Average Error: 0.3 → 0.2
Time: 22.7s
Precision: binary64
Cost: 6848
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
↓
\[\mathsf{fma}\left(-0.12900613773279798 \cdot x, x, 0.954929658551372\right) \cdot x \]
(FPCore (x)
 :precision binary64
 (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))
↓
(FPCore (x)
 :precision binary64
 (* (fma (* -0.12900613773279798 x) x 0.954929658551372) x))
double code(double x) {
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
}
↓
double code(double x) {
	return fma((-0.12900613773279798 * x), x, 0.954929658551372) * x;
}

function code(x)
	return Float64(Float64(0.954929658551372 * x) - Float64(0.12900613773279798 * Float64(Float64(x * x) * x)))
end
↓
function code(x)
	return Float64(fma(Float64(-0.12900613773279798 * x), x, 0.954929658551372) * x)
end

code[x_] := N[(N[(0.954929658551372 * x), $MachinePrecision] - N[(0.12900613773279798 * N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(N[(N[(-0.12900613773279798 * x), $MachinePrecision] * x + 0.954929658551372), $MachinePrecision] * x), $MachinePrecision]

0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
\mathsf{fma}\left(-0.12900613773279798 \cdot x, x, 0.954929658551372\right) \cdot x

Error

Derivation

  1. Initial program 0.3

    \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

  2. Simplified0.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(-0.12900613773279798, {x}^{3}, 0.954929658551372 \cdot x\right)} \]
    Proof

  3. Applied egg-rr0.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(-0.12900613773279798 \cdot x, x, 0.954929658551372\right) \cdot x} \]

Alternatives

Alternative 1
Error0.2
Cost704
\[0.954929658551372 \cdot x - \left(x \cdot x\right) \cdot \left(0.12900613773279798 \cdot x\right) \]
Alternative 2
Error0.2
Cost576
\[\left(0.954929658551372 + -0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x \]
Alternative 3
Error0.2
Cost576
\[\left(\left(-0.12900613773279798 \cdot x\right) \cdot x + 0.954929658551372\right) \cdot x \]
Alternative 4
Error16.4
Cost192
\[0.954929658551372 \cdot x \]

Error

Reproduce

herbie shell --seed 2023010 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))