Average Error: 0.7 → 0.7
Time: 1.8s
Precision: binary64
\[\frac{\log \left(\frac{100}{x}\right) + \left(\left(0.050000000000000003 - 0.0100000000000000002\right) + \frac{0.149999999999999994 \cdot 0.149999999999999994}{2}\right) \cdot 2}{0.149999999999999994 \cdot \sqrt{2}}\]
↓
\[\frac{\log \left(\frac{100}{x}\right) + \left(\left(0.050000000000000003 - 0.0100000000000000002\right) + \frac{0.149999999999999994 \cdot 0.149999999999999994}{2}\right) \cdot 2}{0.149999999999999994 \cdot \sqrt{2}}\]
\frac{\log \left(\frac{100}{x}\right) + \left(\left(0.050000000000000003 - 0.0100000000000000002\right) + \frac{0.149999999999999994 \cdot 0.149999999999999994}{2}\right) \cdot 2}{0.149999999999999994 \cdot \sqrt{2}}
↓
\frac{\log \left(\frac{100}{x}\right) + \left(\left(0.050000000000000003 - 0.0100000000000000002\right) + \frac{0.149999999999999994 \cdot 0.149999999999999994}{2}\right) \cdot 2}{0.149999999999999994 \cdot \sqrt{2}}
double code(double x) {
	return ((double) (((double) (((double) log(((double) (100.0 / x)))) + ((double) (((double) (((double) (0.05 - 0.01)) + ((double) (((double) (0.15 * 0.15)) / 2.0)))) * 2.0)))) / ((double) (0.15 * ((double) sqrt(2.0))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) log(((double) (100.0 / x)))) + ((double) (((double) (((double) (0.05 - 0.01)) + ((double) (((double) (0.15 * 0.15)) / 2.0)))) * 2.0)))) / ((double) (0.15 * ((double) sqrt(2.0))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.7

    \[\frac{\log \left(\frac{100}{x}\right) + \left(\left(0.050000000000000003 - 0.0100000000000000002\right) + \frac{0.149999999999999994 \cdot 0.149999999999999994}{2}\right) \cdot 2}{0.149999999999999994 \cdot \sqrt{2}}\]

  2. Final simplification0.7

    \[\leadsto \frac{\log \left(\frac{100}{x}\right) + \left(\left(0.050000000000000003 - 0.0100000000000000002\right) + \frac{0.149999999999999994 \cdot 0.149999999999999994}{2}\right) \cdot 2}{0.149999999999999994 \cdot \sqrt{2}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ (+ (log (/ 100 x)) (* (+ (- 0.05 0.01) (/ (* 0.15 0.15) 2)) 2)) (* 0.15 (sqrt 2)))"
  :precision binary64
  (/ (+ (log (/ 100.0 x)) (* (+ (- 0.05 0.01) (/ (* 0.15 0.15) 2.0)) 2.0)) (* 0.15 (sqrt 2.0))))