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

Percentage Accurate: 87.7% → 99.7%

Time: 7.4s

Alternatives: 12

Speedup: 1.0×

• 21.5% 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: 87.7% 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: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;x_m \leq 2.9 \cdot 10^{-42}:\\ \;\;\;\;\frac{x_m + x_m \cdot y}{z} - x_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{z} \cdot \left(\left(y - z\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= x_m 2.9e-42)
    (- (/ (+ x_m (* x_m y)) z) x_m)
    (* (/ x_m z) (+ (- y z) 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 (x_m <= 2.9e-42) {
		tmp = ((x_m + (x_m * y)) / z) - x_m;
	} else {
		tmp = (x_m / z) * ((y - z) + 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 (x_m <= 2.9d-42) then
        tmp = ((x_m + (x_m * y)) / z) - x_m
    else
        tmp = (x_m / z) * ((y - z) + 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 (x_m <= 2.9e-42) {
		tmp = ((x_m + (x_m * y)) / z) - x_m;
	} else {
		tmp = (x_m / z) * ((y - z) + 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 x_m <= 2.9e-42:
		tmp = ((x_m + (x_m * y)) / z) - x_m
	else:
		tmp = (x_m / z) * ((y - z) + 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 (x_m <= 2.9e-42)
		tmp = Float64(Float64(Float64(x_m + Float64(x_m * y)) / z) - x_m);
	else
		tmp = Float64(Float64(x_m / z) * Float64(Float64(y - z) + 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 (x_m <= 2.9e-42)
		tmp = ((x_m + (x_m * y)) / z) - x_m;
	else
		tmp = (x_m / z) * ((y - z) + 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[x$95$m, 2.9e-42], N[(N[(N[(x$95$m + N[(x$95$m * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - x$95$m), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 2: 58.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := x_m \cdot \frac{y}{z}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-52}:\\ \;\;\;\;-x_m\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-162}:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-177}:\\ \;\;\;\;-x_m\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-207}:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-140}:\\ \;\;\;\;-x_m\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (* x_m (/ y z))))
   (*
    x_s
    (if (<= y -7.8e+84)
      t_0
      (if (<= y -5.6e-52)
        (- x_m)
        (if (<= y -5.5e-162)
          (/ x_m z)
          (if (<= y -3.9e-177)
            (- x_m)
            (if (<= y 7.2e-207)
              (/ x_m z)
              (if (<= y 4.8e-140)
                (- x_m)
                (if (<= y 1.0) (/ x_m z) 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 = x_m * (y / z);
	double tmp;
	if (y <= -7.8e+84) {
		tmp = t_0;
	} else if (y <= -5.6e-52) {
		tmp = -x_m;
	} else if (y <= -5.5e-162) {
		tmp = x_m / z;
	} else if (y <= -3.9e-177) {
		tmp = -x_m;
	} else if (y <= 7.2e-207) {
		tmp = x_m / z;
	} else if (y <= 4.8e-140) {
		tmp = -x_m;
	} else if (y <= 1.0) {
		tmp = x_m / z;
	} 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 = x_m * (y / z)
    if (y <= (-7.8d+84)) then
        tmp = t_0
    else if (y <= (-5.6d-52)) then
        tmp = -x_m
    else if (y <= (-5.5d-162)) then
        tmp = x_m / z
    else if (y <= (-3.9d-177)) then
        tmp = -x_m
    else if (y <= 7.2d-207) then
        tmp = x_m / z
    else if (y <= 4.8d-140) then
        tmp = -x_m
    else if (y <= 1.0d0) then
        tmp = x_m / z
    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 = x_m * (y / z);
	double tmp;
	if (y <= -7.8e+84) {
		tmp = t_0;
	} else if (y <= -5.6e-52) {
		tmp = -x_m;
	} else if (y <= -5.5e-162) {
		tmp = x_m / z;
	} else if (y <= -3.9e-177) {
		tmp = -x_m;
	} else if (y <= 7.2e-207) {
		tmp = x_m / z;
	} else if (y <= 4.8e-140) {
		tmp = -x_m;
	} else if (y <= 1.0) {
		tmp = x_m / z;
	} 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 = x_m * (y / z)
	tmp = 0
	if y <= -7.8e+84:
		tmp = t_0
	elif y <= -5.6e-52:
		tmp = -x_m
	elif y <= -5.5e-162:
		tmp = x_m / z
	elif y <= -3.9e-177:
		tmp = -x_m
	elif y <= 7.2e-207:
		tmp = x_m / z
	elif y <= 4.8e-140:
		tmp = -x_m
	elif y <= 1.0:
		tmp = x_m / z
	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(x_m * Float64(y / z))
	tmp = 0.0
	if (y <= -7.8e+84)
		tmp = t_0;
	elseif (y <= -5.6e-52)
		tmp = Float64(-x_m);
	elseif (y <= -5.5e-162)
		tmp = Float64(x_m / z);
	elseif (y <= -3.9e-177)
		tmp = Float64(-x_m);
	elseif (y <= 7.2e-207)
		tmp = Float64(x_m / z);
	elseif (y <= 4.8e-140)
		tmp = Float64(-x_m);
	elseif (y <= 1.0)
		tmp = Float64(x_m / z);
	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 = x_m * (y / z);
	tmp = 0.0;
	if (y <= -7.8e+84)
		tmp = t_0;
	elseif (y <= -5.6e-52)
		tmp = -x_m;
	elseif (y <= -5.5e-162)
		tmp = x_m / z;
	elseif (y <= -3.9e-177)
		tmp = -x_m;
	elseif (y <= 7.2e-207)
		tmp = x_m / z;
	elseif (y <= 4.8e-140)
		tmp = -x_m;
	elseif (y <= 1.0)
		tmp = x_m / z;
	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[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -7.8e+84], t$95$0, If[LessEqual[y, -5.6e-52], (-x$95$m), If[LessEqual[y, -5.5e-162], N[(x$95$m / z), $MachinePrecision], If[LessEqual[y, -3.9e-177], (-x$95$m), If[LessEqual[y, 7.2e-207], N[(x$95$m / z), $MachinePrecision], If[LessEqual[y, 4.8e-140], (-x$95$m), If[LessEqual[y, 1.0], N[(x$95$m / z), $MachinePrecision], t$95$0]]]]]]]), $MachinePrecision]]

Derivation

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

Alternative 3: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+17}:\\ \;\;\;\;-x_m\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \frac{x_m}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-47}:\\ \;\;\;\;\frac{x_m}{z}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+182}:\\ \;\;\;\;x_m \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= z -2.6e+17)
    (- x_m)
    (if (<= z 5.2e-105)
      (* y (/ x_m z))
      (if (<= z 6.2e-47)
        (/ x_m z)
        (if (<= z 1.06e+182) (* 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 (z <= -2.6e+17) {
		tmp = -x_m;
	} else if (z <= 5.2e-105) {
		tmp = y * (x_m / z);
	} else if (z <= 6.2e-47) {
		tmp = x_m / z;
	} else if (z <= 1.06e+182) {
		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 (z <= (-2.6d+17)) then
        tmp = -x_m
    else if (z <= 5.2d-105) then
        tmp = y * (x_m / z)
    else if (z <= 6.2d-47) then
        tmp = x_m / z
    else if (z <= 1.06d+182) 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 (z <= -2.6e+17) {
		tmp = -x_m;
	} else if (z <= 5.2e-105) {
		tmp = y * (x_m / z);
	} else if (z <= 6.2e-47) {
		tmp = x_m / z;
	} else if (z <= 1.06e+182) {
		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 z <= -2.6e+17:
		tmp = -x_m
	elif z <= 5.2e-105:
		tmp = y * (x_m / z)
	elif z <= 6.2e-47:
		tmp = x_m / z
	elif z <= 1.06e+182:
		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 (z <= -2.6e+17)
		tmp = Float64(-x_m);
	elseif (z <= 5.2e-105)
		tmp = Float64(y * Float64(x_m / z));
	elseif (z <= 6.2e-47)
		tmp = Float64(x_m / z);
	elseif (z <= 1.06e+182)
		tmp = Float64(x_m * Float64(y / z));
	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)
	tmp = 0.0;
	if (z <= -2.6e+17)
		tmp = -x_m;
	elseif (z <= 5.2e-105)
		tmp = y * (x_m / z);
	elseif (z <= 6.2e-47)
		tmp = x_m / z;
	elseif (z <= 1.06e+182)
		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[LessEqual[z, -2.6e+17], (-x$95$m), If[LessEqual[z, 5.2e-105], N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-47], N[(x$95$m / z), $MachinePrecision], If[LessEqual[z, 1.06e+182], N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision], (-x$95$m)]]]]), $MachinePrecision]

Derivation

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

Alternative 4: 95.2% accurate, 0.8× speedup

Math

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

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 2e-10)))
    (* x_m (+ -1.0 (/ 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 ((y <= -1.0) || !(y <= 2e-10)) {
		tmp = x_m * (-1.0 + (y / 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 <= (-1.0d0)) .or. (.not. (y <= 2d-10))) then
        tmp = x_m * ((-1.0d0) + (y / 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 <= -1.0) || !(y <= 2e-10)) {
		tmp = x_m * (-1.0 + (y / 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 <= -1.0) or not (y <= 2e-10):
		tmp = x_m * (-1.0 + (y / 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 <= -1.0) || !(y <= 2e-10))
		tmp = Float64(x_m * Float64(-1.0 + Float64(y / 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 <= -1.0) || ~((y <= 2e-10)))
		tmp = x_m * (-1.0 + (y / 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, -1.0], N[Not[LessEqual[y, 2e-10]], $MachinePrecision]], N[(x$95$m * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] - x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 5: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 0.215\right):\\ \;\;\;\;x_m \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{z} \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

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 -1.05) (not (<= z 0.215)))
    (* x_m (+ -1.0 (/ 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 tmp;
	if ((z <= -1.05) || !(z <= 0.215)) {
		tmp = x_m * (-1.0 + (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) :: tmp
    if ((z <= (-1.05d0)) .or. (.not. (z <= 0.215d0))) then
        tmp = x_m * ((-1.0d0) + (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 tmp;
	if ((z <= -1.05) || !(z <= 0.215)) {
		tmp = x_m * (-1.0 + (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):
	tmp = 0
	if (z <= -1.05) or not (z <= 0.215):
		tmp = x_m * (-1.0 + (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)
	tmp = 0.0
	if ((z <= -1.05) || !(z <= 0.215))
		tmp = Float64(x_m * Float64(-1.0 + 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)
	tmp = 0.0;
	if ((z <= -1.05) || ~((z <= 0.215)))
		tmp = x_m * (-1.0 + (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_] := N[(x$95$s * If[Or[LessEqual[z, -1.05], N[Not[LessEqual[z, 0.215]], $MachinePrecision]], N[(x$95$m * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 6: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -0.98:\\ \;\;\;\;x_m \cdot \frac{y}{z} - x_m\\ \mathbf{elif}\;z \leq 0.215:\\ \;\;\;\;\frac{x_m}{z} \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x_m \cdot \left(-1 + \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= z -0.98)
    (- (* x_m (/ y z)) x_m)
    (if (<= z 0.215) (* (/ x_m z) (+ y 1.0)) (* x_m (+ -1.0 (/ 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 (z <= -0.98) {
		tmp = (x_m * (y / z)) - x_m;
	} else if (z <= 0.215) {
		tmp = (x_m / z) * (y + 1.0);
	} else {
		tmp = x_m * (-1.0 + (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 (z <= (-0.98d0)) then
        tmp = (x_m * (y / z)) - x_m
    else if (z <= 0.215d0) then
        tmp = (x_m / z) * (y + 1.0d0)
    else
        tmp = x_m * ((-1.0d0) + (y / z))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= -0.98) {
		tmp = (x_m * (y / z)) - x_m;
	} else if (z <= 0.215) {
		tmp = (x_m / z) * (y + 1.0);
	} else {
		tmp = x_m * (-1.0 + (y / z));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if z <= -0.98:
		tmp = (x_m * (y / z)) - x_m
	elif z <= 0.215:
		tmp = (x_m / z) * (y + 1.0)
	else:
		tmp = x_m * (-1.0 + (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 (z <= -0.98)
		tmp = Float64(Float64(x_m * Float64(y / z)) - x_m);
	elseif (z <= 0.215)
		tmp = Float64(Float64(x_m / z) * Float64(y + 1.0));
	else
		tmp = Float64(x_m * Float64(-1.0 + Float64(y / z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (z <= -0.98)
		tmp = (x_m * (y / z)) - x_m;
	elseif (z <= 0.215)
		tmp = (x_m / z) * (y + 1.0);
	else
		tmp = x_m * (-1.0 + (y / z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[z, -0.98], N[(N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision] - x$95$m), $MachinePrecision], If[LessEqual[z, 0.215], N[(N[(x$95$m / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 7: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;x_m \cdot \frac{y}{z} - x_m\\ \mathbf{elif}\;z \leq 0.215:\\ \;\;\;\;\frac{x_m + x_m \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x_m \cdot \left(-1 + \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= z -1.05)
    (- (* x_m (/ y z)) x_m)
    (if (<= z 0.215) (/ (+ x_m (* x_m y)) z) (* x_m (+ -1.0 (/ 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 (z <= -1.05) {
		tmp = (x_m * (y / z)) - x_m;
	} else if (z <= 0.215) {
		tmp = (x_m + (x_m * y)) / z;
	} else {
		tmp = x_m * (-1.0 + (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 (z <= (-1.05d0)) then
        tmp = (x_m * (y / z)) - x_m
    else if (z <= 0.215d0) then
        tmp = (x_m + (x_m * y)) / z
    else
        tmp = x_m * ((-1.0d0) + (y / z))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= -1.05) {
		tmp = (x_m * (y / z)) - x_m;
	} else if (z <= 0.215) {
		tmp = (x_m + (x_m * y)) / z;
	} else {
		tmp = x_m * (-1.0 + (y / z));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if z <= -1.05:
		tmp = (x_m * (y / z)) - x_m
	elif z <= 0.215:
		tmp = (x_m + (x_m * y)) / z
	else:
		tmp = x_m * (-1.0 + (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 (z <= -1.05)
		tmp = Float64(Float64(x_m * Float64(y / z)) - x_m);
	elseif (z <= 0.215)
		tmp = Float64(Float64(x_m + Float64(x_m * y)) / z);
	else
		tmp = Float64(x_m * Float64(-1.0 + Float64(y / z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (z <= -1.05)
		tmp = (x_m * (y / z)) - x_m;
	elseif (z <= 0.215)
		tmp = (x_m + (x_m * y)) / z;
	else
		tmp = x_m * (-1.0 + (y / z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[z, -1.05], N[(N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision] - x$95$m), $MachinePrecision], If[LessEqual[z, 0.215], N[(N[(x$95$m + N[(x$95$m * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x$95$m * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 8: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{x_m}{z}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{x_m}{z} - x_m\\ \mathbf{else}:\\ \;\;\;\;x_m \cdot \frac{y}{z}\\ \end{array} \end{array} \]

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 -7.8e+84)
    (* y (/ x_m z))
    (if (<= y 7.8e+28) (- (/ x_m z) 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) {
	double tmp;
	if (y <= -7.8e+84) {
		tmp = y * (x_m / z);
	} else if (y <= 7.8e+28) {
		tmp = (x_m / z) - x_m;
	} 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 <= (-7.8d+84)) then
        tmp = y * (x_m / z)
    else if (y <= 7.8d+28) then
        tmp = (x_m / z) - x_m
    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 <= -7.8e+84) {
		tmp = y * (x_m / z);
	} else if (y <= 7.8e+28) {
		tmp = (x_m / z) - x_m;
	} 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 <= -7.8e+84:
		tmp = y * (x_m / z)
	elif y <= 7.8e+28:
		tmp = (x_m / z) - x_m
	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 <= -7.8e+84)
		tmp = Float64(y * Float64(x_m / z));
	elseif (y <= 7.8e+28)
		tmp = Float64(Float64(x_m / z) - x_m);
	else
		tmp = Float64(x_m * 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 (y <= -7.8e+84)
		tmp = y * (x_m / z);
	elseif (y <= 7.8e+28)
		tmp = (x_m / z) - x_m;
	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, -7.8e+84], N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+28], N[(N[(x$95$m / z), $MachinePrecision] - x$95$m), $MachinePrecision], N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 9: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{x_m}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+28}:\\ \;\;\;\;\frac{x_m}{z} - x_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\frac{z}{y}}\\ \end{array} \end{array} \]

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 -1.75e+85)
    (* y (/ x_m z))
    (if (<= y 2e+28) (- (/ x_m z) x_m) (/ x_m (/ z y))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -1.75e+85) {
		tmp = y * (x_m / z);
	} else if (y <= 2e+28) {
		tmp = (x_m / z) - x_m;
	} else {
		tmp = x_m / (z / y);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.75d+85)) then
        tmp = y * (x_m / z)
    else if (y <= 2d+28) then
        tmp = (x_m / z) - x_m
    else
        tmp = x_m / (z / y)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -1.75e+85) {
		tmp = y * (x_m / z);
	} else if (y <= 2e+28) {
		tmp = (x_m / z) - x_m;
	} else {
		tmp = x_m / (z / y);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -1.75e+85:
		tmp = y * (x_m / z)
	elif y <= 2e+28:
		tmp = (x_m / z) - x_m
	else:
		tmp = x_m / (z / y)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -1.75e+85)
		tmp = Float64(y * Float64(x_m / z));
	elseif (y <= 2e+28)
		tmp = Float64(Float64(x_m / z) - x_m);
	else
		tmp = Float64(x_m / Float64(z / y));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -1.75e+85)
		tmp = y * (x_m / z);
	elseif (y <= 2e+28)
		tmp = (x_m / z) - x_m;
	else
		tmp = x_m / (z / y);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -1.75e+85], N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+28], N[(N[(x$95$m / z), $MachinePrecision] - x$95$m), $MachinePrecision], N[(x$95$m / N[(z / y), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 10: 96.1% accurate, 1.0× speedup

Math

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

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 (+ (/ (+ y 1.0) z) -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) {
	return x_s * (x_m * (((y + 1.0) / z) + -1.0));
}

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

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

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(Float64(Float64(y + 1.0) / z) + -1.0)))
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 * (((y + 1.0) / z) + -1.0));
end

Wolfram

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

Derivation

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

Alternative 11: 64.8% accurate, 1.3× speedup

Math

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

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 1.0))) (- 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 <= 1.0)) {
		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 <= 1.0d0))) 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 <= 1.0)) {
		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 <= 1.0):
		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 <= 1.0))
		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 <= 1.0)))
		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, 1.0]], $MachinePrecision]], (-x$95$m), N[(x$95$m / z), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 12: 39.0% 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: 99.5% 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 2023348 
(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))