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

Percentage Accurate: 95.6% → 99.7%

Time: 7.4s

Alternatives: 10

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 2 \cdot 10^{-43}:\\ \;\;\;\;x\_m + z \cdot \left(x\_m \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m - x\_m \cdot \left(z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= x_m 2e-43)
    (+ x_m (* z (* x_m (+ -1.0 y))))
    (- x_m (* x_m (* z (- 1.0 y)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 2e-43) {
		tmp = x_m + (z * (x_m * (-1.0 + y)));
	} else {
		tmp = x_m - (x_m * (z * (1.0 - y)));
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
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 <= 2d-43) then
        tmp = x_m + (z * (x_m * ((-1.0d0) + y)))
    else
        tmp = x_m - (x_m * (z * (1.0d0 - y)))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 2e-43) {
		tmp = x_m + (z * (x_m * (-1.0 + y)));
	} else {
		tmp = x_m - (x_m * (z * (1.0 - y)));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if x_m <= 2e-43:
		tmp = x_m + (z * (x_m * (-1.0 + y)))
	else:
		tmp = x_m - (x_m * (z * (1.0 - y)))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 2e-43)
		tmp = Float64(x_m + Float64(z * Float64(x_m * Float64(-1.0 + y))));
	else
		tmp = Float64(x_m - Float64(x_m * Float64(z * Float64(1.0 - y))));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (x_m <= 2e-43)
		tmp = x_m + (z * (x_m * (-1.0 + y)));
	else
		tmp = x_m - (x_m * (z * (1.0 - y)));
	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]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[x$95$m, 2e-43], N[(x$95$m + N[(z * N[(x$95$m * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m - N[(x$95$m * N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 2.00000000000000015e-43

   1. Initial program 96.3%

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

   3. Taylor expanded in z around 0 96.3%

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

   4. Taylor expanded in y around 0 94.6%

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

      1. associate-*r* 94.6%

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

      2. associate-*r* 94.0%

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

      3. *-commutative 94.0%

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

      4. distribute-rgt-out 95.7%

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

      5. distribute-rgt-in 95.7%

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

   6. Simplified 95.7%

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

   if 2.00000000000000015e-43 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-43}:\\ \;\;\;\;x + z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -92 \lor \neg \left(z \leq 2.85 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m + x\_m \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -92.0) (not (<= z 2.85e-5)))
    (* z (* x_m (+ -1.0 y)))
    (+ x_m (* x_m (* z y))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -92.0) || !(z <= 2.85e-5)) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m + (x_m * (z * y));
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
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 ((z <= (-92.0d0)) .or. (.not. (z <= 2.85d-5))) then
        tmp = z * (x_m * ((-1.0d0) + y))
    else
        tmp = x_m + (x_m * (z * y))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -92.0) || !(z <= 2.85e-5)) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m + (x_m * (z * y));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (z <= -92.0) or not (z <= 2.85e-5):
		tmp = z * (x_m * (-1.0 + y))
	else:
		tmp = x_m + (x_m * (z * y))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((z <= -92.0) || !(z <= 2.85e-5))
		tmp = Float64(z * Float64(x_m * Float64(-1.0 + y)));
	else
		tmp = Float64(x_m + Float64(x_m * Float64(z * y)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((z <= -92.0) || ~((z <= 2.85e-5)))
		tmp = z * (x_m * (-1.0 + y));
	else
		tmp = x_m + (x_m * (z * y));
	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]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[z, -92.0], N[Not[LessEqual[z, 2.85e-5]], $MachinePrecision]], N[(z * N[(x$95$m * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m + N[(x$95$m * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -92 or 2.8500000000000002e-5 < z

   1. Initial program 94.7%

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

   3. Taylor expanded in z around inf 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-*r* 98.1%

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

      3. *-commutative 98.1%

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

      4. sub-neg 98.1%

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

      5. metadata-eval 98.1%

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

   5. Simplified 98.1%

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

   if -92 < z < 2.8500000000000002e-5

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in y around inf 98.8%

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

      1. *-commutative 98.8%

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

   6. Simplified 98.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -92 \lor \neg \left(z \leq 2.85 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -92 \lor \neg \left(z \leq 2.85 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -92.0) (not (<= z 2.85e-5)))
    (* z (* x_m (+ -1.0 y)))
    (* x_m (+ 1.0 (* z y))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -92.0) || !(z <= 2.85e-5)) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m * (1.0 + (z * y));
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
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 ((z <= (-92.0d0)) .or. (.not. (z <= 2.85d-5))) then
        tmp = z * (x_m * ((-1.0d0) + y))
    else
        tmp = x_m * (1.0d0 + (z * y))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -92.0) || !(z <= 2.85e-5)) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m * (1.0 + (z * y));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (z <= -92.0) or not (z <= 2.85e-5):
		tmp = z * (x_m * (-1.0 + y))
	else:
		tmp = x_m * (1.0 + (z * y))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((z <= -92.0) || !(z <= 2.85e-5))
		tmp = Float64(z * Float64(x_m * Float64(-1.0 + y)));
	else
		tmp = Float64(x_m * Float64(1.0 + Float64(z * y)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((z <= -92.0) || ~((z <= 2.85e-5)))
		tmp = z * (x_m * (-1.0 + y));
	else
		tmp = x_m * (1.0 + (z * y));
	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]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[z, -92.0], N[Not[LessEqual[z, 2.85e-5]], $MachinePrecision]], N[(z * N[(x$95$m * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -92 or 2.8500000000000002e-5 < z

   1. Initial program 94.7%

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

   3. Taylor expanded in z around inf 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-*r* 98.1%

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

      3. *-commutative 98.1%

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

      4. sub-neg 98.1%

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

      5. metadata-eval 98.1%

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

   5. Simplified 98.1%

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

   if -92 < z < 2.8500000000000002e-5

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-lft-neg-out 98.8%

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

      3. *-commutative 98.8%

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

   5. Simplified 98.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -92 \lor \neg \left(z \leq 2.85 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -50000 \lor \neg \left(y \leq 1.72 \cdot 10^{+47}\right):\\ \;\;\;\;x\_m \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (or (<= y -50000.0) (not (<= y 1.72e+47))) (* x_m (* z y)) x_m)))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -50000.0) || !(y <= 1.72e+47)) {
		tmp = x_m * (z * y);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
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 <= (-50000.0d0)) .or. (.not. (y <= 1.72d+47))) then
        tmp = x_m * (z * y)
    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);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -50000.0) || !(y <= 1.72e+47)) {
		tmp = x_m * (z * y);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (y <= -50000.0) or not (y <= 1.72e+47):
		tmp = x_m * (z * y)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((y <= -50000.0) || !(y <= 1.72e+47))
		tmp = Float64(x_m * Float64(z * y));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((y <= -50000.0) || ~((y <= 1.72e+47)))
		tmp = x_m * (z * y);
	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]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[y, -50000.0], N[Not[LessEqual[y, 1.72e+47]], $MachinePrecision]], N[(x$95$m * N[(z * y), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -5e4 or 1.72000000000000002e47 < y

   1. Initial program 94.7%

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

   3. Taylor expanded in y around inf 77.6%

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

      1. *-commutative 77.6%

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

   5. Simplified 77.6%

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

   if -5e4 < y < 1.72000000000000002e47

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 51.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -50000 \lor \neg \left(y \leq 1.72 \cdot 10^{+47}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+64} \lor \neg \left(y \leq 2.9 \cdot 10^{+34}\right):\\ \;\;\;\;x\_m \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= y -9e+64) (not (<= y 2.9e+34)))
    (* x_m (* z y))
    (* x_m (- 1.0 z)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -9e+64) || !(y <= 2.9e+34)) {
		tmp = x_m * (z * y);
	} else {
		tmp = x_m * (1.0 - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
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 <= (-9d+64)) .or. (.not. (y <= 2.9d+34))) then
        tmp = x_m * (z * y)
    else
        tmp = x_m * (1.0d0 - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -9e+64) || !(y <= 2.9e+34)) {
		tmp = x_m * (z * y);
	} else {
		tmp = x_m * (1.0 - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (y <= -9e+64) or not (y <= 2.9e+34):
		tmp = x_m * (z * y)
	else:
		tmp = x_m * (1.0 - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((y <= -9e+64) || !(y <= 2.9e+34))
		tmp = Float64(x_m * Float64(z * y));
	else
		tmp = Float64(x_m * Float64(1.0 - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((y <= -9e+64) || ~((y <= 2.9e+34)))
		tmp = x_m * (z * y);
	else
		tmp = x_m * (1.0 - 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]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[y, -9e+64], N[Not[LessEqual[y, 2.9e+34]], $MachinePrecision]], N[(x$95$m * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999946e64 or 2.9000000000000001e34 < y

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf 80.7%

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

      1. *-commutative 80.7%

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

   5. Simplified 80.7%

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

   if -8.99999999999999946e64 < y < 2.9000000000000001e34

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.7%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+64} \lor \neg \left(y \leq 2.9 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+64}:\\ \;\;\;\;x\_m \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+35}:\\ \;\;\;\;x\_m \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x\_m \cdot z\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -7.8e+64)
    (* x_m (* z y))
    (if (<= y 2.9e+35) (* x_m (- 1.0 z)) (* y (* x_m z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -7.8e+64) {
		tmp = x_m * (z * y);
	} else if (y <= 2.9e+35) {
		tmp = x_m * (1.0 - z);
	} else {
		tmp = y * (x_m * z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
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 <= (-7.8d+64)) then
        tmp = x_m * (z * y)
    else if (y <= 2.9d+35) then
        tmp = x_m * (1.0d0 - z)
    else
        tmp = y * (x_m * z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -7.8e+64) {
		tmp = x_m * (z * y);
	} else if (y <= 2.9e+35) {
		tmp = x_m * (1.0 - z);
	} else {
		tmp = y * (x_m * z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -7.8e+64:
		tmp = x_m * (z * y)
	elif y <= 2.9e+35:
		tmp = x_m * (1.0 - z)
	else:
		tmp = y * (x_m * z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -7.8e+64)
		tmp = Float64(x_m * Float64(z * y));
	elseif (y <= 2.9e+35)
		tmp = Float64(x_m * Float64(1.0 - z));
	else
		tmp = Float64(y * Float64(x_m * z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -7.8e+64)
		tmp = x_m * (z * y);
	elseif (y <= 2.9e+35)
		tmp = x_m * (1.0 - z);
	else
		tmp = y * (x_m * 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]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -7.8e+64], N[(x$95$m * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+35], N[(x$95$m * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x$95$m * z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -7.7999999999999996e64

   1. Initial program 97.9%

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

   3. Taylor expanded in y around inf 82.4%

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

      1. *-commutative 82.4%

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

   5. Simplified 82.4%

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

   if -7.7999999999999996e64 < y < 2.89999999999999995e35

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.7%

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

   if 2.89999999999999995e35 < y

   1. Initial program 90.9%

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

   3. Taylor expanded in y around inf 80.4%

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

   4. Taylor expanded in y around inf 83.9%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+64}:\\ \;\;\;\;x\_m \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+35}:\\ \;\;\;\;x\_m - x\_m \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x\_m \cdot z\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -7.5e+64)
    (* x_m (* z y))
    (if (<= y 2.45e+35) (- x_m (* x_m z)) (* y (* x_m z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -7.5e+64) {
		tmp = x_m * (z * y);
	} else if (y <= 2.45e+35) {
		tmp = x_m - (x_m * z);
	} else {
		tmp = y * (x_m * z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
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 <= (-7.5d+64)) then
        tmp = x_m * (z * y)
    else if (y <= 2.45d+35) then
        tmp = x_m - (x_m * z)
    else
        tmp = y * (x_m * z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -7.5e+64) {
		tmp = x_m * (z * y);
	} else if (y <= 2.45e+35) {
		tmp = x_m - (x_m * z);
	} else {
		tmp = y * (x_m * z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -7.5e+64:
		tmp = x_m * (z * y)
	elif y <= 2.45e+35:
		tmp = x_m - (x_m * z)
	else:
		tmp = y * (x_m * z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -7.5e+64)
		tmp = Float64(x_m * Float64(z * y));
	elseif (y <= 2.45e+35)
		tmp = Float64(x_m - Float64(x_m * z));
	else
		tmp = Float64(y * Float64(x_m * z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -7.5e+64)
		tmp = x_m * (z * y);
	elseif (y <= 2.45e+35)
		tmp = x_m - (x_m * z);
	else
		tmp = y * (x_m * 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]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -7.5e+64], N[(x$95$m * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e+35], N[(x$95$m - N[(x$95$m * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x$95$m * z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -7.5000000000000005e64

   1. Initial program 97.9%

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

   3. Taylor expanded in y around inf 82.4%

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

      1. *-commutative 82.4%

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

   5. Simplified 82.4%

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

   if -7.5000000000000005e64 < y < 2.45000000000000013e35

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.7%

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

      1. sub-neg 92.7%

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

      2. distribute-rgt-in 92.7%

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

      3. *-un-lft-identity 92.7%

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

   5. Applied egg-rr 92.7%

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

   if 2.45000000000000013e35 < y

   1. Initial program 90.9%

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

   3. Taylor expanded in y around inf 80.4%

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

   4. Taylor expanded in y around inf 83.9%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+35}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+134}:\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= z -2.35e+134)
    (* z (* x_m (+ -1.0 y)))
    (* x_m (+ 1.0 (* z (+ -1.0 y)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= -2.35e+134) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m * (1.0 + (z * (-1.0 + y)));
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
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 (z <= (-2.35d+134)) then
        tmp = z * (x_m * ((-1.0d0) + y))
    else
        tmp = x_m * (1.0d0 + (z * ((-1.0d0) + y)))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= -2.35e+134) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m * (1.0 + (z * (-1.0 + y)));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if z <= -2.35e+134:
		tmp = z * (x_m * (-1.0 + y))
	else:
		tmp = x_m * (1.0 + (z * (-1.0 + y)))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (z <= -2.35e+134)
		tmp = Float64(z * Float64(x_m * Float64(-1.0 + y)));
	else
		tmp = Float64(x_m * Float64(1.0 + Float64(z * Float64(-1.0 + y))));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (z <= -2.35e+134)
		tmp = z * (x_m * (-1.0 + y));
	else
		tmp = x_m * (1.0 + (z * (-1.0 + y)));
	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]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[z, -2.35e+134], N[(z * N[(x$95$m * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 + N[(z * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.35000000000000013e134

   1. Initial program 88.8%

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

   3. Taylor expanded in z around inf 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*r* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -2.35000000000000013e134 < z

   1. Initial program 99.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+134}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+134}:\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m - x\_m \cdot \left(z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= z -3.3e+134)
    (* z (* x_m (+ -1.0 y)))
    (- x_m (* x_m (* z (- 1.0 y)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= -3.3e+134) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m - (x_m * (z * (1.0 - y)));
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
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 (z <= (-3.3d+134)) then
        tmp = z * (x_m * ((-1.0d0) + y))
    else
        tmp = x_m - (x_m * (z * (1.0d0 - y)))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= -3.3e+134) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m - (x_m * (z * (1.0 - y)));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if z <= -3.3e+134:
		tmp = z * (x_m * (-1.0 + y))
	else:
		tmp = x_m - (x_m * (z * (1.0 - y)))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (z <= -3.3e+134)
		tmp = Float64(z * Float64(x_m * Float64(-1.0 + y)));
	else
		tmp = Float64(x_m - Float64(x_m * Float64(z * Float64(1.0 - y))));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (z <= -3.3e+134)
		tmp = z * (x_m * (-1.0 + y));
	else
		tmp = x_m - (x_m * (z * (1.0 - y)));
	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]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[z, -3.3e+134], N[(z * N[(x$95$m * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m - N[(x$95$m * N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e134

   1. Initial program 88.8%

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

   3. Taylor expanded in z around inf 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*r* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -3.3e134 < z

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 99.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+134}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.1% accurate, 9.0× speedup

Math

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

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s x_m))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
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)
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);
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)
def code(x_s, x_m, y, z):
	return x_s * x_m

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
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);
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]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * x$95$m), $MachinePrecision]

Derivation

1. Initial program 97.3%

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

3. Taylor expanded in z around 0 34.2%

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

4. Final simplification 34.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.5% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024078 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

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