Average Error: 0.0 → 0.0
Time: 10.0s
Precision: 64
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(\left(b + c\right) + d\right) \cdot a\]
double f(double a, double b, double c, double d) {
        double r25122618 = a;
        double r25122619 = b;
        double r25122620 = c;
        double r25122621 = r25122619 + r25122620;
        double r25122622 = d;
        double r25122623 = r25122621 + r25122622;
        double r25122624 = r25122618 * r25122623;
        return r25122624;
}
↓
double f(double a, double b, double c, double d) {
        double r25122625 = b;
        double r25122626 = c;
        double r25122627 = r25122625 + r25122626;
        double r25122628 = d;
        double r25122629 = r25122627 + r25122628;
        double r25122630 = a;
        double r25122631 = r25122629 * r25122630;
        return r25122631;
}


a \cdot \left(\left(b + c\right) + d\right)
↓
\left(\left(b + c\right) + d\right) \cdot a

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original0.0
Target0.0
Herbie0.0
\[a \cdot b + a \cdot \left(c + d\right)\]

Derivation

  1. Initial program 0.0

    \[a \cdot \left(\left(b + c\right) + d\right)\]

  2. Final simplification0.0

    \[\leadsto \left(\left(b + c\right) + d\right) \cdot a\]

Reproduce

herbie shell --seed 2019101 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789 a 98765) (<= 0 b 1) (<= 0 c 0.0016773) (<= 0 d 0.0016773))

  :herbie-target
  (+ (* a b) (* a (+ c d)))

  (* a (+ (+ b c) d)))