(- (log (+ (* (exp a) an) (* (exp c) cn))) (log (+ an cn)))

Average Error: 50.2 → 50.2

Time: 13.3s

Precision: binary64

• could not determine a ground truth for program body

  1. a = -9.426156606175285e+27
  2. an = -2.6305831255475505e-188
  3. c = -4.6986329538044373e+55
  4. cn = 7.960518986233747e+131

Math

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

↓

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

C

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

↓

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

Error

Bits error versus a

Bits error versus an

Bits error versus c

Bits error versus cn

Derivation

1. Initial program 50.2

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

2. Final simplification 50.2

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

Reproduce

herbie shell --seed 2020153 
(FPCore (a an c cn)
  :name "(- (log (+ (* (exp a) an) (* (exp c) cn))) (log (+ an cn)))"
  :precision binary64
  (- (log (+ (* (exp a) an) (* (exp c) cn))) (log (+ an cn))))