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

↓

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

(FPCore (x) :precision binary64 (* (* x x) (- 3.0 (* x 2.0))))

↓

(FPCore (x) :precision binary64 (fma -2.0 (pow x 3.0) (* x (* x 3.0))))

double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}

↓

double code(double x) {
	return fma(-2.0, pow(x, 3.0), (x * (x * 3.0)));
}

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

↓

function code(x)
	return fma(-2.0, (x ^ 3.0), Float64(x * Float64(x * 3.0)))
end

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

↓

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

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

↓

\mathsf{fma}\left(-2, {x}^{3}, x \cdot \left(x \cdot 3\right)\right)

Original	0.2
Target	0.2
Herbie	0.1

Derivation

Initial program 0.2
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
Simplified0.2
\[\leadsto \color{blue}{x \cdot \left(x \cdot \mathsf{fma}\left(x, -2, 3\right)\right)} \]
Taylor expanded in x around 0 0.1
\[\leadsto \color{blue}{3 \cdot {x}^{2} + -2 \cdot {x}^{3}} \]
Applied egg-rr8.7
\[\leadsto \color{blue}{\sqrt{\mathsf{fma}\left(-2, {x}^{3}, 3 \cdot \left(x \cdot x\right)\right)} \cdot \sqrt{\mathsf{fma}\left(-2, {x}^{3}, 3 \cdot \left(x \cdot x\right)\right)}} \]
Applied egg-rr0.1
\[\leadsto \color{blue}{\mathsf{fma}\left(-2, {x}^{3}, x \cdot \left(x \cdot 3\right)\right)} \]
Final simplification0.1
\[\leadsto \mathsf{fma}\left(-2, {x}^{3}, x \cdot \left(x \cdot 3\right)\right) \]

Reproduce

herbie shell --seed 2022192 
(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))))

Error

Target

Derivation

Reproduce