Average Error: 0.1 → 0.1
Time: 2.3s
Precision: binary64
\[\sqrt{\log \left(0.900000000000000022 \cdot x\right) - \log 0.900000000000000022}\]
↓
\[\sqrt{\log \left(0.900000000000000022 \cdot x\right) - \log 0.900000000000000022}\]
\sqrt{\log \left(0.900000000000000022 \cdot x\right) - \log 0.900000000000000022}
↓
\sqrt{\log \left(0.900000000000000022 \cdot x\right) - \log 0.900000000000000022}
double code(double x) {
	return ((double) sqrt(((double) (((double) log(((double) (0.9 * x)))) - ((double) log(0.9))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (((double) log(((double) (0.9 * x)))) - ((double) log(0.9))))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\sqrt{\log \left(0.900000000000000022 \cdot x\right) - \log 0.900000000000000022}\]

  2. Final simplification0.1

    \[\leadsto \sqrt{\log \left(0.900000000000000022 \cdot x\right) - \log 0.900000000000000022}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(sqrt (- (log (* 0.9 x)) (log 0.9)))"
  :precision binary64
  (sqrt (- (log (* 0.9 x)) (log 0.9))))