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

Percentage Accurate: 87.9% → 99.5%

Time: 6.9s

Alternatives: 12

Speedup: 0.8×

• 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: 99.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-15} \lor \neg \left(z \leq 9 \cdot 10^{+81}\right):\\ \;\;\;\;x \cdot \frac{y + \left(1 - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.7e-15) (not (<= z 9e+81)))
   (* x (/ (+ y (- 1.0 z)) z))
   (* (/ x z) (+ 1.0 (- y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7e-15) || !(z <= 9e+81)) {
		tmp = x * ((y + (1.0 - z)) / z);
	} else {
		tmp = (x / z) * (1.0 + (y - z));
	}
	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) :: tmp
    if ((z <= (-3.7d-15)) .or. (.not. (z <= 9d+81))) then
        tmp = x * ((y + (1.0d0 - z)) / z)
    else
        tmp = (x / z) * (1.0d0 + (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7e-15) || !(z <= 9e+81)) {
		tmp = x * ((y + (1.0 - z)) / z);
	} else {
		tmp = (x / z) * (1.0 + (y - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.7e-15) or not (z <= 9e+81):
		tmp = x * ((y + (1.0 - z)) / z)
	else:
		tmp = (x / z) * (1.0 + (y - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.7e-15) || !(z <= 9e+81))
		tmp = Float64(x * Float64(Float64(y + Float64(1.0 - z)) / z));
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 + Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.7e-15) || ~((z <= 9e+81)))
		tmp = x * ((y + (1.0 - z)) / z);
	else
		tmp = (x / z) * (1.0 + (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.7e-15], N[Not[LessEqual[z, 9e+81]], $MachinePrecision]], N[(x * N[(N[(y + N[(1.0 - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+50}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-167}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-238}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 440:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -2e+50)
     (- x)
     (if (<= z -4.5e-14)
       t_0
       (if (<= z -2.25e-91)
         (/ x z)
         (if (<= z -4.9e-167)
           t_0
           (if (<= z -9e-238)
             (/ x z)
             (if (<= z 3.1e-100)
               t_0
               (if (<= z 2.1e-67) (/ x z) (if (<= z 440.0) t_0 (- x)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -2e+50) {
		tmp = -x;
	} else if (z <= -4.5e-14) {
		tmp = t_0;
	} else if (z <= -2.25e-91) {
		tmp = x / z;
	} else if (z <= -4.9e-167) {
		tmp = t_0;
	} else if (z <= -9e-238) {
		tmp = x / z;
	} else if (z <= 3.1e-100) {
		tmp = t_0;
	} else if (z <= 2.1e-67) {
		tmp = x / z;
	} else if (z <= 440.0) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	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 = y * (x / z)
    if (z <= (-2d+50)) then
        tmp = -x
    else if (z <= (-4.5d-14)) then
        tmp = t_0
    else if (z <= (-2.25d-91)) then
        tmp = x / z
    else if (z <= (-4.9d-167)) then
        tmp = t_0
    else if (z <= (-9d-238)) then
        tmp = x / z
    else if (z <= 3.1d-100) then
        tmp = t_0
    else if (z <= 2.1d-67) then
        tmp = x / z
    else if (z <= 440.0d0) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -2e+50) {
		tmp = -x;
	} else if (z <= -4.5e-14) {
		tmp = t_0;
	} else if (z <= -2.25e-91) {
		tmp = x / z;
	} else if (z <= -4.9e-167) {
		tmp = t_0;
	} else if (z <= -9e-238) {
		tmp = x / z;
	} else if (z <= 3.1e-100) {
		tmp = t_0;
	} else if (z <= 2.1e-67) {
		tmp = x / z;
	} else if (z <= 440.0) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -2e+50:
		tmp = -x
	elif z <= -4.5e-14:
		tmp = t_0
	elif z <= -2.25e-91:
		tmp = x / z
	elif z <= -4.9e-167:
		tmp = t_0
	elif z <= -9e-238:
		tmp = x / z
	elif z <= 3.1e-100:
		tmp = t_0
	elif z <= 2.1e-67:
		tmp = x / z
	elif z <= 440.0:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -2e+50)
		tmp = Float64(-x);
	elseif (z <= -4.5e-14)
		tmp = t_0;
	elseif (z <= -2.25e-91)
		tmp = Float64(x / z);
	elseif (z <= -4.9e-167)
		tmp = t_0;
	elseif (z <= -9e-238)
		tmp = Float64(x / z);
	elseif (z <= 3.1e-100)
		tmp = t_0;
	elseif (z <= 2.1e-67)
		tmp = Float64(x / z);
	elseif (z <= 440.0)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -2e+50)
		tmp = -x;
	elseif (z <= -4.5e-14)
		tmp = t_0;
	elseif (z <= -2.25e-91)
		tmp = x / z;
	elseif (z <= -4.9e-167)
		tmp = t_0;
	elseif (z <= -9e-238)
		tmp = x / z;
	elseif (z <= 3.1e-100)
		tmp = t_0;
	elseif (z <= 2.1e-67)
		tmp = x / z;
	elseif (z <= 440.0)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+50], (-x), If[LessEqual[z, -4.5e-14], t$95$0, If[LessEqual[z, -2.25e-91], N[(x / z), $MachinePrecision], If[LessEqual[z, -4.9e-167], t$95$0, If[LessEqual[z, -9e-238], N[(x / z), $MachinePrecision], If[LessEqual[z, 3.1e-100], t$95$0, If[LessEqual[z, 2.1e-67], N[(x / z), $MachinePrecision], If[LessEqual[z, 440.0], t$95$0, (-x)]]]]]]]]]

Derivation

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

Alternative 3: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+50}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-162}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-240}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-115}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 440:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -1.65e+50)
     (- x)
     (if (<= z -4.5e-14)
       (* x (/ y z))
       (if (<= z -2.8e-90)
         (/ x z)
         (if (<= z -5.5e-162)
           t_0
           (if (<= z -1.4e-240)
             (/ x z)
             (if (<= z 2.1e-115)
               t_0
               (if (<= z 2.3e-68) (/ x z) (if (<= z 440.0) t_0 (- x)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -1.65e+50) {
		tmp = -x;
	} else if (z <= -4.5e-14) {
		tmp = x * (y / z);
	} else if (z <= -2.8e-90) {
		tmp = x / z;
	} else if (z <= -5.5e-162) {
		tmp = t_0;
	} else if (z <= -1.4e-240) {
		tmp = x / z;
	} else if (z <= 2.1e-115) {
		tmp = t_0;
	} else if (z <= 2.3e-68) {
		tmp = x / z;
	} else if (z <= 440.0) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	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 = y * (x / z)
    if (z <= (-1.65d+50)) then
        tmp = -x
    else if (z <= (-4.5d-14)) then
        tmp = x * (y / z)
    else if (z <= (-2.8d-90)) then
        tmp = x / z
    else if (z <= (-5.5d-162)) then
        tmp = t_0
    else if (z <= (-1.4d-240)) then
        tmp = x / z
    else if (z <= 2.1d-115) then
        tmp = t_0
    else if (z <= 2.3d-68) then
        tmp = x / z
    else if (z <= 440.0d0) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -1.65e+50) {
		tmp = -x;
	} else if (z <= -4.5e-14) {
		tmp = x * (y / z);
	} else if (z <= -2.8e-90) {
		tmp = x / z;
	} else if (z <= -5.5e-162) {
		tmp = t_0;
	} else if (z <= -1.4e-240) {
		tmp = x / z;
	} else if (z <= 2.1e-115) {
		tmp = t_0;
	} else if (z <= 2.3e-68) {
		tmp = x / z;
	} else if (z <= 440.0) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -1.65e+50:
		tmp = -x
	elif z <= -4.5e-14:
		tmp = x * (y / z)
	elif z <= -2.8e-90:
		tmp = x / z
	elif z <= -5.5e-162:
		tmp = t_0
	elif z <= -1.4e-240:
		tmp = x / z
	elif z <= 2.1e-115:
		tmp = t_0
	elif z <= 2.3e-68:
		tmp = x / z
	elif z <= 440.0:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -1.65e+50)
		tmp = Float64(-x);
	elseif (z <= -4.5e-14)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -2.8e-90)
		tmp = Float64(x / z);
	elseif (z <= -5.5e-162)
		tmp = t_0;
	elseif (z <= -1.4e-240)
		tmp = Float64(x / z);
	elseif (z <= 2.1e-115)
		tmp = t_0;
	elseif (z <= 2.3e-68)
		tmp = Float64(x / z);
	elseif (z <= 440.0)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -1.65e+50)
		tmp = -x;
	elseif (z <= -4.5e-14)
		tmp = x * (y / z);
	elseif (z <= -2.8e-90)
		tmp = x / z;
	elseif (z <= -5.5e-162)
		tmp = t_0;
	elseif (z <= -1.4e-240)
		tmp = x / z;
	elseif (z <= 2.1e-115)
		tmp = t_0;
	elseif (z <= 2.3e-68)
		tmp = x / z;
	elseif (z <= 440.0)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+50], (-x), If[LessEqual[z, -4.5e-14], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-90], N[(x / z), $MachinePrecision], If[LessEqual[z, -5.5e-162], t$95$0, If[LessEqual[z, -1.4e-240], N[(x / z), $MachinePrecision], If[LessEqual[z, 2.1e-115], t$95$0, If[LessEqual[z, 2.3e-68], N[(x / z), $MachinePrecision], If[LessEqual[z, 440.0], t$95$0, (-x)]]]]]]]]]

Derivation

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

Alternative 4: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-19} \lor \neg \left(z \leq 3.2 \cdot 10^{-49}\right):\\ \;\;\;\;x \cdot \frac{y + \left(1 - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5e-19) (not (<= z 3.2e-49)))
   (* x (/ (+ y (- 1.0 z)) z))
   (/ (+ x (* x y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-19) || !(z <= 3.2e-49)) {
		tmp = x * ((y + (1.0 - z)) / z);
	} else {
		tmp = (x + (x * y)) / z;
	}
	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) :: tmp
    if ((z <= (-5d-19)) .or. (.not. (z <= 3.2d-49))) then
        tmp = x * ((y + (1.0d0 - z)) / z)
    else
        tmp = (x + (x * y)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-19) || !(z <= 3.2e-49)) {
		tmp = x * ((y + (1.0 - z)) / z);
	} else {
		tmp = (x + (x * y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5e-19) or not (z <= 3.2e-49):
		tmp = x * ((y + (1.0 - z)) / z)
	else:
		tmp = (x + (x * y)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5e-19) || !(z <= 3.2e-49))
		tmp = Float64(x * Float64(Float64(y + Float64(1.0 - z)) / z));
	else
		tmp = Float64(Float64(x + Float64(x * y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5e-19) || ~((z <= 3.2e-49)))
		tmp = x * ((y + (1.0 - z)) / z);
	else
		tmp = (x + (x * y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5e-19], N[Not[LessEqual[z, 3.2e-49]], $MachinePrecision]], N[(x * N[(N[(y + N[(1.0 - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

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

Alternative 5: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot y + x \cdot \left(1 - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.5e-54)
   (/ (+ (* x y) (* x (- 1.0 z))) z)
   (* (/ x z) (+ 1.0 (- y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.5e-54) {
		tmp = ((x * y) + (x * (1.0 - z))) / z;
	} else {
		tmp = (x / z) * (1.0 + (y - z));
	}
	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) :: tmp
    if (x <= 1.5d-54) then
        tmp = ((x * y) + (x * (1.0d0 - z))) / z
    else
        tmp = (x / z) * (1.0d0 + (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.5e-54) {
		tmp = ((x * y) + (x * (1.0 - z))) / z;
	} else {
		tmp = (x / z) * (1.0 + (y - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.5e-54:
		tmp = ((x * y) + (x * (1.0 - z))) / z
	else:
		tmp = (x / z) * (1.0 + (y - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.5e-54)
		tmp = Float64(Float64(Float64(x * y) + Float64(x * Float64(1.0 - z))) / z);
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 + Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.5e-54)
		tmp = ((x * y) + (x * (1.0 - z))) / z;
	else
		tmp = (x / z) * (1.0 + (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.5e-54], N[(N[(N[(x * y), $MachinePrecision] + N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 6: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+52}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 0.0045:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.6e+52)
   (- x)
   (if (<= z 0.0045) (/ (+ x (* x y)) z) (- (/ x z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e+52) {
		tmp = -x;
	} else if (z <= 0.0045) {
		tmp = (x + (x * y)) / z;
	} else {
		tmp = (x / z) - x;
	}
	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) :: tmp
    if (z <= (-5.6d+52)) then
        tmp = -x
    else if (z <= 0.0045d0) then
        tmp = (x + (x * y)) / z
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e+52) {
		tmp = -x;
	} else if (z <= 0.0045) {
		tmp = (x + (x * y)) / z;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.6e+52:
		tmp = -x
	elif z <= 0.0045:
		tmp = (x + (x * y)) / z
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.6e+52)
		tmp = Float64(-x);
	elseif (z <= 0.0045)
		tmp = Float64(Float64(x + Float64(x * y)) / z);
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.6e+52)
		tmp = -x;
	elseif (z <= 0.0045)
		tmp = (x + (x * y)) / z;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.6e+52], (-x), If[LessEqual[z, 0.0045], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

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

Alternative 7: 93.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \left(y - z\right)\\ \mathbf{if}\;x \leq 1.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot t_0}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (- y z))))
   (if (<= x 1.4e-54) (/ (* x t_0) z) (* (/ x z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (y - z);
	double tmp;
	if (x <= 1.4e-54) {
		tmp = (x * t_0) / z;
	} else {
		tmp = (x / z) * 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 - z)
    if (x <= 1.4d-54) then
        tmp = (x * t_0) / z
    else
        tmp = (x / z) * 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 - z);
	double tmp;
	if (x <= 1.4e-54) {
		tmp = (x * t_0) / z;
	} else {
		tmp = (x / z) * t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (y - z)
	tmp = 0
	if x <= 1.4e-54:
		tmp = (x * t_0) / z
	else:
		tmp = (x / z) * t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(y - z))
	tmp = 0.0
	if (x <= 1.4e-54)
		tmp = Float64(Float64(x * t_0) / z);
	else
		tmp = Float64(Float64(x / z) * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (y - z);
	tmp = 0.0;
	if (x <= 1.4e-54)
		tmp = (x * t_0) / z;
	else
		tmp = (x / z) * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.4e-54], N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * t$95$0), $MachinePrecision]]]

Derivation

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

Alternative 8: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -70000 \lor \neg \left(y \leq 4.6 \cdot 10^{+67}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -70000.0) (not (<= y 4.6e+67))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -70000.0) || !(y <= 4.6e+67)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	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) :: tmp
    if ((y <= (-70000.0d0)) .or. (.not. (y <= 4.6d+67))) then
        tmp = y * (x / z)
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -70000.0) || !(y <= 4.6e+67)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -70000.0) or not (y <= 4.6e+67):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -70000.0) || !(y <= 4.6e+67))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -70000.0) || ~((y <= 4.6e+67)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -70000.0], N[Not[LessEqual[y, 4.6e+67]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

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

Alternative 9: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -940000 \lor \neg \left(y \leq 4.7 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -940000.0) (not (<= y 4.7e+67))) (/ (* x y) z) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -940000.0) || !(y <= 4.7e+67)) {
		tmp = (x * y) / z;
	} else {
		tmp = (x / z) - x;
	}
	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) :: tmp
    if ((y <= (-940000.0d0)) .or. (.not. (y <= 4.7d+67))) then
        tmp = (x * y) / z
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -940000.0) || !(y <= 4.7e+67)) {
		tmp = (x * y) / z;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -940000.0) or not (y <= 4.7e+67):
		tmp = (x * y) / z
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -940000.0) || !(y <= 4.7e+67))
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -940000.0) || ~((y <= 4.7e+67)))
		tmp = (x * y) / z;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -940000.0], N[Not[LessEqual[y, 4.7e+67]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

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

Alternative 10: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4200000:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4200000.0)
   (/ y (/ z x))
   (if (<= y 4.6e+67) (- (/ x z) x) (* y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4200000.0) {
		tmp = y / (z / x);
	} else if (y <= 4.6e+67) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (x / z);
	}
	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) :: tmp
    if (y <= (-4200000.0d0)) then
        tmp = y / (z / x)
    else if (y <= 4.6d+67) then
        tmp = (x / z) - x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4200000.0) {
		tmp = y / (z / x);
	} else if (y <= 4.6e+67) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4200000.0:
		tmp = y / (z / x)
	elif y <= 4.6e+67:
		tmp = (x / z) - x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4200000.0)
		tmp = Float64(y / Float64(z / x));
	elseif (y <= 4.6e+67)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4200000.0)
		tmp = y / (z / x);
	elseif (y <= 4.6e+67)
		tmp = (x / z) - x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4200000.0], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+67], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 11: 63.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5e-14) (not (<= z 1.0))) (- x) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-14) || !(z <= 1.0)) {
		tmp = -x;
	} else {
		tmp = x / z;
	}
	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) :: tmp
    if ((z <= (-4.5d-14)) .or. (.not. (z <= 1.0d0))) then
        tmp = -x
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-14) || !(z <= 1.0)) {
		tmp = -x;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.5e-14) or not (z <= 1.0):
		tmp = -x
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.5e-14) || !(z <= 1.0))
		tmp = Float64(-x);
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.5e-14) || ~((z <= 1.0)))
		tmp = -x;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.5e-14], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], (-x), N[(x / z), $MachinePrecision]]

Derivation

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

Alternative 12: 38.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-x)

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 2023347 
(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))