Rosa's Benchmark

Average Error: 0.2 → 0.2

Time: 7.4s

Precision: binary64

Cost: 13184

Math

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

↓

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

FPCore

(FPCore (x)
 :precision binary64
 (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

↓

(FPCore (x)
 :precision binary64
 (fma x 0.954929658551372 (* (pow x 3.0) -0.12900613773279798)))

C

double code(double x) {
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
}

↓

double code(double x) {
	return fma(x, 0.954929658551372, (pow(x, 3.0) * -0.12900613773279798));
}

Julia

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

↓

function code(x)
	return fma(x, 0.954929658551372, Float64((x ^ 3.0) * -0.12900613773279798))
end

Wolfram

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

↓

code[x_] := N[(x * 0.954929658551372 + N[(N[Power[x, 3.0], $MachinePrecision] * -0.12900613773279798), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.2

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

2. Applied egg-rr 0.2

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

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	0.2
Cost	6912

\[x \cdot 0.954929658551372 + {x}^{3} \cdot -0.12900613773279798 \]

Alternative 2
Error	0.2
Cost	576

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

Alternative 3
Error	0.2
Cost	576

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

Alternative 4
Error	16.5
Cost	192

\[x \cdot 0.954929658551372 \]

Reproduce

herbie shell --seed 2022308 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))