Average Error: 0.1 → 0
Time: 746.0ms
Precision: binary64
\[\left(x \cdot x\right) \cdot x \]
↓
\[{x}^{3} \]
(FPCore (x) :precision binary64 (* (* x x) x))
↓
(FPCore (x) :precision binary64 (pow x 3.0))
double code(double x) {
	return (x * x) * x;
}
↓
double code(double x) {
	return pow(x, 3.0);
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * x) * x
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = x ** 3.0d0
end function

public static double code(double x) {
	return (x * x) * x;
}
↓
public static double code(double x) {
	return Math.pow(x, 3.0);
}

def code(x):
	return (x * x) * x
↓
def code(x):
	return math.pow(x, 3.0)

function code(x)
	return Float64(Float64(x * x) * x)
end
↓
function code(x)
	return x ^ 3.0
end

function tmp = code(x)
	tmp = (x * x) * x;
end
↓
function tmp = code(x)
	tmp = x ^ 3.0;
end

code[x_] := N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]
↓
code[x_] := N[Power[x, 3.0], $MachinePrecision]

\left(x \cdot x\right) \cdot x
↓
{x}^{3}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0
Herbie0
\[{x}^{3} \]

Derivation

  1. Initial program 0.1

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

  2. Simplified0

    \[\leadsto \color{blue}{{x}^{3}} \]

  3. Final simplification0

    \[\leadsto {x}^{3} \]

Reproduce

herbie shell --seed 2022150 
(FPCore (x)
  :name "math.cube on real"
  :precision binary64

  :herbie-target
  (pow x 3.0)

  (* (* x x) x))