Main:bigenough1 from B

Average Error: 0.0 → 0

Time: 1.6s

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 0.0

   \[x + x \cdot x \]

2. Simplified 0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, x\right)} \]
   Proof
   (fma.f64 x x x): 0 points increase in error, 0 points decrease in error
   (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x x) x)): 3 points increase in error, 0 points decrease in error
   (Rewrite<= +-commutative_binary64 (+.f64 x (*.f64 x x))): 0 points increase in error, 0 points decrease in error

3. Final simplification 0

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

Alternatives

Alternative 1
Error	1.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -336.42660365535187:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 0.10266196555053207:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 2
Error	0.0
Cost	320

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

Alternative 3
Error	21.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022291 
(FPCore (x)
  :name "Main:bigenough1 from B"
  :precision binary64
  (+ x (* x x)))