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

Percentage Accurate: 96.4% → 98.9%

Time: 7.3s

Alternatives: 7

Speedup: 0.3×

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: 96.4% 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: 98.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ \begin{array}{l} t_0 := x\_m \cdot \left(1 - y \cdot z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+211} \lor \neg \left(t\_0 \leq 10^{+293}\right):\\ \;\;\;\;x\_m - z \cdot \left(x\_m \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m - x\_m \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (* x_m (- 1.0 (* y z)))))
   (*
    x_s
    (if (or (<= t_0 -4e+211) (not (<= t_0 1e+293)))
      (- x_m (* z (* x_m y)))
      (- x_m (* x_m (* y z)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
assert(x_m < y && y < z);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (1.0 - (y * z));
	double tmp;
	if ((t_0 <= -4e+211) || !(t_0 <= 1e+293)) {
		tmp = x_m - (z * (x_m * y));
	} else {
		tmp = x_m - (x_m * (y * z));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x_m * (1.0d0 - (y * z))
    if ((t_0 <= (-4d+211)) .or. (.not. (t_0 <= 1d+293))) then
        tmp = x_m - (z * (x_m * y))
    else
        tmp = x_m - (x_m * (y * z))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
assert x_m < y && y < z;
public static double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (1.0 - (y * z));
	double tmp;
	if ((t_0 <= -4e+211) || !(t_0 <= 1e+293)) {
		tmp = x_m - (z * (x_m * y));
	} else {
		tmp = x_m - (x_m * (y * z));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
[x_m, y, z] = sort([x_m, y, z])
def code(x_s, x_m, y, z):
	t_0 = x_m * (1.0 - (y * z))
	tmp = 0
	if (t_0 <= -4e+211) or not (t_0 <= 1e+293):
		tmp = x_m - (z * (x_m * y))
	else:
		tmp = x_m - (x_m * (y * z))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
x_m, y, z = sort([x_m, y, z])
function code(x_s, x_m, y, z)
	t_0 = Float64(x_m * Float64(1.0 - Float64(y * z)))
	tmp = 0.0
	if ((t_0 <= -4e+211) || !(t_0 <= 1e+293))
		tmp = Float64(x_m - Float64(z * Float64(x_m * y)));
	else
		tmp = Float64(x_m - Float64(x_m * Float64(y * z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
x_m, y, z = num2cell(sort([x_m, y, z])){:}
function tmp_2 = code(x_s, x_m, y, z)
	t_0 = x_m * (1.0 - (y * z));
	tmp = 0.0;
	if ((t_0 <= -4e+211) || ~((t_0 <= 1e+293)))
		tmp = x_m - (z * (x_m * y));
	else
		tmp = x_m - (x_m * (y * z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(x$95$m * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[Or[LessEqual[t$95$0, -4e+211], N[Not[LessEqual[t$95$0, 1e+293]], $MachinePrecision]], N[(x$95$m - N[(z * N[(x$95$m * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m - N[(x$95$m * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 y z))) < -3.9999999999999998e211 or 9.9999999999999992e292 < (*.f64 x (-.f64 1 (*.f64 y z)))

   1. Initial program 87.0%

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

   3. Taylor expanded in y around 0 87.0%

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

      1. mul-1-neg 87.0%

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

   5. Simplified 87.0%

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

      1. unsub-neg 87.0%

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

      2. *-commutative 87.0%

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

      3. associate-*l* 88.4%

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

   7. Applied egg-rr 88.4%

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

      1. rem-cube-cbrt 88.1%

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

   9. Applied egg-rr 88.1%

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

       1. rem-cube-cbrt 88.4%

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

       2. *-commutative 88.4%

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

       3. associate-*r* 98.5%

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

   11. Applied egg-rr 98.5%

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

   if -3.9999999999999998e211 < (*.f64 x (-.f64 1 (*.f64 y z))) < 9.9999999999999992e292

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

   5. Simplified 99.8%

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

      1. unsub-neg 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l* 93.8%

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

   7. Applied egg-rr 93.8%

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

   8. Taylor expanded in y around 0 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - y \cdot z\right) \leq -4 \cdot 10^{+211} \lor \neg \left(x \cdot \left(1 - y \cdot z\right) \leq 10^{+293}\right):\\ \;\;\;\;x - z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 8 \cdot 10^{-28}:\\ \;\;\;\;x\_m - \sqrt{x\_m} \cdot \left(y \cdot \left(z \cdot \sqrt{x\_m}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m - x\_m \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= x_m 8e-28)
    (- x_m (* (sqrt x_m) (* y (* z (sqrt x_m)))))
    (- x_m (* x_m (* y z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
assert(x_m < y && y < z);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 8e-28) {
		tmp = x_m - (sqrt(x_m) * (y * (z * sqrt(x_m))));
	} else {
		tmp = x_m - (x_m * (y * z));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x_m <= 8d-28) then
        tmp = x_m - (sqrt(x_m) * (y * (z * sqrt(x_m))))
    else
        tmp = x_m - (x_m * (y * z))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
assert x_m < y && y < z;
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 8e-28) {
		tmp = x_m - (Math.sqrt(x_m) * (y * (z * Math.sqrt(x_m))));
	} else {
		tmp = x_m - (x_m * (y * z));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
[x_m, y, z] = sort([x_m, y, z])
def code(x_s, x_m, y, z):
	tmp = 0
	if x_m <= 8e-28:
		tmp = x_m - (math.sqrt(x_m) * (y * (z * math.sqrt(x_m))))
	else:
		tmp = x_m - (x_m * (y * z))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
x_m, y, z = sort([x_m, y, z])
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 8e-28)
		tmp = Float64(x_m - Float64(sqrt(x_m) * Float64(y * Float64(z * sqrt(x_m)))));
	else
		tmp = Float64(x_m - Float64(x_m * Float64(y * z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
x_m, y, z = num2cell(sort([x_m, y, z])){:}
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (x_m <= 8e-28)
		tmp = x_m - (sqrt(x_m) * (y * (z * sqrt(x_m))));
	else
		tmp = x_m - (x_m * (y * z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[x$95$m, 8e-28], N[(x$95$m - N[(N[Sqrt[x$95$m], $MachinePrecision] * N[(y * N[(z * N[Sqrt[x$95$m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m - N[(x$95$m * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 7.99999999999999977e-28

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0 94.5%

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

      1. mul-1-neg 94.5%

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

   5. Simplified 94.5%

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

      1. add-cube-cbrt 94.0%

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

      2. pow3 94.0%

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

      3. *-commutative 94.0%

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

      4. associate-*l* 93.2%

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

   7. Applied egg-rr 93.2%

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

      1. rem-cube-cbrt 93.7%

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

      2. associate-*r* 94.5%

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

      3. add-sqr-sqrt 27.2%

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

      4. associate-*r* 27.2%

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

   9. Applied egg-rr 27.2%

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

   10. Taylor expanded in y around 0 27.2%

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

       1. *-commutative 27.2%

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

       2. associate-*r* 29.6%

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

   12. Simplified 29.6%

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

   if 7.99999999999999977e-28 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

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

   5. Simplified 99.9%

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

      1. unsub-neg 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l* 89.2%

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

   7. Applied egg-rr 89.2%

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

   8. Taylor expanded in y around 0 99.9%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{-28}:\\ \;\;\;\;x - \sqrt{x} \cdot \left(y \cdot \left(z \cdot \sqrt{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ \begin{array}{l} t_0 := x\_m \cdot \left(y \cdot \left(-z\right)\right)\\ t_1 := y \cdot \left(x\_m \cdot \left(-z\right)\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot z \leq -1000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 0.2:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;y \cdot z \leq 10^{+286}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (* x_m (* y (- z)))) (t_1 (* y (* x_m (- z)))))
   (*
    x_s
    (if (<= (* y z) -1e+164)
      t_1
      (if (<= (* y z) -1000000.0)
        t_0
        (if (<= (* y z) 0.2) x_m (if (<= (* y z) 1e+286) t_0 t_1)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
assert(x_m < y && y < z);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (y * -z);
	double t_1 = y * (x_m * -z);
	double tmp;
	if ((y * z) <= -1e+164) {
		tmp = t_1;
	} else if ((y * z) <= -1000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.2) {
		tmp = x_m;
	} else if ((y * z) <= 1e+286) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x_m * (y * -z)
    t_1 = y * (x_m * -z)
    if ((y * z) <= (-1d+164)) then
        tmp = t_1
    else if ((y * z) <= (-1000000.0d0)) then
        tmp = t_0
    else if ((y * z) <= 0.2d0) then
        tmp = x_m
    else if ((y * z) <= 1d+286) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
assert x_m < y && y < z;
public static double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (y * -z);
	double t_1 = y * (x_m * -z);
	double tmp;
	if ((y * z) <= -1e+164) {
		tmp = t_1;
	} else if ((y * z) <= -1000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.2) {
		tmp = x_m;
	} else if ((y * z) <= 1e+286) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
[x_m, y, z] = sort([x_m, y, z])
def code(x_s, x_m, y, z):
	t_0 = x_m * (y * -z)
	t_1 = y * (x_m * -z)
	tmp = 0
	if (y * z) <= -1e+164:
		tmp = t_1
	elif (y * z) <= -1000000.0:
		tmp = t_0
	elif (y * z) <= 0.2:
		tmp = x_m
	elif (y * z) <= 1e+286:
		tmp = t_0
	else:
		tmp = t_1
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
x_m, y, z = sort([x_m, y, z])
function code(x_s, x_m, y, z)
	t_0 = Float64(x_m * Float64(y * Float64(-z)))
	t_1 = Float64(y * Float64(x_m * Float64(-z)))
	tmp = 0.0
	if (Float64(y * z) <= -1e+164)
		tmp = t_1;
	elseif (Float64(y * z) <= -1000000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 0.2)
		tmp = x_m;
	elseif (Float64(y * z) <= 1e+286)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
x_m, y, z = num2cell(sort([x_m, y, z])){:}
function tmp_2 = code(x_s, x_m, y, z)
	t_0 = x_m * (y * -z);
	t_1 = y * (x_m * -z);
	tmp = 0.0;
	if ((y * z) <= -1e+164)
		tmp = t_1;
	elseif ((y * z) <= -1000000.0)
		tmp = t_0;
	elseif ((y * z) <= 0.2)
		tmp = x_m;
	elseif ((y * z) <= 1e+286)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(x$95$m * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(x$95$m * (-z)), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[N[(y * z), $MachinePrecision], -1e+164], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], -1000000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 0.2], x$95$m, If[LessEqual[N[(y * z), $MachinePrecision], 1e+286], t$95$0, t$95$1]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -1e164 or 1.00000000000000003e286 < (*.f64 y z)

   1. Initial program 78.9%

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

   3. Taylor expanded in y around 0 78.9%

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

      1. mul-1-neg 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in y around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r* 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

   8. Simplified 99.9%

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

   if -1e164 < (*.f64 y z) < -1e6 or 0.20000000000000001 < (*.f64 y z) < 1.00000000000000003e286

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 95.1%

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

      1. mul-1-neg 95.1%

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

      2. distribute-rgt-neg-in 95.1%

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

      3. distribute-rgt-neg-in 95.1%

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

   5. Simplified 95.1%

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

   if -1e6 < (*.f64 y z) < 0.20000000000000001

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 96.8%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+164}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \cdot z \leq -1000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 0.2:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 10^{+286}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+164} \lor \neg \left(y \cdot z \leq 10^{+286}\right):\\ \;\;\;\;y \cdot \left(x\_m \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= (* y z) -1e+164) (not (<= (* y z) 1e+286)))
    (* y (* x_m (- z)))
    (* x_m (- 1.0 (* y z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
assert(x_m < y && y < z);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (((y * z) <= -1e+164) || !((y * z) <= 1e+286)) {
		tmp = y * (x_m * -z);
	} else {
		tmp = x_m * (1.0 - (y * z));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((y * z) <= (-1d+164)) .or. (.not. ((y * z) <= 1d+286))) then
        tmp = y * (x_m * -z)
    else
        tmp = x_m * (1.0d0 - (y * z))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
assert x_m < y && y < z;
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (((y * z) <= -1e+164) || !((y * z) <= 1e+286)) {
		tmp = y * (x_m * -z);
	} else {
		tmp = x_m * (1.0 - (y * z));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
[x_m, y, z] = sort([x_m, y, z])
def code(x_s, x_m, y, z):
	tmp = 0
	if ((y * z) <= -1e+164) or not ((y * z) <= 1e+286):
		tmp = y * (x_m * -z)
	else:
		tmp = x_m * (1.0 - (y * z))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
x_m, y, z = sort([x_m, y, z])
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -1e+164) || !(Float64(y * z) <= 1e+286))
		tmp = Float64(y * Float64(x_m * Float64(-z)));
	else
		tmp = Float64(x_m * Float64(1.0 - Float64(y * z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
x_m, y, z = num2cell(sort([x_m, y, z])){:}
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (((y * z) <= -1e+164) || ~(((y * z) <= 1e+286)))
		tmp = y * (x_m * -z);
	else
		tmp = x_m * (1.0 - (y * z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[N[(y * z), $MachinePrecision], -1e+164], N[Not[LessEqual[N[(y * z), $MachinePrecision], 1e+286]], $MachinePrecision]], N[(y * N[(x$95$m * (-z)), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1e164 or 1.00000000000000003e286 < (*.f64 y z)

   1. Initial program 78.9%

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

   3. Taylor expanded in y around 0 78.9%

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

      1. mul-1-neg 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in y around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r* 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

   8. Simplified 99.9%

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

   if -1e164 < (*.f64 y z) < 1.00000000000000003e286

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+164} \lor \neg \left(y \cdot z \leq 10^{+286}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+164} \lor \neg \left(y \cdot z \leq 10^{+286}\right):\\ \;\;\;\;y \cdot \left(x\_m \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m - x\_m \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= (* y z) -1e+164) (not (<= (* y z) 1e+286)))
    (* y (* x_m (- z)))
    (- x_m (* x_m (* y z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
assert(x_m < y && y < z);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (((y * z) <= -1e+164) || !((y * z) <= 1e+286)) {
		tmp = y * (x_m * -z);
	} else {
		tmp = x_m - (x_m * (y * z));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((y * z) <= (-1d+164)) .or. (.not. ((y * z) <= 1d+286))) then
        tmp = y * (x_m * -z)
    else
        tmp = x_m - (x_m * (y * z))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
assert x_m < y && y < z;
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (((y * z) <= -1e+164) || !((y * z) <= 1e+286)) {
		tmp = y * (x_m * -z);
	} else {
		tmp = x_m - (x_m * (y * z));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
[x_m, y, z] = sort([x_m, y, z])
def code(x_s, x_m, y, z):
	tmp = 0
	if ((y * z) <= -1e+164) or not ((y * z) <= 1e+286):
		tmp = y * (x_m * -z)
	else:
		tmp = x_m - (x_m * (y * z))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
x_m, y, z = sort([x_m, y, z])
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -1e+164) || !(Float64(y * z) <= 1e+286))
		tmp = Float64(y * Float64(x_m * Float64(-z)));
	else
		tmp = Float64(x_m - Float64(x_m * Float64(y * z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
x_m, y, z = num2cell(sort([x_m, y, z])){:}
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (((y * z) <= -1e+164) || ~(((y * z) <= 1e+286)))
		tmp = y * (x_m * -z);
	else
		tmp = x_m - (x_m * (y * z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[N[(y * z), $MachinePrecision], -1e+164], N[Not[LessEqual[N[(y * z), $MachinePrecision], 1e+286]], $MachinePrecision]], N[(y * N[(x$95$m * (-z)), $MachinePrecision]), $MachinePrecision], N[(x$95$m - N[(x$95$m * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1e164 or 1.00000000000000003e286 < (*.f64 y z)

   1. Initial program 78.9%

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

   3. Taylor expanded in y around 0 78.9%

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

      1. mul-1-neg 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in y around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r* 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

   8. Simplified 99.9%

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

   if -1e164 < (*.f64 y z) < 1.00000000000000003e286

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

   5. Simplified 99.8%

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

      1. unsub-neg 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l* 90.7%

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

   7. Applied egg-rr 90.7%

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

   8. Taylor expanded in y around 0 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+164} \lor \neg \left(y \cdot z \leq 10^{+286}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1000000 \lor \neg \left(y \cdot z \leq 0.2\right):\\ \;\;\;\;x\_m \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= (* y z) -1000000.0) (not (<= (* y z) 0.2)))
    (* x_m (* y (- z)))
    x_m)))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
assert(x_m < y && y < z);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (((y * z) <= -1000000.0) || !((y * z) <= 0.2)) {
		tmp = x_m * (y * -z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((y * z) <= (-1000000.0d0)) .or. (.not. ((y * z) <= 0.2d0))) then
        tmp = x_m * (y * -z)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
assert x_m < y && y < z;
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (((y * z) <= -1000000.0) || !((y * z) <= 0.2)) {
		tmp = x_m * (y * -z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
[x_m, y, z] = sort([x_m, y, z])
def code(x_s, x_m, y, z):
	tmp = 0
	if ((y * z) <= -1000000.0) or not ((y * z) <= 0.2):
		tmp = x_m * (y * -z)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
x_m, y, z = sort([x_m, y, z])
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -1000000.0) || !(Float64(y * z) <= 0.2))
		tmp = Float64(x_m * Float64(y * Float64(-z)));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
x_m, y, z = num2cell(sort([x_m, y, z])){:}
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (((y * z) <= -1000000.0) || ~(((y * z) <= 0.2)))
		tmp = x_m * (y * -z);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[N[(y * z), $MachinePrecision], -1000000.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 0.2]], $MachinePrecision]], N[(x$95$m * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1e6 or 0.20000000000000001 < (*.f64 y z)

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 89.1%

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

      1. mul-1-neg 89.1%

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

      2. distribute-rgt-neg-in 89.1%

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

      3. distribute-rgt-neg-in 89.1%

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

   5. Simplified 89.1%

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

   if -1e6 < (*.f64 y z) < 0.20000000000000001

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 96.8%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1000000 \lor \neg \left(y \cdot z \leq 0.2\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x\_s \cdot x\_m \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z) :precision binary64 (* x_s x_m))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
assert(x_m < y && y < z);
double code(double x_s, double x_m, double y, double z) {
	return x_s * x_m;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * x_m
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
assert x_m < y && y < z;
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * x_m;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
[x_m, y, z] = sort([x_m, y, z])
def code(x_s, x_m, y, z):
	return x_s * x_m

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
x_m, y, z = sort([x_m, y, z])
function code(x_s, x_m, y, z)
	return Float64(x_s * x_m)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
x_m, y, z = num2cell(sort([x_m, y, z])){:}
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * x_m;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * x$95$m), $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 52.8%

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

4. Final simplification 52.8%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024027 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))