Average Error: 0.0 → 0.0
Time: 975.0ms
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\mathsf{fma}\left(x, x, {x}^{3}\right)\right)\right)\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\mathsf{fma}\left(x, x, {x}^{3}\right)\right)\right)
double code(double x) {
	return ((x * (x * x)) + (x * x));
}
↓
double code(double x) {
	return expm1(log1p(fma(x, x, pow(x, 3.0))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, {x}^{3}\right)}\]
  3. Using strategy rm

  4. Applied expm1-log1p-u0.0

    \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\mathsf{fma}\left(x, x, {x}^{3}\right)\right)\right)}\]

  5. Final simplification0.0

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\mathsf{fma}\left(x, x, {x}^{3}\right)\right)\right)\]

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

  :herbie-target
  (* (* (+ 1 x) x) x)

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