Average Error: 0.1 → 0.0

Time: 1.4s

Precision: binary64

Cost: 6528

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

↓

\[{x}^{3} \]

(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}

Try it out

In
Out

Enter valid numbers for all inputs

Target

\[{x}^{3} \]

Initial program 0.1
\[\left(x \cdot x\right) \cdot x \]
Simplified0.0
\[\leadsto \color{blue}{{x}^{3}} \]
Proof
(pow.f64 x 3): 0 points increase in error, 0 points decrease in error
(Rewrite=> unpow3_binary64 (*.f64 (*.f64 x x) x)): 30 points increase in error, 0 points decrease in error
Final simplification0.0
\[\leadsto {x}^{3} \]

Alternative 1
Error	0.1
Cost	320

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

herbie shell --seed 2022295 
(FPCore (x)
  :name "math.cube on real"
  :precision binary64

  :herbie-target
  (pow x 3.0)

  (* (* x x) x))