Main:bigenough1 from B

Average Error: 0.02% → 0%

Time: 1.1s

Precision: binary64

Cost: 6592

Math

\[x + x \cdot x \]

↓

\[\mathsf{fma}\left(x, x, x\right) \]

FPCore

(FPCore (x) :precision binary64 (+ x (* x x)))

↓

(FPCore (x) :precision binary64 (fma x x x))

C

double code(double x) {
	return x + (x * x);
}

↓

double code(double x) {
	return fma(x, x, x);
}

Julia

function code(x)
	return Float64(x + Float64(x * x))
end

↓

function code(x)
	return fma(x, x, x)
end

Wolfram

code[x_] := N[(x + N[(x * x), $MachinePrecision]), $MachinePrecision]

↓

code[x_] := N[(x * x + x), $MachinePrecision]

Derivation

1. Initial program 0.02

   \[x + x \cdot x \]

2. Simplified 0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, x\right)} \]
   Proof

   [Start] 0.02	\[ x + x \cdot x \]
   +-commutative [=>] 0.02	\[ \color{blue}{x \cdot x + x} \]
   fma-def [=>] 0	\[ \color{blue}{\mathsf{fma}\left(x, x, x\right)} \]

3. Final simplification 0

   \[\leadsto \mathsf{fma}\left(x, x, x\right) \]

Alternatives

Alternative 1
Error	2.88%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 2
Error	0.02%
Cost	320

\[x \cdot \left(x + 1\right) \]

Alternative 3
Error	0.02%
Cost	320

\[x + x \cdot x \]

Alternative 4
Error	33.32%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x)
  :name "Main:bigenough1 from B"
  :precision binary64
  (+ x (* x x)))