Average Error: 0.0 → 0.0
Time: 1.6s
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 r105208 = a;
        double r105209 = b;
        double r105210 = c;
        double r105211 = r105209 + r105210;
        double r105212 = d;
        double r105213 = r105211 + r105212;
        double r105214 = r105208 * r105213;
        return r105214;
}
↓
double f(double a, double b, double c, double d) {
        double r105215 = a;
        double r105216 = b;
        double r105217 = c;
        double r105218 = r105216 + r105217;
        double r105219 = r105215 * r105218;
        double r105220 = d;
        double r105221 = r105215 * r105220;
        double r105222 = r105219 + r105221;
        return r105222;
}

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 2020024 
(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)))