Average Error: 0.2 → 0.1
Time: 1.6s
Precision: binary64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
↓
\[3 \cdot {x}^{2} + {x}^{3} \cdot -2 \]
(FPCore (x) :precision binary64 (* (* x x) (- 3.0 (* x 2.0))))
↓
(FPCore (x) :precision binary64 (+ (* 3.0 (pow x 2.0)) (* (pow x 3.0) -2.0)))
double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}
↓
double code(double x) {
	return (3.0 * pow(x, 2.0)) + (pow(x, 3.0) * -2.0);
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * x) * (3.0d0 - (x * 2.0d0))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = (3.0d0 * (x ** 2.0d0)) + ((x ** 3.0d0) * (-2.0d0))
end function

public static double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}
↓
public static double code(double x) {
	return (3.0 * Math.pow(x, 2.0)) + (Math.pow(x, 3.0) * -2.0);
}

def code(x):
	return (x * x) * (3.0 - (x * 2.0))
↓
def code(x):
	return (3.0 * math.pow(x, 2.0)) + (math.pow(x, 3.0) * -2.0)

function code(x)
	return Float64(Float64(x * x) * Float64(3.0 - Float64(x * 2.0)))
end
↓
function code(x)
	return Float64(Float64(3.0 * (x ^ 2.0)) + Float64((x ^ 3.0) * -2.0))
end

function tmp = code(x)
	tmp = (x * x) * (3.0 - (x * 2.0));
end
↓
function tmp = code(x)
	tmp = (3.0 * (x ^ 2.0)) + ((x ^ 3.0) * -2.0);
end

code[x_] := N[(N[(x * x), $MachinePrecision] * N[(3.0 - N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(N[(3.0 * N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[Power[x, 3.0], $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]

\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
3 \cdot {x}^{2} + {x}^{3} \cdot -2

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.1
\[x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right) \]

Derivation

  1. Initial program 0.2

    \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]

  2. Simplified0.2

    \[\leadsto \color{blue}{x \cdot \left(x \cdot \mathsf{fma}\left(x, -2, 3\right)\right)} \]

  3. Taylor expanded in x around 0 0.1

    \[\leadsto \color{blue}{3 \cdot {x}^{2} - 2 \cdot {x}^{3}} \]

  4. Final simplification0.1

    \[\leadsto 3 \cdot {x}^{2} + {x}^{3} \cdot -2 \]

Reproduce

herbie shell --seed 2022166 
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"
  :precision binary64

  :herbie-target
  (* x (* x (- 3.0 (* x 2.0))))

  (* (* x x) (- 3.0 (* x 2.0))))