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

Percentage Accurate: 95.8% → 98.9%

Time: 8.7s

Alternatives: 10

Speedup: 0.8×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0021:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.0021)
   (* z (* x (+ y -1.0)))
   (if (<= z 1.0) (+ x (* x (* y z))) (* z (- (* y x) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0021) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 1.0) {
		tmp = x + (x * (y * z));
	} else {
		tmp = z * ((y * x) - 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 <= (-0.0021d0)) then
        tmp = z * (x * (y + (-1.0d0)))
    else if (z <= 1.0d0) then
        tmp = x + (x * (y * z))
    else
        tmp = z * ((y * x) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0021) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 1.0) {
		tmp = x + (x * (y * z));
	} else {
		tmp = z * ((y * x) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.0021:
		tmp = z * (x * (y + -1.0))
	elif z <= 1.0:
		tmp = x + (x * (y * z))
	else:
		tmp = z * ((y * x) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.0021)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (z <= 1.0)
		tmp = Float64(x + Float64(x * Float64(y * z)));
	else
		tmp = Float64(z * Float64(Float64(y * x) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.0021)
		tmp = z * (x * (y + -1.0));
	elseif (z <= 1.0)
		tmp = x + (x * (y * z));
	else
		tmp = z * ((y * x) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.0021], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.00209999999999999987

   1. Initial program 90.6%

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

   2. Taylor expanded in z around inf 89.0%

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

      1. *-commutative 89.0%

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

      2. associate-*l* 98.2%

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

      3. sub-neg 98.2%

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

      4. metadata-eval 98.2%

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

   4. Simplified 98.2%

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

   if -0.00209999999999999987 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   if 1 < z

   1. Initial program 92.0%

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

   2. Taylor expanded in z around inf 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-*l* 99.3%

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

      3. sub-neg 99.3%

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

      4. metadata-eval 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in y around 0 99.3%

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

      1. neg-mul-1 99.3%

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

      2. +-commutative 99.3%

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

      3. fma-def 99.3%

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

      4. fma-neg 99.3%

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

   7. Simplified 99.3%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0021:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \]

Alternative 2: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+219}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* y z))))
   (if (<= z -1.35e+219)
     t_0
     (if (<= z -3.6e+186)
       t_1
       (if (<= z -1.0)
         t_0
         (if (<= z 1.2e-62) x (if (<= z 1.35e+41) 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 <= -1.35e+219) {
		tmp = t_0;
	} else if (z <= -3.6e+186) {
		tmp = t_1;
	} else if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1.2e-62) {
		tmp = x;
	} else if (z <= 1.35e+41) {
		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 <= (-1.35d+219)) then
        tmp = t_0
    else if (z <= (-3.6d+186)) then
        tmp = t_1
    else if (z <= (-1.0d0)) then
        tmp = t_0
    else if (z <= 1.2d-62) then
        tmp = x
    else if (z <= 1.35d+41) 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 <= -1.35e+219) {
		tmp = t_0;
	} else if (z <= -3.6e+186) {
		tmp = t_1;
	} else if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1.2e-62) {
		tmp = x;
	} else if (z <= 1.35e+41) {
		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 <= -1.35e+219:
		tmp = t_0
	elif z <= -3.6e+186:
		tmp = t_1
	elif z <= -1.0:
		tmp = t_0
	elif z <= 1.2e-62:
		tmp = x
	elif z <= 1.35e+41:
		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 <= -1.35e+219)
		tmp = t_0;
	elseif (z <= -3.6e+186)
		tmp = t_1;
	elseif (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1.2e-62)
		tmp = x;
	elseif (z <= 1.35e+41)
		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 <= -1.35e+219)
		tmp = t_0;
	elseif (z <= -3.6e+186)
		tmp = t_1;
	elseif (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1.2e-62)
		tmp = x;
	elseif (z <= 1.35e+41)
		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, -1.35e+219], t$95$0, If[LessEqual[z, -3.6e+186], t$95$1, If[LessEqual[z, -1.0], t$95$0, If[LessEqual[z, 1.2e-62], x, If[LessEqual[z, 1.35e+41], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3499999999999999e219 or -3.6000000000000002e186 < z < -1 or 1.35e41 < z

   1. Initial program 92.1%

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

   2. Taylor expanded in y around 0 65.0%

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

      1. sub-neg 65.0%

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

      2. distribute-rgt-in 65.0%

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

      3. *-lft-identity 65.0%

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

      4. distribute-lft-neg-out 65.0%

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

      5. *-commutative 65.0%

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

      6. unsub-neg 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in z around inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. *-commutative 64.7%

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

      3. distribute-rgt-neg-in 64.7%

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

   7. Simplified 64.7%

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

   if -1.3499999999999999e219 < z < -3.6000000000000002e186 or 1.19999999999999992e-62 < z < 1.35e41

   1. Initial program 90.0%

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

   2. Taylor expanded in y around inf 64.9%

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

      1. *-commutative 64.9%

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

   4. Simplified 64.9%

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

   if -1 < z < 1.19999999999999992e-62

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 78.4%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+219}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 97.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 50.6%

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

   2. Taylor expanded in y around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. unsub-neg 50.6%

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

      3. *-commutative 50.6%

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

   4. Simplified 50.6%

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

   5. Taylor expanded in y around inf 50.6%

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

      1. *-commutative 50.6%

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

      2. associate-*r* 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.9%

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

   7. Simplified 99.9%

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

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

   1. Initial program 98.4%

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

   2. Taylor expanded in y around 0 98.4%

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

      1. mul-1-neg 98.4%

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

      2. unsub-neg 98.4%

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

      3. *-commutative 98.4%

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

   4. Simplified 98.4%

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

4. Final simplification 98.5%

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

Alternative 4: 97.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 50.6%

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

   2. Taylor expanded in y around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. unsub-neg 50.6%

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

      3. *-commutative 50.6%

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

   4. Simplified 50.6%

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

   5. Taylor expanded in y around inf 50.6%

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

      1. *-commutative 50.6%

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

      2. associate-*r* 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.9%

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

   7. Simplified 99.9%

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

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

   1. Initial program 98.4%

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

4. Final simplification 98.5%

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

Alternative 5: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot x\right)\\ t_1 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -9.4 \cdot 10^{+185}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+99}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z x))) (t_1 (* z (- x))))
   (if (<= z -9.4e+185)
     t_0
     (if (<= z -1.0)
       t_1
       (if (<= z 1.36e-62) x (if (<= z 1.75e+99) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * x);
	double t_1 = z * -x;
	double tmp;
	if (z <= -9.4e+185) {
		tmp = t_0;
	} else if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 1.36e-62) {
		tmp = x;
	} else if (z <= 1.75e+99) {
		tmp = t_0;
	} 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 = y * (z * x)
    t_1 = z * -x
    if (z <= (-9.4d+185)) then
        tmp = t_0
    else if (z <= (-1.0d0)) then
        tmp = t_1
    else if (z <= 1.36d-62) then
        tmp = x
    else if (z <= 1.75d+99) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z * x);
	double t_1 = z * -x;
	double tmp;
	if (z <= -9.4e+185) {
		tmp = t_0;
	} else if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 1.36e-62) {
		tmp = x;
	} else if (z <= 1.75e+99) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * x)
	t_1 = z * -x
	tmp = 0
	if z <= -9.4e+185:
		tmp = t_0
	elif z <= -1.0:
		tmp = t_1
	elif z <= 1.36e-62:
		tmp = x
	elif z <= 1.75e+99:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * x))
	t_1 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -9.4e+185)
		tmp = t_0;
	elseif (z <= -1.0)
		tmp = t_1;
	elseif (z <= 1.36e-62)
		tmp = x;
	elseif (z <= 1.75e+99)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * x);
	t_1 = z * -x;
	tmp = 0.0;
	if (z <= -9.4e+185)
		tmp = t_0;
	elseif (z <= -1.0)
		tmp = t_1;
	elseif (z <= 1.36e-62)
		tmp = x;
	elseif (z <= 1.75e+99)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[z, -9.4e+185], t$95$0, If[LessEqual[z, -1.0], t$95$1, If[LessEqual[z, 1.36e-62], x, If[LessEqual[z, 1.75e+99], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.39999999999999945e185 or 1.35999999999999999e-62 < z < 1.7499999999999999e99

   1. Initial program 86.9%

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

   2. Taylor expanded in y around inf 58.0%

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

      1. mul-1-neg 58.0%

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

      2. distribute-lft-neg-out 58.0%

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

      3. *-commutative 58.0%

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

   4. Simplified 58.0%

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

      1. *-commutative 58.0%

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

      2. cancel-sign-sub 58.0%

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

      3. *-commutative 58.0%

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

      4. +-commutative 58.0%

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

      5. add-cube-cbrt 57.5%

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

      6. associate-*l* 57.5%

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

      7. fma-def 57.5%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(\sqrt[3]{z} \cdot \sqrt[3]{z}, \sqrt[3]{z} \cdot y, 1\right)} \]

      8. pow2 57.5%

         \[\leadsto x \cdot \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z} \cdot y, 1\right) \]

   6. Applied egg-rr 57.5%

      \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot y, 1\right)} \]

   7. Taylor expanded in y around inf 52.2%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. pow-base-1 52.2%

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

      2. *-commutative 52.2%

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

      3. *-lft-identity 52.2%

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

      4. associate-*r* 68.4%

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

      5. *-commutative 68.4%

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

   9. Simplified 68.4%

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

   if -9.39999999999999945e185 < z < -1 or 1.7499999999999999e99 < z

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0 67.7%

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

      1. sub-neg 67.7%

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

      2. distribute-rgt-in 67.7%

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

      3. *-lft-identity 67.7%

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

      4. distribute-lft-neg-out 67.7%

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

      5. *-commutative 67.7%

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

      6. unsub-neg 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in z around inf 67.3%

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

      1. mul-1-neg 67.3%

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

      2. *-commutative 67.3%

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

      3. distribute-rgt-neg-in 67.3%

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

   7. Simplified 67.3%

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

   if -1 < z < 1.35999999999999999e-62

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 78.4%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 6: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-23} \lor \neg \left(z \leq 1.36 \cdot 10^{-62}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.7e-23) (not (<= z 1.36e-62)))
   (* z (* x (+ y -1.0)))
   (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.7e-23) || !(z <= 1.36e-62)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.7d-23)) .or. (.not. (z <= 1.36d-62))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x - (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.7e-23) || !(z <= 1.36e-62)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.7e-23) or not (z <= 1.36e-62):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.7e-23) || !(z <= 1.36e-62))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.7e-23) || ~((z <= 1.36e-62)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.7e-23], N[Not[LessEqual[z, 1.36e-62]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999985e-23 or 1.35999999999999999e-62 < z

   1. Initial program 92.1%

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

   2. Taylor expanded in z around inf 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-*l* 95.5%

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

      3. sub-neg 95.5%

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

      4. metadata-eval 95.5%

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

   4. Simplified 95.5%

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

   if -2.69999999999999985e-23 < z < 1.35999999999999999e-62

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.9%

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

      1. sub-neg 81.9%

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

      2. distribute-rgt-in 81.9%

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

      3. *-lft-identity 81.9%

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

      4. distribute-lft-neg-out 81.9%

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

      5. *-commutative 81.9%

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

      6. unsub-neg 81.9%

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

   4. Simplified 81.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-23} \lor \neg \left(z \leq 1.36 \cdot 10^{-62}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]

Alternative 7: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.7 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-63}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.7e-23)
   (* z (* x (+ y -1.0)))
   (if (<= z 3.1e-63) (- x (* z x)) (* z (- (* y x) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.7e-23) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 3.1e-63) {
		tmp = x - (z * x);
	} else {
		tmp = z * ((y * x) - 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 <= (-9.7d-23)) then
        tmp = z * (x * (y + (-1.0d0)))
    else if (z <= 3.1d-63) then
        tmp = x - (z * x)
    else
        tmp = z * ((y * x) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.7e-23) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 3.1e-63) {
		tmp = x - (z * x);
	} else {
		tmp = z * ((y * x) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.7e-23:
		tmp = z * (x * (y + -1.0))
	elif z <= 3.1e-63:
		tmp = x - (z * x)
	else:
		tmp = z * ((y * x) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.7e-23)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (z <= 3.1e-63)
		tmp = Float64(x - Float64(z * x));
	else
		tmp = Float64(z * Float64(Float64(y * x) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.7e-23)
		tmp = z * (x * (y + -1.0));
	elseif (z <= 3.1e-63)
		tmp = x - (z * x);
	else
		tmp = z * ((y * x) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.7e-23], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-63], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.7000000000000003e-23

   1. Initial program 91.3%

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

   2. Taylor expanded in z around inf 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-*l* 95.9%

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

      3. sub-neg 95.9%

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

      4. metadata-eval 95.9%

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

   4. Simplified 95.9%

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

   if -9.7000000000000003e-23 < z < 3.09999999999999984e-63

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.9%

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

      1. sub-neg 81.9%

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

      2. distribute-rgt-in 81.9%

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

      3. *-lft-identity 81.9%

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

      4. distribute-lft-neg-out 81.9%

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

      5. *-commutative 81.9%

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

      6. unsub-neg 81.9%

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

   4. Simplified 81.9%

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

   if 3.09999999999999984e-63 < z

   1. Initial program 92.8%

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

   2. Taylor expanded in z around inf 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-*l* 95.2%

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

      3. sub-neg 95.2%

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

      4. metadata-eval 95.2%

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

   4. Simplified 95.2%

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

   5. Taylor expanded in y around 0 95.2%

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

      1. neg-mul-1 95.2%

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

      2. +-commutative 95.2%

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

      3. fma-def 95.2%

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

      4. fma-neg 95.2%

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

   7. Simplified 95.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.7 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-63}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \]

Alternative 8: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+52} \lor \neg \left(y \leq 2.1 \cdot 10^{+59}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.6e+52) (not (<= y 2.1e+59))) (* y (* z x)) (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.6e+52) || !(y <= 2.1e+59)) {
		tmp = y * (z * x);
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.6d+52)) .or. (.not. (y <= 2.1d+59))) then
        tmp = y * (z * x)
    else
        tmp = x - (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.6e+52) || !(y <= 2.1e+59)) {
		tmp = y * (z * x);
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.6e+52) or not (y <= 2.1e+59):
		tmp = y * (z * x)
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.6e+52) || !(y <= 2.1e+59))
		tmp = Float64(y * Float64(z * x));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.6e+52) || ~((y <= 2.1e+59)))
		tmp = y * (z * x);
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.6e+52], N[Not[LessEqual[y, 2.1e+59]], $MachinePrecision]], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e52 or 2.09999999999999984e59 < y

   1. Initial program 87.1%

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

   2. Taylor expanded in y around inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. distribute-lft-neg-out 87.1%

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

      3. *-commutative 87.1%

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

   4. Simplified 87.1%

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

      1. *-commutative 87.1%

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

      2. cancel-sign-sub 87.1%

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

      3. *-commutative 87.1%

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

      4. +-commutative 87.1%

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

      5. add-cube-cbrt 86.2%

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

      6. associate-*l* 86.3%

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

      7. fma-def 86.3%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(\sqrt[3]{z} \cdot \sqrt[3]{z}, \sqrt[3]{z} \cdot y, 1\right)} \]

      8. pow2 86.3%

         \[\leadsto x \cdot \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z} \cdot y, 1\right) \]

   6. Applied egg-rr 86.3%

      \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot y, 1\right)} \]

   7. Taylor expanded in y around inf 70.7%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. pow-base-1 70.7%

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

      2. *-commutative 70.7%

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

      3. *-lft-identity 70.7%

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

      4. associate-*r* 81.9%

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

      5. *-commutative 81.9%

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

   9. Simplified 81.9%

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

   if -2.6e52 < y < 2.09999999999999984e59

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 94.0%

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

      1. sub-neg 94.0%

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

      2. distribute-rgt-in 94.0%

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

      3. *-lft-identity 94.0%

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

      4. distribute-lft-neg-out 94.0%

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

      5. *-commutative 94.0%

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

      6. unsub-neg 94.0%

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

   4. Simplified 94.0%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+52} \lor \neg \left(y \leq 2.1 \cdot 10^{+59}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]

Alternative 9: 64.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 4.9\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 4.9))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 4.9)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 4.9d0))) then
        tmp = z * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 4.9)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 4.9):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 4.9))
		tmp = Float64(z * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 4.9)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 4.9]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 4.9000000000000004 < z

   1. Initial program 91.1%

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

   2. Taylor expanded in y around 0 59.1%

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

      1. sub-neg 59.1%

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

      2. distribute-rgt-in 59.1%

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

      3. *-lft-identity 59.1%

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

      4. distribute-lft-neg-out 59.1%

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

      5. *-commutative 59.1%

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

      6. unsub-neg 59.1%

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

   4. Simplified 59.1%

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

   5. Taylor expanded in z around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. *-commutative 58.5%

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

      3. distribute-rgt-neg-in 58.5%

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

   7. Simplified 58.5%

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

   if -1 < z < 4.9000000000000004

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 75.2%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 4.9\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 38.0% 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 95.2%

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

2. Taylor expanded in z around 0 36.5%

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

3. Final simplification 36.5%

   \[\leadsto x \]

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 2023287 
(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))))