Average Error: 30.9 → 0.1
Time: 1.2s
Precision: binary64
\[\log \left(x \cdot x\right) \cdot x - \log x\]
↓
\[\left(\left(x + x\right) + -1\right) \cdot \log x\]
\log \left(x \cdot x\right) \cdot x - \log x
↓
\left(\left(x + x\right) + -1\right) \cdot \log x
double code(double x) {
	return ((double) (((double) (((double) log(((double) (x * x)))) * x)) - ((double) log(x))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (x + x)) + -1.0)) * ((double) log(x))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.9

    \[\log \left(x \cdot x\right) \cdot x - \log x\]

  2. Simplified0.1

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

  3. Final simplification0.1

    \[\leadsto \left(\left(x + x\right) + -1\right) \cdot \log x\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (* (log (* x x)) x) (log x))"
  :precision binary64
  (- (* (log (* x x)) x) (log x)))