Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.0016773000000000001 \land 0.0 \le d \le 0.0016773000000000001\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot \left(b + c\right) + a \cdot d\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot \left(b + c\right) + a \cdot d
double f(double a, double b, double c, double d) {
        double r83991 = a;
        double r83992 = b;
        double r83993 = c;
        double r83994 = r83992 + r83993;
        double r83995 = d;
        double r83996 = r83994 + r83995;
        double r83997 = r83991 * r83996;
        return r83997;
}
↓
double f(double a, double b, double c, double d) {
        double r83998 = a;
        double r83999 = b;
        double r84000 = c;
        double r84001 = r83999 + r84000;
        double r84002 = r83998 * r84001;
        double r84003 = d;
        double r84004 = r83998 * r84003;
        double r84005 = r84002 + r84004;
        return r84005;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{a \cdot \left(b + c\right) + a \cdot d}\]

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020018 
(FPCore (a b c d)
  :name "Expression, p14"
  :precision binary64
  :pre (and (<= 56789 a 98765) (<= 0.0 b 1) (<= 0.0 c 0.0016773) (<= 0.0 d 0.0016773))

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

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