Average Error: 0.0 → 0.0
Time: 8.3s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot b + \left(c + d\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot b + \left(c + d\right) \cdot a
double f(double a, double b, double c, double d) {
        double r1810311 = a;
        double r1810312 = b;
        double r1810313 = c;
        double r1810314 = r1810312 + r1810313;
        double r1810315 = d;
        double r1810316 = r1810314 + r1810315;
        double r1810317 = r1810311 * r1810316;
        return r1810317;
}
↓
double f(double a, double b, double c, double d) {
        double r1810318 = a;
        double r1810319 = b;
        double r1810320 = r1810318 * r1810319;
        double r1810321 = c;
        double r1810322 = d;
        double r1810323 = r1810321 + r1810322;
        double r1810324 = r1810323 * r1810318;
        double r1810325 = r1810320 + r1810324;
        return r1810325;
}

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. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Applied associate-+l+0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019153 +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)))