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

Percentage Accurate: 96.2% → 98.2%

Time: 8.2s

Alternatives: 13

Speedup: 1.0×

• 20.7% 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: 96.2% 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: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(\left(1 + y \cdot z\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 3.7e+15) (* x (- (+ 1.0 (* y z)) z)) (* (+ y -1.0) (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.7e+15) {
		tmp = x * ((1.0 + (y * z)) - z);
	} else {
		tmp = (y + -1.0) * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 3.7d+15) then
        tmp = x * ((1.0d0 + (y * z)) - z)
    else
        tmp = (y + (-1.0d0)) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.7e+15) {
		tmp = x * ((1.0 + (y * z)) - z);
	} else {
		tmp = (y + -1.0) * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 3.7e+15:
		tmp = x * ((1.0 + (y * z)) - z)
	else:
		tmp = (y + -1.0) * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 3.7e+15)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(y * z)) - z));
	else
		tmp = Float64(Float64(y + -1.0) * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 3.7e+15)
		tmp = x * ((1.0 + (y * z)) - z);
	else
		tmp = (y + -1.0) * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 3.7e+15], N[(x * N[(N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.7e15

   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 98.9%

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

   if 3.7e15 < z

   1. Initial program 91.9%

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

   3. Taylor expanded in y around 0 91.9%

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

   4. Taylor expanded in z around inf 91.9%

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

      1. sub-neg 91.9%

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

      2. metadata-eval 91.9%

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

      3. associate-*r* 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(\left(1 + y \cdot z\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+276}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* y z))))
   (if (<= z -1.7e+276)
     t_0
     (if (<= z -1.45e-27)
       t_1
       (if (<= z 4.2e-43) x (if (<= z 1.25e+28) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -1.7e+276) {
		tmp = t_0;
	} else if (z <= -1.45e-27) {
		tmp = t_1;
	} else if (z <= 4.2e-43) {
		tmp = x;
	} else if (z <= 1.25e+28) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * -x
    t_1 = x * (y * z)
    if (z <= (-1.7d+276)) then
        tmp = t_0
    else if (z <= (-1.45d-27)) then
        tmp = t_1
    else if (z <= 4.2d-43) then
        tmp = x
    else if (z <= 1.25d+28) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -1.7e+276) {
		tmp = t_0;
	} else if (z <= -1.45e-27) {
		tmp = t_1;
	} else if (z <= 4.2e-43) {
		tmp = x;
	} else if (z <= 1.25e+28) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = x * (y * z)
	tmp = 0
	if z <= -1.7e+276:
		tmp = t_0
	elif z <= -1.45e-27:
		tmp = t_1
	elif z <= 4.2e-43:
		tmp = x
	elif z <= 1.25e+28:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -1.7e+276)
		tmp = t_0;
	elseif (z <= -1.45e-27)
		tmp = t_1;
	elseif (z <= 4.2e-43)
		tmp = x;
	elseif (z <= 1.25e+28)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -1.7e+276)
		tmp = t_0;
	elseif (z <= -1.45e-27)
		tmp = t_1;
	elseif (z <= 4.2e-43)
		tmp = x;
	elseif (z <= 1.25e+28)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+276], t$95$0, If[LessEqual[z, -1.45e-27], t$95$1, If[LessEqual[z, 4.2e-43], x, If[LessEqual[z, 1.25e+28], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.69999999999999992e276 or 1.24999999999999989e28 < z

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0 66.4%

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

   4. Taylor expanded in z around inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. distribute-rgt-neg-out 66.4%

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

   6. Simplified 66.4%

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

   if -1.69999999999999992e276 < z < -1.45000000000000002e-27 or 4.2000000000000001e-43 < z < 1.24999999999999989e28

   1. Initial program 97.3%

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

   3. Taylor expanded in y around inf 62.6%

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

      1. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   if -1.45000000000000002e-27 < z < 4.2000000000000001e-43

   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 80.2%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+276}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+25} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.3e+25) (not (<= z 1.0)))
   (* (* x z) (+ y -1.0))
   (* x (+ 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.3e+25) || !(z <= 1.0)) {
		tmp = (x * z) * (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 <= (-4.3d+25)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x * z) * (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 <= -4.3e+25) || !(z <= 1.0)) {
		tmp = (x * z) * (y + -1.0);
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.3e+25) or not (z <= 1.0):
		tmp = (x * z) * (y + -1.0)
	else:
		tmp = x * (1.0 + (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.3e+25) || !(z <= 1.0))
		tmp = Float64(Float64(x * z) * 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 <= -4.3e+25) || ~((z <= 1.0)))
		tmp = (x * z) * (y + -1.0);
	else
		tmp = x * (1.0 + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.3e+25], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x * z), $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 < -4.29999999999999998e25 or 1 < z

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0 94.6%

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

   4. Taylor expanded in z around inf 94.4%

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

      1. sub-neg 94.4%

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

      2. metadata-eval 94.4%

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

      3. associate-*r* 99.8%

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

   6. Simplified 99.8%

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

   if -4.29999999999999998e25 < 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 98.5%

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

      1. *-commutative 98.5%

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

      2. *-commutative 98.5%

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

      3. distribute-rgt1-in 98.5%

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

   6. Applied egg-rr 98.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+25} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-35} \lor \neg \left(z \leq 2.5 \cdot 10^{-43}\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.2e-35) (not (<= z 2.5e-43))) (* (* x z) (+ y -1.0)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e-35) || !(z <= 2.5e-43)) {
		tmp = (x * z) * (y + -1.0);
	} 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 <= (-4.2d-35)) .or. (.not. (z <= 2.5d-43))) then
        tmp = (x * z) * (y + (-1.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e-35) || !(z <= 2.5e-43)) {
		tmp = (x * z) * (y + -1.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.2e-35) or not (z <= 2.5e-43):
		tmp = (x * z) * (y + -1.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.2e-35) || !(z <= 2.5e-43))
		tmp = Float64(Float64(x * z) * Float64(y + -1.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.2e-35) || ~((z <= 2.5e-43)))
		tmp = (x * z) * (y + -1.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.2e-35], N[Not[LessEqual[z, 2.5e-43]], $MachinePrecision]], N[(N[(x * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e-35 or 2.50000000000000009e-43 < z

   1. Initial program 95.1%

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

   3. Taylor expanded in y around 0 95.2%

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

   4. Taylor expanded in z around inf 91.7%

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

      1. sub-neg 91.7%

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

      2. metadata-eval 91.7%

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

      3. associate-*r* 96.4%

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

   6. Simplified 96.4%

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

   if -4.2e-35 < z < 2.50000000000000009e-43

   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 80.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-35} \lor \neg \left(z \leq 2.5 \cdot 10^{-43}\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-35} \lor \neg \left(z \leq 4.3 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e-35) (not (<= z 4.3e-42))) (* x (* z (+ y -1.0))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e-35) || !(z <= 4.3e-42)) {
		tmp = x * (z * (y + -1.0));
	} 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 <= (-1d-35)) .or. (.not. (z <= 4.3d-42))) then
        tmp = x * (z * (y + (-1.0d0)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e-35) || !(z <= 4.3e-42)) {
		tmp = x * (z * (y + -1.0));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1e-35) or not (z <= 4.3e-42):
		tmp = x * (z * (y + -1.0))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1e-35) || !(z <= 4.3e-42))
		tmp = Float64(x * Float64(z * Float64(y + -1.0)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1e-35) || ~((z <= 4.3e-42)))
		tmp = x * (z * (y + -1.0));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1e-35], N[Not[LessEqual[z, 4.3e-42]], $MachinePrecision]], N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000001e-35 or 4.3000000000000001e-42 < z

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf 91.7%

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

   if -1.00000000000000001e-35 < z < 4.3000000000000001e-42

   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 80.6%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-35} \lor \neg \left(z \leq 4.3 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \left(y \cdot z - z\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.1e-35)
   (* x (- (* y z) z))
   (if (<= z 5.5e-41) x (* x (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.1e-35) {
		tmp = x * ((y * z) - z);
	} else if (z <= 5.5e-41) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-3.1d-35)) then
        tmp = x * ((y * z) - z)
    else if (z <= 5.5d-41) then
        tmp = x
    else
        tmp = 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 (z <= -3.1e-35) {
		tmp = x * ((y * z) - z);
	} else if (z <= 5.5e-41) {
		tmp = x;
	} else {
		tmp = x * (z * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.1e-35:
		tmp = x * ((y * z) - z)
	elif z <= 5.5e-41:
		tmp = x
	else:
		tmp = x * (z * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.1e-35)
		tmp = Float64(x * Float64(Float64(y * z) - z));
	elseif (z <= 5.5e-41)
		tmp = x;
	else
		tmp = Float64(x * Float64(z * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.1e-35)
		tmp = x * ((y * z) - z);
	elseif (z <= 5.5e-41)
		tmp = x;
	else
		tmp = x * (z * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.1e-35], N[(x * N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-41], x, N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.10000000000000012e-35

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 94.5%

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

      1. distribute-rgt-out-- 94.5%

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

      2. *-un-lft-identity 94.5%

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

   5. Applied egg-rr 94.5%

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

   if -3.10000000000000012e-35 < z < 5.50000000000000022e-41

   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 80.6%

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

   if 5.50000000000000022e-41 < z

   1. Initial program 93.2%

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

   3. Taylor expanded in z around inf 88.9%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \left(y \cdot z - z\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+68} \lor \neg \left(y \leq 9 \cdot 10^{+60}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.25e+68) (not (<= y 9e+60))) (* x (* y z)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.25e+68) || !(y <= 9e+60)) {
		tmp = x * (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 <= (-1.25d+68)) .or. (.not. (y <= 9d+60))) then
        tmp = x * (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 <= -1.25e+68) || !(y <= 9e+60)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.25e+68) or not (y <= 9e+60):
		tmp = x * (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.25e+68) || !(y <= 9e+60))
		tmp = Float64(x * 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 <= -1.25e+68) || ~((y <= 9e+60)))
		tmp = x * (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.25e+68], N[Not[LessEqual[y, 9e+60]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2500000000000001e68 or 9.00000000000000026e60 < y

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf 72.1%

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

      1. *-commutative 72.1%

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

   5. Simplified 72.1%

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

   if -1.2500000000000001e68 < y < 9.00000000000000026e60

   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 96.8%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+68} \lor \neg \left(y \leq 9 \cdot 10^{+60}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 10^{+61}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.3e+68)
   (* z (* y x))
   (if (<= y 1e+61) (- x (* x z)) (* x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e+68) {
		tmp = z * (y * x);
	} else if (y <= 1e+61) {
		tmp = x - (x * 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 <= (-1.3d+68)) then
        tmp = z * (y * x)
    else if (y <= 1d+61) then
        tmp = x - (x * 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 <= -1.3e+68) {
		tmp = z * (y * x);
	} else if (y <= 1e+61) {
		tmp = x - (x * z);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.3e+68:
		tmp = z * (y * x)
	elif y <= 1e+61:
		tmp = x - (x * z)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.3e+68)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 1e+61)
		tmp = Float64(x - Float64(x * 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 <= -1.3e+68)
		tmp = z * (y * x);
	elseif (y <= 1e+61)
		tmp = x - (x * z);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.3e+68], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+61], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2999999999999999e68

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf 75.6%

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

      1. associate-*r* 77.7%

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

   5. Simplified 77.7%

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

   if -1.2999999999999999e68 < y < 9.99999999999999949e60

   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 0 100.0%

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

      1. sub-neg 100.0%

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

      2. associate-+l+ 100.0%

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

      3. sub-neg 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. distribute-rgt-out-- 99.9%

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

      6. +-commutative 99.9%

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

      7. distribute-rgt-out 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. *-commutative 100.0%

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

      10. associate-*r* 100.0%

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

      11. *-commutative 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 96.8%

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

      1. neg-mul-1 96.8%

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

      2. distribute-lft-neg-in 96.8%

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

   8. Simplified 96.8%

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

      1. +-commutative 96.8%

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

      2. distribute-lft-neg-out 96.8%

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

      3. unsub-neg 96.8%

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

      4. *-commutative 96.8%

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

   10. Applied egg-rr 96.8%

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

   if 9.99999999999999949e60 < y

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf 70.0%

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

      1. *-commutative 70.0%

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

   5. Simplified 70.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 10^{+61}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+67}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8e+67)
   (* z (* y x))
   (if (<= y 9e+60) (* x (- 1.0 z)) (* x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+67) {
		tmp = z * (y * x);
	} else if (y <= 9e+60) {
		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 <= (-8d+67)) then
        tmp = z * (y * x)
    else if (y <= 9d+60) 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 <= -8e+67) {
		tmp = z * (y * x);
	} else if (y <= 9e+60) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8e+67:
		tmp = z * (y * x)
	elif y <= 9e+60:
		tmp = x * (1.0 - z)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8e+67)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 9e+60)
		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 <= -8e+67)
		tmp = z * (y * x);
	elseif (y <= 9e+60)
		tmp = x * (1.0 - z);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8e+67], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+60], 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 < -7.99999999999999986e67

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf 75.6%

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

      1. associate-*r* 77.7%

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

   5. Simplified 77.7%

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

   if -7.99999999999999986e67 < y < 9.00000000000000026e60

   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 96.8%

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

   if 9.00000000000000026e60 < y

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf 70.0%

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

      1. *-commutative 70.0%

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

   5. Simplified 70.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+67}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+25} \lor \neg \left(z \leq 1.05\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.3e+25) (not (<= z 1.05))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.3e+25) || !(z <= 1.05)) {
		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 <= (-4.3d+25)) .or. (.not. (z <= 1.05d0))) 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 <= -4.3e+25) || !(z <= 1.05)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.3e+25) or not (z <= 1.05):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.3e+25) || !(z <= 1.05))
		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 <= -4.3e+25) || ~((z <= 1.05)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.3e+25], N[Not[LessEqual[z, 1.05]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.29999999999999998e25 or 1.05000000000000004 < z

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0 57.4%

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

   4. Taylor expanded in z around inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. distribute-rgt-neg-out 57.4%

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

   6. Simplified 57.4%

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

   if -4.29999999999999998e25 < z < 1.05000000000000004

   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 73.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+25} \lor \neg \left(z \leq 1.05\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 4e+15) (* x (+ 1.0 (* z (+ y -1.0)))) (* (* x z) (+ y -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 4e+15) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = (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 (z <= 4d+15) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = (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 (z <= 4e+15) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = (x * z) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 4e+15:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = (x * z) * (y + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 4e+15)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(Float64(x * z) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 4e+15)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = (x * z) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 4e+15], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4e15

   1. Initial program 98.9%

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

   if 4e15 < z

   1. Initial program 91.9%

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

   3. Taylor expanded in y around 0 91.9%

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

   4. Taylor expanded in z around inf 91.9%

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

      1. sub-neg 91.9%

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

      2. metadata-eval 91.9%

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

      3. associate-*r* 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((x * z) * (y + (-1.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

3. Taylor expanded in y around 0 97.3%

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

   1. sub-neg 97.3%

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

   2. associate-+l+ 97.3%

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

   3. sub-neg 97.3%

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

   4. *-un-lft-identity 97.3%

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

   5. distribute-rgt-out-- 97.3%

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

   6. +-commutative 97.3%

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

   7. distribute-rgt-out 97.3%

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

   8. *-un-lft-identity 97.3%

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

   9. *-commutative 97.3%

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

   10. associate-*r* 98.2%

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

   11. *-commutative 98.2%

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

   12. sub-neg 98.2%

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

   13. metadata-eval 98.2%

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

5. Applied egg-rr 98.2%

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

6. Final simplification 98.2%

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

Alternative 13: 38.5% 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 97.3%

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

3. Taylor expanded in z around 0 39.7%

   \[\leadsto \color{blue}{x} \]
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 2024135 
(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))))