Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.1% → 97.2%

Time: 5.8s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ y z)) z))

C

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

Java

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

Python

def code(x, y, z):
	return (x * (y + z)) / z

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ y z)) z))

C

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

Java

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

Python

def code(x, y, z):
	return (x * (y + z)) / z

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x_m \cdot \left(y + z\right)}{z} \leq -4 \cdot 10^{+53}:\\ \;\;\;\;\frac{1}{z \cdot \frac{\frac{1}{y}}{x_m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\frac{z}{y + z}}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= (/ (* x_m (+ y z)) z) -4e+53)
    (/ 1.0 (* z (/ (/ 1.0 y) x_m)))
    (/ x_m (/ z (+ y 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 (((x_m * (y + z)) / z) <= -4e+53) {
		tmp = 1.0 / (z * ((1.0 / y) / x_m));
	} else {
		tmp = x_m / (z / (y + 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 (((x_m * (y + z)) / z) <= (-4d+53)) then
        tmp = 1.0d0 / (z * ((1.0d0 / y) / x_m))
    else
        tmp = x_m / (z / (y + 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 (((x_m * (y + z)) / z) <= -4e+53) {
		tmp = 1.0 / (z * ((1.0 / y) / x_m));
	} else {
		tmp = x_m / (z / (y + 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 ((x_m * (y + z)) / z) <= -4e+53:
		tmp = 1.0 / (z * ((1.0 / y) / x_m))
	else:
		tmp = x_m / (z / (y + 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 (Float64(Float64(x_m * Float64(y + z)) / z) <= -4e+53)
		tmp = Float64(1.0 / Float64(z * Float64(Float64(1.0 / y) / x_m)));
	else
		tmp = Float64(x_m / Float64(z / Float64(y + 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 (((x_m * (y + z)) / z) <= -4e+53)
		tmp = 1.0 / (z * ((1.0 / y) / x_m));
	else
		tmp = x_m / (z / (y + z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[N[(N[(x$95$m * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], -4e+53], N[(1.0 / N[(z * N[(N[(1.0 / y), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -50000:\\ \;\;\;\;\frac{y}{\frac{z}{x_m}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-84}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;y \leq 3700000000000:\\ \;\;\;\;x_m \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+18}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+165}:\\ \;\;\;\;y \cdot \frac{x_m}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -50000.0)
    (/ y (/ z x_m))
    (if (<= y 7.2e-84)
      x_m
      (if (<= y 3700000000000.0)
        (* x_m (/ y z))
        (if (<= y 7.2e+18)
          x_m
          (if (<= y 2e+165) (* y (/ x_m z)) (/ (* x_m y) 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 <= -50000.0) {
		tmp = y / (z / x_m);
	} else if (y <= 7.2e-84) {
		tmp = x_m;
	} else if (y <= 3700000000000.0) {
		tmp = x_m * (y / z);
	} else if (y <= 7.2e+18) {
		tmp = x_m;
	} else if (y <= 2e+165) {
		tmp = y * (x_m / z);
	} else {
		tmp = (x_m * y) / 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 <= (-50000.0d0)) then
        tmp = y / (z / x_m)
    else if (y <= 7.2d-84) then
        tmp = x_m
    else if (y <= 3700000000000.0d0) then
        tmp = x_m * (y / z)
    else if (y <= 7.2d+18) then
        tmp = x_m
    else if (y <= 2d+165) then
        tmp = y * (x_m / z)
    else
        tmp = (x_m * y) / z
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -50000.0) {
		tmp = y / (z / x_m);
	} else if (y <= 7.2e-84) {
		tmp = x_m;
	} else if (y <= 3700000000000.0) {
		tmp = x_m * (y / z);
	} else if (y <= 7.2e+18) {
		tmp = x_m;
	} else if (y <= 2e+165) {
		tmp = y * (x_m / z);
	} else {
		tmp = (x_m * y) / 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 <= -50000.0:
		tmp = y / (z / x_m)
	elif y <= 7.2e-84:
		tmp = x_m
	elif y <= 3700000000000.0:
		tmp = x_m * (y / z)
	elif y <= 7.2e+18:
		tmp = x_m
	elif y <= 2e+165:
		tmp = y * (x_m / z)
	else:
		tmp = (x_m * y) / 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 <= -50000.0)
		tmp = Float64(y / Float64(z / x_m));
	elseif (y <= 7.2e-84)
		tmp = x_m;
	elseif (y <= 3700000000000.0)
		tmp = Float64(x_m * Float64(y / z));
	elseif (y <= 7.2e+18)
		tmp = x_m;
	elseif (y <= 2e+165)
		tmp = Float64(y * Float64(x_m / z));
	else
		tmp = Float64(Float64(x_m * y) / 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 <= -50000.0)
		tmp = y / (z / x_m);
	elseif (y <= 7.2e-84)
		tmp = x_m;
	elseif (y <= 3700000000000.0)
		tmp = x_m * (y / z);
	elseif (y <= 7.2e+18)
		tmp = x_m;
	elseif (y <= 2e+165)
		tmp = y * (x_m / z);
	else
		tmp = (x_m * y) / z;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -50000.0], N[(y / N[(z / x$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-84], x$95$m, If[LessEqual[y, 3700000000000.0], N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+18], x$95$m, If[LessEqual[y, 2e+165], N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m * y), $MachinePrecision] / z), $MachinePrecision]]]]]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 97.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x_m \cdot \left(y + z\right)}{z} \leq -5 \cdot 10^{+51}:\\ \;\;\;\;\frac{x_m \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\frac{z}{y + z}}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= (/ (* x_m (+ y z)) z) -5e+51)
    (/ (* x_m y) z)
    (/ x_m (/ z (+ y 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 (((x_m * (y + z)) / z) <= -5e+51) {
		tmp = (x_m * y) / z;
	} else {
		tmp = x_m / (z / (y + 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 (((x_m * (y + z)) / z) <= (-5d+51)) then
        tmp = (x_m * y) / z
    else
        tmp = x_m / (z / (y + 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 (((x_m * (y + z)) / z) <= -5e+51) {
		tmp = (x_m * y) / z;
	} else {
		tmp = x_m / (z / (y + 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 ((x_m * (y + z)) / z) <= -5e+51:
		tmp = (x_m * y) / z
	else:
		tmp = x_m / (z / (y + 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 (Float64(Float64(x_m * Float64(y + z)) / z) <= -5e+51)
		tmp = Float64(Float64(x_m * y) / z);
	else
		tmp = Float64(x_m / Float64(z / Float64(y + 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 (((x_m * (y + z)) / z) <= -5e+51)
		tmp = (x_m * y) / z;
	else
		tmp = x_m / (z / (y + z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[N[(N[(x$95$m * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], -5e+51], N[(N[(x$95$m * y), $MachinePrecision] / z), $MachinePrecision], N[(x$95$m / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -25000000000000 \lor \neg \left(y \leq 5.9 \cdot 10^{-83} \lor \neg \left(y \leq 290000000000\right) \land y \leq 8.5 \cdot 10^{+26}\right):\\ \;\;\;\;x_m \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

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 (<= y -25000000000000.0)
          (not
           (or (<= y 5.9e-83)
               (and (not (<= y 290000000000.0)) (<= y 8.5e+26)))))
    (* x_m (/ y 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 ((y <= -25000000000000.0) || !((y <= 5.9e-83) || (!(y <= 290000000000.0) && (y <= 8.5e+26)))) {
		tmp = x_m * (y / 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 ((y <= (-25000000000000.0d0)) .or. (.not. (y <= 5.9d-83) .or. (.not. (y <= 290000000000.0d0)) .and. (y <= 8.5d+26))) then
        tmp = x_m * (y / z)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -25000000000000.0) || !((y <= 5.9e-83) || (!(y <= 290000000000.0) && (y <= 8.5e+26)))) {
		tmp = x_m * (y / z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (y <= -25000000000000.0) or not ((y <= 5.9e-83) or (not (y <= 290000000000.0) and (y <= 8.5e+26))):
		tmp = x_m * (y / 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 ((y <= -25000000000000.0) || !((y <= 5.9e-83) || (!(y <= 290000000000.0) && (y <= 8.5e+26))))
		tmp = Float64(x_m * Float64(y / 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 ((y <= -25000000000000.0) || ~(((y <= 5.9e-83) || (~((y <= 290000000000.0)) && (y <= 8.5e+26)))))
		tmp = x_m * (y / z);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[y, -25000000000000.0], N[Not[Or[LessEqual[y, 5.9e-83], And[N[Not[LessEqual[y, 290000000000.0]], $MachinePrecision], LessEqual[y, 8.5e+26]]]], $MachinePrecision]], N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := y \cdot \frac{x_m}{z}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3200000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-83}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;y \leq 120000000000:\\ \;\;\;\;x_m \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+21}:\\ \;\;\;\;x_m\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (* y (/ x_m z))))
   (*
    x_s
    (if (<= y -3200000.0)
      t_0
      (if (<= y 3.2e-83)
        x_m
        (if (<= y 120000000000.0)
          (* x_m (/ y z))
          (if (<= y 1.1e+21) x_m t_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 = y * (x_m / z);
	double tmp;
	if (y <= -3200000.0) {
		tmp = t_0;
	} else if (y <= 3.2e-83) {
		tmp = x_m;
	} else if (y <= 120000000000.0) {
		tmp = x_m * (y / z);
	} else if (y <= 1.1e+21) {
		tmp = x_m;
	} else {
		tmp = t_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 = y * (x_m / z)
    if (y <= (-3200000.0d0)) then
        tmp = t_0
    else if (y <= 3.2d-83) then
        tmp = x_m
    else if (y <= 120000000000.0d0) then
        tmp = x_m * (y / z)
    else if (y <= 1.1d+21) then
        tmp = x_m
    else
        tmp = t_0
    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 = y * (x_m / z);
	double tmp;
	if (y <= -3200000.0) {
		tmp = t_0;
	} else if (y <= 3.2e-83) {
		tmp = x_m;
	} else if (y <= 120000000000.0) {
		tmp = x_m * (y / z);
	} else if (y <= 1.1e+21) {
		tmp = x_m;
	} else {
		tmp = t_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 = y * (x_m / z)
	tmp = 0
	if y <= -3200000.0:
		tmp = t_0
	elif y <= 3.2e-83:
		tmp = x_m
	elif y <= 120000000000.0:
		tmp = x_m * (y / z)
	elif y <= 1.1e+21:
		tmp = x_m
	else:
		tmp = t_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(y * Float64(x_m / z))
	tmp = 0.0
	if (y <= -3200000.0)
		tmp = t_0;
	elseif (y <= 3.2e-83)
		tmp = x_m;
	elseif (y <= 120000000000.0)
		tmp = Float64(x_m * Float64(y / z));
	elseif (y <= 1.1e+21)
		tmp = x_m;
	else
		tmp = t_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 = y * (x_m / z);
	tmp = 0.0;
	if (y <= -3200000.0)
		tmp = t_0;
	elseif (y <= 3.2e-83)
		tmp = x_m;
	elseif (y <= 120000000000.0)
		tmp = x_m * (y / z);
	elseif (y <= 1.1e+21)
		tmp = x_m;
	else
		tmp = t_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[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -3200000.0], t$95$0, If[LessEqual[y, 3.2e-83], x$95$m, If[LessEqual[y, 120000000000.0], N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+21], x$95$m, t$95$0]]]]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -35000000:\\ \;\;\;\;\frac{y}{\frac{z}{x_m}}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-83}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;y \leq 2150000000000:\\ \;\;\;\;x_m \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+19}:\\ \;\;\;\;x_m\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x_m}{z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -35000000.0)
    (/ y (/ z x_m))
    (if (<= y 5.8e-83)
      x_m
      (if (<= y 2150000000000.0)
        (* x_m (/ y z))
        (if (<= y 1.3e+19) x_m (* 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 <= -35000000.0) {
		tmp = y / (z / x_m);
	} else if (y <= 5.8e-83) {
		tmp = x_m;
	} else if (y <= 2150000000000.0) {
		tmp = x_m * (y / z);
	} else if (y <= 1.3e+19) {
		tmp = x_m;
	} 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 <= (-35000000.0d0)) then
        tmp = y / (z / x_m)
    else if (y <= 5.8d-83) then
        tmp = x_m
    else if (y <= 2150000000000.0d0) then
        tmp = x_m * (y / z)
    else if (y <= 1.3d+19) then
        tmp = x_m
    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 <= -35000000.0) {
		tmp = y / (z / x_m);
	} else if (y <= 5.8e-83) {
		tmp = x_m;
	} else if (y <= 2150000000000.0) {
		tmp = x_m * (y / z);
	} else if (y <= 1.3e+19) {
		tmp = x_m;
	} 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 <= -35000000.0:
		tmp = y / (z / x_m)
	elif y <= 5.8e-83:
		tmp = x_m
	elif y <= 2150000000000.0:
		tmp = x_m * (y / z)
	elif y <= 1.3e+19:
		tmp = x_m
	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 <= -35000000.0)
		tmp = Float64(y / Float64(z / x_m));
	elseif (y <= 5.8e-83)
		tmp = x_m;
	elseif (y <= 2150000000000.0)
		tmp = Float64(x_m * Float64(y / z));
	elseif (y <= 1.3e+19)
		tmp = x_m;
	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 <= -35000000.0)
		tmp = y / (z / x_m);
	elseif (y <= 5.8e-83)
		tmp = x_m;
	elseif (y <= 2150000000000.0)
		tmp = x_m * (y / z);
	elseif (y <= 1.3e+19)
		tmp = x_m;
	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, -35000000.0], N[(y / N[(z / x$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-83], x$95$m, If[LessEqual[y, 2150000000000.0], N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+19], x$95$m, N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 90.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+133}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+179}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x_m}{z}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= z -1.8e+133) x_m (if (<= z 8.2e+179) (* (+ y z) (/ 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 <= -1.8e+133) {
		tmp = x_m;
	} else if (z <= 8.2e+179) {
		tmp = (y + z) * (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 <= (-1.8d+133)) then
        tmp = x_m
    else if (z <= 8.2d+179) then
        tmp = (y + z) * (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 <= -1.8e+133) {
		tmp = x_m;
	} else if (z <= 8.2e+179) {
		tmp = (y + z) * (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 <= -1.8e+133:
		tmp = x_m
	elif z <= 8.2e+179:
		tmp = (y + z) * (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 <= -1.8e+133)
		tmp = x_m;
	elseif (z <= 8.2e+179)
		tmp = Float64(Float64(y + z) * Float64(x_m / 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 <= -1.8e+133)
		tmp = x_m;
	elseif (z <= 8.2e+179)
		tmp = (y + z) * (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[LessEqual[z, -1.8e+133], x$95$m, If[LessEqual[z, 8.2e+179], N[(N[(y + z), $MachinePrecision] * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 96.1% accurate, 1.0× speedup

Math

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

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 (* x_m (/ y z)))))

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 + (x_m * (y / z)));
}

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 + (x_m * (y / z)))
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 + (x_m * (y / z)));
}

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 + (x_m * (y / z)))

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * Float64(x_m + Float64(x_m * Float64(y / z))))
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 + (x_m * (y / z)));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * N[(x$95$m + N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 51.4% accurate, 7.0× 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 96.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{z}{y + z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ x (/ z (+ y z))))

C

double code(double x, double y, double z) {
	return x / (z / (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 / (z / (y + z))
end function

Java

public static double code(double x, double y, double z) {
	return x / (z / (y + z));
}

Python

def code(x, y, z):
	return x / (z / (y + z))

Julia

function code(x, y, z)
	return Float64(x / Float64(z / Float64(y + z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x / (z / (y + z));
end

Wolfram

code[x_, y_, z_] := N[(x / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024008 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (/ x (/ z (+ y z)))

  (/ (* x (+ y z)) z))