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

Percentage Accurate: 96.0% → 97.8%

Time: 7.6s

Alternatives: 6

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x * (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 - (y * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x * (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 - (y * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+191}:\\ \;\;\;\;\left(\left(-x\right) \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-z, y, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -1e+191) (* (* (- x) y) z) (* x (fma (- z) y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+191) {
		tmp = (-x * y) * z;
	} else {
		tmp = x * fma(-z, y, 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -1e+191)
		tmp = Float64(Float64(Float64(-x) * y) * z);
	else
		tmp = Float64(x * fma(Float64(-z), y, 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -1e+191], N[(N[((-x) * y), $MachinePrecision] * z), $MachinePrecision], N[(x * N[((-z) * y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.00000000000000007e191

   1. Initial program 83.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 83.7

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

   5. Applied rewrites 83.7%

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

   7. Applied rewrites 65.1%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 99.8

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

   10. Applied rewrites 99.8%

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

   if -1.00000000000000007e191 < (*.f64 y z)

   1. Initial program 98.5%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-neg-in N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 98.6

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

   4. Applied rewrites 98.6%

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

Alternative 2: 94.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ \mathbf{if}\;t\_0 \leq -0.02 \lor \neg \left(t\_0 \leq 2\right):\\ \;\;\;\;\left(\left(-x\right) \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))))
   (if (or (<= t_0 -0.02) (not (<= t_0 2.0))) (* (* (- x) z) y) (* x 1.0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if ((t_0 <= -0.02) || !(t_0 <= 2.0)) {
		tmp = (-x * z) * y;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y * z)
    if ((t_0 <= (-0.02d0)) .or. (.not. (t_0 <= 2.0d0))) then
        tmp = (-x * z) * y
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if ((t_0 <= -0.02) || !(t_0 <= 2.0)) {
		tmp = (-x * z) * y;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y * z)
	tmp = 0
	if (t_0 <= -0.02) or not (t_0 <= 2.0):
		tmp = (-x * z) * y
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	tmp = 0.0
	if ((t_0 <= -0.02) || !(t_0 <= 2.0))
		tmp = Float64(Float64(Float64(-x) * z) * y);
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	tmp = 0.0;
	if ((t_0 <= -0.02) || ~((t_0 <= 2.0)))
		tmp = (-x * z) * y;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -0.02], N[Not[LessEqual[t$95$0, 2.0]], $MachinePrecision]], N[(N[((-x) * z), $MachinePrecision] * y), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -0.0200000000000000004 or 2 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 88.9

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

   5. Applied rewrites 88.9%

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

   7. Applied rewrites 59.6%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 88.6

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

   10. Applied rewrites 88.6%

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

   12. Applied rewrites 88.2%

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

   if -0.0200000000000000004 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto x \cdot \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.0%

      \[\leadsto x \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq -0.02 \lor \neg \left(1 - y \cdot z \leq 2\right):\\ \;\;\;\;\left(\left(-x\right) \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ \mathbf{if}\;t\_0 \leq -0.02 \lor \neg \left(t\_0 \leq 2\right):\\ \;\;\;\;\left(\left(-x\right) \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))))
   (if (or (<= t_0 -0.02) (not (<= t_0 2.0))) (* (* (- x) y) z) (* x 1.0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if ((t_0 <= -0.02) || !(t_0 <= 2.0)) {
		tmp = (-x * y) * z;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y * z)
    if ((t_0 <= (-0.02d0)) .or. (.not. (t_0 <= 2.0d0))) then
        tmp = (-x * y) * z
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if ((t_0 <= -0.02) || !(t_0 <= 2.0)) {
		tmp = (-x * y) * z;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y * z)
	tmp = 0
	if (t_0 <= -0.02) or not (t_0 <= 2.0):
		tmp = (-x * y) * z
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	tmp = 0.0
	if ((t_0 <= -0.02) || !(t_0 <= 2.0))
		tmp = Float64(Float64(Float64(-x) * y) * z);
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	tmp = 0.0;
	if ((t_0 <= -0.02) || ~((t_0 <= 2.0)))
		tmp = (-x * y) * z;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -0.02], N[Not[LessEqual[t$95$0, 2.0]], $MachinePrecision]], N[(N[((-x) * y), $MachinePrecision] * z), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -0.0200000000000000004 or 2 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 88.9

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

   5. Applied rewrites 88.9%

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

   7. Applied rewrites 59.6%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 88.6

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

   10. Applied rewrites 88.6%

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

   if -0.0200000000000000004 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto x \cdot \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.0%

      \[\leadsto x \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq -0.02 \lor \neg \left(1 - y \cdot z \leq 2\right):\\ \;\;\;\;\left(\left(-x\right) \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -400000:\\ \;\;\;\;\left(\left(-x\right) \cdot z\right) \cdot y\\ \mathbf{elif}\;y \cdot z \leq 0.04:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(-y\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -400000.0)
   (* (* (- x) z) y)
   (if (<= (* y z) 0.04) (* x 1.0) (* x (* (- y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -400000.0) {
		tmp = (-x * z) * y;
	} else if ((y * z) <= 0.04) {
		tmp = x * 1.0;
	} else {
		tmp = x * (-y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y * z) <= (-400000.0d0)) then
        tmp = (-x * z) * y
    else if ((y * z) <= 0.04d0) then
        tmp = x * 1.0d0
    else
        tmp = x * (-y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -400000.0) {
		tmp = (-x * z) * y;
	} else if ((y * z) <= 0.04) {
		tmp = x * 1.0;
	} else {
		tmp = x * (-y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -400000.0:
		tmp = (-x * z) * y
	elif (y * z) <= 0.04:
		tmp = x * 1.0
	else:
		tmp = x * (-y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -400000.0)
		tmp = Float64(Float64(Float64(-x) * z) * y);
	elseif (Float64(y * z) <= 0.04)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(x * Float64(Float64(-y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -400000.0)
		tmp = (-x * z) * y;
	elseif ((y * z) <= 0.04)
		tmp = x * 1.0;
	else
		tmp = x * (-y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -400000.0], N[(N[((-x) * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.04], N[(x * 1.0), $MachinePrecision], N[(x * N[((-y) * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -4e5

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 88.0

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

   5. Applied rewrites 88.0%

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

   7. Applied rewrites 64.1%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 90.2

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

   10. Applied rewrites 90.2%

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

   12. Applied rewrites 89.9%

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

   if -4e5 < (*.f64 y z) < 0.0400000000000000008

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto x \cdot \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.0%

      \[\leadsto x \cdot \color{blue}{1} \]

   if 0.0400000000000000008 < (*.f64 y z)

   1. Initial program 94.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 90.1

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

   5. Applied rewrites 90.1%

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

Alternative 5: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+191}:\\ \;\;\;\;\left(\left(-x\right) \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -1e+191) (* (* (- x) y) z) (* x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+191) {
		tmp = (-x * y) * z;
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y * z) <= (-1d+191)) then
        tmp = (-x * y) * z
    else
        tmp = x * (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+191) {
		tmp = (-x * y) * z;
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -1e+191:
		tmp = (-x * y) * z
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -1e+191)
		tmp = Float64(Float64(Float64(-x) * y) * z);
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -1e+191)
		tmp = (-x * y) * z;
	else
		tmp = x * (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -1e+191], N[(N[((-x) * y), $MachinePrecision] * z), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.00000000000000007e191

   1. Initial program 83.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 83.7

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

   5. Applied rewrites 83.7%

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

   7. Applied rewrites 65.1%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 99.8

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

   10. Applied rewrites 99.8%

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

   if -1.00000000000000007e191 < (*.f64 y z)

   1. Initial program 98.5%

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

Alternative 6: 50.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ x \cdot 1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

3. Taylor expanded in y around 0

   \[\leadsto x \cdot \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 49.7%

   \[\leadsto x \cdot \color{blue}{1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024324 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))