Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Percentage Accurate: 85.1% → 96.1%

Time: 4.8s

Alternatives: 8

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

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)) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;x_m \leq 1.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{x_m \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x_m \cdot \left(1 - \frac{z}{y}\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= x_m 1.8e-72) (/ (* x_m (- y z)) y) (* x_m (- 1.0 (/ z y))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 1.8e-72) {
		tmp = (x_m * (y - z)) / y;
	} else {
		tmp = x_m * (1.0 - (z / y));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x_m <= 1.8d-72) then
        tmp = (x_m * (y - z)) / y
    else
        tmp = x_m * (1.0d0 - (z / y))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 1.8e-72) {
		tmp = (x_m * (y - z)) / y;
	} else {
		tmp = x_m * (1.0 - (z / y));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if x_m <= 1.8e-72:
		tmp = (x_m * (y - z)) / y
	else:
		tmp = x_m * (1.0 - (z / y))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 1.8e-72)
		tmp = Float64(Float64(x_m * Float64(y - z)) / y);
	else
		tmp = Float64(x_m * Float64(1.0 - Float64(z / y)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (x_m <= 1.8e-72)
		tmp = (x_m * (y - z)) / y;
	else
		tmp = x_m * (1.0 - (z / y));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[x$95$m, 1.8e-72], N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 2: 68.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-158}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-13}:\\ \;\;\;\;x_m \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -1.32e-158) x_m (if (<= y 5.6e-13) (* x_m (/ (- z) y)) x_m))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -1.32e-158) {
		tmp = x_m;
	} else if (y <= 5.6e-13) {
		tmp = x_m * (-z / y);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.32d-158)) then
        tmp = x_m
    else if (y <= 5.6d-13) then
        tmp = x_m * (-z / y)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -1.32e-158) {
		tmp = x_m;
	} else if (y <= 5.6e-13) {
		tmp = x_m * (-z / y);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -1.32e-158:
		tmp = x_m
	elif y <= 5.6e-13:
		tmp = x_m * (-z / y)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -1.32e-158)
		tmp = x_m;
	elseif (y <= 5.6e-13)
		tmp = Float64(x_m * Float64(Float64(-z) / y));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -1.32e-158)
		tmp = x_m;
	elseif (y <= 5.6e-13)
		tmp = x_m * (-z / y);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -1.32e-158], x$95$m, If[LessEqual[y, 5.6e-13], N[(x$95$m * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

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

Alternative 3: 69.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{-158}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-15}:\\ \;\;\;\;z \cdot \frac{-x_m}{y}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -1.56e-158) x_m (if (<= y 1.55e-15) (* z (/ (- x_m) y)) x_m))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -1.56e-158) {
		tmp = x_m;
	} else if (y <= 1.55e-15) {
		tmp = z * (-x_m / y);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.56d-158)) then
        tmp = x_m
    else if (y <= 1.55d-15) then
        tmp = z * (-x_m / y)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -1.56e-158) {
		tmp = x_m;
	} else if (y <= 1.55e-15) {
		tmp = z * (-x_m / y);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -1.56e-158:
		tmp = x_m
	elif y <= 1.55e-15:
		tmp = z * (-x_m / y)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -1.56e-158)
		tmp = x_m;
	elseif (y <= 1.55e-15)
		tmp = Float64(z * Float64(Float64(-x_m) / y));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -1.56e-158)
		tmp = x_m;
	elseif (y <= 1.55e-15)
		tmp = z * (-x_m / y);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -1.56e-158], x$95$m, If[LessEqual[y, 1.55e-15], N[(z * N[((-x$95$m) / y), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

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

Alternative 4: 52.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-193}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \frac{x_m}{y}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= y -8.5e-193) x_m (if (<= y 3.9e-134) (* y (/ x_m y)) x_m))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -8.5e-193) {
		tmp = x_m;
	} else if (y <= 3.9e-134) {
		tmp = y * (x_m / y);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8.5d-193)) then
        tmp = x_m
    else if (y <= 3.9d-134) then
        tmp = y * (x_m / y)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -8.5e-193) {
		tmp = x_m;
	} else if (y <= 3.9e-134) {
		tmp = y * (x_m / y);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -8.5e-193:
		tmp = x_m
	elif y <= 3.9e-134:
		tmp = y * (x_m / y)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -8.5e-193)
		tmp = x_m;
	elseif (y <= 3.9e-134)
		tmp = Float64(y * Float64(x_m / y));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -8.5e-193)
		tmp = x_m;
	elseif (y <= 3.9e-134)
		tmp = y * (x_m / y);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -8.5e-193], x$95$m, If[LessEqual[y, 3.9e-134], N[(y * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

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

Alternative 5: 52.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-193}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-132}:\\ \;\;\;\;\frac{y}{\frac{y}{x_m}}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= y -6.8e-193) x_m (if (<= y 1.8e-132) (/ y (/ y x_m)) x_m))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -6.8e-193) {
		tmp = x_m;
	} else if (y <= 1.8e-132) {
		tmp = y / (y / x_m);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.8d-193)) then
        tmp = x_m
    else if (y <= 1.8d-132) then
        tmp = y / (y / x_m)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -6.8e-193) {
		tmp = x_m;
	} else if (y <= 1.8e-132) {
		tmp = y / (y / x_m);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -6.8e-193:
		tmp = x_m
	elif y <= 1.8e-132:
		tmp = y / (y / x_m)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -6.8e-193)
		tmp = x_m;
	elseif (y <= 1.8e-132)
		tmp = Float64(y / Float64(y / x_m));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -6.8e-193)
		tmp = x_m;
	elseif (y <= 1.8e-132)
		tmp = y / (y / x_m);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -6.8e-193], x$95$m, If[LessEqual[y, 1.8e-132], N[(y / N[(y / x$95$m), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

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

Alternative 6: 94.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 3 \cdot 10^{+136}:\\ \;\;\;\;x_m \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x_m}{y}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= z 3e+136) (* x_m (- 1.0 (/ z y))) (* z (/ (- x_m) y)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= 3e+136) {
		tmp = x_m * (1.0 - (z / y));
	} else {
		tmp = z * (-x_m / y);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 3d+136) then
        tmp = x_m * (1.0d0 - (z / y))
    else
        tmp = z * (-x_m / y)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= 3e+136) {
		tmp = x_m * (1.0 - (z / y));
	} else {
		tmp = z * (-x_m / y);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if z <= 3e+136:
		tmp = x_m * (1.0 - (z / y))
	else:
		tmp = z * (-x_m / y)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (z <= 3e+136)
		tmp = Float64(x_m * Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(z * Float64(Float64(-x_m) / y));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (z <= 3e+136)
		tmp = x_m * (1.0 - (z / y));
	else
		tmp = z * (-x_m / y);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[z, 3e+136], N[(x$95$m * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[((-x$95$m) / y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 7: 95.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 3.4 \cdot 10^{+135}:\\ \;\;\;\;x_m \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x_m}{y}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= z 3.4e+135) (* x_m (- 1.0 (/ z y))) (* (- y z) (/ x_m y)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= 3.4e+135) {
		tmp = x_m * (1.0 - (z / y));
	} else {
		tmp = (y - z) * (x_m / y);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 3.4d+135) then
        tmp = x_m * (1.0d0 - (z / y))
    else
        tmp = (y - z) * (x_m / y)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= 3.4e+135) {
		tmp = x_m * (1.0 - (z / y));
	} else {
		tmp = (y - z) * (x_m / y);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if z <= 3.4e+135:
		tmp = x_m * (1.0 - (z / y))
	else:
		tmp = (y - z) * (x_m / y)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (z <= 3.4e+135)
		tmp = Float64(x_m * Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(Float64(y - z) * Float64(x_m / y));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (z <= 3.4e+135)
		tmp = x_m * (1.0 - (z / y));
	else
		tmp = (y - z) * (x_m / y);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[z, 3.4e+135], N[(x$95$m * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 8: 50.6% accurate, 7.0× speedup

Math

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

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s x_m))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * x_m;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * x_m
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * x_m;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	return x_s * x_m

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * x_m)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * x_m;
end

Wolfram

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

Derivation

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

Developer target: 96.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -2.060202331921739e+104)
   (- x (/ (* z x) y))
   (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (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 < (-2.060202331921739d+104)) then
        tmp = x - ((z * x) / y)
    else if (z < 1.6939766013828526d+213) then
        tmp = x / (y / (y - z))
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -2.060202331921739e+104:
		tmp = x - ((z * x) / y)
	elif z < 1.6939766013828526e+213:
		tmp = x / (y / (y - z))
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -2.060202331921739e+104)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	elseif (z < 1.6939766013828526e+213)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -2.060202331921739e+104)
		tmp = x - ((z * x) / y);
	elseif (z < 1.6939766013828526e+213)
		tmp = x / (y / (y - z));
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -2.060202331921739e+104], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Less[z, 1.6939766013828526e+213], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023348 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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