Rosa's Benchmark

Percentage Accurate: 99.8% → 99.8%

Time: 6.8s

Precision: binary64

Cost: 6848

• 33.2% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

function code(x)
	return Float64(x * fma(Float64(x * x), -0.12900613773279798, 0.954929658551372))
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 * N[(N[(x * x), $MachinePrecision] * -0.12900613773279798 + 0.954929658551372), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

2. Simplified 99.8%

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

   [Start] 99.8	\[ 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
   associate-*r* [=>] 99.8	\[ 0.954929658551372 \cdot x - \color{blue}{\left(0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x} \]
   distribute-rgt-out-- [=>] 99.8	\[ \color{blue}{x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right)} \]
   sub-neg [=>] 99.8	\[ x \cdot \color{blue}{\left(0.954929658551372 + \left(-0.12900613773279798 \cdot \left(x \cdot x\right)\right)\right)} \]
   +-commutative [=>] 99.8	\[ x \cdot \color{blue}{\left(\left(-0.12900613773279798 \cdot \left(x \cdot x\right)\right) + 0.954929658551372\right)} \]
   *-commutative [=>] 99.8	\[ x \cdot \left(\left(-\color{blue}{\left(x \cdot x\right) \cdot 0.12900613773279798}\right) + 0.954929658551372\right) \]
   distribute-rgt-neg-in [=>] 99.8	\[ x \cdot \left(\color{blue}{\left(x \cdot x\right) \cdot \left(-0.12900613773279798\right)} + 0.954929658551372\right) \]
   fma-def [=>] 99.8	\[ x \cdot \color{blue}{\mathsf{fma}\left(x \cdot x, -0.12900613773279798, 0.954929658551372\right)} \]
   metadata-eval [=>] 99.8	\[ x \cdot \mathsf{fma}\left(x \cdot x, \color{blue}{-0.12900613773279798}, 0.954929658551372\right) \]

3. Final simplification 99.8%

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

Alternatives

Alternative 1
Accuracy	98.7%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -2.7 \lor \neg \left(x \leq 2.7\right):\\ \;\;\;\;x \cdot \left(\left(x \cdot x\right) \cdot -0.12900613773279798\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.954929658551372\\ \end{array} \]

Alternative 2
Accuracy	99.8%
Cost	576

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

Alternative 3
Accuracy	50.3%
Cost	192

\[x \cdot 0.954929658551372 \]

Reproduce

herbie shell --seed 2023161 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))