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

Percentage Accurate: 95.5% → 99.5%

Time: 8.2s

Alternatives: 8

Speedup: 0.6×

• 21.3% 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: 95.5% 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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+300}:\\ \;\;\;\;x \cdot \left(1 - \left(z - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)) (t_1 (* z (* x y))))
   (if (<= t_0 (- INFINITY))
     t_1
     (if (<= t_0 5e+300) (* x (- 1.0 (- z (* y z)))) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double t_1 = z * (x * y);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= 5e+300) {
		tmp = x * (1.0 - (z - (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double t_1 = z * (x * y);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= 5e+300) {
		tmp = x * (1.0 - (z - (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * z
	t_1 = z * (x * y)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= 5e+300:
		tmp = x * (1.0 - (z - (y * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= 5e+300)
		tmp = Float64(x * Float64(1.0 - Float64(z - Float64(y * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	t_1 = z * (x * y);
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= 5e+300)
		tmp = x * (1.0 - (z - (y * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, 5e+300], N[(x * N[(1.0 - N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -inf.0 or 5.00000000000000026e300 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 63.8%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 63.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 63.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x \cdot y\right), \color{blue}{z}\right) \]

      4. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   7. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 5.00000000000000026e300

   1. Initial program 99.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(z \cdot \color{blue}{\left(1 - y\right)}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right)\right) \]

      3. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(z \cdot 1 + \color{blue}{z \cdot \left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      4. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\mathsf{fma}\left(z, \color{blue}{1}, z \cdot \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\mathsf{fma}\left(z, 1, \mathsf{neg}\left(z \cdot y\right)\right)\right)\right)\right) \]

      6. fmm-undef N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(z \cdot 1 - \color{blue}{z \cdot y}\right)\right)\right) \]

      7. *-rgt-identity N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(z - \color{blue}{z} \cdot y\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \color{blue}{\left(z \cdot y\right)}\right)\right)\right) \]

      9. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right)\right)\right) \]

   4. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 5 \cdot 10^{+300}:\\ \;\;\;\;x \cdot \left(1 - \left(z - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+300}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)) (t_1 (* z (* x y))))
   (if (<= t_0 (- INFINITY))
     t_1
     (if (<= t_0 5e+300) (* x (+ 1.0 (* z (+ y -1.0)))) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double t_1 = z * (x * y);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= 5e+300) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double t_1 = z * (x * y);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= 5e+300) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * z
	t_1 = z * (x * y)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= 5e+300:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= 5e+300)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	t_1 = z * (x * y);
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= 5e+300)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, 5e+300], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -inf.0 or 5.00000000000000026e300 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 63.8%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 63.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 63.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x \cdot y\right), \color{blue}{z}\right) \]

      4. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   7. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 5.00000000000000026e300

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 5 \cdot 10^{+300}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.8e+119)
   (* y (* x z))
   (if (<= y 1.3e+36) (* x (- 1.0 z)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e+119) {
		tmp = y * (x * z);
	} else if (y <= 1.3e+36) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	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 <= (-6.8d+119)) then
        tmp = y * (x * z)
    else if (y <= 1.3d+36) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e+119) {
		tmp = y * (x * z);
	} else if (y <= 1.3e+36) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.8e+119:
		tmp = y * (x * z)
	elif y <= 1.3e+36:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.8e+119)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 1.3e+36)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.8e+119)
		tmp = y * (x * z);
	elseif (y <= 1.3e+36)
		tmp = x * (1.0 - z);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.8e+119], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+36], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.80000000000000027e119

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 70.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 70.9%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 88.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Applied egg-rr 88.4%

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

   if -6.80000000000000027e119 < y < 1.3000000000000001e36

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 - z\right)}\right) \]

      2. --lowering--.f64 94.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   5. Simplified 94.4%

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

   if 1.3000000000000001e36 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 72.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 72.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x \cdot y\right), \color{blue}{z}\right) \]

      4. *-lowering-*.f64 81.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   7. Applied egg-rr 81.1%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+120}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x y))))
   (if (<= y -1.1e+120) t_0 (if (<= y 3.8e+36) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * y);
	double tmp;
	if (y <= -1.1e+120) {
		tmp = t_0;
	} else if (y <= 3.8e+36) {
		tmp = x * (1.0 - 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 = z * (x * y)
    if (y <= (-1.1d+120)) then
        tmp = t_0
    else if (y <= 3.8d+36) then
        tmp = x * (1.0d0 - 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 = z * (x * y);
	double tmp;
	if (y <= -1.1e+120) {
		tmp = t_0;
	} else if (y <= 3.8e+36) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * y)
	tmp = 0
	if y <= -1.1e+120:
		tmp = t_0
	elif y <= 3.8e+36:
		tmp = x * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (y <= -1.1e+120)
		tmp = t_0;
	elseif (y <= 3.8e+36)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * y);
	tmp = 0.0;
	if (y <= -1.1e+120)
		tmp = t_0;
	elseif (y <= 3.8e+36)
		tmp = x * (1.0 - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+120], t$95$0, If[LessEqual[y, 3.8e+36], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1000000000000001e120 or 3.80000000000000025e36 < y

   1. Initial program 85.3%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 71.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 71.5%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x \cdot y\right), \color{blue}{z}\right) \]

      4. *-lowering-*.f64 82.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   7. Applied egg-rr 82.6%

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

   if -1.1000000000000001e120 < y < 3.80000000000000025e36

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 - z\right)}\right) \]

      2. --lowering--.f64 94.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   5. Simplified 94.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+120}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+119}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y z))))
   (if (<= y -4.8e+119) t_0 (if (<= y 1.8e+36) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if (y <= -4.8e+119) {
		tmp = t_0;
	} else if (y <= 1.8e+36) {
		tmp = x * (1.0 - 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 * (y * z)
    if (y <= (-4.8d+119)) then
        tmp = t_0
    else if (y <= 1.8d+36) then
        tmp = x * (1.0d0 - 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 * (y * z);
	double tmp;
	if (y <= -4.8e+119) {
		tmp = t_0;
	} else if (y <= 1.8e+36) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * z)
	tmp = 0
	if y <= -4.8e+119:
		tmp = t_0
	elif y <= 1.8e+36:
		tmp = x * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -4.8e+119)
		tmp = t_0;
	elseif (y <= 1.8e+36)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y * z);
	tmp = 0.0;
	if (y <= -4.8e+119)
		tmp = t_0;
	elseif (y <= 1.8e+36)
		tmp = x * (1.0 - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+119], t$95$0, If[LessEqual[y, 1.8e+36], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e119 or 1.7999999999999999e36 < y

   1. Initial program 85.3%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 71.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 71.5%

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

   if -4.8e119 < y < 1.7999999999999999e36

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 - z\right)}\right) \]

      2. --lowering--.f64 94.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   5. Simplified 94.4%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y z))))
   (if (<= z -1.45e-19) t_0 (if (<= z 1.7e-24) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if (z <= -1.45e-19) {
		tmp = t_0;
	} else if (z <= 1.7e-24) {
		tmp = x;
	} 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 * (y * z)
    if (z <= (-1.45d-19)) then
        tmp = t_0
    else if (z <= 1.7d-24) then
        tmp = x
    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 * (y * z);
	double tmp;
	if (z <= -1.45e-19) {
		tmp = t_0;
	} else if (z <= 1.7e-24) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * z)
	tmp = 0
	if z <= -1.45e-19:
		tmp = t_0
	elif z <= 1.7e-24:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -1.45e-19)
		tmp = t_0;
	elseif (z <= 1.7e-24)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y * z);
	tmp = 0.0;
	if (z <= -1.45e-19)
		tmp = t_0;
	elseif (z <= 1.7e-24)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e-19], t$95$0, If[LessEqual[z, 1.7e-24], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e-19 or 1.69999999999999996e-24 < z

   1. Initial program 89.9%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 41.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 41.5%

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

   if -1.45e-19 < z < 1.69999999999999996e-24

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 81.6%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.8 \cdot 10^{-74}:\\ \;\;\;\;x + z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(z - y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 6.8e-74) (+ x (* z (* x (+ y -1.0)))) (* x (- 1.0 (- z (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 6.8e-74) {
		tmp = x + (z * (x * (y + -1.0)));
	} else {
		tmp = x * (1.0 - (z - (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 (x <= 6.8d-74) then
        tmp = x + (z * (x * (y + (-1.0d0))))
    else
        tmp = x * (1.0d0 - (z - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 6.8e-74) {
		tmp = x + (z * (x * (y + -1.0)));
	} else {
		tmp = x * (1.0 - (z - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 6.8e-74:
		tmp = x + (z * (x * (y + -1.0)))
	else:
		tmp = x * (1.0 - (z - (y * z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 6.8e-74)
		tmp = Float64(x + Float64(z * Float64(x * Float64(y + -1.0))));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 6.8e-74)
		tmp = x + (z * (x * (y + -1.0)));
	else
		tmp = x * (1.0 - (z - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 6.8e-74], N[(x + N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.8000000000000001e-74

   1. Initial program 91.9%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. fma-define N/A

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

      4. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{neg}\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)\right) \]

      5. fmm-undef N/A

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

      6. *-lft-identity N/A

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

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\left(1 - y\right) \cdot z\right), \color{blue}{x}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(1 - y\right), z\right), x\right)\right) \]

      10. --lowering--.f64 91.9%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, y\right), z\right), x\right)\right) \]

   4. Applied egg-rr 91.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(x \cdot \color{blue}{\left(\left(1 - y\right) \cdot z\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(x \cdot \left(1 - y\right)\right) \cdot \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(x \cdot \left(1 - y\right)\right), \color{blue}{z}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(1 - y\right)\right), z\right)\right) \]

      5. --lowering--.f64 96.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, y\right)\right), z\right)\right) \]

   6. Applied egg-rr 96.6%

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

   if 6.8000000000000001e-74 < x

   1. Initial program 99.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(z \cdot \color{blue}{\left(1 - y\right)}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right)\right) \]

      3. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(z \cdot 1 + \color{blue}{z \cdot \left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      4. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\mathsf{fma}\left(z, \color{blue}{1}, z \cdot \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\mathsf{fma}\left(z, 1, \mathsf{neg}\left(z \cdot y\right)\right)\right)\right)\right) \]

      6. fmm-undef N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(z \cdot 1 - \color{blue}{z \cdot y}\right)\right)\right) \]

      7. *-rgt-identity N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(z - \color{blue}{z} \cdot y\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \color{blue}{\left(z \cdot y\right)}\right)\right)\right) \]

      9. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right)\right)\right) \]

   4. Applied egg-rr 99.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.8 \cdot 10^{-74}:\\ \;\;\;\;x + z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(z - y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 94.4%

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

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 38.8%

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

Developer Target 1: 99.7% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024150 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

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

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