Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I

Percentage Accurate: 96.5% → 98.2%

Time: 4.8s

Alternatives: 6

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x * (1.0 - (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 = x * (1.0d0 - (y * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x * (1.0 - (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 = x * (1.0d0 - (y * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) (- INFINITY)) (* z (* y (- x))) (- x (* (* y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -((double) INFINITY)) {
		tmp = z * (y * -x);
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -Double.POSITIVE_INFINITY) {
		tmp = z * (y * -x);
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -math.inf:
		tmp = z * (y * -x)
	else:
		tmp = x - ((y * z) * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= Float64(-Inf))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = Float64(x - Float64(Float64(y * z) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -Inf)
		tmp = z * (y * -x);
	else
		tmp = x - ((y * z) * x);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -inf.0

   1. Initial program 70.7%

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

      1. flip3-- 0.0%

         \[\leadsto x \cdot \color{blue}{\frac{{1}^{3} - {\left(y \cdot z\right)}^{3}}{1 \cdot 1 + \left(\left(y \cdot z\right) \cdot \left(y \cdot z\right) + 1 \cdot \left(y \cdot z\right)\right)}} \]

      2. associate-*r/ 0.0%

         \[\leadsto \color{blue}{\frac{x \cdot \left({1}^{3} - {\left(y \cdot z\right)}^{3}\right)}{1 \cdot 1 + \left(\left(y \cdot z\right) \cdot \left(y \cdot z\right) + 1 \cdot \left(y \cdot z\right)\right)}} \]

      3. metadata-eval 0.0%

         \[\leadsto \frac{x \cdot \left(\color{blue}{1} - {\left(y \cdot z\right)}^{3}\right)}{1 \cdot 1 + \left(\left(y \cdot z\right) \cdot \left(y \cdot z\right) + 1 \cdot \left(y \cdot z\right)\right)} \]

      4. metadata-eval 0.0%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{3}\right)}{\color{blue}{1} + \left(\left(y \cdot z\right) \cdot \left(y \cdot z\right) + 1 \cdot \left(y \cdot z\right)\right)} \]

      5. distribute-rgt-out 0.0%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{3}\right)}{1 + \color{blue}{\left(y \cdot z\right) \cdot \left(y \cdot z + 1\right)}} \]

      6. +-commutative 0.0%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{3}\right)}{1 + \left(y \cdot z\right) \cdot \color{blue}{\left(1 + y \cdot z\right)}} \]

   3. Applied egg-rr 0.0%

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

      1. associate-/l* 0.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{1 + \left(y \cdot z\right) \cdot \left(1 + y \cdot z\right)}{1 - {\left(y \cdot z\right)}^{3}}}} \]

   5. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{1 + \left(y \cdot z\right) \cdot \left(1 + y \cdot z\right)}{1 - {\left(y \cdot z\right)}^{3}}}} \]

   6. Taylor expanded in y around inf 70.7%

      \[\leadsto \frac{x}{\color{blue}{\frac{-1}{y \cdot z}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 70.7%

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

      2. associate-*r* 100.0%

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

      3. div-inv 100.0%

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

      4. metadata-eval 100.0%

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

   8. Applied egg-rr 100.0%

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

   if -inf.0 < (*.f64 y z)

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. distribute-rgt-in 98.3%

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

      3. *-un-lft-identity 98.3%

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

      4. distribute-rgt-neg-in 98.3%

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

   3. Applied egg-rr 98.3%

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

4. Final simplification 98.4%

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

Alternative 2: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+230}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -1e+230) (* y (* z (- x))) (* x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+230) {
		tmp = y * (z * -x);
	} else {
		tmp = x * (1.0 - (y * 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 ((y * z) <= (-1d+230)) then
        tmp = y * (z * -x)
    else
        tmp = x * (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+230) {
		tmp = y * (z * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -1e+230:
		tmp = y * (z * -x)
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -1e+230)
		tmp = Float64(y * Float64(z * Float64(-x)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -1e+230)
		tmp = y * (z * -x);
	else
		tmp = x * (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -1e+230], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.0000000000000001e230

   1. Initial program 82.5%

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

   2. Taylor expanded in y around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

      3. distribute-lft-neg-out 99.8%

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

      4. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   if -1.0000000000000001e230 < (*.f64 y z)

   1. Initial program 98.2%

      \[x \cdot \left(1 - y \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+230}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 3: 98.2% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) (- INFINITY)) (* z (* y (- x))) (* x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -((double) INFINITY)) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -Double.POSITIVE_INFINITY) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -math.inf:
		tmp = z * (y * -x)
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= Float64(-Inf))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -Inf)
		tmp = z * (y * -x);
	else
		tmp = x * (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -inf.0

   1. Initial program 70.7%

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

      1. flip3-- 0.0%

         \[\leadsto x \cdot \color{blue}{\frac{{1}^{3} - {\left(y \cdot z\right)}^{3}}{1 \cdot 1 + \left(\left(y \cdot z\right) \cdot \left(y \cdot z\right) + 1 \cdot \left(y \cdot z\right)\right)}} \]

      2. associate-*r/ 0.0%

         \[\leadsto \color{blue}{\frac{x \cdot \left({1}^{3} - {\left(y \cdot z\right)}^{3}\right)}{1 \cdot 1 + \left(\left(y \cdot z\right) \cdot \left(y \cdot z\right) + 1 \cdot \left(y \cdot z\right)\right)}} \]

      3. metadata-eval 0.0%

         \[\leadsto \frac{x \cdot \left(\color{blue}{1} - {\left(y \cdot z\right)}^{3}\right)}{1 \cdot 1 + \left(\left(y \cdot z\right) \cdot \left(y \cdot z\right) + 1 \cdot \left(y \cdot z\right)\right)} \]

      4. metadata-eval 0.0%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{3}\right)}{\color{blue}{1} + \left(\left(y \cdot z\right) \cdot \left(y \cdot z\right) + 1 \cdot \left(y \cdot z\right)\right)} \]

      5. distribute-rgt-out 0.0%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{3}\right)}{1 + \color{blue}{\left(y \cdot z\right) \cdot \left(y \cdot z + 1\right)}} \]

      6. +-commutative 0.0%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{3}\right)}{1 + \left(y \cdot z\right) \cdot \color{blue}{\left(1 + y \cdot z\right)}} \]

   3. Applied egg-rr 0.0%

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

      1. associate-/l* 0.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{1 + \left(y \cdot z\right) \cdot \left(1 + y \cdot z\right)}{1 - {\left(y \cdot z\right)}^{3}}}} \]

   5. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{1 + \left(y \cdot z\right) \cdot \left(1 + y \cdot z\right)}{1 - {\left(y \cdot z\right)}^{3}}}} \]

   6. Taylor expanded in y around inf 70.7%

      \[\leadsto \frac{x}{\color{blue}{\frac{-1}{y \cdot z}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 70.7%

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

      2. associate-*r* 100.0%

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

      3. div-inv 100.0%

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

      4. metadata-eval 100.0%

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

   8. Applied egg-rr 100.0%

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

   if -inf.0 < (*.f64 y z)

   1. Initial program 98.3%

      \[x \cdot \left(1 - y \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

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

Alternative 4: 70.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+41} \lor \neg \left(y \leq 2.4 \cdot 10^{-103}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e+41) (not (<= y 2.4e-103))) (* (* y z) (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+41) || !(y <= 2.4e-103)) {
		tmp = (y * z) * -x;
	} else {
		tmp = 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 ((y <= (-1d+41)) .or. (.not. (y <= 2.4d-103))) then
        tmp = (y * z) * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+41) || !(y <= 2.4e-103)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e+41) or not (y <= 2.4e-103):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e+41) || !(y <= 2.4e-103))
		tmp = Float64(Float64(y * z) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1e+41) || ~((y <= 2.4e-103)))
		tmp = (y * z) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e+41], N[Not[LessEqual[y, 2.4e-103]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000001e41 or 2.4000000000000002e-103 < y

   1. Initial program 93.5%

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

   2. Taylor expanded in y around inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. associate-*r* 64.1%

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

      3. distribute-lft-neg-in 64.1%

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

      4. distribute-rgt-neg-out 64.1%

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

      5. *-commutative 64.1%

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

   4. Simplified 64.1%

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

   if -1.00000000000000001e41 < y < 2.4000000000000002e-103

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 74.4%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+41} \lor \neg \left(y \leq 2.4 \cdot 10^{-103}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 70.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+100} \lor \neg \left(y \leq 3.75 \cdot 10^{-103}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.4e+100) (not (<= y 3.75e-103))) (* y (* z (- x))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+100) || !(y <= 3.75e-103)) {
		tmp = y * (z * -x);
	} else {
		tmp = 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 ((y <= (-2.4d+100)) .or. (.not. (y <= 3.75d-103))) then
        tmp = y * (z * -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+100) || !(y <= 3.75e-103)) {
		tmp = y * (z * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.4e+100) or not (y <= 3.75e-103):
		tmp = y * (z * -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.4e+100) || !(y <= 3.75e-103))
		tmp = Float64(y * Float64(z * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.4e+100) || ~((y <= 3.75e-103)))
		tmp = y * (z * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.4e+100], N[Not[LessEqual[y, 3.75e-103]], $MachinePrecision]], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.40000000000000012e100 or 3.75e-103 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. distribute-rgt-neg-in 67.8%

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

      3. distribute-lft-neg-out 67.8%

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

      4. *-commutative 67.8%

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

   4. Simplified 67.8%

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

   if -2.40000000000000012e100 < y < 3.75e-103

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 72.2%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+100} \lor \neg \left(y \leq 3.75 \cdot 10^{-103}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 51.1% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 96.6%

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

2. Taylor expanded in y around 0 52.1%

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

3. Final simplification 52.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023228 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))