Main:bigenough1 from B

Average Error: 0.0 → 0

Time: 695.0ms

Precision: binary64

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]

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[x + x \cdot x \]

2. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2022165 
(FPCore (x)
  :name "Main:bigenough1 from B"
  :precision binary64
  (+ x (* x x)))