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

Percentage Accurate: 95.8% → 98.7%

Time: 7.4s

Alternatives: 12

Speedup: 0.5×

• 21.1% 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: 95.8% 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: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.95) (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 <= -0.95) || !(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 <= (-0.95d0)) .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 <= -0.95) || !(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 <= -0.95) 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 <= -0.95) || !(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 <= -0.95) || ~((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, -0.95], 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 < -0.94999999999999996 or 1 < z

   1. Initial program 90.0%

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

   3. Taylor expanded in z around inf 89.3%

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

      1. associate-*r* 99.2%

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

      2. *-commutative 99.2%

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

      3. sub-neg 99.2%

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

      4. metadata-eval 99.2%

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

   5. Simplified 99.2%

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

   if -0.94999999999999996 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.0%

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

      1. neg-mul-1 99.0%

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

   5. Simplified 99.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+208}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) -1e+208)
   (* (* z x) (+ y -1.0))
   (+ x (* x (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -1e+208) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x + (x * (z * (y + -1.0)));
	}
	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) :: tmp
    if (((1.0d0 - y) * z) <= (-1d+208)) then
        tmp = (z * x) * (y + (-1.0d0))
    else
        tmp = x + (x * (z * (y + (-1.0d0))))
    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+208) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x + (x * (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= -1e+208:
		tmp = (z * x) * (y + -1.0)
	else:
		tmp = x + (x * (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= -1e+208)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	else
		tmp = Float64(x + Float64(x * Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= -1e+208)
		tmp = (z * x) * (y + -1.0);
	else
		tmp = x + (x * (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], -1e+208], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -9.9999999999999998e207

   1. Initial program 80.0%

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

   3. Taylor expanded in z around inf 80.0%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -9.9999999999999998e207 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0 98.1%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+208}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+208}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) -1e+208)
   (* (* z x) (+ y -1.0))
   (* x (+ 1.0 (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -1e+208) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	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) :: tmp
    if (((1.0d0 - y) * z) <= (-1d+208)) then
        tmp = (z * x) * (y + (-1.0d0))
    else
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    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+208) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= -1e+208:
		tmp = (z * x) * (y + -1.0)
	else:
		tmp = x * (1.0 + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= -1e+208)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= -1e+208)
		tmp = (z * x) * (y + -1.0);
	else
		tmp = x * (1.0 + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], -1e+208], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -9.9999999999999998e207

   1. Initial program 80.0%

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

   3. Taylor expanded in z around inf 80.0%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -9.9999999999999998e207 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 98.1%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+208}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1) (not (<= z 1.0)))
   (* (* z x) (+ y -1.0))
   (+ x (* z (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1) || !(z <= 1.0)) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x + (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 ((z <= (-1.1d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (z * x) * (y + (-1.0d0))
    else
        tmp = x + (z * (y * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1) || !(z <= 1.0)) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x + (z * (y * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1) or not (z <= 1.0):
		tmp = (z * x) * (y + -1.0)
	else:
		tmp = x + (z * (y * x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1) || !(z <= 1.0))
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	else
		tmp = Float64(x + Float64(z * Float64(y * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.1) || ~((z <= 1.0)))
		tmp = (z * x) * (y + -1.0);
	else
		tmp = x + (z * (y * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001 or 1 < z

   1. Initial program 90.0%

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

   3. Taylor expanded in z around inf 89.3%

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

      1. associate-*r* 99.2%

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

      2. *-commutative 99.2%

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

      3. sub-neg 99.2%

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

      4. metadata-eval 99.2%

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

   5. Simplified 99.2%

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

   if -1.1000000000000001 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in y around inf 99.1%

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

      1. associate-*r* 92.1%

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

      2. *-commutative 92.1%

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

   6. Simplified 92.1%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-11} \lor \neg \left(z \leq 1.85 \cdot 10^{-22}\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4e-11) (not (<= z 1.85e-22)))
   (* (* z x) (+ y -1.0))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e-11) || !(z <= 1.85e-22)) {
		tmp = (z * x) * (y + -1.0);
	} 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 ((z <= (-4d-11)) .or. (.not. (z <= 1.85d-22))) then
        tmp = (z * x) * (y + (-1.0d0))
    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 ((z <= -4e-11) || !(z <= 1.85e-22)) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4e-11) or not (z <= 1.85e-22):
		tmp = (z * x) * (y + -1.0)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4e-11) || !(z <= 1.85e-22))
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4e-11) || ~((z <= 1.85e-22)))
		tmp = (z * x) * (y + -1.0);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4e-11], N[Not[LessEqual[z, 1.85e-22]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999976e-11 or 1.85e-22 < z

   1. Initial program 90.5%

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

   3. Taylor expanded in z around inf 88.5%

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

      1. associate-*r* 97.9%

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

      2. *-commutative 97.9%

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

      3. sub-neg 97.9%

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

      4. metadata-eval 97.9%

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

   5. Simplified 97.9%

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

   if -3.99999999999999976e-11 < z < 1.85e-22

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 82.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-11} \lor \neg \left(z \leq 1.85 \cdot 10^{-22}\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+21} \lor \neg \left(y \leq 1.4 \cdot 10^{+21}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.05e+21) (not (<= y 1.4e+21))) (* y (* z x)) (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e+21) || !(y <= 1.4e+21)) {
		tmp = y * (z * x);
	} else {
		tmp = x - (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 <= (-1.05d+21)) .or. (.not. (y <= 1.4d+21))) then
        tmp = y * (z * x)
    else
        tmp = x - (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e+21) || !(y <= 1.4e+21)) {
		tmp = y * (z * x);
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.05e+21) or not (y <= 1.4e+21):
		tmp = y * (z * x)
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.05e+21) || !(y <= 1.4e+21))
		tmp = Float64(y * Float64(z * x));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.05e+21) || ~((y <= 1.4e+21)))
		tmp = y * (z * x);
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.05e+21], N[Not[LessEqual[y, 1.4e+21]], $MachinePrecision]], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e21 or 1.4e21 < y

   1. Initial program 87.5%

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

   3. Taylor expanded in z around inf 67.6%

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

      1. associate-*r* 79.0%

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

      2. *-commutative 79.0%

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

      3. sub-neg 79.0%

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

      4. metadata-eval 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in y around inf 79.0%

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

   if -1.05e21 < y < 1.4e21

   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 96.9%

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

      1. sub-neg 96.9%

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

      2. distribute-rgt-in 96.9%

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

      3. *-un-lft-identity 96.9%

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

      4. distribute-lft-neg-in 96.9%

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

      5. unsub-neg 96.9%

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

   5. Applied egg-rr 96.9%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+21} \lor \neg \left(y \leq 1.4 \cdot 10^{+21}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+21} \lor \neg \left(y \leq 3.65 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.8e+21) (not (<= y 3.65e+22))) (* y (* z x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.8e+21) || !(y <= 3.65e+22)) {
		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 <= (-2.8d+21)) .or. (.not. (y <= 3.65d+22))) 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 <= -2.8e+21) || !(y <= 3.65e+22)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.8e+21) or not (y <= 3.65e+22):
		tmp = y * (z * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.8e+21) || !(y <= 3.65e+22))
		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 <= -2.8e+21) || ~((y <= 3.65e+22)))
		tmp = y * (z * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.8e+21], N[Not[LessEqual[y, 3.65e+22]], $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 < -2.8e21 or 3.6499999999999999e22 < y

   1. Initial program 87.5%

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

   3. Taylor expanded in z around inf 67.6%

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

      1. associate-*r* 79.0%

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

      2. *-commutative 79.0%

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

      3. sub-neg 79.0%

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

      4. metadata-eval 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in y around inf 79.0%

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

   if -2.8e21 < y < 3.6499999999999999e22

   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 96.9%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+21} \lor \neg \left(y \leq 3.65 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+21} \lor \neg \left(y \leq 1.12 \cdot 10^{+21}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8e+21) (not (<= y 1.12e+21))) (* z (* y x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8e+21) || !(y <= 1.12e+21)) {
		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 <= (-8d+21)) .or. (.not. (y <= 1.12d+21))) 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 <= -8e+21) || !(y <= 1.12e+21)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8e+21) or not (y <= 1.12e+21):
		tmp = z * (y * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8e+21) || !(y <= 1.12e+21))
		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 <= -8e+21) || ~((y <= 1.12e+21)))
		tmp = z * (y * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8e+21], N[Not[LessEqual[y, 1.12e+21]], $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 < -8e21 or 1.12e21 < y

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. *-commutative 67.6%

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

      3. associate-*l* 76.4%

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

   5. Simplified 76.4%

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

   if -8e21 < y < 1.12e21

   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 96.9%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+21} \lor \neg \left(y \leq 1.12 \cdot 10^{+21}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 4.5 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 4.5e+14))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 4.5e+14)) {
		tmp = x * -z;
	} 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 <= 4.5d+14))) then
        tmp = x * -z
    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 <= 4.5e+14)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 4.5e+14):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 4.5e+14))
		tmp = Float64(x * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 4.5e+14)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 4.5e+14]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 4.5e14 < z

   1. Initial program 89.8%

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

   3. Taylor expanded in z around inf 89.0%

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

   4. Taylor expanded in y around 0 59.5%

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

      1. mul-1-neg 59.5%

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

      2. *-commutative 59.5%

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

      3. distribute-rgt-neg-in 59.5%

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

   6. Simplified 59.5%

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

   if -1 < z < 4.5e14

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 76.5%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 4.5 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.3 \cdot 10^{+194}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 4.3e+194) (* x (- 1.0 z)) (* z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.3e+194) {
		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 <= 4.3d+194) 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 <= 4.3e+194) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4.3e+194:
		tmp = x * (1.0 - z)
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4.3e+194)
		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 <= 4.3e+194)
		tmp = x * (1.0 - z);
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4.3e+194], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.29999999999999994e194

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0 75.6%

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

   if 4.29999999999999994e194 < y

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf 76.5%

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

   4. Taylor expanded in y around 0 0.8%

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

      1. mul-1-neg 0.8%

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

      2. *-commutative 0.8%

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

      3. distribute-rgt-neg-in 0.8%

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

   6. Simplified 0.8%

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

      1. add-sqr-sqrt 0.6%

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

      2. sqrt-unprod 26.6%

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

      3. sqr-neg 26.6%

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

      4. sqrt-unprod 18.2%

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

      5. add-sqr-sqrt 28.3%

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

      6. pow1 28.3%

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

   8. Applied egg-rr 28.3%

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

      1. unpow1 28.3%

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

      2. *-commutative 28.3%

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

   10. Simplified 28.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.3 \cdot 10^{+194}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 5.5e-16) x (* z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 5.5e-16) {
		tmp = x;
	} 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 (z <= 5.5d-16) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 5.5e-16) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 5.5e-16:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 5.5e-16)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 5.5e-16)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 5.5e-16], x, N[(z * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.49999999999999964e-16

   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 51.2%

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

   if 5.49999999999999964e-16 < z

   1. Initial program 89.0%

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

   3. Taylor expanded in z around inf 88.9%

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

   4. Taylor expanded in y around 0 49.8%

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

      1. mul-1-neg 49.8%

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

      2. *-commutative 49.8%

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

      3. distribute-rgt-neg-in 49.8%

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

   6. Simplified 49.8%

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

      1. add-sqr-sqrt 23.7%

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

      2. sqrt-unprod 25.2%

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

      3. sqr-neg 25.2%

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

      4. sqrt-unprod 4.4%

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

      5. add-sqr-sqrt 13.7%

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

      6. pow1 13.7%

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

   8. Applied egg-rr 13.7%

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

      1. unpow1 13.7%

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

      2. *-commutative 13.7%

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

   10. Simplified 13.7%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.2% 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 94.8%

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

3. Taylor expanded in z around 0 39.8%

   \[\leadsto \color{blue}{x} \]
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 2024133 
(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))))