Average Error: 29.0 → 0
Time: 1.1s
Precision: binary64
Cost: 64
\[\left(1 + x\right) - x \]
↓
\[1 \]
(FPCore (x) :precision binary64 (- (+ 1.0 x) x))
↓
(FPCore (x) :precision binary64 1.0)
double code(double x) {
	return (1.0 + x) - x;
}
↓
double code(double x) {
	return 1.0;
}

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

public static double code(double x) {
	return (1.0 + x) - x;
}
↓
public static double code(double x) {
	return 1.0;
}

def code(x):
	return (1.0 + x) - x
↓
def code(x):
	return 1.0

function code(x)
	return Float64(Float64(1.0 + x) - x)
end
↓
function code(x)
	return 1.0
end

function tmp = code(x)
	tmp = (1.0 + x) - x;
end
↓
function tmp = code(x)
	tmp = 1.0;
end

code[x_] := N[(N[(1.0 + x), $MachinePrecision] - x), $MachinePrecision]
↓
code[x_] := 1.0

\left(1 + x\right) - x
↓
1

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.0

    \[\left(1 + x\right) - x \]

  2. Simplified0

    \[\leadsto \color{blue}{1} \]
    Proof
    1: 0 points increase in error, 0 points decrease in error
    (Rewrite<= metadata-eval (+.f64 1 0)): 0 points increase in error, 0 points decrease in error
    (+.f64 1 (Rewrite<= +-inverses_binary64 (-.f64 x x))): 0 points increase in error, 0 points decrease in error
    (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 1 x) x)): 117 points increase in error, 0 points decrease in error

  3. Final simplification0

    \[\leadsto 1 \]

Reproduce

herbie shell --seed 2022294 
(FPCore (x)
  :name "Cancel like terms"
  :precision binary64
  (- (+ 1.0 x) x))