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

Percentage Accurate: 96.1% → 98.9%

Time: 8.6s

Alternatives: 12

Speedup: 0.5×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.1% 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: 98.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := x\_m \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;x\_m \cdot \left(1 - z\right) + x\_m \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x\_m \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (* x_m (+ 1.0 (* z (+ y -1.0))))))
   (*
    x_s
    (if (<= t_0 -1e+226)
      (* z (* x_m (+ y -1.0)))
      (if (<= t_0 5e+299)
        (+ (* x_m (- 1.0 z)) (* x_m (* y z)))
        (* (* x_m z) (+ y -1.0)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= -1e+226) {
		tmp = z * (x_m * (y + -1.0));
	} else if (t_0 <= 5e+299) {
		tmp = (x_m * (1.0 - z)) + (x_m * (y * z));
	} else {
		tmp = (x_m * z) * (y + -1.0);
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x_m * (1.0d0 + (z * (y + (-1.0d0))))
    if (t_0 <= (-1d+226)) then
        tmp = z * (x_m * (y + (-1.0d0)))
    else if (t_0 <= 5d+299) then
        tmp = (x_m * (1.0d0 - z)) + (x_m * (y * z))
    else
        tmp = (x_m * z) * (y + (-1.0d0))
    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 t_0 = x_m * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= -1e+226) {
		tmp = z * (x_m * (y + -1.0));
	} else if (t_0 <= 5e+299) {
		tmp = (x_m * (1.0 - z)) + (x_m * (y * z));
	} else {
		tmp = (x_m * z) * (y + -1.0);
	}
	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):
	t_0 = x_m * (1.0 + (z * (y + -1.0)))
	tmp = 0
	if t_0 <= -1e+226:
		tmp = z * (x_m * (y + -1.0))
	elif t_0 <= 5e+299:
		tmp = (x_m * (1.0 - z)) + (x_m * (y * z))
	else:
		tmp = (x_m * z) * (y + -1.0)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	t_0 = Float64(x_m * Float64(1.0 + Float64(z * Float64(y + -1.0))))
	tmp = 0.0
	if (t_0 <= -1e+226)
		tmp = Float64(z * Float64(x_m * Float64(y + -1.0)));
	elseif (t_0 <= 5e+299)
		tmp = Float64(Float64(x_m * Float64(1.0 - z)) + Float64(x_m * Float64(y * z)));
	else
		tmp = Float64(Float64(x_m * z) * Float64(y + -1.0));
	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)
	t_0 = x_m * (1.0 + (z * (y + -1.0)));
	tmp = 0.0;
	if (t_0 <= -1e+226)
		tmp = z * (x_m * (y + -1.0));
	elseif (t_0 <= 5e+299)
		tmp = (x_m * (1.0 - z)) + (x_m * (y * z));
	else
		tmp = (x_m * z) * (y + -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]
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(x$95$m * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, -1e+226], N[(z * N[(x$95$m * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+299], N[(N[(x$95$m * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(x$95$m * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < -9.99999999999999961e225

   1. Initial program 86.8%

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

   3. Taylor expanded in y around 0 78.8%

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

   4. Taylor expanded in z around inf 84.3%

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

   5. Taylor expanded in x around 0 84.4%

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

   if -9.99999999999999961e225 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < 5.0000000000000003e299

   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 0 99.9%

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

   if 5.0000000000000003e299 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z)))

   1. Initial program 70.3%

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

   3. Taylor expanded in y around 0 70.3%

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

   4. Taylor expanded in z around inf 70.3%

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

      1. sub-neg 70.3%

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

      2. metadata-eval 70.3%

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

      3. associate-*r* 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right) \leq -1 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right) \leq 5 \cdot 10^{+299}:\\ \;\;\;\;x \cdot \left(1 - z\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := x\_m \cdot \left(y \cdot z\right)\\ t_1 := x\_m \cdot \left(-z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-96}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-86}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 760000 \lor \neg \left(z \leq 3.8 \cdot 10^{+141}\right) \land z \leq 3.4 \cdot 10^{+177}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (* x_m (* y z))) (t_1 (* x_m (- z))))
   (*
    x_s
    (if (<= z -1.45e+19)
      t_1
      (if (<= z -3.6e-96)
        t_0
        (if (<= z 2.5e-86)
          x_m
          (if (or (<= z 760000.0) (and (not (<= z 3.8e+141)) (<= z 3.4e+177)))
            t_0
            t_1)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (y * z);
	double t_1 = x_m * -z;
	double tmp;
	if (z <= -1.45e+19) {
		tmp = t_1;
	} else if (z <= -3.6e-96) {
		tmp = t_0;
	} else if (z <= 2.5e-86) {
		tmp = x_m;
	} else if ((z <= 760000.0) || (!(z <= 3.8e+141) && (z <= 3.4e+177))) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x_m * (y * z)
    t_1 = x_m * -z
    if (z <= (-1.45d+19)) then
        tmp = t_1
    else if (z <= (-3.6d-96)) then
        tmp = t_0
    else if (z <= 2.5d-86) then
        tmp = x_m
    else if ((z <= 760000.0d0) .or. (.not. (z <= 3.8d+141)) .and. (z <= 3.4d+177)) 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);
public static double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (y * z);
	double t_1 = x_m * -z;
	double tmp;
	if (z <= -1.45e+19) {
		tmp = t_1;
	} else if (z <= -3.6e-96) {
		tmp = t_0;
	} else if (z <= 2.5e-86) {
		tmp = x_m;
	} else if ((z <= 760000.0) || (!(z <= 3.8e+141) && (z <= 3.4e+177))) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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):
	t_0 = x_m * (y * z)
	t_1 = x_m * -z
	tmp = 0
	if z <= -1.45e+19:
		tmp = t_1
	elif z <= -3.6e-96:
		tmp = t_0
	elif z <= 2.5e-86:
		tmp = x_m
	elif (z <= 760000.0) or (not (z <= 3.8e+141) and (z <= 3.4e+177)):
		tmp = t_0
	else:
		tmp = t_1
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	t_0 = Float64(x_m * Float64(y * z))
	t_1 = Float64(x_m * Float64(-z))
	tmp = 0.0
	if (z <= -1.45e+19)
		tmp = t_1;
	elseif (z <= -3.6e-96)
		tmp = t_0;
	elseif (z <= 2.5e-86)
		tmp = x_m;
	elseif ((z <= 760000.0) || (!(z <= 3.8e+141) && (z <= 3.4e+177)))
		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);
function tmp_2 = code(x_s, x_m, y, z)
	t_0 = x_m * (y * z);
	t_1 = x_m * -z;
	tmp = 0.0;
	if (z <= -1.45e+19)
		tmp = t_1;
	elseif (z <= -3.6e-96)
		tmp = t_0;
	elseif (z <= 2.5e-86)
		tmp = x_m;
	elseif ((z <= 760000.0) || (~((z <= 3.8e+141)) && (z <= 3.4e+177)))
		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]
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[(x$95$m * (-z)), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -1.45e+19], t$95$1, If[LessEqual[z, -3.6e-96], t$95$0, If[LessEqual[z, 2.5e-86], x$95$m, If[Or[LessEqual[z, 760000.0], And[N[Not[LessEqual[z, 3.8e+141]], $MachinePrecision], LessEqual[z, 3.4e+177]]], t$95$0, t$95$1]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45e19 or 7.6e5 < z < 3.79999999999999976e141 or 3.3999999999999998e177 < z

   1. Initial program 87.2%

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

   3. Taylor expanded in z around inf 86.4%

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

   4. Taylor expanded in y around 0 62.3%

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

      1. mul-1-neg 62.3%

         \[\leadsto \color{blue}{-x \cdot z} \]

      2. *-commutative 62.3%

         \[\leadsto -\color{blue}{z \cdot x} \]

      3. distribute-rgt-neg-in 62.3%

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

   6. Simplified 62.3%

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

   if -1.45e19 < z < -3.60000000000000008e-96 or 2.4999999999999999e-86 < z < 7.6e5 or 3.79999999999999976e141 < z < 3.3999999999999998e177

   1. Initial program 96.6%

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

   3. Taylor expanded in y around inf 62.9%

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

      1. *-commutative 62.9%

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

   5. Simplified 62.9%

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

   if -3.60000000000000008e-96 < z < 2.4999999999999999e-86

   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 83.7%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 760000 \lor \neg \left(z \leq 3.8 \cdot 10^{+141}\right) \land z \leq 3.4 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := x\_m \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(x\_m \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (* x_m (+ 1.0 (* z (+ y -1.0))))))
   (*
    x_s
    (if (<= t_0 -1e+226)
      (* z (* x_m (+ y -1.0)))
      (if (<= t_0 5e+299) t_0 (* (* x_m z) (+ y -1.0)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= -1e+226) {
		tmp = z * (x_m * (y + -1.0));
	} else if (t_0 <= 5e+299) {
		tmp = t_0;
	} else {
		tmp = (x_m * z) * (y + -1.0);
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x_m * (1.0d0 + (z * (y + (-1.0d0))))
    if (t_0 <= (-1d+226)) then
        tmp = z * (x_m * (y + (-1.0d0)))
    else if (t_0 <= 5d+299) then
        tmp = t_0
    else
        tmp = (x_m * z) * (y + (-1.0d0))
    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 t_0 = x_m * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= -1e+226) {
		tmp = z * (x_m * (y + -1.0));
	} else if (t_0 <= 5e+299) {
		tmp = t_0;
	} else {
		tmp = (x_m * z) * (y + -1.0);
	}
	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):
	t_0 = x_m * (1.0 + (z * (y + -1.0)))
	tmp = 0
	if t_0 <= -1e+226:
		tmp = z * (x_m * (y + -1.0))
	elif t_0 <= 5e+299:
		tmp = t_0
	else:
		tmp = (x_m * z) * (y + -1.0)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	t_0 = Float64(x_m * Float64(1.0 + Float64(z * Float64(y + -1.0))))
	tmp = 0.0
	if (t_0 <= -1e+226)
		tmp = Float64(z * Float64(x_m * Float64(y + -1.0)));
	elseif (t_0 <= 5e+299)
		tmp = t_0;
	else
		tmp = Float64(Float64(x_m * z) * Float64(y + -1.0));
	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)
	t_0 = x_m * (1.0 + (z * (y + -1.0)));
	tmp = 0.0;
	if (t_0 <= -1e+226)
		tmp = z * (x_m * (y + -1.0));
	elseif (t_0 <= 5e+299)
		tmp = t_0;
	else
		tmp = (x_m * z) * (y + -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]
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(x$95$m * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, -1e+226], N[(z * N[(x$95$m * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+299], t$95$0, N[(N[(x$95$m * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < -9.99999999999999961e225

   1. Initial program 86.8%

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

   3. Taylor expanded in y around 0 78.8%

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

   4. Taylor expanded in z around inf 84.3%

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

   5. Taylor expanded in x around 0 84.4%

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

   if -9.99999999999999961e225 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < 5.0000000000000003e299

   1. Initial program 99.8%

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

   if 5.0000000000000003e299 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z)))

   1. Initial program 70.3%

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

   3. Taylor expanded in y around 0 70.3%

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

   4. Taylor expanded in z around inf 70.3%

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

      1. sub-neg 70.3%

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

      2. metadata-eval 70.3%

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

      3. associate-*r* 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right) \leq -1 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right) \leq 5 \cdot 10^{+299}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := x\_m \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;x\_m \cdot \left(\left(1 + y \cdot z\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x\_m \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (* x_m (+ 1.0 (* z (+ y -1.0))))))
   (*
    x_s
    (if (<= t_0 -1e+226)
      (* z (* x_m (+ y -1.0)))
      (if (<= t_0 5e+299)
        (* x_m (- (+ 1.0 (* y z)) z))
        (* (* x_m z) (+ y -1.0)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= -1e+226) {
		tmp = z * (x_m * (y + -1.0));
	} else if (t_0 <= 5e+299) {
		tmp = x_m * ((1.0 + (y * z)) - z);
	} else {
		tmp = (x_m * z) * (y + -1.0);
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x_m * (1.0d0 + (z * (y + (-1.0d0))))
    if (t_0 <= (-1d+226)) then
        tmp = z * (x_m * (y + (-1.0d0)))
    else if (t_0 <= 5d+299) then
        tmp = x_m * ((1.0d0 + (y * z)) - z)
    else
        tmp = (x_m * z) * (y + (-1.0d0))
    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 t_0 = x_m * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= -1e+226) {
		tmp = z * (x_m * (y + -1.0));
	} else if (t_0 <= 5e+299) {
		tmp = x_m * ((1.0 + (y * z)) - z);
	} else {
		tmp = (x_m * z) * (y + -1.0);
	}
	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):
	t_0 = x_m * (1.0 + (z * (y + -1.0)))
	tmp = 0
	if t_0 <= -1e+226:
		tmp = z * (x_m * (y + -1.0))
	elif t_0 <= 5e+299:
		tmp = x_m * ((1.0 + (y * z)) - z)
	else:
		tmp = (x_m * z) * (y + -1.0)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	t_0 = Float64(x_m * Float64(1.0 + Float64(z * Float64(y + -1.0))))
	tmp = 0.0
	if (t_0 <= -1e+226)
		tmp = Float64(z * Float64(x_m * Float64(y + -1.0)));
	elseif (t_0 <= 5e+299)
		tmp = Float64(x_m * Float64(Float64(1.0 + Float64(y * z)) - z));
	else
		tmp = Float64(Float64(x_m * z) * Float64(y + -1.0));
	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)
	t_0 = x_m * (1.0 + (z * (y + -1.0)));
	tmp = 0.0;
	if (t_0 <= -1e+226)
		tmp = z * (x_m * (y + -1.0));
	elseif (t_0 <= 5e+299)
		tmp = x_m * ((1.0 + (y * z)) - z);
	else
		tmp = (x_m * z) * (y + -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]
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(x$95$m * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, -1e+226], N[(z * N[(x$95$m * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+299], N[(x$95$m * N[(N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < -9.99999999999999961e225

   1. Initial program 86.8%

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

   3. Taylor expanded in y around 0 78.8%

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

   4. Taylor expanded in z around inf 84.3%

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

   5. Taylor expanded in x around 0 84.4%

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

   if -9.99999999999999961e225 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < 5.0000000000000003e299

   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 0 99.9%

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

   if 5.0000000000000003e299 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z)))

   1. Initial program 70.3%

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

   3. Taylor expanded in y around 0 70.3%

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

   4. Taylor expanded in z around inf 70.3%

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

      1. sub-neg 70.3%

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

      2. metadata-eval 70.3%

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

      3. associate-*r* 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right) \leq -1 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right) \leq 5 \cdot 10^{+299}:\\ \;\;\;\;x \cdot \left(\left(1 + y \cdot z\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+95} \lor \neg \left(y \leq -3.2 \cdot 10^{+49}\right) \land \left(y \leq -3.1 \cdot 10^{+31} \lor \neg \left(y \leq 5.5 \cdot 10^{+36}\right)\right):\\ \;\;\;\;z \cdot \left(x\_m \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= y -7.4e+95)
          (and (not (<= y -3.2e+49))
               (or (<= y -3.1e+31) (not (<= y 5.5e+36)))))
    (* z (* x_m 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 <= -7.4e+95) || (!(y <= -3.2e+49) && ((y <= -3.1e+31) || !(y <= 5.5e+36)))) {
		tmp = z * (x_m * 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 <= (-7.4d+95)) .or. (.not. (y <= (-3.2d+49))) .and. (y <= (-3.1d+31)) .or. (.not. (y <= 5.5d+36))) then
        tmp = z * (x_m * 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 <= -7.4e+95) || (!(y <= -3.2e+49) && ((y <= -3.1e+31) || !(y <= 5.5e+36)))) {
		tmp = z * (x_m * 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 <= -7.4e+95) or (not (y <= -3.2e+49) and ((y <= -3.1e+31) or not (y <= 5.5e+36))):
		tmp = z * (x_m * 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 <= -7.4e+95) || (!(y <= -3.2e+49) && ((y <= -3.1e+31) || !(y <= 5.5e+36))))
		tmp = Float64(z * Float64(x_m * 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 <= -7.4e+95) || (~((y <= -3.2e+49)) && ((y <= -3.1e+31) || ~((y <= 5.5e+36)))))
		tmp = z * (x_m * 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, -7.4e+95], And[N[Not[LessEqual[y, -3.2e+49]], $MachinePrecision], Or[LessEqual[y, -3.1e+31], N[Not[LessEqual[y, 5.5e+36]], $MachinePrecision]]]], N[(z * N[(x$95$m * y), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -7.4000000000000003e95 or -3.20000000000000014e49 < y < -3.1000000000000002e31 or 5.5000000000000002e36 < y

   1. Initial program 85.4%

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

   3. Taylor expanded in y around 0 79.2%

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

   4. Taylor expanded in z around inf 76.1%

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

   5. Taylor expanded in y around inf 76.1%

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

   if -7.4000000000000003e95 < y < -3.20000000000000014e49 or -3.1000000000000002e31 < y < 5.5000000000000002e36

   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 95.5%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+95} \lor \neg \left(y \leq -3.2 \cdot 10^{+49}\right) \land \left(y \leq -3.1 \cdot 10^{+31} \lor \neg \left(y \leq 5.5 \cdot 10^{+36}\right)\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+95} \lor \neg \left(y \leq -1.75 \cdot 10^{+51} \lor \neg \left(y \leq -2.8 \cdot 10^{+30}\right) \land y \leq 7 \cdot 10^{+36}\right):\\ \;\;\;\;y \cdot \left(x\_m \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= y -4.4e+95)
          (not (or (<= y -1.75e+51) (and (not (<= y -2.8e+30)) (<= y 7e+36)))))
    (* y (* x_m z))
    (* 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 <= -4.4e+95) || !((y <= -1.75e+51) || (!(y <= -2.8e+30) && (y <= 7e+36)))) {
		tmp = y * (x_m * z);
	} 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 <= (-4.4d+95)) .or. (.not. (y <= (-1.75d+51)) .or. (.not. (y <= (-2.8d+30))) .and. (y <= 7d+36))) then
        tmp = y * (x_m * z)
    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 <= -4.4e+95) || !((y <= -1.75e+51) || (!(y <= -2.8e+30) && (y <= 7e+36)))) {
		tmp = y * (x_m * z);
	} 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 <= -4.4e+95) or not ((y <= -1.75e+51) or (not (y <= -2.8e+30) and (y <= 7e+36))):
		tmp = y * (x_m * z)
	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 <= -4.4e+95) || !((y <= -1.75e+51) || (!(y <= -2.8e+30) && (y <= 7e+36))))
		tmp = Float64(y * Float64(x_m * z));
	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 <= -4.4e+95) || ~(((y <= -1.75e+51) || (~((y <= -2.8e+30)) && (y <= 7e+36)))))
		tmp = y * (x_m * z);
	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, -4.4e+95], N[Not[Or[LessEqual[y, -1.75e+51], And[N[Not[LessEqual[y, -2.8e+30]], $MachinePrecision], LessEqual[y, 7e+36]]]], $MachinePrecision]], N[(y * N[(x$95$m * z), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999998e95 or -1.75e51 < y < -2.79999999999999983e30 or 6.9999999999999996e36 < y

   1. Initial program 85.4%

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

   3. Taylor expanded in y around inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. distribute-lft-neg-out 85.4%

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

      3. *-commutative 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in z around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-*r* 76.9%

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

   8. Simplified 76.9%

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

   if -4.3999999999999998e95 < y < -1.75e51 or -2.79999999999999983e30 < y < 6.9999999999999996e36

   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 95.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+95} \lor \neg \left(y \leq -1.75 \cdot 10^{+51} \lor \neg \left(y \leq -2.8 \cdot 10^{+30}\right) \land y \leq 7 \cdot 10^{+36}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-65} \lor \neg \left(z \leq 1.2 \cdot 10^{-49}\right):\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -6.2e-65) (not (<= z 1.2e-49)))
    (* z (* x_m (+ y -1.0)))
    (* 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 ((z <= -6.2e-65) || !(z <= 1.2e-49)) {
		tmp = z * (x_m * (y + -1.0));
	} 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 ((z <= (-6.2d-65)) .or. (.not. (z <= 1.2d-49))) then
        tmp = z * (x_m * (y + (-1.0d0)))
    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 ((z <= -6.2e-65) || !(z <= 1.2e-49)) {
		tmp = z * (x_m * (y + -1.0));
	} 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 (z <= -6.2e-65) or not (z <= 1.2e-49):
		tmp = z * (x_m * (y + -1.0))
	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 ((z <= -6.2e-65) || !(z <= 1.2e-49))
		tmp = Float64(z * Float64(x_m * Float64(y + -1.0)));
	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 ((z <= -6.2e-65) || ~((z <= 1.2e-49)))
		tmp = z * (x_m * (y + -1.0));
	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[z, -6.2e-65], N[Not[LessEqual[z, 1.2e-49]], $MachinePrecision]], N[(z * N[(x$95$m * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000032e-65 or 1.19999999999999996e-49 < z

   1. Initial program 89.6%

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

   3. Taylor expanded in y around 0 83.2%

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

   4. Taylor expanded in z around inf 92.2%

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

   5. Taylor expanded in x around 0 92.2%

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

   if -6.20000000000000032e-65 < z < 1.19999999999999996e-49

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 79.2%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-65} \lor \neg \left(z \leq 1.2 \cdot 10^{-49}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-99} \lor \neg \left(z \leq 1.7 \cdot 10^{-45}\right):\\ \;\;\;\;\left(x\_m \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -8.6e-99) (not (<= z 1.7e-45)))
    (* (* x_m z) (+ y -1.0))
    (* 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 ((z <= -8.6e-99) || !(z <= 1.7e-45)) {
		tmp = (x_m * z) * (y + -1.0);
	} 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 ((z <= (-8.6d-99)) .or. (.not. (z <= 1.7d-45))) then
        tmp = (x_m * z) * (y + (-1.0d0))
    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 ((z <= -8.6e-99) || !(z <= 1.7e-45)) {
		tmp = (x_m * z) * (y + -1.0);
	} 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 (z <= -8.6e-99) or not (z <= 1.7e-45):
		tmp = (x_m * z) * (y + -1.0)
	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 ((z <= -8.6e-99) || !(z <= 1.7e-45))
		tmp = Float64(Float64(x_m * z) * Float64(y + -1.0));
	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 ((z <= -8.6e-99) || ~((z <= 1.7e-45)))
		tmp = (x_m * z) * (y + -1.0);
	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[z, -8.6e-99], N[Not[LessEqual[z, 1.7e-45]], $MachinePrecision]], N[(N[(x$95$m * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -8.5999999999999998e-99 or 1.70000000000000002e-45 < z

   1. Initial program 90.1%

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

   3. Taylor expanded in y around 0 90.1%

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

   4. Taylor expanded in z around inf 81.1%

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

      1. sub-neg 81.1%

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

      2. metadata-eval 81.1%

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

      3. associate-*r* 90.8%

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

   6. Simplified 90.8%

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

   if -8.5999999999999998e-99 < z < 1.70000000000000002e-45

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 81.6%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-99} \lor \neg \left(z \leq 1.7 \cdot 10^{-45}\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3200:\\ \;\;\;\;\left(x\_m \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\_m + x\_m \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= z -3200.0)
    (* (* x_m z) (+ y -1.0))
    (if (<= z 1.0) (+ x_m (* x_m (* y z))) (* z (* x_m (+ y -1.0)))))))

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 <= -3200.0) {
		tmp = (x_m * z) * (y + -1.0);
	} else if (z <= 1.0) {
		tmp = x_m + (x_m * (y * z));
	} else {
		tmp = z * (x_m * (y + -1.0));
	}
	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 <= (-3200.0d0)) then
        tmp = (x_m * z) * (y + (-1.0d0))
    else if (z <= 1.0d0) then
        tmp = x_m + (x_m * (y * z))
    else
        tmp = z * (x_m * (y + (-1.0d0)))
    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 <= -3200.0) {
		tmp = (x_m * z) * (y + -1.0);
	} else if (z <= 1.0) {
		tmp = x_m + (x_m * (y * z));
	} else {
		tmp = z * (x_m * (y + -1.0));
	}
	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 <= -3200.0:
		tmp = (x_m * z) * (y + -1.0)
	elif z <= 1.0:
		tmp = x_m + (x_m * (y * z))
	else:
		tmp = z * (x_m * (y + -1.0))
	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 <= -3200.0)
		tmp = Float64(Float64(x_m * z) * Float64(y + -1.0));
	elseif (z <= 1.0)
		tmp = Float64(x_m + Float64(x_m * Float64(y * z)));
	else
		tmp = Float64(z * Float64(x_m * Float64(y + -1.0)));
	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 <= -3200.0)
		tmp = (x_m * z) * (y + -1.0);
	elseif (z <= 1.0)
		tmp = x_m + (x_m * (y * z));
	else
		tmp = z * (x_m * (y + -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]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[z, -3200.0], N[(N[(x$95$m * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x$95$m + N[(x$95$m * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x$95$m * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -3200

   1. Initial program 87.2%

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

   3. Taylor expanded in y around 0 87.2%

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

   4. Taylor expanded in z around inf 86.1%

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

      1. sub-neg 86.1%

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

      2. metadata-eval 86.1%

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

      3. associate-*r* 98.8%

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

   6. Simplified 98.8%

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

   if -3200 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 98.3%

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

      1. mul-1-neg 98.3%

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

      2. distribute-lft-neg-out 98.3%

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

      3. *-commutative 98.3%

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

   5. Simplified 98.3%

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

      1. flip-- 94.6%

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

      2. flip-- 98.3%

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

      3. *-commutative 98.3%

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

      4. cancel-sign-sub 98.3%

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

      5. *-commutative 98.3%

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

      6. distribute-rgt-in 98.3%

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

      7. *-un-lft-identity 98.3%

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

      8. *-commutative 98.3%

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

   7. Applied egg-rr 98.3%

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

   if 1 < z

   1. Initial program 87.9%

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

   3. Taylor expanded in y around 0 81.0%

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

   4. Taylor expanded in z around inf 97.8%

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

   5. Taylor expanded in x around 0 97.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3200:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+159} \lor \neg \left(y \leq 5.1 \cdot 10^{+36}\right):\\ \;\;\;\;x\_m \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= y -6.5e+159) (not (<= y 5.1e+36)))
    (* x_m (* y z))
    (* 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 <= -6.5e+159) || !(y <= 5.1e+36)) {
		tmp = x_m * (y * z);
	} 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 <= (-6.5d+159)) .or. (.not. (y <= 5.1d+36))) then
        tmp = x_m * (y * z)
    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 <= -6.5e+159) || !(y <= 5.1e+36)) {
		tmp = x_m * (y * z);
	} 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 <= -6.5e+159) or not (y <= 5.1e+36):
		tmp = x_m * (y * z)
	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 <= -6.5e+159) || !(y <= 5.1e+36))
		tmp = Float64(x_m * Float64(y * z));
	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 <= -6.5e+159) || ~((y <= 5.1e+36)))
		tmp = x_m * (y * z);
	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, -6.5e+159], N[Not[LessEqual[y, 5.1e+36]], $MachinePrecision]], N[(x$95$m * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000001e159 or 5.09999999999999973e36 < y

   1. Initial program 87.7%

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

   3. Taylor expanded in y around inf 70.2%

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

      1. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   if -6.5000000000000001e159 < y < 5.09999999999999973e36

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0 87.3%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+159} \lor \neg \left(y \leq 5.1 \cdot 10^{+36}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3200 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x\_m \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (or (<= z -3200.0) (not (<= z 1.0))) (* x_m (- z)) 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 ((z <= -3200.0) || !(z <= 1.0)) {
		tmp = x_m * -z;
	} 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 ((z <= (-3200.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x_m * -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);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -3200.0) || !(z <= 1.0)) {
		tmp = x_m * -z;
	} 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 (z <= -3200.0) or not (z <= 1.0):
		tmp = x_m * -z
	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 ((z <= -3200.0) || !(z <= 1.0))
		tmp = Float64(x_m * 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);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((z <= -3200.0) || ~((z <= 1.0)))
		tmp = x_m * -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]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[z, -3200.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x$95$m * (-z)), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3200 or 1 < z

   1. Initial program 87.6%

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

   3. Taylor expanded in z around inf 86.0%

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

   4. Taylor expanded in y around 0 55.7%

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

      1. mul-1-neg 55.7%

         \[\leadsto \color{blue}{-x \cdot z} \]

      2. *-commutative 55.7%

         \[\leadsto -\color{blue}{z \cdot x} \]

      3. distribute-rgt-neg-in 55.7%

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

   6. Simplified 55.7%

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

   if -3200 < z < 1

   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 69.5%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3200 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.3% 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 1 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 93.6%

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

3. Taylor expanded in z around 0 35.5%

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

4. Final simplification 35.5%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.7% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024044 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (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))))