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

Percentage Accurate: 88.6% → 99.9%

Time: 7.8s

Alternatives: 11

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: 88.6% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-290} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-290) (not (<= t_0 0.0))) t_0 (* z (/ (- (- x) y) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-290) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((-x - y) / 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 <= (-1d-290)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((-x - y) / 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 <= -1e-290) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((-x - y) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-290) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * ((-x - y) / 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 <= -1e-290) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(Float64(Float64(-x) - y) / 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 <= -1e-290) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * ((-x - y) / 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, -1e-290], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 2: 66.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t_0}\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)))
   (if (<= x -2.6e-111)
     t_1
     (if (<= x 5.5e-67)
       (/ y t_0)
       (if (<= x 5.4e+54) (* z (/ (- (- x) y) y)) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double tmp;
	if (x <= -2.6e-111) {
		tmp = t_1;
	} else if (x <= 5.5e-67) {
		tmp = y / t_0;
	} else if (x <= 5.4e+54) {
		tmp = z * ((-x - y) / y);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = x / t_0
    if (x <= (-2.6d-111)) then
        tmp = t_1
    else if (x <= 5.5d-67) then
        tmp = y / t_0
    else if (x <= 5.4d+54) then
        tmp = z * ((-x - y) / y)
    else
        tmp = t_1
    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 t_1 = x / t_0;
	double tmp;
	if (x <= -2.6e-111) {
		tmp = t_1;
	} else if (x <= 5.5e-67) {
		tmp = y / t_0;
	} else if (x <= 5.4e+54) {
		tmp = z * ((-x - y) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	tmp = 0
	if x <= -2.6e-111:
		tmp = t_1
	elif x <= 5.5e-67:
		tmp = y / t_0
	elif x <= 5.4e+54:
		tmp = z * ((-x - y) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(x / t_0)
	tmp = 0.0
	if (x <= -2.6e-111)
		tmp = t_1;
	elseif (x <= 5.5e-67)
		tmp = Float64(y / t_0);
	elseif (x <= 5.4e+54)
		tmp = Float64(z * Float64(Float64(Float64(-x) - y) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = x / t_0;
	tmp = 0.0;
	if (x <= -2.6e-111)
		tmp = t_1;
	elseif (x <= 5.5e-67)
		tmp = y / t_0;
	elseif (x <= 5.4e+54)
		tmp = z * ((-x - y) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[x, -2.6e-111], t$95$1, If[LessEqual[x, 5.5e-67], N[(y / t$95$0), $MachinePrecision], If[LessEqual[x, 5.4e+54], N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

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

Alternative 3: 66.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t_0}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-62}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+54}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)))
   (if (<= x -7.6e-112)
     t_1
     (if (<= x 2.4e-62)
       (/ y t_0)
       (if (<= x 5.2e+54) (/ (- z) (/ y (+ x y))) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double tmp;
	if (x <= -7.6e-112) {
		tmp = t_1;
	} else if (x <= 2.4e-62) {
		tmp = y / t_0;
	} else if (x <= 5.2e+54) {
		tmp = -z / (y / (x + y));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = x / t_0
    if (x <= (-7.6d-112)) then
        tmp = t_1
    else if (x <= 2.4d-62) then
        tmp = y / t_0
    else if (x <= 5.2d+54) then
        tmp = -z / (y / (x + y))
    else
        tmp = t_1
    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 t_1 = x / t_0;
	double tmp;
	if (x <= -7.6e-112) {
		tmp = t_1;
	} else if (x <= 2.4e-62) {
		tmp = y / t_0;
	} else if (x <= 5.2e+54) {
		tmp = -z / (y / (x + y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	tmp = 0
	if x <= -7.6e-112:
		tmp = t_1
	elif x <= 2.4e-62:
		tmp = y / t_0
	elif x <= 5.2e+54:
		tmp = -z / (y / (x + y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(x / t_0)
	tmp = 0.0
	if (x <= -7.6e-112)
		tmp = t_1;
	elseif (x <= 2.4e-62)
		tmp = Float64(y / t_0);
	elseif (x <= 5.2e+54)
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = x / t_0;
	tmp = 0.0;
	if (x <= -7.6e-112)
		tmp = t_1;
	elseif (x <= 2.4e-62)
		tmp = y / t_0;
	elseif (x <= 5.2e+54)
		tmp = -z / (y / (x + y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[x, -7.6e-112], t$95$1, If[LessEqual[x, 2.4e-62], N[(y / t$95$0), $MachinePrecision], If[LessEqual[x, 5.2e+54], N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

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

Alternative 4: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-58}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+49} \lor \neg \left(y \leq 5.2 \cdot 10^{+75}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.5e+54)
   (- z)
   (if (<= y 5.1e-58)
     (+ x y)
     (if (<= y 2.4e+23)
       (* x (/ (- z) y))
       (if (or (<= y 1.02e+49) (not (<= y 5.2e+75))) (- z) (+ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e+54) {
		tmp = -z;
	} else if (y <= 5.1e-58) {
		tmp = x + y;
	} else if (y <= 2.4e+23) {
		tmp = x * (-z / y);
	} else if ((y <= 1.02e+49) || !(y <= 5.2e+75)) {
		tmp = -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 (y <= (-7.5d+54)) then
        tmp = -z
    else if (y <= 5.1d-58) then
        tmp = x + y
    else if (y <= 2.4d+23) then
        tmp = x * (-z / y)
    else if ((y <= 1.02d+49) .or. (.not. (y <= 5.2d+75))) then
        tmp = -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 (y <= -7.5e+54) {
		tmp = -z;
	} else if (y <= 5.1e-58) {
		tmp = x + y;
	} else if (y <= 2.4e+23) {
		tmp = x * (-z / y);
	} else if ((y <= 1.02e+49) || !(y <= 5.2e+75)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.5e+54:
		tmp = -z
	elif y <= 5.1e-58:
		tmp = x + y
	elif y <= 2.4e+23:
		tmp = x * (-z / y)
	elif (y <= 1.02e+49) or not (y <= 5.2e+75):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.5e+54)
		tmp = Float64(-z);
	elseif (y <= 5.1e-58)
		tmp = Float64(x + y);
	elseif (y <= 2.4e+23)
		tmp = Float64(x * Float64(Float64(-z) / y));
	elseif ((y <= 1.02e+49) || !(y <= 5.2e+75))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.5e+54)
		tmp = -z;
	elseif (y <= 5.1e-58)
		tmp = x + y;
	elseif (y <= 2.4e+23)
		tmp = x * (-z / y);
	elseif ((y <= 1.02e+49) || ~((y <= 5.2e+75)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.5e+54], (-z), If[LessEqual[y, 5.1e-58], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.4e+23], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.02e+49], N[Not[LessEqual[y, 5.2e+75]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]]]]

Derivation

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

Alternative 5: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-58}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+48} \lor \neg \left(y \leq 1.6 \cdot 10^{+77}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.1e+54)
   (- z)
   (if (<= y 5.1e-58)
     (+ x y)
     (if (<= y 4.3e+23)
       (* z (/ (- x) y))
       (if (or (<= y 5.2e+48) (not (<= y 1.6e+77))) (- z) (+ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e+54) {
		tmp = -z;
	} else if (y <= 5.1e-58) {
		tmp = x + y;
	} else if (y <= 4.3e+23) {
		tmp = z * (-x / y);
	} else if ((y <= 5.2e+48) || !(y <= 1.6e+77)) {
		tmp = -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 (y <= (-2.1d+54)) then
        tmp = -z
    else if (y <= 5.1d-58) then
        tmp = x + y
    else if (y <= 4.3d+23) then
        tmp = z * (-x / y)
    else if ((y <= 5.2d+48) .or. (.not. (y <= 1.6d+77))) then
        tmp = -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 (y <= -2.1e+54) {
		tmp = -z;
	} else if (y <= 5.1e-58) {
		tmp = x + y;
	} else if (y <= 4.3e+23) {
		tmp = z * (-x / y);
	} else if ((y <= 5.2e+48) || !(y <= 1.6e+77)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.1e+54:
		tmp = -z
	elif y <= 5.1e-58:
		tmp = x + y
	elif y <= 4.3e+23:
		tmp = z * (-x / y)
	elif (y <= 5.2e+48) or not (y <= 1.6e+77):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.1e+54)
		tmp = Float64(-z);
	elseif (y <= 5.1e-58)
		tmp = Float64(x + y);
	elseif (y <= 4.3e+23)
		tmp = Float64(z * Float64(Float64(-x) / y));
	elseif ((y <= 5.2e+48) || !(y <= 1.6e+77))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.1e+54)
		tmp = -z;
	elseif (y <= 5.1e-58)
		tmp = x + y;
	elseif (y <= 4.3e+23)
		tmp = z * (-x / y);
	elseif ((y <= 5.2e+48) || ~((y <= 1.6e+77)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.1e+54], (-z), If[LessEqual[y, 5.1e-58], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.3e+23], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 5.2e+48], N[Not[LessEqual[y, 1.6e+77]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]]]]

Derivation

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

Alternative 6: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{+56}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-79}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+48} \lor \neg \left(y \leq 7.5 \cdot 10^{+75}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.7e+56)
   (- z)
   (if (<= y 2.15e-79)
     (+ x y)
     (if (<= y 3.8e+23)
       (/ x (- 1.0 (/ y z)))
       (if (or (<= y 7e+48) (not (<= y 7.5e+75))) (- z) (+ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.7e+56) {
		tmp = -z;
	} else if (y <= 2.15e-79) {
		tmp = x + y;
	} else if (y <= 3.8e+23) {
		tmp = x / (1.0 - (y / z));
	} else if ((y <= 7e+48) || !(y <= 7.5e+75)) {
		tmp = -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 (y <= (-6.7d+56)) then
        tmp = -z
    else if (y <= 2.15d-79) then
        tmp = x + y
    else if (y <= 3.8d+23) then
        tmp = x / (1.0d0 - (y / z))
    else if ((y <= 7d+48) .or. (.not. (y <= 7.5d+75))) then
        tmp = -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 (y <= -6.7e+56) {
		tmp = -z;
	} else if (y <= 2.15e-79) {
		tmp = x + y;
	} else if (y <= 3.8e+23) {
		tmp = x / (1.0 - (y / z));
	} else if ((y <= 7e+48) || !(y <= 7.5e+75)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.7e+56:
		tmp = -z
	elif y <= 2.15e-79:
		tmp = x + y
	elif y <= 3.8e+23:
		tmp = x / (1.0 - (y / z))
	elif (y <= 7e+48) or not (y <= 7.5e+75):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.7e+56)
		tmp = Float64(-z);
	elseif (y <= 2.15e-79)
		tmp = Float64(x + y);
	elseif (y <= 3.8e+23)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif ((y <= 7e+48) || !(y <= 7.5e+75))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.7e+56)
		tmp = -z;
	elseif (y <= 2.15e-79)
		tmp = x + y;
	elseif (y <= 3.8e+23)
		tmp = x / (1.0 - (y / z));
	elseif ((y <= 7e+48) || ~((y <= 7.5e+75)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.7e+56], (-z), If[LessEqual[y, 2.15e-79], N[(x + y), $MachinePrecision], If[LessEqual[y, 3.8e+23], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 7e+48], N[Not[LessEqual[y, 7.5e+75]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]]]]

Derivation

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

Alternative 7: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t_0}\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.15:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;x \leq 1.92 \cdot 10^{+40}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)))
   (if (<= x -3.8e-111)
     t_1
     (if (<= x 1.15) (/ y t_0) (if (<= x 1.92e+40) (- z) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double tmp;
	if (x <= -3.8e-111) {
		tmp = t_1;
	} else if (x <= 1.15) {
		tmp = y / t_0;
	} else if (x <= 1.92e+40) {
		tmp = -z;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = x / t_0
    if (x <= (-3.8d-111)) then
        tmp = t_1
    else if (x <= 1.15d0) then
        tmp = y / t_0
    else if (x <= 1.92d+40) then
        tmp = -z
    else
        tmp = t_1
    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 t_1 = x / t_0;
	double tmp;
	if (x <= -3.8e-111) {
		tmp = t_1;
	} else if (x <= 1.15) {
		tmp = y / t_0;
	} else if (x <= 1.92e+40) {
		tmp = -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	tmp = 0
	if x <= -3.8e-111:
		tmp = t_1
	elif x <= 1.15:
		tmp = y / t_0
	elif x <= 1.92e+40:
		tmp = -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(x / t_0)
	tmp = 0.0
	if (x <= -3.8e-111)
		tmp = t_1;
	elseif (x <= 1.15)
		tmp = Float64(y / t_0);
	elseif (x <= 1.92e+40)
		tmp = Float64(-z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = x / t_0;
	tmp = 0.0;
	if (x <= -3.8e-111)
		tmp = t_1;
	elseif (x <= 1.15)
		tmp = y / t_0;
	elseif (x <= 1.92e+40)
		tmp = -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[x, -3.8e-111], t$95$1, If[LessEqual[x, 1.15], N[(y / t$95$0), $MachinePrecision], If[LessEqual[x, 1.92e+40], (-z), t$95$1]]]]]

Derivation

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

Alternative 8: 65.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+57} \lor \neg \left(y \leq 2.3 \cdot 10^{-58}\right) \land \left(y \leq 2.1 \cdot 10^{+50} \lor \neg \left(y \leq 3.2 \cdot 10^{+76}\right)\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.9e+57)
         (and (not (<= y 2.3e-58)) (or (<= y 2.1e+50) (not (<= y 3.2e+76)))))
   (- z)
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.9e+57) || (!(y <= 2.3e-58) && ((y <= 2.1e+50) || !(y <= 3.2e+76)))) {
		tmp = -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 ((y <= (-5.9d+57)) .or. (.not. (y <= 2.3d-58)) .and. (y <= 2.1d+50) .or. (.not. (y <= 3.2d+76))) then
        tmp = -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 ((y <= -5.9e+57) || (!(y <= 2.3e-58) && ((y <= 2.1e+50) || !(y <= 3.2e+76)))) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.9e+57) or (not (y <= 2.3e-58) and ((y <= 2.1e+50) or not (y <= 3.2e+76))):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.9e+57) || (!(y <= 2.3e-58) && ((y <= 2.1e+50) || !(y <= 3.2e+76))))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.9e+57) || (~((y <= 2.3e-58)) && ((y <= 2.1e+50) || ~((y <= 3.2e+76)))))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.9e+57], And[N[Not[LessEqual[y, 2.3e-58]], $MachinePrecision], Or[LessEqual[y, 2.1e+50], N[Not[LessEqual[y, 3.2e+76]], $MachinePrecision]]]], (-z), N[(x + y), $MachinePrecision]]

Derivation

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

Alternative 9: 57.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1350 \lor \neg \left(y \leq 3.2 \cdot 10^{-58}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1350.0) (not (<= y 3.2e-58))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1350.0) || !(y <= 3.2e-58)) {
		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 <= (-1350.0d0)) .or. (.not. (y <= 3.2d-58))) 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 <= -1350.0) || !(y <= 3.2e-58)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1350.0) or not (y <= 3.2e-58):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1350.0) || !(y <= 3.2e-58))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1350.0) || ~((y <= 3.2e-58)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1350.0], N[Not[LessEqual[y, 3.2e-58]], $MachinePrecision]], (-z), x]

Derivation

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

Alternative 10: 40.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-109}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.12e-113) x (if (<= x 1.35e-109) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.12e-113) {
		tmp = x;
	} else if (x <= 1.35e-109) {
		tmp = y;
	} 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 (x <= (-1.12d-113)) then
        tmp = x
    else if (x <= 1.35d-109) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.12e-113) {
		tmp = x;
	} else if (x <= 1.35e-109) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.12e-113:
		tmp = x
	elif x <= 1.35e-109:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.12e-113)
		tmp = x;
	elseif (x <= 1.35e-109)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.12e-113)
		tmp = x;
	elseif (x <= 1.35e-109)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.12e-113], x, If[LessEqual[x, 1.35e-109], y, x]]

Derivation

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

Alternative 11: 35.1% 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: 93.5% 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 2024008 
(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))))