(log (/ (+ (* (exp a) an) (* (exp c) cn)) (+ an bn)))

Average Error: 33.1 → 33.1

Time: 4.7s

Precision: binary64

• could not determine a ground truth for program body

  1. a = -2.45306454334614e+41
  2. an = 3.490121281110349e-223
  3. c = -2.0600520594623638e+217
  4. cn = -9.121802075917386e-45
  5. bn = -2101194269202.4614

Math

\[\log \left(\frac{e^{a} \cdot an + e^{c} \cdot cn}{an + bn}\right)\]

↓

\[\log \left(\frac{e^{a} \cdot an + e^{c} \cdot cn}{an + bn}\right)\]

C

double code(double a, double an, double c, double cn, double bn) {
	return ((double) log(((double) (((double) (((double) (((double) exp(a)) * an)) + ((double) (((double) exp(c)) * cn)))) / ((double) (an + bn))))));
}

↓

double code(double a, double an, double c, double cn, double bn) {
	return ((double) log(((double) (((double) (((double) (((double) exp(a)) * an)) + ((double) (((double) exp(c)) * cn)))) / ((double) (an + bn))))));
}

Error

Bits error versus a

Bits error versus an

Bits error versus c

Bits error versus cn

Bits error versus bn

Derivation

1. Initial program 33.1

   \[\log \left(\frac{e^{a} \cdot an + e^{c} \cdot cn}{an + bn}\right)\]

2. Final simplification 33.1

   \[\leadsto \log \left(\frac{e^{a} \cdot an + e^{c} \cdot cn}{an + bn}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a an c cn bn)
  :name "(log (/ (+ (* (exp a) an) (* (exp c) cn)) (+ an bn)))"
  :precision binary64
  (log (/ (+ (* (exp a) an) (* (exp c) cn)) (+ an bn))))