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

Percentage Accurate: 95.9% → 97.9%

Time: 7.0s

Alternatives: 11

Speedup: 0.5×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 10^{+308}:\\ \;\;\;\;x \cdot \left(\left(1 + y \cdot z\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) 1e+308) (* x (- (+ 1.0 (* y z)) z)) (* z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 1e+308) {
		tmp = x * ((1.0 + (y * z)) - z);
	} else {
		tmp = z * (y * 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 (((1.0d0 - y) * z) <= 1d+308) then
        tmp = x * ((1.0d0 + (y * z)) - z)
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 1e+308) {
		tmp = x * ((1.0 + (y * z)) - z);
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= 1e+308:
		tmp = x * ((1.0 + (y * z)) - z)
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= 1e+308)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(y * z)) - z));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= 1e+308)
		tmp = x * ((1.0 + (y * z)) - z);
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], 1e+308], N[(x * N[(N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 1e308

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 98.8%

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

   if 1e308 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 68.4%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

      3. associate-*l* 99.8%

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

   5. Simplified 99.8%

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

Alternative 2: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 10^{+308}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) 1e+308) (* x (+ 1.0 (* z (+ y -1.0)))) (* z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 1e+308) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (y * 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 (((1.0d0 - y) * z) <= 1d+308) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 1e+308) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= 1e+308:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= 1e+308)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= 1e+308)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], 1e+308], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 1e308

   1. Initial program 98.8%

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

   if 1e308 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 68.4%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

      3. associate-*l* 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 10^{+308}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -710 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -710.0) (not (<= z 1.0)))
   (* (* z x) (+ y -1.0))
   (* x (+ 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -710.0) || !(z <= 1.0)) {
		tmp = (z * x) * (y + -1.0);
	} 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 ((z <= (-710.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (z * x) * (y + (-1.0d0))
    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 ((z <= -710.0) || !(z <= 1.0)) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -710.0) or not (z <= 1.0):
		tmp = (z * x) * (y + -1.0)
	else:
		tmp = x * (1.0 + (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -710.0) || !(z <= 1.0))
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	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 ((z <= -710.0) || ~((z <= 1.0)))
		tmp = (z * x) * (y + -1.0);
	else
		tmp = x * (1.0 + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -710.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -710 or 1 < z

   1. Initial program 93.3%

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

   3. Taylor expanded in z around inf 92.2%

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

      1. associate-*r* 98.8%

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

      2. *-commutative 98.8%

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

      3. sub-neg 98.8%

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

      4. metadata-eval 98.8%

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

   5. Simplified 98.8%

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

   if -710 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 98.4%

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

      1. neg-mul-1 98.4%

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

   5. Simplified 98.4%

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

      1. cancel-sign-sub 98.4%

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

      2. +-commutative 98.4%

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

   7. Applied egg-rr 98.4%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -710 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+19} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.1e+19) (not (<= y 1.0)))
   (* x (+ 1.0 (* y z)))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e+19) || !(y <= 1.0)) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = x * (1.0 - 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 <= (-3.1d+19)) .or. (.not. (y <= 1.0d0))) then
        tmp = x * (1.0d0 + (y * z))
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e+19) || !(y <= 1.0)) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.1e+19) or not (y <= 1.0):
		tmp = x * (1.0 + (y * z))
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.1e+19) || !(y <= 1.0))
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.1e+19) || ~((y <= 1.0)))
		tmp = x * (1.0 + (y * z));
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.1e+19], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1e19 or 1 < y

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf 91.7%

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

      1. neg-mul-1 91.7%

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

   5. Simplified 91.7%

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

      1. cancel-sign-sub 91.7%

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

      2. +-commutative 91.7%

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

   7. Applied egg-rr 91.7%

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

   if -3.1e19 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+19} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+120} \lor \neg \left(y \leq 7.2 \cdot 10^{+40}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6e+120) (not (<= y 7.2e+40))) (* y (* z x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6e+120) || !(y <= 7.2e+40)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - 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 <= (-6d+120)) .or. (.not. (y <= 7.2d+40))) then
        tmp = y * (z * x)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6e+120) || !(y <= 7.2e+40)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6e+120) or not (y <= 7.2e+40):
		tmp = y * (z * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6e+120) || !(y <= 7.2e+40))
		tmp = Float64(y * Float64(z * x));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6e+120) || ~((y <= 7.2e+40)))
		tmp = y * (z * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6e+120], N[Not[LessEqual[y, 7.2e+40]], $MachinePrecision]], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6e120 or 7.19999999999999993e40 < y

   1. Initial program 91.6%

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

   3. Taylor expanded in z around inf 76.3%

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

      1. associate-*r* 79.7%

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

      2. *-commutative 79.7%

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

      3. sub-neg 79.7%

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

      4. metadata-eval 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in y around inf 79.7%

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

   if -6e120 < y < 7.19999999999999993e40

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 92.4%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+120} \lor \neg \left(y \leq 7.2 \cdot 10^{+40}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+120} \lor \neg \left(y \leq 5.5 \cdot 10^{+39}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.1e+120) (not (<= y 5.5e+39))) (* z (* y x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.1e+120) || !(y <= 5.5e+39)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - 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 <= (-5.1d+120)) .or. (.not. (y <= 5.5d+39))) then
        tmp = z * (y * x)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.1e+120) || !(y <= 5.5e+39)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.1e+120) or not (y <= 5.5e+39):
		tmp = z * (y * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.1e+120) || !(y <= 5.5e+39))
		tmp = Float64(z * Float64(y * x));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.1e+120) || ~((y <= 5.5e+39)))
		tmp = z * (y * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.1e+120], N[Not[LessEqual[y, 5.5e+39]], $MachinePrecision]], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.10000000000000027e120 or 5.4999999999999997e39 < y

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf 76.3%

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

      1. *-commutative 76.3%

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

      2. *-commutative 76.3%

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

      3. associate-*l* 75.4%

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

   5. Simplified 75.4%

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

   if -5.10000000000000027e120 < y < 5.4999999999999997e39

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 92.4%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+120} \lor \neg \left(y \leq 5.5 \cdot 10^{+39}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.9e+120)
   (* y (* z x))
   (if (<= y 2.1e+49) (* x (- 1.0 z)) (* x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.9e+120) {
		tmp = y * (z * x);
	} else if (y <= 2.1e+49) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (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 <= (-4.9d+120)) then
        tmp = y * (z * x)
    else if (y <= 2.1d+49) then
        tmp = x * (1.0d0 - z)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.9e+120) {
		tmp = y * (z * x);
	} else if (y <= 2.1e+49) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.9e+120:
		tmp = y * (z * x)
	elif y <= 2.1e+49:
		tmp = x * (1.0 - z)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.9e+120)
		tmp = Float64(y * Float64(z * x));
	elseif (y <= 2.1e+49)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.9e+120)
		tmp = y * (z * x);
	elseif (y <= 2.1e+49)
		tmp = x * (1.0 - z);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.9e+120], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+49], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9000000000000001e120

   1. Initial program 88.0%

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

   3. Taylor expanded in z around inf 81.0%

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

      1. associate-*r* 85.6%

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

      2. *-commutative 85.6%

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

      3. sub-neg 85.6%

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

      4. metadata-eval 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in y around inf 85.6%

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

   if -4.9000000000000001e120 < y < 2.10000000000000011e49

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 91.9%

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

   if 2.10000000000000011e49 < y

   1. Initial program 97.4%

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

   3. Taylor expanded in y around inf 75.1%

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

      1. *-commutative 75.1%

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

      2. *-commutative 75.1%

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

   5. Simplified 75.1%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = 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 ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = 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 ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0 58.6%

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

   4. Taylor expanded in z around inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. distribute-rgt-neg-out 57.6%

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

   6. Simplified 57.6%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 80.0%

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

4. Final simplification 68.7%

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

Alternative 9: 41.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+124} \lor \neg \left(z \leq 1.2 \cdot 10^{+28}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1e+124) (not (<= z 1.2e+28))) (* z x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e+124) || !(z <= 1.2e+28)) {
		tmp = 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 ((z <= (-1.1d+124)) .or. (.not. (z <= 1.2d+28))) then
        tmp = 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 ((z <= -1.1e+124) || !(z <= 1.2e+28)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1e+124) or not (z <= 1.2e+28):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1e+124) || !(z <= 1.2e+28))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.1e+124) || ~((z <= 1.2e+28)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1e+124], N[Not[LessEqual[z, 1.2e+28]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e124 or 1.19999999999999991e28 < z

   1. Initial program 91.5%

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

   3. Taylor expanded in y around 0 53.5%

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

   4. Taylor expanded in z around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. distribute-rgt-neg-out 53.5%

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

   6. Simplified 53.5%

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

      1. neg-sub0 53.5%

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

      2. sub-neg 53.5%

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

      3. add-sqr-sqrt 24.9%

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

      4. sqrt-unprod 23.8%

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

      5. sqr-neg 23.8%

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

      6. sqrt-unprod 7.7%

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

      7. add-sqr-sqrt 15.1%

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

   8. Applied egg-rr 15.1%

      \[\leadsto x \cdot \color{blue}{\left(0 + z\right)} \]
   9. Step-by-step derivation

      1. +-lft-identity 15.1%

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

   10. Simplified 15.1%

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

   if -1.1e124 < z < 1.19999999999999991e28

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 62.4%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+124} \lor \neg \left(z \leq 1.2 \cdot 10^{+28}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.8e+53) (* x (- 1.0 z)) (* z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.8e+53) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * 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 <= 1.8d+53) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.8e+53) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.8e+53:
		tmp = x * (1.0 - z)
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.8e+53)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.8e+53)
		tmp = x * (1.0 - z);
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.8e+53], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.8e53

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0 78.4%

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

   if 1.8e53 < y

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0 21.8%

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

   4. Taylor expanded in z around inf 1.4%

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

      1. mul-1-neg 1.4%

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

      2. distribute-rgt-neg-out 1.4%

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

   6. Simplified 1.4%

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

      1. neg-sub0 1.4%

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

      2. sub-neg 1.4%

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

      3. add-sqr-sqrt 0.8%

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

      4. sqrt-unprod 23.1%

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

      5. sqr-neg 23.1%

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

      6. sqrt-unprod 15.1%

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

      7. add-sqr-sqrt 32.6%

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

   8. Applied egg-rr 32.6%

      \[\leadsto x \cdot \color{blue}{\left(0 + z\right)} \]
   9. Step-by-step derivation

      1. +-lft-identity 32.6%

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

   10. Simplified 32.6%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.7% accurate, 9.0× 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%

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

3. Taylor expanded in z around 0 41.4%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ t_1 := x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{if}\;t\_0 < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z))))
        (t_1 (+ x (* (- 1.0 y) (* (- z) x)))))
   (if (< t_0 -1.618195973607049e+50)
     t_1
     (if (< t_0 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = x * (1.0d0 - ((1.0d0 - y) * z))
    t_1 = x + ((1.0d0 - y) * (-z * x))
    if (t_0 < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (t_0 < 3.892237649663903d+134) then
        tmp = ((x * y) * z) - ((x * z) - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	t_1 = x + ((1.0 - y) * (-z * x))
	tmp = 0
	if t_0 < -1.618195973607049e+50:
		tmp = t_1
	elif t_0 < 3.892237649663903e+134:
		tmp = ((x * y) * z) - ((x * z) - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	t_1 = Float64(x + Float64(Float64(1.0 - y) * Float64(Float64(-z) * x)))
	tmp = 0.0
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = Float64(Float64(Float64(x * y) * z) - Float64(Float64(x * z) - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	t_1 = x + ((1.0 - y) * (-z * x));
	tmp = 0.0;
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = ((x * y) * z) - ((x * z) - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(N[(1.0 - y), $MachinePrecision] * N[((-z) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$0, -1.618195973607049e+50], t$95$1, If[Less[t$95$0, 3.892237649663903e+134], N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024141 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- 1 (* (- 1 y) z))) -161819597360704900000000000000000000000000000000000) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 389223764966390300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x))))))

  (* x (- 1.0 (* (- 1.0 y) z))))