Average Error: 0.0 → 0.0
Time: 1.5s
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}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[1 - \frac{y}{x} \]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x} \]
  2. 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)): 5 points increase in error, 0 points decrease in error
  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022291 
(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))