fabs fraction 1

Average Error: 1.7 → 1.7

Time: 7.6s

Precision: binary64

Cost: 7104

Math

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

↓

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

FPCore

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

↓

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

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) {
	return fabs((((x + 4.0) / y) - ((x / 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 = 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
    code = abs((((x + 4.0d0) / y) - ((x / y) * z)))
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) {
	return Math.abs((((x + 4.0) / y) - ((x / y) * z)));
}

Python

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

↓

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

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

MATLAB

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

↓

function tmp = code(x, y, z)
	tmp = abs((((x + 4.0) / y) - ((x / y) * z)));
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_] := N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 1.7

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

2. Final simplification 1.7

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

Alternatives

Alternative 1
Error	12.3
Cost	7644

\[\begin{array}{l} t_0 := \left|x \cdot \frac{z}{y}\right|\\ t_1 := \left|\frac{z}{\frac{y}{x}}\right|\\ t_2 := \left|\frac{x + 4}{y}\right|\\ \mathbf{if}\;z \leq -1.4404033504866865 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1809152312201316 \cdot 10^{+95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.283726085342735 \cdot 10^{+73}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.0491518327847735 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 10^{+215}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	12.5
Cost	7644

\[\begin{array}{l} t_0 := \left|x \cdot \frac{z}{y}\right|\\ t_1 := \left|\frac{x + 4}{y}\right|\\ t_2 := \left|\frac{x}{y} \cdot z\right|\\ \mathbf{if}\;z \leq -1.4404033504866865 \cdot 10^{+115}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;z \leq -1.1809152312201316 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.283726085342735 \cdot 10^{+73}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.0491518327847735 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{+215}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	12.7
Cost	7512

\[\begin{array}{l} t_0 := \left|\frac{x + 4}{y}\right|\\ \mathbf{if}\;z \leq -1.4404033504866865 \cdot 10^{+115}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;z \leq -1.1809152312201316 \cdot 10^{+95}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.283726085342735 \cdot 10^{+73}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;z \leq 2.0491518327847735 \cdot 10^{+22}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+131}:\\ \;\;\;\;\left|\frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+194}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x \cdot z}{y}\right|\\ \end{array} \]

Alternative 4
Error	2.7
Cost	7240

\[\begin{array}{l} t_0 := \left|\frac{4}{y} - \frac{z}{\frac{y}{x}}\right|\\ \mathbf{if}\;z \leq -133247.2111898633:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.753450746434506 \cdot 10^{-21}:\\ \;\;\;\;\left|\frac{x + 4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	2.6
Cost	7108

\[\begin{array}{l} \mathbf{if}\;z \leq -4.283726085342735 \cdot 10^{+73}:\\ \;\;\;\;\left|\frac{4}{y} - \frac{z}{\frac{y}{x}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x \cdot z + \left(-4 - x\right)}{y}\right|\\ \end{array} \]

Alternative 6
Error	1.8
Cost	7104

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

Alternative 7
Error	19.4
Cost	6988

\[\begin{array}{l} t_0 := \left|\frac{x}{y}\right|\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+59}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.0357721671583626 \cdot 10^{-23}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \leq 3.668101731883291 \cdot 10^{-10}:\\ \;\;\;\;\frac{4}{\left|y\right|}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	19.3
Cost	6856

\[\begin{array}{l} t_0 := \left|\frac{x}{y}\right|\\ \mathbf{if}\;x \leq -28345.69961408105:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.668101731883291 \cdot 10^{-10}:\\ \;\;\;\;\frac{4}{\left|y\right|}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	47.2
Cost	6592

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

Reproduce

herbie shell --seed 2022300 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))