math.cube on real

Average Error: 0.1 → 0.0

Time: 6.6s

Precision: binary64

Cost: 6528

Math

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

↓

\[{x}^{3} \]

FPCore

(FPCore (x) :precision binary64 (* (* x x) x))

↓

(FPCore (x) :precision binary64 (pow x 3.0))

C

double code(double x) {
	return (x * x) * x;
}

↓

double code(double x) {
	return pow(x, 3.0);
}

Fortran

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

Java

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

↓

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

Python

def code(x):
	return (x * x) * x

↓

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

Julia

function code(x)
	return Float64(Float64(x * x) * x)
end

↓

function code(x)
	return x ^ 3.0
end

MATLAB

function tmp = code(x)
	tmp = (x * x) * x;
end

↓

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

Wolfram

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

↓

code[x_] := N[Power[x, 3.0], $MachinePrecision]

Target

Original	0.1
Target	0.0
Herbie	0.0

\[{x}^{3} \]

Derivation

1. Initial program 0.1

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

2. Taylor expanded in x around 0 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.2
Cost	1728

\[\begin{array}{l} t_0 := x \cdot \left(x \cdot x\right)\\ \frac{t_0 \cdot 0.75 + \frac{x \cdot \left(\left(x \cdot x\right) \cdot 9\right)}{4}}{4} + \frac{t_0}{4} \end{array} \]

Alternative 2
Error	0.1
Cost	320

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

Reproduce

herbie shell --seed 2023100 
(FPCore (x)
  :name "math.cube on real"
  :precision binary64

  :herbie-target
  (pow x 3.0)

  (* (* x x) x))