fabs fraction 1

Average Error: 1.4 → 0.5

Time: 10.2s

Precision: binary64

Cost: 7368

Math

\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

↓

\[\begin{array}{l} t_0 := \frac{x + 4}{y}\\ \mathbf{if}\;x \leq -6.062350352892886 \cdot 10^{-118}:\\ \;\;\;\;\left|t_0 - \frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;x \leq 10^{+90}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|t_0 - \frac{z}{\frac{y}{x}}\right|\\ \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x 4.0) y)))
   (if (<= x -6.062350352892886e-118)
     (fabs (- t_0 (* (/ x y) z)))
     (if (<= x 1e+90)
       (fabs (/ (- (+ x 4.0) (* x z)) y))
       (fabs (- t_0 (/ z (/ y x))))))))

C

double code(double x, double y, double z) {
	return fabs((((x + 4.0) / y) - ((x / y) * z)));
}

↓

double code(double x, double y, double z) {
	double t_0 = (x + 4.0) / y;
	double tmp;
	if (x <= -6.062350352892886e-118) {
		tmp = fabs((t_0 - ((x / y) * z)));
	} else if (x <= 1e+90) {
		tmp = fabs((((x + 4.0) - (x * z)) / y));
	} else {
		tmp = fabs((t_0 - (z / (y / 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
    code = abs((((x + 4.0d0) / y) - ((x / y) * z)))
end function

↓

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 + 4.0d0) / y
    if (x <= (-6.062350352892886d-118)) then
        tmp = abs((t_0 - ((x / y) * z)))
    else if (x <= 1d+90) then
        tmp = abs((((x + 4.0d0) - (x * z)) / y))
    else
        tmp = abs((t_0 - (z / (y / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	return Math.abs((((x + 4.0) / y) - ((x / y) * z)));
}

↓

public static double code(double x, double y, double z) {
	double t_0 = (x + 4.0) / y;
	double tmp;
	if (x <= -6.062350352892886e-118) {
		tmp = Math.abs((t_0 - ((x / y) * z)));
	} else if (x <= 1e+90) {
		tmp = Math.abs((((x + 4.0) - (x * z)) / y));
	} else {
		tmp = Math.abs((t_0 - (z / (y / x))));
	}
	return tmp;
}

Python

def code(x, y, z):
	return math.fabs((((x + 4.0) / y) - ((x / y) * z)))

↓

def code(x, y, z):
	t_0 = (x + 4.0) / y
	tmp = 0
	if x <= -6.062350352892886e-118:
		tmp = math.fabs((t_0 - ((x / y) * z)))
	elif x <= 1e+90:
		tmp = math.fabs((((x + 4.0) - (x * z)) / y))
	else:
		tmp = math.fabs((t_0 - (z / (y / x))))
	return tmp

Julia

function code(x, y, z)
	return abs(Float64(Float64(Float64(x + 4.0) / y) - Float64(Float64(x / y) * z)))
end

↓

function code(x, y, z)
	t_0 = Float64(Float64(x + 4.0) / y)
	tmp = 0.0
	if (x <= -6.062350352892886e-118)
		tmp = abs(Float64(t_0 - Float64(Float64(x / y) * z)));
	elseif (x <= 1e+90)
		tmp = abs(Float64(Float64(Float64(x + 4.0) - Float64(x * z)) / y));
	else
		tmp = abs(Float64(t_0 - Float64(z / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z)
	tmp = abs((((x + 4.0) / y) - ((x / y) * z)));
end

↓

function tmp_2 = code(x, y, z)
	t_0 = (x + 4.0) / y;
	tmp = 0.0;
	if (x <= -6.062350352892886e-118)
		tmp = abs((t_0 - ((x / y) * z)));
	elseif (x <= 1e+90)
		tmp = abs((((x + 4.0) - (x * z)) / y));
	else
		tmp = abs((t_0 - (z / (y / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + 4.0), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[x, -6.062350352892886e-118], N[Abs[N[(t$95$0 - N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 1e+90], N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(t$95$0 - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.06235035289288624e-118

   1. Initial program 1.0

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   if -6.06235035289288624e-118 < x < 9.99999999999999966e89

   1. Initial program 2.0

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Applied egg-rr 0.3

      \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   if 9.99999999999999966e89 < x

   1. Initial program 0.1

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Applied egg-rr 0.1

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{z}{\frac{y}{x}}}\right| \]
3. Recombined 3 regimes into one program.

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.062350352892886 \cdot 10^{-118}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;x \leq 10^{+90}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{z}{\frac{y}{x}}\right|\\ \end{array} \]

Alternatives

Alternative 1
Error	28.9
Cost	8040

\[\begin{array}{l} t_0 := \left|\frac{x}{y}\right|\\ t_1 := \left|x \cdot \frac{z}{y}\right|\\ t_2 := \left|\frac{-4}{y}\right|\\ \mathbf{if}\;z \leq -4.2060613478808176 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.2518771220378959 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.0153878531438772 \cdot 10^{-91}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.5867882404080174 \cdot 10^{-191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.006245100227897 \cdot 10^{-267}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.468529510587328 \cdot 10^{-147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.470894342030933 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.083835872083797 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+110}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+167}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	28.9
Cost	8040

\[\begin{array}{l} t_0 := \left|\frac{x}{y}\right|\\ t_1 := \left|\frac{-4}{y}\right|\\ \mathbf{if}\;z \leq -4.2060613478808176 \cdot 10^{+36}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;z \leq -1.2518771220378959 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.0153878531438772 \cdot 10^{-91}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.5867882404080174 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.006245100227897 \cdot 10^{-267}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.468529510587328 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.470894342030933 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.083835872083797 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+110}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{\frac{y}{z}}\right|\\ \end{array} \]

Alternative 3
Error	0.3
Cost	7368

\[\begin{array}{l} \mathbf{if}\;x \leq -1.464136504053415 \cdot 10^{+32}:\\ \;\;\;\;\left|\frac{x}{\frac{y}{1 - z}}\right|\\ \mathbf{elif}\;x \leq 10^{+90}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{z}{\frac{y}{x}}\right|\\ \end{array} \]

Alternative 4
Error	12.1
Cost	7248

\[\begin{array}{l} t_0 := \left|\frac{x + 4}{y}\right|\\ \mathbf{if}\;z \leq -4.2060613478808176 \cdot 10^{+36}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;z \leq 3.083835872083797 \cdot 10^{+54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+110}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+167}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{\frac{y}{z}}\right|\\ \end{array} \]

Alternative 5
Error	11.9
Cost	7248

\[\begin{array}{l} t_0 := \left|\frac{x + 4}{y}\right|\\ \mathbf{if}\;z \leq -4.2060613478808176 \cdot 10^{+36}:\\ \;\;\;\;\left|\frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;z \leq 3.083835872083797 \cdot 10^{+54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+110}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+167}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{\frac{y}{z}}\right|\\ \end{array} \]

Alternative 6
Error	0.5
Cost	7240

\[\begin{array}{l} t_0 := \left|\frac{x}{\frac{y}{1 - z}}\right|\\ \mathbf{if}\;x \leq -1.464136504053415 \cdot 10^{+32}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 10^{+150}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	4.2
Cost	7112

\[\begin{array}{l} t_0 := \left|\frac{4 - x \cdot z}{y}\right|\\ \mathbf{if}\;z \leq -437574739.26678383:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.9753376586326061:\\ \;\;\;\;\left|\frac{x + 4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	1.1
Cost	7112

\[\begin{array}{l} t_0 := \left|\frac{x}{\frac{y}{1 - z}}\right|\\ \mathbf{if}\;x \leq -185549631904.90997:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.003460331485035759:\\ \;\;\;\;\left|\frac{4 - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	19.4
Cost	6988

\[\begin{array}{l} t_0 := \left|\frac{x}{y}\right|\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.864886182142133 \cdot 10^{-34}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;x \leq 0.0738665516299867:\\ \;\;\;\;\left|\frac{-4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 10
Error	18.8
Cost	6856

\[\begin{array}{l} t_0 := \left|\frac{x}{y}\right|\\ \mathbf{if}\;x \leq -185549631904.90997:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.0738665516299867:\\ \;\;\;\;\left|\frac{-4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Error	47.5
Cost	6592

\[\left|\frac{x}{y}\right| \]

Reproduce

herbie shell --seed 2022316 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))