Rosa's Benchmark

Percentage Accurate: 99.8% → 99.8%

Time: 7.3s

Precision: binary64

Cost: 6976

• 34.0% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x) {
	return fma((x * x), (x * -0.12900613773279798), (x * 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 fma(Float64(x * x), Float64(x * -0.12900613773279798), Float64(x * 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[(N[(x * x), $MachinePrecision] * N[(x * -0.12900613773279798), $MachinePrecision] + N[(x * 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 99.7%

   \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(x \cdot x, -0.12900613773279798, 0.954929658551372\right)} \]
   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* [=>] 99.7%	\[ 0.954929658551372 \cdot x - \color{blue}{\left(0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x} \]
   distribute-rgt-out-- [=>] 99.7%	\[ \color{blue}{x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right)} \]
   sub-neg [=>] 99.7%	\[ x \cdot \color{blue}{\left(0.954929658551372 + \left(-0.12900613773279798 \cdot \left(x \cdot x\right)\right)\right)} \]
   +-commutative [=>] 99.7%	\[ x \cdot \color{blue}{\left(\left(-0.12900613773279798 \cdot \left(x \cdot x\right)\right) + 0.954929658551372\right)} \]
   *-commutative [=>] 99.7%	\[ x \cdot \left(\left(-\color{blue}{\left(x \cdot x\right) \cdot 0.12900613773279798}\right) + 0.954929658551372\right) \]
   distribute-rgt-neg-in [=>] 99.7%	\[ x \cdot \left(\color{blue}{\left(x \cdot x\right) \cdot \left(-0.12900613773279798\right)} + 0.954929658551372\right) \]
   fma-def [=>] 99.7%	\[ x \cdot \color{blue}{\mathsf{fma}\left(x \cdot x, -0.12900613773279798, 0.954929658551372\right)} \]
   metadata-eval [=>] 99.7%	\[ x \cdot \mathsf{fma}\left(x \cdot x, \color{blue}{-0.12900613773279798}, 0.954929658551372\right) \]

3. Applied egg-rr 99.8%

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

   [Start] 99.7%	\[ x \cdot \mathsf{fma}\left(x \cdot x, -0.12900613773279798, 0.954929658551372\right) \]
   fma-udef [=>] 99.7%	\[ x \cdot \color{blue}{\left(\left(x \cdot x\right) \cdot -0.12900613773279798 + 0.954929658551372\right)} \]
   distribute-rgt-in [=>] 99.7%	\[ \color{blue}{\left(\left(x \cdot x\right) \cdot -0.12900613773279798\right) \cdot x + 0.954929658551372 \cdot x} \]
   *-commutative [=>] 99.7%	\[ \color{blue}{\left(-0.12900613773279798 \cdot \left(x \cdot x\right)\right)} \cdot x + 0.954929658551372 \cdot x \]
   associate-*r* [<=] 99.8%	\[ \color{blue}{-0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)} + 0.954929658551372 \cdot x \]
   *-commutative [<=] 99.8%	\[ \color{blue}{\left(\left(x \cdot x\right) \cdot x\right) \cdot -0.12900613773279798} + 0.954929658551372 \cdot x \]
   associate-*l* [=>] 99.8%	\[ \color{blue}{\left(x \cdot x\right) \cdot \left(x \cdot -0.12900613773279798\right)} + 0.954929658551372 \cdot x \]
   fma-def [=>] 99.8%	\[ \color{blue}{\mathsf{fma}\left(x \cdot x, x \cdot -0.12900613773279798, 0.954929658551372 \cdot x\right)} \]
   *-commutative [=>] 99.8%	\[ \mathsf{fma}\left(x \cdot x, x \cdot -0.12900613773279798, \color{blue}{x \cdot 0.954929658551372}\right) \]

4. Final simplification 99.8%

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

Alternatives

Alternative 1
Accuracy	99.8%
Cost	6976

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

Alternative 2
Accuracy	98.9%
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 3
Accuracy	99.8%
Cost	704

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

Alternative 4
Accuracy	99.8%
Cost	576

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

Alternative 5
Accuracy	5.1%
Cost	192

\[x \cdot -0.954929658551372 \]

Alternative 6
Accuracy	49.4%
Cost	192

\[x \cdot 0.954929658551372 \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))