Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A

Percentage Accurate: 87.9% → 99.9%

Time: 6.4s

Alternatives: 10

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 87.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-302} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-302) (not (<= t_0 0.0))) t_0 (/ (- z) (/ y (+ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-302) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	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 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-5d-302)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z / (y / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-302) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-302) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z / (y / (x + y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -5e-302) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -5e-302) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z / (y / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5e-302], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 2: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{-27}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-84}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ x y) (+ 1.0 (/ y z)))))
   (if (<= z -9.8e-27)
     t_0
     (if (<= z 5.2e-84)
       (/ (* z (- (- y) x)) y)
       (if (<= z 3.3e-49)
         (/ x (- 1.0 (/ y z)))
         (if (<= z 5e-11) (* (+ x y) (/ (- z) y)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) * (1.0 + (y / z));
	double tmp;
	if (z <= -9.8e-27) {
		tmp = t_0;
	} else if (z <= 5.2e-84) {
		tmp = (z * (-y - x)) / y;
	} else if (z <= 3.3e-49) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 5e-11) {
		tmp = (x + y) * (-z / y);
	} 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 = (x + y) * (1.0d0 + (y / z))
    if (z <= (-9.8d-27)) then
        tmp = t_0
    else if (z <= 5.2d-84) then
        tmp = (z * (-y - x)) / y
    else if (z <= 3.3d-49) then
        tmp = x / (1.0d0 - (y / z))
    else if (z <= 5d-11) then
        tmp = (x + y) * (-z / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) * (1.0 + (y / z));
	double tmp;
	if (z <= -9.8e-27) {
		tmp = t_0;
	} else if (z <= 5.2e-84) {
		tmp = (z * (-y - x)) / y;
	} else if (z <= 3.3e-49) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 5e-11) {
		tmp = (x + y) * (-z / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) * (1.0 + (y / z))
	tmp = 0
	if z <= -9.8e-27:
		tmp = t_0
	elif z <= 5.2e-84:
		tmp = (z * (-y - x)) / y
	elif z <= 3.3e-49:
		tmp = x / (1.0 - (y / z))
	elif z <= 5e-11:
		tmp = (x + y) * (-z / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)))
	tmp = 0.0
	if (z <= -9.8e-27)
		tmp = t_0;
	elseif (z <= 5.2e-84)
		tmp = Float64(Float64(z * Float64(Float64(-y) - x)) / y);
	elseif (z <= 3.3e-49)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (z <= 5e-11)
		tmp = Float64(Float64(x + y) * Float64(Float64(-z) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) * (1.0 + (y / z));
	tmp = 0.0;
	if (z <= -9.8e-27)
		tmp = t_0;
	elseif (z <= 5.2e-84)
		tmp = (z * (-y - x)) / y;
	elseif (z <= 3.3e-49)
		tmp = x / (1.0 - (y / z));
	elseif (z <= 5e-11)
		tmp = (x + y) * (-z / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e-27], t$95$0, If[LessEqual[z, 5.2e-84], N[(N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 3.3e-49], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-11], N[(N[(x + y), $MachinePrecision] * N[((-z) / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

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

Alternative 3: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-84}:\\ \;\;\;\;\left(-z\right) - \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-11}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.2e-27)
   (+ x y)
   (if (<= z 5.5e-84)
     (- (- z) (/ x (/ y z)))
     (if (<= z 2.4e-49)
       (/ x (- 1.0 (/ y z)))
       (if (<= z 1.32e-11) (* (+ x y) (/ (- z) y)) (+ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.2e-27) {
		tmp = x + y;
	} else if (z <= 5.5e-84) {
		tmp = -z - (x / (y / z));
	} else if (z <= 2.4e-49) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 1.32e-11) {
		tmp = (x + y) * (-z / y);
	} else {
		tmp = x + y;
	}
	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 <= (-9.2d-27)) then
        tmp = x + y
    else if (z <= 5.5d-84) then
        tmp = -z - (x / (y / z))
    else if (z <= 2.4d-49) then
        tmp = x / (1.0d0 - (y / z))
    else if (z <= 1.32d-11) then
        tmp = (x + y) * (-z / y)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.2e-27) {
		tmp = x + y;
	} else if (z <= 5.5e-84) {
		tmp = -z - (x / (y / z));
	} else if (z <= 2.4e-49) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 1.32e-11) {
		tmp = (x + y) * (-z / y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.2e-27:
		tmp = x + y
	elif z <= 5.5e-84:
		tmp = -z - (x / (y / z))
	elif z <= 2.4e-49:
		tmp = x / (1.0 - (y / z))
	elif z <= 1.32e-11:
		tmp = (x + y) * (-z / y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.2e-27)
		tmp = Float64(x + y);
	elseif (z <= 5.5e-84)
		tmp = Float64(Float64(-z) - Float64(x / Float64(y / z)));
	elseif (z <= 2.4e-49)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (z <= 1.32e-11)
		tmp = Float64(Float64(x + y) * Float64(Float64(-z) / y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.2e-27)
		tmp = x + y;
	elseif (z <= 5.5e-84)
		tmp = -z - (x / (y / z));
	elseif (z <= 2.4e-49)
		tmp = x / (1.0 - (y / z));
	elseif (z <= 1.32e-11)
		tmp = (x + y) * (-z / y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.2e-27], N[(x + y), $MachinePrecision], If[LessEqual[z, 5.5e-84], N[((-z) - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-49], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.32e-11], N[(N[(x + y), $MachinePrecision] * N[((-z) / y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

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

Alternative 4: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-26}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-13}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e-26)
   (+ x y)
   (if (<= z 7.5e-84)
     (/ (- z) (/ y (+ x y)))
     (if (<= z 5.7e-49)
       (/ x (- 1.0 (/ y z)))
       (if (<= z 5.5e-13) (* (+ x y) (/ (- z) y)) (+ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e-26) {
		tmp = x + y;
	} else if (z <= 7.5e-84) {
		tmp = -z / (y / (x + y));
	} else if (z <= 5.7e-49) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 5.5e-13) {
		tmp = (x + y) * (-z / y);
	} else {
		tmp = x + y;
	}
	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 <= (-1.1d-26)) then
        tmp = x + y
    else if (z <= 7.5d-84) then
        tmp = -z / (y / (x + y))
    else if (z <= 5.7d-49) then
        tmp = x / (1.0d0 - (y / z))
    else if (z <= 5.5d-13) then
        tmp = (x + y) * (-z / y)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e-26) {
		tmp = x + y;
	} else if (z <= 7.5e-84) {
		tmp = -z / (y / (x + y));
	} else if (z <= 5.7e-49) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 5.5e-13) {
		tmp = (x + y) * (-z / y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e-26:
		tmp = x + y
	elif z <= 7.5e-84:
		tmp = -z / (y / (x + y))
	elif z <= 5.7e-49:
		tmp = x / (1.0 - (y / z))
	elif z <= 5.5e-13:
		tmp = (x + y) * (-z / y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e-26)
		tmp = Float64(x + y);
	elseif (z <= 7.5e-84)
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	elseif (z <= 5.7e-49)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (z <= 5.5e-13)
		tmp = Float64(Float64(x + y) * Float64(Float64(-z) / y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1e-26)
		tmp = x + y;
	elseif (z <= 7.5e-84)
		tmp = -z / (y / (x + y));
	elseif (z <= 5.7e-49)
		tmp = x / (1.0 - (y / z));
	elseif (z <= 5.5e-13)
		tmp = (x + y) * (-z / y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e-26], N[(x + y), $MachinePrecision], If[LessEqual[z, 7.5e-84], N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e-49], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-13], N[(N[(x + y), $MachinePrecision] * N[((-z) / y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

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

Alternative 5: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-86}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-12}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.6e-27)
   (+ x y)
   (if (<= z 2.75e-86)
     (/ (* z (- (- y) x)) y)
     (if (<= z 2.4e-49)
       (/ x (- 1.0 (/ y z)))
       (if (<= z 3.6e-12) (* (+ x y) (/ (- z) y)) (+ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.6e-27) {
		tmp = x + y;
	} else if (z <= 2.75e-86) {
		tmp = (z * (-y - x)) / y;
	} else if (z <= 2.4e-49) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 3.6e-12) {
		tmp = (x + y) * (-z / y);
	} else {
		tmp = x + y;
	}
	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 <= (-7.6d-27)) then
        tmp = x + y
    else if (z <= 2.75d-86) then
        tmp = (z * (-y - x)) / y
    else if (z <= 2.4d-49) then
        tmp = x / (1.0d0 - (y / z))
    else if (z <= 3.6d-12) then
        tmp = (x + y) * (-z / y)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.6e-27) {
		tmp = x + y;
	} else if (z <= 2.75e-86) {
		tmp = (z * (-y - x)) / y;
	} else if (z <= 2.4e-49) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 3.6e-12) {
		tmp = (x + y) * (-z / y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.6e-27:
		tmp = x + y
	elif z <= 2.75e-86:
		tmp = (z * (-y - x)) / y
	elif z <= 2.4e-49:
		tmp = x / (1.0 - (y / z))
	elif z <= 3.6e-12:
		tmp = (x + y) * (-z / y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.6e-27)
		tmp = Float64(x + y);
	elseif (z <= 2.75e-86)
		tmp = Float64(Float64(z * Float64(Float64(-y) - x)) / y);
	elseif (z <= 2.4e-49)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (z <= 3.6e-12)
		tmp = Float64(Float64(x + y) * Float64(Float64(-z) / y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.6e-27)
		tmp = x + y;
	elseif (z <= 2.75e-86)
		tmp = (z * (-y - x)) / y;
	elseif (z <= 2.4e-49)
		tmp = x / (1.0 - (y / z));
	elseif (z <= 3.6e-12)
		tmp = (x + y) * (-z / y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.6e-27], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.75e-86], N[(N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 2.4e-49], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-12], N[(N[(x + y), $MachinePrecision] * N[((-z) / y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

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

Alternative 6: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+123}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-109}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= y -4.4e+123)
     (- z)
     (if (<= y 2.5e-229)
       t_0
       (if (<= y 3e-109) (+ x y) (if (<= y 6e+26) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -4.4e+123) {
		tmp = -z;
	} else if (y <= 2.5e-229) {
		tmp = t_0;
	} else if (y <= 3e-109) {
		tmp = x + y;
	} else if (y <= 6e+26) {
		tmp = t_0;
	} else {
		tmp = -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) :: t_0
    real(8) :: tmp
    t_0 = x / (1.0d0 - (y / z))
    if (y <= (-4.4d+123)) then
        tmp = -z
    else if (y <= 2.5d-229) then
        tmp = t_0
    else if (y <= 3d-109) then
        tmp = x + y
    else if (y <= 6d+26) then
        tmp = t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -4.4e+123) {
		tmp = -z;
	} else if (y <= 2.5e-229) {
		tmp = t_0;
	} else if (y <= 3e-109) {
		tmp = x + y;
	} else if (y <= 6e+26) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	tmp = 0
	if y <= -4.4e+123:
		tmp = -z
	elif y <= 2.5e-229:
		tmp = t_0
	elif y <= 3e-109:
		tmp = x + y
	elif y <= 6e+26:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -4.4e+123)
		tmp = Float64(-z);
	elseif (y <= 2.5e-229)
		tmp = t_0;
	elseif (y <= 3e-109)
		tmp = Float64(x + y);
	elseif (y <= 6e+26)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -4.4e+123)
		tmp = -z;
	elseif (y <= 2.5e-229)
		tmp = t_0;
	elseif (y <= 3e-109)
		tmp = x + y;
	elseif (y <= 6e+26)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+123], (-z), If[LessEqual[y, 2.5e-229], t$95$0, If[LessEqual[y, 3e-109], N[(x + y), $MachinePrecision], If[LessEqual[y, 6e+26], t$95$0, (-z)]]]]]

Derivation

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

Alternative 7: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-209}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{-193}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.2e-27)
   (+ x y)
   (if (<= z -6e-209)
     (* (+ x y) (/ (- z) y))
     (if (<= z 1.48e-193)
       (- z)
       (if (<= z 2.2e+25) (/ x (- 1.0 (/ y z))) (+ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.2e-27) {
		tmp = x + y;
	} else if (z <= -6e-209) {
		tmp = (x + y) * (-z / y);
	} else if (z <= 1.48e-193) {
		tmp = -z;
	} else if (z <= 2.2e+25) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = x + y;
	}
	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 <= (-6.2d-27)) then
        tmp = x + y
    else if (z <= (-6d-209)) then
        tmp = (x + y) * (-z / y)
    else if (z <= 1.48d-193) then
        tmp = -z
    else if (z <= 2.2d+25) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.2e-27) {
		tmp = x + y;
	} else if (z <= -6e-209) {
		tmp = (x + y) * (-z / y);
	} else if (z <= 1.48e-193) {
		tmp = -z;
	} else if (z <= 2.2e+25) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.2e-27:
		tmp = x + y
	elif z <= -6e-209:
		tmp = (x + y) * (-z / y)
	elif z <= 1.48e-193:
		tmp = -z
	elif z <= 2.2e+25:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.2e-27)
		tmp = Float64(x + y);
	elseif (z <= -6e-209)
		tmp = Float64(Float64(x + y) * Float64(Float64(-z) / y));
	elseif (z <= 1.48e-193)
		tmp = Float64(-z);
	elseif (z <= 2.2e+25)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.2e-27)
		tmp = x + y;
	elseif (z <= -6e-209)
		tmp = (x + y) * (-z / y);
	elseif (z <= 1.48e-193)
		tmp = -z;
	elseif (z <= 2.2e+25)
		tmp = x / (1.0 - (y / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.2e-27], N[(x + y), $MachinePrecision], If[LessEqual[z, -6e-209], N[(N[(x + y), $MachinePrecision] * N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.48e-193], (-z), If[LessEqual[z, 2.2e+25], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

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

Alternative 8: 61.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-27} \lor \neg \left(z \leq 5.5 \cdot 10^{-85}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.3e-27) (not (<= z 5.5e-85))) (+ x y) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.3e-27) || !(z <= 5.5e-85)) {
		tmp = x + y;
	} else {
		tmp = -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 <= (-5.3d-27)) .or. (.not. (z <= 5.5d-85))) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.3e-27) || !(z <= 5.5e-85)) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.3e-27) or not (z <= 5.5e-85):
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.3e-27) || !(z <= 5.5e-85))
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.3e-27) || ~((z <= 5.5e-85)))
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.3e-27], N[Not[LessEqual[z, 5.5e-85]], $MachinePrecision]], N[(x + y), $MachinePrecision], (-z)]

Derivation

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

Alternative 9: 58.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+53} \lor \neg \left(y \leq 9.5 \cdot 10^{-40}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.2e+53) (not (<= y 9.5e-40))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.2e+53) || !(y <= 9.5e-40)) {
		tmp = -z;
	} 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) :: tmp
    if ((y <= (-8.2d+53)) .or. (.not. (y <= 9.5d-40))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.2e+53) || !(y <= 9.5e-40)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.2e+53) or not (y <= 9.5e-40):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.2e+53) || !(y <= 9.5e-40))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8.2e+53) || ~((y <= 9.5e-40)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.2e+53], N[Not[LessEqual[y, 9.5e-40]], $MachinePrecision]], (-z), x]

Derivation

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

Alternative 10: 35.4% accurate, 9.0× 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 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: 94.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (+ y x) (- y)) z)))
   (if (< y -3.7429310762689856e+171)
     t_0
     (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / 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 = ((y + x) / -y) * z
    if (y < (-3.7429310762689856d+171)) then
        tmp = t_0
    else if (y < 3.5534662456086734d+168) then
        tmp = (x + y) / (1.0d0 - (y / 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 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y + x) / -y) * z
	tmp = 0
	if y < -3.7429310762689856e+171:
		tmp = t_0
	elif y < 3.5534662456086734e+168:
		tmp = (x + y) / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y + x) / Float64(-y)) * z)
	tmp = 0.0
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y + x) / -y) * z;
	tmp = 0.0;
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = (x + y) / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision] * z), $MachinePrecision]}, If[Less[y, -3.7429310762689856e+171], t$95$0, If[Less[y, 3.5534662456086734e+168], N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023343 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

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