Average Error: 0.0 → 0.0
Time: 12.1s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[d \cdot a + \left(b + c\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
d \cdot a + \left(b + c\right) \cdot a
double f(double a, double b, double c, double d) {
        double r1728480 = a;
        double r1728481 = b;
        double r1728482 = c;
        double r1728483 = r1728481 + r1728482;
        double r1728484 = d;
        double r1728485 = r1728483 + r1728484;
        double r1728486 = r1728480 * r1728485;
        return r1728486;
}
↓
double f(double a, double b, double c, double d) {
        double r1728487 = d;
        double r1728488 = a;
        double r1728489 = r1728487 * r1728488;
        double r1728490 = b;
        double r1728491 = c;
        double r1728492 = r1728490 + r1728491;
        double r1728493 = r1728492 * r1728488;
        double r1728494 = r1728489 + r1728493;
        return r1728494;
}

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

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

Reproduce

herbie shell --seed 2019152 +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)))