Average Error: 0.0 → 0
Time: 810.0ms
Precision: 64
\[x \cdot \left(x - 1\right)\]
↓
\[\mathsf{fma}\left(x, x, x \cdot \left(-1\right)\right)\]
x \cdot \left(x - 1\right)
↓
\mathsf{fma}\left(x, x, x \cdot \left(-1\right)\right)
double code(double x) {
	return (x * (x - 1.0));
}
↓
double code(double x) {
	return fma(x, x, (x * -1.0));
}

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
\[x \cdot x - x\]

Derivation

  1. Initial program 0.0

    \[x \cdot \left(x - 1\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto x \cdot \color{blue}{\left(x + \left(-1\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{x \cdot x + x \cdot \left(-1\right)}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{{x}^{2}} + x \cdot \left(-1\right)\]
  6. Using strategy rm

  7. Applied unpow20.0

    \[\leadsto \color{blue}{x \cdot x} + x \cdot \left(-1\right)\]

  8. Applied fma-def0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, x \cdot \left(-1\right)\right)}\]

  9. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, x, x \cdot \left(-1\right)\right)\]

Reproduce

herbie shell --seed 2020105 +o rules:numerics
(FPCore (x)
  :name "Statistics.Correlation.Kendall:numOfTiesBy from math-functions-0.1.5.2"
  :precision binary64

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

  (* x (- x 1)))