Average Error: 0.0 → 0.0

Time: 2.0s

Precision: binary64

Cost: 320

\[\frac{x - y}{x} \]

↓

\[1 - \frac{y}{x} \]

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

\frac{x - y}{x}

↓

1 - \frac{y}{x}

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	0.0
Target	0.0
Herbie	0.0

\[1 - \frac{y}{x} \]

Derivation

Initial program 0.0
\[\frac{x - y}{x} \]
Simplified0.0
\[\leadsto \color{blue}{1 - \frac{y}{x}} \]
Proof
(-.f64 1 (/.f64 y x)): 0 points increase in error, 0 points decrease in error
(-.f64 (Rewrite<= *-inverses_binary64 (/.f64 x x)) (/.f64 y x)): 0 points increase in error, 0 points decrease in error
(Rewrite<= div-sub_binary64 (/.f64 (-.f64 x y) x)): 3 points increase in error, 2 points decrease in error
Final simplification0.0
\[\leadsto 1 - \frac{y}{x} \]

Alternatives

Alternative 1
Error	19.5
Cost	520

\[\begin{array}{l} t_0 := \frac{-y}{x}\\ \mathbf{if}\;y \leq -9044100853676149000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.408641106180247 \cdot 10^{-107}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	26.6
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022294 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- 1.0 (/ y x))

  (/ (- x y) x))