Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3

Percentage Accurate: 87.9% → 99.6%

Time: 5.5s

Alternatives: 10

Speedup: 1.0×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / 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) + 1.0d0)) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 87.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / 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) + 1.0d0)) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;x_m \leq 1.25 \cdot 10^{-142}:\\ \;\;\;\;\frac{x_m \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{z} \cdot \left(y + 1\right) - x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= x_m 1.25e-142)
    (/ (* x_m (+ (- y z) 1.0)) z)
    (- (* (/ x_m z) (+ y 1.0)) 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 (x_m <= 1.25e-142) {
		tmp = (x_m * ((y - z) + 1.0)) / z;
	} else {
		tmp = ((x_m / z) * (y + 1.0)) - 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 (x_m <= 1.25d-142) then
        tmp = (x_m * ((y - z) + 1.0d0)) / z
    else
        tmp = ((x_m / z) * (y + 1.0d0)) - 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 (x_m <= 1.25e-142) {
		tmp = (x_m * ((y - z) + 1.0)) / z;
	} else {
		tmp = ((x_m / z) * (y + 1.0)) - 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 x_m <= 1.25e-142:
		tmp = (x_m * ((y - z) + 1.0)) / z
	else:
		tmp = ((x_m / z) * (y + 1.0)) - 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 (x_m <= 1.25e-142)
		tmp = Float64(Float64(x_m * Float64(Float64(y - z) + 1.0)) / z);
	else
		tmp = Float64(Float64(Float64(x_m / z) * Float64(y + 1.0)) - 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 (x_m <= 1.25e-142)
		tmp = (x_m * ((y - z) + 1.0)) / z;
	else
		tmp = ((x_m / z) * (y + 1.0)) - 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[x$95$m, 1.25e-142], N[(N[(x$95$m * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(x$95$m / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] - x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 2: 65.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := y \cdot \frac{x_m}{z}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+36}:\\ \;\;\;\;-x_m\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-75}:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-191}:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-308}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-149}:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-35}:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+35}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x_m\\ \end{array} \end{array} \end{array} \]

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 (<= z -9e+36)
      (- x_m)
      (if (<= z -3.8e-29)
        t_0
        (if (<= z -3.8e-75)
          (/ x_m z)
          (if (<= z -2.5e-100)
            t_0
            (if (<= z -1.6e-191)
              (/ x_m z)
              (if (<= z -3.9e-308)
                t_0
                (if (<= z 5.5e-149)
                  (/ x_m z)
                  (if (<= z 3.35e-100)
                    t_0
                    (if (<= z 1.4e-35)
                      (/ x_m z)
                      (if (<= z 7.5e+35) t_0 (- 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 t_0 = y * (x_m / z);
	double tmp;
	if (z <= -9e+36) {
		tmp = -x_m;
	} else if (z <= -3.8e-29) {
		tmp = t_0;
	} else if (z <= -3.8e-75) {
		tmp = x_m / z;
	} else if (z <= -2.5e-100) {
		tmp = t_0;
	} else if (z <= -1.6e-191) {
		tmp = x_m / z;
	} else if (z <= -3.9e-308) {
		tmp = t_0;
	} else if (z <= 5.5e-149) {
		tmp = x_m / z;
	} else if (z <= 3.35e-100) {
		tmp = t_0;
	} else if (z <= 1.4e-35) {
		tmp = x_m / z;
	} else if (z <= 7.5e+35) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y * (x_m / z)
    if (z <= (-9d+36)) then
        tmp = -x_m
    else if (z <= (-3.8d-29)) then
        tmp = t_0
    else if (z <= (-3.8d-75)) then
        tmp = x_m / z
    else if (z <= (-2.5d-100)) then
        tmp = t_0
    else if (z <= (-1.6d-191)) then
        tmp = x_m / z
    else if (z <= (-3.9d-308)) then
        tmp = t_0
    else if (z <= 5.5d-149) then
        tmp = x_m / z
    else if (z <= 3.35d-100) then
        tmp = t_0
    else if (z <= 1.4d-35) then
        tmp = x_m / z
    else if (z <= 7.5d+35) then
        tmp = t_0
    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 t_0 = y * (x_m / z);
	double tmp;
	if (z <= -9e+36) {
		tmp = -x_m;
	} else if (z <= -3.8e-29) {
		tmp = t_0;
	} else if (z <= -3.8e-75) {
		tmp = x_m / z;
	} else if (z <= -2.5e-100) {
		tmp = t_0;
	} else if (z <= -1.6e-191) {
		tmp = x_m / z;
	} else if (z <= -3.9e-308) {
		tmp = t_0;
	} else if (z <= 5.5e-149) {
		tmp = x_m / z;
	} else if (z <= 3.35e-100) {
		tmp = t_0;
	} else if (z <= 1.4e-35) {
		tmp = x_m / z;
	} else if (z <= 7.5e+35) {
		tmp = t_0;
	} 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):
	t_0 = y * (x_m / z)
	tmp = 0
	if z <= -9e+36:
		tmp = -x_m
	elif z <= -3.8e-29:
		tmp = t_0
	elif z <= -3.8e-75:
		tmp = x_m / z
	elif z <= -2.5e-100:
		tmp = t_0
	elif z <= -1.6e-191:
		tmp = x_m / z
	elif z <= -3.9e-308:
		tmp = t_0
	elif z <= 5.5e-149:
		tmp = x_m / z
	elif z <= 3.35e-100:
		tmp = t_0
	elif z <= 1.4e-35:
		tmp = x_m / z
	elif z <= 7.5e+35:
		tmp = t_0
	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)
	t_0 = Float64(y * Float64(x_m / z))
	tmp = 0.0
	if (z <= -9e+36)
		tmp = Float64(-x_m);
	elseif (z <= -3.8e-29)
		tmp = t_0;
	elseif (z <= -3.8e-75)
		tmp = Float64(x_m / z);
	elseif (z <= -2.5e-100)
		tmp = t_0;
	elseif (z <= -1.6e-191)
		tmp = Float64(x_m / z);
	elseif (z <= -3.9e-308)
		tmp = t_0;
	elseif (z <= 5.5e-149)
		tmp = Float64(x_m / z);
	elseif (z <= 3.35e-100)
		tmp = t_0;
	elseif (z <= 1.4e-35)
		tmp = Float64(x_m / z);
	elseif (z <= 7.5e+35)
		tmp = t_0;
	else
		tmp = Float64(-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)
	t_0 = y * (x_m / z);
	tmp = 0.0;
	if (z <= -9e+36)
		tmp = -x_m;
	elseif (z <= -3.8e-29)
		tmp = t_0;
	elseif (z <= -3.8e-75)
		tmp = x_m / z;
	elseif (z <= -2.5e-100)
		tmp = t_0;
	elseif (z <= -1.6e-191)
		tmp = x_m / z;
	elseif (z <= -3.9e-308)
		tmp = t_0;
	elseif (z <= 5.5e-149)
		tmp = x_m / z;
	elseif (z <= 3.35e-100)
		tmp = t_0;
	elseif (z <= 1.4e-35)
		tmp = x_m / z;
	elseif (z <= 7.5e+35)
		tmp = t_0;
	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_] := Block[{t$95$0 = N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -9e+36], (-x$95$m), If[LessEqual[z, -3.8e-29], t$95$0, If[LessEqual[z, -3.8e-75], N[(x$95$m / z), $MachinePrecision], If[LessEqual[z, -2.5e-100], t$95$0, If[LessEqual[z, -1.6e-191], N[(x$95$m / z), $MachinePrecision], If[LessEqual[z, -3.9e-308], t$95$0, If[LessEqual[z, 5.5e-149], N[(x$95$m / z), $MachinePrecision], If[LessEqual[z, 3.35e-100], t$95$0, If[LessEqual[z, 1.4e-35], N[(x$95$m / z), $MachinePrecision], If[LessEqual[z, 7.5e+35], t$95$0, (-x$95$m)]]]]]]]]]]), $MachinePrecision]]

Derivation

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

Alternative 3: 63.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := y \cdot \frac{x_m}{z}\\ t_1 := x_m \cdot \frac{y}{z}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+36}:\\ \;\;\;\;-x_m\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-75}:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-99}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-191}:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-307}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-151}:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-29}:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-x_m\\ \end{array} \end{array} \end{array} \]

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))) (t_1 (* x_m (/ y z))))
   (*
    x_s
    (if (<= z -1.2e+36)
      (- x_m)
      (if (<= z -7.8e-31)
        t_1
        (if (<= z -3.1e-75)
          (/ x_m z)
          (if (<= z -1.4e-99)
            t_0
            (if (<= z -7e-191)
              (/ x_m z)
              (if (<= z 6.5e-307)
                t_0
                (if (<= z 1.45e-151)
                  (/ x_m z)
                  (if (<= z 1.8e-100)
                    t_0
                    (if (<= z 2.4e-29)
                      (/ x_m z)
                      (if (<= z 6.2e+147) t_1 (- 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 t_0 = y * (x_m / z);
	double t_1 = x_m * (y / z);
	double tmp;
	if (z <= -1.2e+36) {
		tmp = -x_m;
	} else if (z <= -7.8e-31) {
		tmp = t_1;
	} else if (z <= -3.1e-75) {
		tmp = x_m / z;
	} else if (z <= -1.4e-99) {
		tmp = t_0;
	} else if (z <= -7e-191) {
		tmp = x_m / z;
	} else if (z <= 6.5e-307) {
		tmp = t_0;
	} else if (z <= 1.45e-151) {
		tmp = x_m / z;
	} else if (z <= 1.8e-100) {
		tmp = t_0;
	} else if (z <= 2.4e-29) {
		tmp = x_m / z;
	} else if (z <= 6.2e+147) {
		tmp = t_1;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (x_m / z)
    t_1 = x_m * (y / z)
    if (z <= (-1.2d+36)) then
        tmp = -x_m
    else if (z <= (-7.8d-31)) then
        tmp = t_1
    else if (z <= (-3.1d-75)) then
        tmp = x_m / z
    else if (z <= (-1.4d-99)) then
        tmp = t_0
    else if (z <= (-7d-191)) then
        tmp = x_m / z
    else if (z <= 6.5d-307) then
        tmp = t_0
    else if (z <= 1.45d-151) then
        tmp = x_m / z
    else if (z <= 1.8d-100) then
        tmp = t_0
    else if (z <= 2.4d-29) then
        tmp = x_m / z
    else if (z <= 6.2d+147) then
        tmp = t_1
    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 t_0 = y * (x_m / z);
	double t_1 = x_m * (y / z);
	double tmp;
	if (z <= -1.2e+36) {
		tmp = -x_m;
	} else if (z <= -7.8e-31) {
		tmp = t_1;
	} else if (z <= -3.1e-75) {
		tmp = x_m / z;
	} else if (z <= -1.4e-99) {
		tmp = t_0;
	} else if (z <= -7e-191) {
		tmp = x_m / z;
	} else if (z <= 6.5e-307) {
		tmp = t_0;
	} else if (z <= 1.45e-151) {
		tmp = x_m / z;
	} else if (z <= 1.8e-100) {
		tmp = t_0;
	} else if (z <= 2.4e-29) {
		tmp = x_m / z;
	} else if (z <= 6.2e+147) {
		tmp = t_1;
	} 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):
	t_0 = y * (x_m / z)
	t_1 = x_m * (y / z)
	tmp = 0
	if z <= -1.2e+36:
		tmp = -x_m
	elif z <= -7.8e-31:
		tmp = t_1
	elif z <= -3.1e-75:
		tmp = x_m / z
	elif z <= -1.4e-99:
		tmp = t_0
	elif z <= -7e-191:
		tmp = x_m / z
	elif z <= 6.5e-307:
		tmp = t_0
	elif z <= 1.45e-151:
		tmp = x_m / z
	elif z <= 1.8e-100:
		tmp = t_0
	elif z <= 2.4e-29:
		tmp = x_m / z
	elif z <= 6.2e+147:
		tmp = t_1
	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)
	t_0 = Float64(y * Float64(x_m / z))
	t_1 = Float64(x_m * Float64(y / z))
	tmp = 0.0
	if (z <= -1.2e+36)
		tmp = Float64(-x_m);
	elseif (z <= -7.8e-31)
		tmp = t_1;
	elseif (z <= -3.1e-75)
		tmp = Float64(x_m / z);
	elseif (z <= -1.4e-99)
		tmp = t_0;
	elseif (z <= -7e-191)
		tmp = Float64(x_m / z);
	elseif (z <= 6.5e-307)
		tmp = t_0;
	elseif (z <= 1.45e-151)
		tmp = Float64(x_m / z);
	elseif (z <= 1.8e-100)
		tmp = t_0;
	elseif (z <= 2.4e-29)
		tmp = Float64(x_m / z);
	elseif (z <= 6.2e+147)
		tmp = t_1;
	else
		tmp = Float64(-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)
	t_0 = y * (x_m / z);
	t_1 = x_m * (y / z);
	tmp = 0.0;
	if (z <= -1.2e+36)
		tmp = -x_m;
	elseif (z <= -7.8e-31)
		tmp = t_1;
	elseif (z <= -3.1e-75)
		tmp = x_m / z;
	elseif (z <= -1.4e-99)
		tmp = t_0;
	elseif (z <= -7e-191)
		tmp = x_m / z;
	elseif (z <= 6.5e-307)
		tmp = t_0;
	elseif (z <= 1.45e-151)
		tmp = x_m / z;
	elseif (z <= 1.8e-100)
		tmp = t_0;
	elseif (z <= 2.4e-29)
		tmp = x_m / z;
	elseif (z <= 6.2e+147)
		tmp = t_1;
	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_] := Block[{t$95$0 = N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -1.2e+36], (-x$95$m), If[LessEqual[z, -7.8e-31], t$95$1, If[LessEqual[z, -3.1e-75], N[(x$95$m / z), $MachinePrecision], If[LessEqual[z, -1.4e-99], t$95$0, If[LessEqual[z, -7e-191], N[(x$95$m / z), $MachinePrecision], If[LessEqual[z, 6.5e-307], t$95$0, If[LessEqual[z, 1.45e-151], N[(x$95$m / z), $MachinePrecision], If[LessEqual[z, 1.8e-100], t$95$0, If[LessEqual[z, 2.4e-29], N[(x$95$m / z), $MachinePrecision], If[LessEqual[z, 6.2e+147], t$95$1, (-x$95$m)]]]]]]]]]]), $MachinePrecision]]]

Derivation

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

Alternative 4: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-75} \lor \neg \left(z \leq 9.5 \cdot 10^{-19}\right):\\ \;\;\;\;x_m \cdot \left(\frac{y + 1}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m \cdot \left(y + 1\right)}{z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -1.8e-75) (not (<= z 9.5e-19)))
    (* x_m (+ (/ (+ y 1.0) z) -1.0))
    (/ (* x_m (+ y 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 <= -1.8e-75) || !(z <= 9.5e-19)) {
		tmp = x_m * (((y + 1.0) / z) + -1.0);
	} else {
		tmp = (x_m * (y + 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 <= (-1.8d-75)) .or. (.not. (z <= 9.5d-19))) then
        tmp = x_m * (((y + 1.0d0) / z) + (-1.0d0))
    else
        tmp = (x_m * (y + 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 <= -1.8e-75) || !(z <= 9.5e-19)) {
		tmp = x_m * (((y + 1.0) / z) + -1.0);
	} else {
		tmp = (x_m * (y + 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 <= -1.8e-75) or not (z <= 9.5e-19):
		tmp = x_m * (((y + 1.0) / z) + -1.0)
	else:
		tmp = (x_m * (y + 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 <= -1.8e-75) || !(z <= 9.5e-19))
		tmp = Float64(x_m * Float64(Float64(Float64(y + 1.0) / z) + -1.0));
	else
		tmp = Float64(Float64(x_m * Float64(y + 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 <= -1.8e-75) || ~((z <= 9.5e-19)))
		tmp = x_m * (((y + 1.0) / z) + -1.0);
	else
		tmp = (x_m * (y + 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, -1.8e-75], N[Not[LessEqual[z, 9.5e-19]], $MachinePrecision]], N[(x$95$m * N[(N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 5: 95.0% accurate, 0.8× speedup

Math

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

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

Derivation

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

Alternative 6: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+23} \lor \neg \left(y \leq 6.2 \cdot 10^{+75}\right):\\ \;\;\;\;y \cdot \frac{x_m}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{z} - x_m\\ \end{array} \end{array} \]

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 -4.1e+23) (not (<= y 6.2e+75)))
    (* y (/ x_m 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 ((y <= -4.1e+23) || !(y <= 6.2e+75)) {
		tmp = y * (x_m / z);
	} else {
		tmp = (x_m / z) - 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 <= (-4.1d+23)) .or. (.not. (y <= 6.2d+75))) then
        tmp = y * (x_m / z)
    else
        tmp = (x_m / z) - 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 <= -4.1e+23) || !(y <= 6.2e+75)) {
		tmp = y * (x_m / z);
	} else {
		tmp = (x_m / z) - 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 <= -4.1e+23) or not (y <= 6.2e+75):
		tmp = y * (x_m / z)
	else:
		tmp = (x_m / z) - 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 <= -4.1e+23) || !(y <= 6.2e+75))
		tmp = Float64(y * Float64(x_m / z));
	else
		tmp = Float64(Float64(x_m / z) - 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 <= -4.1e+23) || ~((y <= 6.2e+75)))
		tmp = y * (x_m / z);
	else
		tmp = (x_m / z) - 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, -4.1e+23], N[Not[LessEqual[y, 6.2e+75]], $MachinePrecision]], N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] - x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 7: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+23}:\\ \;\;\;\;\frac{x_m \cdot y}{z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{x_m}{z} - x_m\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x_m}{z}\\ \end{array} \end{array} \]

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 -4.1e+23)
    (/ (* x_m y) z)
    (if (<= y 4.2e+80) (- (/ x_m z) 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 <= -4.1e+23) {
		tmp = (x_m * y) / z;
	} else if (y <= 4.2e+80) {
		tmp = (x_m / z) - 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 <= (-4.1d+23)) then
        tmp = (x_m * y) / z
    else if (y <= 4.2d+80) then
        tmp = (x_m / z) - 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 <= -4.1e+23) {
		tmp = (x_m * y) / z;
	} else if (y <= 4.2e+80) {
		tmp = (x_m / z) - 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 <= -4.1e+23:
		tmp = (x_m * y) / z
	elif y <= 4.2e+80:
		tmp = (x_m / z) - 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 <= -4.1e+23)
		tmp = Float64(Float64(x_m * y) / z);
	elseif (y <= 4.2e+80)
		tmp = Float64(Float64(x_m / z) - 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 <= -4.1e+23)
		tmp = (x_m * y) / z;
	elseif (y <= 4.2e+80)
		tmp = (x_m / z) - 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, -4.1e+23], N[(N[(x$95$m * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 4.2e+80], N[(N[(x$95$m / z), $MachinePrecision] - x$95$m), $MachinePrecision], N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 8: 98.0% accurate, 1.0× speedup

Math

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

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 z) (+ y 1.0)) 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 / z) * (y + 1.0)) - 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 / z) * (y + 1.0d0)) - 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 / z) * (y + 1.0)) - 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 / z) * (y + 1.0)) - 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 * Float64(Float64(Float64(x_m / z) * Float64(y + 1.0)) - 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 / z) * (y + 1.0)) - 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 * N[(N[(N[(x$95$m / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] - x$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 9: 63.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 8.2 \cdot 10^{-8}\right):\\ \;\;\;\;-x_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (or (<= z -1.0) (not (<= z 8.2e-8))) (- x_m) (/ 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 ((z <= -1.0) || !(z <= 8.2e-8)) {
		tmp = -x_m;
	} else {
		tmp = 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 ((z <= (-1.0d0)) .or. (.not. (z <= 8.2d-8))) then
        tmp = -x_m
    else
        tmp = 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 ((z <= -1.0) || !(z <= 8.2e-8)) {
		tmp = -x_m;
	} else {
		tmp = 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 (z <= -1.0) or not (z <= 8.2e-8):
		tmp = -x_m
	else:
		tmp = 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 ((z <= -1.0) || !(z <= 8.2e-8))
		tmp = Float64(-x_m);
	else
		tmp = 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 ((z <= -1.0) || ~((z <= 8.2e-8)))
		tmp = -x_m;
	else
		tmp = 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[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 8.2e-8]], $MachinePrecision]], (-x$95$m), N[(x$95$m / z), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 10: 38.7% accurate, 4.5× speedup

Math

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

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)))

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 * Float64(-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: 99.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (+ 1.0 y) (/ x z)) x)))
   (if (< x -2.71483106713436e-162)
     t_0
     (if (< x 3.874108816439546e-197)
       (* (* x (+ (- y z) 1.0)) (/ 1.0 z))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} else {
		tmp = t_0;
	}
	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) :: tmp
    t_0 = ((1.0d0 + y) * (x / z)) - x
    if (x < (-2.71483106713436d-162)) then
        tmp = t_0
    else if (x < 3.874108816439546d-197) then
        tmp = (x * ((y - z) + 1.0d0)) * (1.0d0 / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((1.0 + y) * (x / z)) - x
	tmp = 0
	if x < -2.71483106713436e-162:
		tmp = t_0
	elif x < 3.874108816439546e-197:
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(1.0 + y) * Float64(x / z)) - x)
	tmp = 0.0
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) * Float64(1.0 / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((1.0 + y) * (x / z)) - x;
	tmp = 0.0;
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(1.0 + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[Less[x, -2.71483106713436e-162], t$95$0, If[Less[x, 3.874108816439546e-197], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023350 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

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