e+304) {
		tmp = t_0;
	} else {
		tmp = x * (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * (1.0 - x)) + (x * z)
	tmp = 0
	if t_0 <= 1e+304:
		tmp = t_0
	else:
		tmp = x * (z - y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) + Float64(x * z))
	tmp = 0.0
	if (t_0 <= 1e+304)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * (1.0 - x)) + (x * z);
	tmp = 0.0;
	if (t_0 <= 1e+304)
		tmp = t_0;
	else
		tmp = x * (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 1e+304], t$95$0, N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (-.f64 1 x) y) (*.f64 x z)) < 9.9999999999999994e303

   1. Initial program 100.0%

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

   if 9.9999999999999994e303 < (+.f64 (*.f64 (-.f64 1 x) y) (*.f64 x z))

   1. Initial program 82.8%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(1 - x\right) + x \cdot z \leq 10^{+304}:\\ \;\;\;\;y \cdot \left(1 - x\right) + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 3: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{+148}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-54}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-20}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+168}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+268}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= x -1.95e+148)
     t_0
     (if (<= x -1.18e-54)
       (* x z)
       (if (<= x 5.5e-20)
         y
         (if (<= x 3.2e+168) (* x z) (if (<= x 3.5e+268) t_0 (* x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (x <= -1.95e+148) {
		tmp = t_0;
	} else if (x <= -1.18e-54) {
		tmp = x * z;
	} else if (x <= 5.5e-20) {
		tmp = y;
	} else if (x <= 3.2e+168) {
		tmp = x * z;
	} else if (x <= 3.5e+268) {
		tmp = t_0;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * -x
    if (x <= (-1.95d+148)) then
        tmp = t_0
    else if (x <= (-1.18d-54)) then
        tmp = x * z
    else if (x <= 5.5d-20) then
        tmp = y
    else if (x <= 3.2d+168) then
        tmp = x * z
    else if (x <= 3.5d+268) then
        tmp = t_0
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (x <= -1.95e+148) {
		tmp = t_0;
	} else if (x <= -1.18e-54) {
		tmp = x * z;
	} else if (x <= 5.5e-20) {
		tmp = y;
	} else if (x <= 3.2e+168) {
		tmp = x * z;
	} else if (x <= 3.5e+268) {
		tmp = t_0;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if x <= -1.95e+148:
		tmp = t_0
	elif x <= -1.18e-54:
		tmp = x * z
	elif x <= 5.5e-20:
		tmp = y
	elif x <= 3.2e+168:
		tmp = x * z
	elif x <= 3.5e+268:
		tmp = t_0
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (x <= -1.95e+148)
		tmp = t_0;
	elseif (x <= -1.18e-54)
		tmp = Float64(x * z);
	elseif (x <= 5.5e-20)
		tmp = y;
	elseif (x <= 3.2e+168)
		tmp = Float64(x * z);
	elseif (x <= 3.5e+268)
		tmp = t_0;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -x;
	tmp = 0.0;
	if (x <= -1.95e+148)
		tmp = t_0;
	elseif (x <= -1.18e-54)
		tmp = x * z;
	elseif (x <= 5.5e-20)
		tmp = y;
	elseif (x <= 3.2e+168)
		tmp = x * z;
	elseif (x <= 3.5e+268)
		tmp = t_0;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[x, -1.95e+148], t$95$0, If[LessEqual[x, -1.18e-54], N[(x * z), $MachinePrecision], If[LessEqual[x, 5.5e-20], y, If[LessEqual[x, 3.2e+168], N[(x * z), $MachinePrecision], If[LessEqual[x, 3.5e+268], t$95$0, N[(x * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.95000000000000001e148 or 3.2000000000000001e168 < x < 3.49999999999999972e268

   1. Initial program 91.9%

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

   2. Taylor expanded in y around inf 68.7%

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

      1. distribute-lft-out-- 68.7%

         \[\leadsto \color{blue}{y \cdot 1 - y \cdot x} \]

      2. *-rgt-identity 68.7%

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

   4. Simplified 68.7%

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

   5. Taylor expanded in x around inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. distribute-rgt-neg-out 68.7%

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

   7. Simplified 68.7%

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

   if -1.95000000000000001e148 < x < -1.17999999999999996e-54 or 5.4999999999999996e-20 < x < 3.2000000000000001e168 or 3.49999999999999972e268 < x

   1. Initial program 98.8%

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

   2. Taylor expanded in y around 0 64.0%

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

   if -1.17999999999999996e-54 < x < 5.4999999999999996e-20

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.0%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-54}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-20}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+168}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+268}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 4: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-54} \lor \neg \left(x \leq 2.15 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e-54) (not (<= x 2.15e-17))) (* x (- z y)) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e-54) || !(x <= 2.15e-17)) {
		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 <= (-3.8d-54)) .or. (.not. (x <= 2.15d-17))) 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 <= -3.8e-54) || !(x <= 2.15e-17)) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e-54) or not (x <= 2.15e-17):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e-54) || !(x <= 2.15e-17))
		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 <= -3.8e-54) || ~((x <= 2.15e-17)))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e-54], N[Not[LessEqual[x, 2.15e-17]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -3.8000000000000002e-54 or 2.15000000000000012e-17 < x

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 96.8%

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

      1. mul-1-neg 96.8%

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

      2. unsub-neg 96.8%

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

   4. Simplified 96.8%

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

   if -3.8000000000000002e-54 < x < 2.15000000000000012e-17

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.0%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-54} \lor \neg \left(x \leq 2.15 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-54} \lor \neg \left(x \leq 0.0035\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e-54) (not (<= x 0.0035))) (* x (- z y)) (- y (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e-54) || !(x <= 0.0035)) {
		tmp = x * (z - y);
	} else {
		tmp = y - (x * 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 <= (-3.8d-54)) .or. (.not. (x <= 0.0035d0))) then
        tmp = x * (z - y)
    else
        tmp = y - (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e-54) || !(x <= 0.0035)) {
		tmp = x * (z - y);
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e-54) or not (x <= 0.0035):
		tmp = x * (z - y)
	else:
		tmp = y - (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e-54) || !(x <= 0.0035))
		tmp = Float64(x * Float64(z - y));
	else
		tmp = Float64(y - Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.8e-54) || ~((x <= 0.0035)))
		tmp = x * (z - y);
	else
		tmp = y - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e-54], N[Not[LessEqual[x, 0.0035]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8000000000000002e-54 or 0.00350000000000000007 < x

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf 99.0%

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

      1. mul-1-neg 99.0%

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

      2. unsub-neg 99.0%

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

   4. Simplified 99.0%

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

   if -3.8000000000000002e-54 < x < 0.00350000000000000007

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 83.2%

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

      1. distribute-lft-out-- 83.2%

         \[\leadsto \color{blue}{y \cdot 1 - y \cdot x} \]

      2. *-rgt-identity 83.2%

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

   4. Simplified 83.2%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-54} \lor \neg \left(x \leq 0.0035\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \]

Alternative 6: 61.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-55}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.6e-55) (* x z) (if (<= x 1.5e-17) y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.6e-55) {
		tmp = x * z;
	} else if (x <= 1.5e-17) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-6.6d-55)) then
        tmp = x * z
    else if (x <= 1.5d-17) then
        tmp = y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.6e-55) {
		tmp = x * z;
	} else if (x <= 1.5e-17) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.6e-55:
		tmp = x * z
	elif x <= 1.5e-17:
		tmp = y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.6e-55)
		tmp = Float64(x * z);
	elseif (x <= 1.5e-17)
		tmp = y;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.6e-55)
		tmp = x * z;
	elseif (x <= 1.5e-17)
		tmp = y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.6e-55], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.5e-17], y, N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5999999999999999e-55 or 1.50000000000000003e-17 < x

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 54.4%

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

   if -6.5999999999999999e-55 < x < 1.50000000000000003e-17

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.0%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-55}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 7: 36.5% 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 98.0%

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

2. Taylor expanded in x around 0 41.9%

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

3. Final simplification 41.9%

   \[\leadsto y \]

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 2023229 
(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)))