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

Percentage Accurate: 96.0% → 96.8%

Time: 10.1s

Alternatives: 9

Speedup: 0.8×

• 20.8% 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: 96.0% 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: 96.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 9.4 \cdot 10^{+54}\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1) (not (<= z 9.4e+54)))
   (* (+ y -1.0) (* x z))
   (* x (+ 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1) || !(z <= 9.4e+54)) {
		tmp = (y + -1.0) * (x * z);
	} 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 <= (-1.1d0)) .or. (.not. (z <= 9.4d+54))) then
        tmp = (y + (-1.0d0)) * (x * z)
    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 <= -1.1) || !(z <= 9.4e+54)) {
		tmp = (y + -1.0) * (x * z);
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1) or not (z <= 9.4e+54):
		tmp = (y + -1.0) * (x * z)
	else:
		tmp = x * (1.0 + (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1) || !(z <= 9.4e+54))
		tmp = Float64(Float64(y + -1.0) * Float64(x * z));
	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 <= -1.1) || ~((z <= 9.4e+54)))
		tmp = (y + -1.0) * (x * z);
	else
		tmp = x * (1.0 + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1], N[Not[LessEqual[z, 9.4e+54]], $MachinePrecision]], N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001 or 9.39999999999999985e54 < z

   1. Initial program 93.5%

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

   2. Taylor expanded in z around inf 93.1%

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

      1. associate-*r* 99.6%

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

      2. *-commutative 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

   4. Simplified 99.6%

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

   if -1.1000000000000001 < z < 9.39999999999999985e54

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. distribute-lft-neg-out 99.1%

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

      3. *-commutative 99.1%

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

   4. Simplified 99.1%

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

   5. Taylor expanded in z around 0 99.1%

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

      1. *-commutative 99.1%

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

      2. distribute-rgt1-in 99.1%

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

   7. Applied egg-rr 99.1%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 9.4 \cdot 10^{+54}\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]

Alternative 2: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = (y + -1.0) * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

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

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = (y + -1.0) * (x * z)
	else:
		tmp = t_0
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = (y + -1.0) * (x * z);
	else
		tmp = t_0;
	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]}, If[LessEqual[t$95$0, (-Infinity)], N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < -inf.0

   1. Initial program 81.8%

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

   2. Taylor expanded in z around inf 81.8%

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

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   if -inf.0 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z)))

   1. Initial program 99.1%

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

4. Final simplification 99.2%

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

Alternative 3: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+181}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -27.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -9.5e+181)
     (* y (* x z))
     (if (<= z -27.5)
       t_0
       (if (<= z 1.25e-48) x (if (<= z 7.2e+84) (* x (* y z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -9.5e+181) {
		tmp = y * (x * z);
	} else if (z <= -27.5) {
		tmp = t_0;
	} else if (z <= 1.25e-48) {
		tmp = x;
	} else if (z <= 7.2e+84) {
		tmp = x * (y * z);
	} 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) :: tmp
    t_0 = x * -z
    if (z <= (-9.5d+181)) then
        tmp = y * (x * z)
    else if (z <= (-27.5d0)) then
        tmp = t_0
    else if (z <= 1.25d-48) then
        tmp = x
    else if (z <= 7.2d+84) then
        tmp = x * (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -9.5e+181) {
		tmp = y * (x * z);
	} else if (z <= -27.5) {
		tmp = t_0;
	} else if (z <= 1.25e-48) {
		tmp = x;
	} else if (z <= 7.2e+84) {
		tmp = x * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -9.5e+181:
		tmp = y * (x * z)
	elif z <= -27.5:
		tmp = t_0
	elif z <= 1.25e-48:
		tmp = x
	elif z <= 7.2e+84:
		tmp = x * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -9.5e+181)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -27.5)
		tmp = t_0;
	elseif (z <= 1.25e-48)
		tmp = x;
	elseif (z <= 7.2e+84)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -9.5e+181)
		tmp = y * (x * z);
	elseif (z <= -27.5)
		tmp = t_0;
	elseif (z <= 1.25e-48)
		tmp = x;
	elseif (z <= 7.2e+84)
		tmp = x * (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -9.5e+181], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -27.5], t$95$0, If[LessEqual[z, 1.25e-48], x, If[LessEqual[z, 7.2e+84], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.50000000000000032e181

   1. Initial program 88.9%

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

      1. flip-- 88.9%

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

      2. associate-*l/ 84.9%

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

      3. metadata-eval 84.9%

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

   3. Applied egg-rr 84.9%

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

   4. Taylor expanded in y around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-*r* 74.9%

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

   6. Simplified 74.9%

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

   if -9.50000000000000032e181 < z < -27.5 or 7.1999999999999999e84 < z

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 94.8%

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

      1. *-commutative 94.8%

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

      2. associate-*l* 99.5%

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

      3. sub-neg 99.5%

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

      4. metadata-eval 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in y around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. distribute-rgt-neg-in 70.4%

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

   7. Simplified 70.4%

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

   if -27.5 < z < 1.25e-48

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.3%

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

   if 1.25e-48 < z < 7.1999999999999999e84

   1. Initial program 95.6%

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

   2. Taylor expanded in y around inf 70.4%

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

      1. *-commutative 70.4%

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

   4. Simplified 70.4%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+181}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -27.5:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+182}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -27.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+87}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -2.6e+182)
     (* y (* x z))
     (if (<= z -27.5)
       t_0
       (if (<= z 1.04e-48) x (if (<= z 3.8e+87) (* z (* x y)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -2.6e+182) {
		tmp = y * (x * z);
	} else if (z <= -27.5) {
		tmp = t_0;
	} else if (z <= 1.04e-48) {
		tmp = x;
	} else if (z <= 3.8e+87) {
		tmp = z * (x * y);
	} 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) :: tmp
    t_0 = x * -z
    if (z <= (-2.6d+182)) then
        tmp = y * (x * z)
    else if (z <= (-27.5d0)) then
        tmp = t_0
    else if (z <= 1.04d-48) then
        tmp = x
    else if (z <= 3.8d+87) then
        tmp = z * (x * y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -2.6e+182) {
		tmp = y * (x * z);
	} else if (z <= -27.5) {
		tmp = t_0;
	} else if (z <= 1.04e-48) {
		tmp = x;
	} else if (z <= 3.8e+87) {
		tmp = z * (x * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -2.6e+182:
		tmp = y * (x * z)
	elif z <= -27.5:
		tmp = t_0
	elif z <= 1.04e-48:
		tmp = x
	elif z <= 3.8e+87:
		tmp = z * (x * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -2.6e+182)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -27.5)
		tmp = t_0;
	elseif (z <= 1.04e-48)
		tmp = x;
	elseif (z <= 3.8e+87)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -2.6e+182)
		tmp = y * (x * z);
	elseif (z <= -27.5)
		tmp = t_0;
	elseif (z <= 1.04e-48)
		tmp = x;
	elseif (z <= 3.8e+87)
		tmp = z * (x * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -2.6e+182], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -27.5], t$95$0, If[LessEqual[z, 1.04e-48], x, If[LessEqual[z, 3.8e+87], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e182

   1. Initial program 88.9%

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

      1. flip-- 88.9%

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

      2. associate-*l/ 84.9%

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

      3. metadata-eval 84.9%

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

   3. Applied egg-rr 84.9%

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

   4. Taylor expanded in y around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-*r* 74.9%

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

   6. Simplified 74.9%

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

   if -2.6e182 < z < -27.5 or 3.80000000000000011e87 < z

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 94.8%

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

      1. *-commutative 94.8%

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

      2. associate-*l* 99.5%

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

      3. sub-neg 99.5%

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

      4. metadata-eval 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in y around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. distribute-rgt-neg-in 70.4%

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

   7. Simplified 70.4%

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

   if -27.5 < z < 1.03999999999999998e-48

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.3%

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

   if 1.03999999999999998e-48 < z < 3.80000000000000011e87

   1. Initial program 95.6%

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

      1. flip-- 82.4%

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

      2. associate-*l/ 78.0%

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

      3. metadata-eval 78.0%

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

   3. Applied egg-rr 78.0%

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

   4. Taylor expanded in y around inf 70.4%

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

      1. *-commutative 70.4%

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

      2. *-commutative 70.4%

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

      3. associate-*l* 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+182}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -27.5:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+87}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 5: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -27.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -27.5)
     t_0
     (if (<= z 9.2e-49) x (if (<= z 7e+84) (* x (* y z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -27.5) {
		tmp = t_0;
	} else if (z <= 9.2e-49) {
		tmp = x;
	} else if (z <= 7e+84) {
		tmp = x * (y * z);
	} 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) :: tmp
    t_0 = x * -z
    if (z <= (-27.5d0)) then
        tmp = t_0
    else if (z <= 9.2d-49) then
        tmp = x
    else if (z <= 7d+84) then
        tmp = x * (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -27.5) {
		tmp = t_0;
	} else if (z <= 9.2e-49) {
		tmp = x;
	} else if (z <= 7e+84) {
		tmp = x * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -27.5:
		tmp = t_0
	elif z <= 9.2e-49:
		tmp = x
	elif z <= 7e+84:
		tmp = x * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -27.5)
		tmp = t_0;
	elseif (z <= 9.2e-49)
		tmp = x;
	elseif (z <= 7e+84)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -27.5)
		tmp = t_0;
	elseif (z <= 9.2e-49)
		tmp = x;
	elseif (z <= 7e+84)
		tmp = x * (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -27.5], t$95$0, If[LessEqual[z, 9.2e-49], x, If[LessEqual[z, 7e+84], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -27.5 or 6.9999999999999998e84 < z

   1. Initial program 93.8%

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

   2. Taylor expanded in z around inf 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l* 99.5%

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

      3. sub-neg 99.5%

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

      4. metadata-eval 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in y around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. distribute-rgt-neg-in 65.2%

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

   7. Simplified 65.2%

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

   if -27.5 < z < 9.1999999999999996e-49

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.3%

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

   if 9.1999999999999996e-49 < z < 6.9999999999999998e84

   1. Initial program 95.6%

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

   2. Taylor expanded in y around inf 70.4%

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

      1. *-commutative 70.4%

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

   4. Simplified 70.4%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -27.5:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 6: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-25} \lor \neg \left(z \leq 1.25 \cdot 10^{-48}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.3e-25) (not (<= z 1.25e-48)))
   (* z (* x (+ y -1.0)))
   (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e-25) || !(z <= 1.25e-48)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x - (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 <= (-1.3d-25)) .or. (.not. (z <= 1.25d-48))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x - (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e-25) || !(z <= 1.25e-48)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.3e-25) or not (z <= 1.25e-48):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.3e-25) || !(z <= 1.25e-48))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.3e-25) || ~((z <= 1.25e-48)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.3e-25], N[Not[LessEqual[z, 1.25e-48]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e-25 or 1.25e-48 < z

   1. Initial program 94.4%

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

   2. Taylor expanded in z around inf 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-*l* 96.0%

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

      3. sub-neg 96.0%

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

      4. metadata-eval 96.0%

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

   4. Simplified 96.0%

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

   if -1.3e-25 < z < 1.25e-48

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 81.5%

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

      1. sub-neg 81.5%

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

      2. distribute-rgt-in 81.5%

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

      3. *-lft-identity 81.5%

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

      4. distribute-lft-neg-out 81.5%

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

      5. *-commutative 81.5%

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

      6. unsub-neg 81.5%

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

   4. Simplified 81.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-25} \lor \neg \left(z \leq 1.25 \cdot 10^{-48}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]

Alternative 7: 81.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+124}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+143}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e+124)
   (* z (* x y))
   (if (<= y 7.6e+143) (- x (* x z)) (* y (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+124) {
		tmp = z * (x * y);
	} else if (y <= 7.6e+143) {
		tmp = x - (x * z);
	} else {
		tmp = y * (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 (y <= (-1.9d+124)) then
        tmp = z * (x * y)
    else if (y <= 7.6d+143) then
        tmp = x - (x * z)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+124) {
		tmp = z * (x * y);
	} else if (y <= 7.6e+143) {
		tmp = x - (x * z);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e+124:
		tmp = z * (x * y)
	elif y <= 7.6e+143:
		tmp = x - (x * z)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e+124)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 7.6e+143)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e+124)
		tmp = z * (x * y);
	elseif (y <= 7.6e+143)
		tmp = x - (x * z);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e+124], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e+143], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8999999999999999e124

   1. Initial program 92.7%

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

      1. flip-- 58.9%

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

      2. associate-*l/ 53.7%

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

      3. metadata-eval 53.7%

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

   3. Applied egg-rr 53.7%

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

   4. Taylor expanded in y around inf 82.2%

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

      1. *-commutative 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-*l* 87.0%

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

   6. Simplified 87.0%

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

   if -1.8999999999999999e124 < y < 7.60000000000000001e143

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.8%

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

      1. sub-neg 87.8%

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

      2. distribute-rgt-in 87.8%

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

      3. *-lft-identity 87.8%

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

      4. distribute-lft-neg-out 87.8%

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

      5. *-commutative 87.8%

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

      6. unsub-neg 87.8%

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

   4. Simplified 87.8%

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

   if 7.60000000000000001e143 < y

   1. Initial program 84.0%

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

      1. flip-- 49.3%

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

      2. associate-*l/ 46.1%

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

      3. metadata-eval 46.1%

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

   3. Applied egg-rr 46.1%

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

   4. Taylor expanded in y around inf 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-*r* 93.6%

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

   6. Simplified 93.6%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+124}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+143}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 8: 64.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -27.5 \lor \neg \left(z \leq 29000000000\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -27.5) (not (<= z 29000000000.0))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -27.5) || !(z <= 29000000000.0)) {
		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 <= (-27.5d0)) .or. (.not. (z <= 29000000000.0d0))) 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 <= -27.5) || !(z <= 29000000000.0)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -27.5) or not (z <= 29000000000.0):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -27.5) || !(z <= 29000000000.0))
		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 <= -27.5) || ~((z <= 29000000000.0)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -27.5], N[Not[LessEqual[z, 29000000000.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -27.5 or 2.9e10 < z

   1. Initial program 93.7%

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

   2. Taylor expanded in z around inf 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-*l* 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in y around 0 63.0%

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

      1. mul-1-neg 63.0%

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

      2. distribute-rgt-neg-in 63.0%

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

   7. Simplified 63.0%

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

   if -27.5 < z < 2.9e10

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 75.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -27.5 \lor \neg \left(z \leq 29000000000\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 38.8% 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 97.0%

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

2. Taylor expanded in z around 0 42.5%

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

3. Final simplification 42.5%

   \[\leadsto x \]

Developer target: 99.7% accurate, 0.3× 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 2023279 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

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