Average Error: 0.0 → 0.0
Time: 12.3s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(b + c\right) \cdot a + a \cdot d\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(b + c\right) \cdot a + a \cdot d
double f(double a, double b, double c, double d) {
        double r86250 = a;
        double r86251 = b;
        double r86252 = c;
        double r86253 = r86251 + r86252;
        double r86254 = d;
        double r86255 = r86253 + r86254;
        double r86256 = r86250 * r86255;
        return r86256;
}
↓
double f(double a, double b, double c, double d) {
        double r86257 = b;
        double r86258 = c;
        double r86259 = r86257 + r86258;
        double r86260 = a;
        double r86261 = r86259 * r86260;
        double r86262 = d;
        double r86263 = r86260 * r86262;
        double r86264 = r86261 + r86263;
        return r86264;
}

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 
(FPCore (a b c d)
  :name "Expression, p14"
  :precision binary64
  :pre (and (<= 56789 a 98765) (<= 0.0 b 1) (<= 0.0 c 0.0016773000000000001) (<= 0.0 d 0.0016773000000000001))

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

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