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

Percentage Accurate: 95.8% → 97.6%

Time: 6.7s

Alternatives: 5

Speedup: 1.0×

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: 95.8% 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: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 7.4 \cdot 10^{-90}:\\ \;\;\;\;x\_m - \left(x\_m \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\_m - \left(z \cdot y\right) \cdot x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) 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 7.4e-90) (- x_m (* (* x_m z) y)) (- x_m (* (* z y) 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 (x_m <= 7.4e-90) {
		tmp = x_m - ((x_m * z) * y);
	} else {
		tmp = x_m - ((z * y) * 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 (x_m <= 7.4d-90) then
        tmp = x_m - ((x_m * z) * y)
    else
        tmp = x_m - ((z * y) * 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 (x_m <= 7.4e-90) {
		tmp = x_m - ((x_m * z) * y);
	} else {
		tmp = x_m - ((z * y) * 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 x_m <= 7.4e-90:
		tmp = x_m - ((x_m * z) * y)
	else:
		tmp = x_m - ((z * y) * 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 (x_m <= 7.4e-90)
		tmp = Float64(x_m - Float64(Float64(x_m * z) * y));
	else
		tmp = Float64(x_m - Float64(Float64(z * y) * 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 (x_m <= 7.4e-90)
		tmp = x_m - ((x_m * z) * y);
	else
		tmp = x_m - ((z * y) * 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[LessEqual[x$95$m, 7.4e-90], N[(x$95$m - N[(N[(x$95$m * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x$95$m - N[(N[(z * y), $MachinePrecision] * x$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 7.40000000000000035e-90

   1. Initial program 96.5%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. distribute-rgt-in N/A

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

      5. *-lft-identity N/A

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

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

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

      7. unsub-neg N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 96.5

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 96.5

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

   4. Applied rewrites 96.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 94.3

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

   6. Applied rewrites 94.3%

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

   if 7.40000000000000035e-90 < x

   1. Initial program 99.9%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. distribute-rgt-in N/A

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

      5. *-lft-identity N/A

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

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

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

      7. unsub-neg N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 99.9

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

Alternative 2: 93.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4 \lor \neg \left(y \cdot z \leq 0.002\right):\\ \;\;\;\;x\_m \cdot \left(\left(-y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot 1\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) 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) -4.0) (not (<= (* y z) 0.002)))
    (* x_m (* (- y) z))
    (* x_m 1.0))))

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) <= -4.0) || !((y * z) <= 0.002)) {
		tmp = x_m * (-y * z);
	} else {
		tmp = x_m * 1.0;
	}
	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) <= (-4.0d0)) .or. (.not. ((y * z) <= 0.002d0))) then
        tmp = x_m * (-y * z)
    else
        tmp = x_m * 1.0d0
    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) <= -4.0) || !((y * z) <= 0.002)) {
		tmp = x_m * (-y * z);
	} else {
		tmp = x_m * 1.0;
	}
	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) <= -4.0) or not ((y * z) <= 0.002):
		tmp = x_m * (-y * z)
	else:
		tmp = x_m * 1.0
	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) <= -4.0) || !(Float64(y * z) <= 0.002))
		tmp = Float64(x_m * Float64(Float64(-y) * z));
	else
		tmp = Float64(x_m * 1.0);
	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) <= -4.0) || ~(((y * z) <= 0.002)))
		tmp = x_m * (-y * z);
	else
		tmp = x_m * 1.0;
	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], -4.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 0.002]], $MachinePrecision]], N[(x$95$m * N[((-y) * z), $MachinePrecision]), $MachinePrecision], N[(x$95$m * 1.0), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -4 or 2e-3 < (*.f64 y z)

   1. Initial program 95.4%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 92.9

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

   5. Applied rewrites 92.9%

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

   if -4 < (*.f64 y z) < 2e-3

   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 98.7%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4 \lor \neg \left(y \cdot z \leq 0.002\right):\\ \;\;\;\;x \cdot \left(\left(-y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 7.4 \cdot 10^{-90}:\\ \;\;\;\;x\_m - \left(x\_m \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) 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 7.4e-90) (- x_m (* (* x_m z) y)) (* 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 (x_m <= 7.4e-90) {
		tmp = x_m - ((x_m * z) * y);
	} 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 (x_m <= 7.4d-90) then
        tmp = x_m - ((x_m * z) * y)
    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 (x_m <= 7.4e-90) {
		tmp = x_m - ((x_m * z) * y);
	} 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 x_m <= 7.4e-90:
		tmp = x_m - ((x_m * z) * y)
	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 (x_m <= 7.4e-90)
		tmp = Float64(x_m - Float64(Float64(x_m * z) * y));
	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 (x_m <= 7.4e-90)
		tmp = x_m - ((x_m * z) * y);
	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[LessEqual[x$95$m, 7.4e-90], N[(x$95$m - N[(N[(x$95$m * z), $MachinePrecision] * y), $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 x < 7.40000000000000035e-90

   1. Initial program 96.5%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. distribute-rgt-in N/A

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

      5. *-lft-identity N/A

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

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

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

      7. unsub-neg N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 96.5

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 96.5

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

   4. Applied rewrites 96.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 94.3

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

   6. Applied rewrites 94.3%

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

   if 7.40000000000000035e-90 < x

   1. Initial program 99.9%

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

Alternative 4: 95.8% accurate, 1.0× speedup

Math

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

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) 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 (- 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) {
	return x_s * (x_m * (1.0 - (y * z)));
}

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 * (1.0d0 - (y * z)))
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 * (1.0 - (y * z)));
}

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 * (1.0 - (y * z)))

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 * Float64(x_m * Float64(1.0 - Float64(y * z))))
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 * (1.0 - (y * z)));
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 * N[(x$95$m * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.6%

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

Alternative 5: 51.1% accurate, 2.3× speedup

Math

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

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) 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 1.0)))

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 * 1.0);
}

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 * 1.0d0)
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 * 1.0);
}

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 * 1.0)

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 * Float64(x_m * 1.0))
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 * 1.0);
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 * N[(x$95$m * 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.6%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 49.0%

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

Reproduce

herbie shell --seed 2024317 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))