Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B

Average Error: 0.01% → 0.01%

Time: 1.6s

Precision: binary64

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

function code(x, y)
	return Float64(fma(x, y, x) + y)
end

Wolfram

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

↓

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

Derivation

1. Initial program 0.01

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

2. Simplified 0.01

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

Reproduce

herbie shell --seed 2023136 
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))