Average Error: 0.0 → 0.0
Time: 981.0ms
Precision: binary64
\[0 \leq x \land x \leq 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x \]
↓
\[x \cdot \mathsf{fma}\left(x, x, x\right) \]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
x \cdot \mathsf{fma}\left(x, x, x\right)

(FPCore (x) :precision binary64 (+ (* x (* x x)) (* x x)))
↓
(FPCore (x) :precision binary64 (* x (fma x x x)))
double code(double x) {
	return (x * (x * x)) + (x * x);
}
↓
double code(double x) {
	return x * fma(x, x, x);
}

Error

Bits error versus x

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(1 + x\right) \cdot x\right) \cdot x \]

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021307 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (and (<= 0.0 x) (<= x 2.0))

  :herbie-target
  (* (* (+ 1.0 x) x) x)

  (+ (* x (* x x)) (* x x)))