Average Error: 0.2 → 0.1
Time: 8.2s
Precision: binary64
Cost: 6848
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x \]
↓
\[\mathsf{fma}\left(x, 6, x \cdot \left(x \cdot -9\right)\right) \]
(FPCore (x) :precision binary64 (* (* 3.0 (- 2.0 (* x 3.0))) x))
↓
(FPCore (x) :precision binary64 (fma x 6.0 (* x (* x -9.0))))
double code(double x) {
	return (3.0 * (2.0 - (x * 3.0))) * x;
}
↓
double code(double x) {
	return fma(x, 6.0, (x * (x * -9.0)));
}

function code(x)
	return Float64(Float64(3.0 * Float64(2.0 - Float64(x * 3.0))) * x)
end
↓
function code(x)
	return fma(x, 6.0, Float64(x * Float64(x * -9.0)))
end

code[x_] := N[(N[(3.0 * N[(2.0 - N[(x * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]
↓
code[x_] := N[(x * 6.0 + N[(x * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
\mathsf{fma}\left(x, 6, x \cdot \left(x \cdot -9\right)\right)

Error

Target

Original0.2
Target0.2
Herbie0.1
\[6 \cdot x - 9 \cdot \left(x \cdot x\right) \]

Derivation

  1. Initial program 0.2

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

  2. Applied egg-rr11.0

    \[\leadsto \color{blue}{{\left(\sqrt{3 \cdot \left(2 - 3 \cdot x\right)}\right)}^{2}} \cdot x \]

  3. Applied egg-rr0.9

    \[\leadsto \color{blue}{\left({\left(\sqrt{3}\right)}^{2} \cdot \left(2 + x \cdot -3\right)\right)} \cdot x \]

  4. Applied egg-rr0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, 6, x \cdot \left(x \cdot -9\right)\right)} \]

  5. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(x, 6, x \cdot \left(x \cdot -9\right)\right) \]

Alternatives

Alternative 1
Error2.1
Cost712
\[\begin{array}{l} \mathbf{if}\;x \leq -140.1741965090909:\\ \;\;\;\;-9 \cdot \left(x \cdot x\right)\\ \mathbf{elif}\;x \leq 7.357464671497419 \cdot 10^{-7}:\\ \;\;\;\;x \cdot 6\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{-0.1111111111111111}{x}}{x}}\\ \end{array} \]
Alternative 2
Error2.1
Cost584
\[\begin{array}{l} t_0 := -9 \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -140.1741965090909:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.357464671497419 \cdot 10^{-7}:\\ \;\;\;\;x \cdot 6\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error0.2
Cost448
\[x \cdot \left(6 + x \cdot -9\right) \]
Alternative 4
Error21.1
Cost192
\[x \cdot 6 \]
Alternative 5
Error62.1
Cost64
\[4 \]

Error

Reproduce

herbie shell --seed 2022300 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"
  :precision binary64

  :herbie-target
  (- (* 6.0 x) (* 9.0 (* x x)))

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