Average Error: 0 → 0
Time: 1.1s
Precision: binary64
Cost: 192
\[\left(\left(\left(x + x\right) + x\right) + x\right) + x \]
↓
\[x \cdot 5 \]
(FPCore (x) :precision binary64 (+ (+ (+ (+ x x) x) x) x))
↓
(FPCore (x) :precision binary64 (* x 5.0))
double code(double x) {
	return (((x + x) + x) + x) + x;
}
↓
double code(double x) {
	return x * 5.0;
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (((x + x) + x) + x) + x
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = x * 5.0d0
end function

public static double code(double x) {
	return (((x + x) + x) + x) + x;
}
↓
public static double code(double x) {
	return x * 5.0;
}

def code(x):
	return (((x + x) + x) + x) + x
↓
def code(x):
	return x * 5.0

function code(x)
	return Float64(Float64(Float64(Float64(x + x) + x) + x) + x)
end
↓
function code(x)
	return Float64(x * 5.0)
end

function tmp = code(x)
	tmp = (((x + x) + x) + x) + x;
end
↓
function tmp = code(x)
	tmp = x * 5.0;
end

code[x_] := N[(N[(N[(N[(x + x), $MachinePrecision] + x), $MachinePrecision] + x), $MachinePrecision] + x), $MachinePrecision]
↓
code[x_] := N[(x * 5.0), $MachinePrecision]

\left(\left(\left(x + x\right) + x\right) + x\right) + x
↓
x \cdot 5

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0

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

  2. Simplified0

    \[\leadsto \color{blue}{x \cdot 5} \]
    Proof
    (*.f64 x 5): 0 points increase in error, 0 points decrease in error
    (*.f64 x (Rewrite<= metadata-eval (+.f64 2 3))): 0 points increase in error, 0 points decrease in error
    (*.f64 x (+.f64 2 (Rewrite<= metadata-eval (+.f64 2 1)))): 0 points increase in error, 0 points decrease in error
    (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 2 x) (*.f64 (+.f64 2 1) x))): 72 points increase in error, 0 points decrease in error
    (+.f64 (Rewrite<= count-2_binary64 (+.f64 x x)) (*.f64 (+.f64 2 1) x)): 0 points increase in error, 0 points decrease in error
    (+.f64 (+.f64 x x) (Rewrite<= distribute-rgt1-in_binary64 (+.f64 x (*.f64 2 x)))): 0 points increase in error, 0 points decrease in error
    (+.f64 (+.f64 x x) (+.f64 x (Rewrite<= count-2_binary64 (+.f64 x x)))): 0 points increase in error, 0 points decrease in error
    (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 x x) x) (+.f64 x x))): 0 points increase in error, 0 points decrease in error
    (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 (+.f64 x x) x) x) x)): 0 points increase in error, 72 points decrease in error

  3. Final simplification0

    \[\leadsto x \cdot 5 \]

Reproduce

herbie shell --seed 2022291 
(FPCore (x)
  :name "Main:i from "
  :precision binary64
  (+ (+ (+ (+ x x) x) x) x))