Average Error: 0.0 → 0.0
Time: 8.8s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.0016773000000000001 \land 0.0 \le d \le 0.0016773000000000001\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot b + a \cdot \left(c + d\right)\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot b + a \cdot \left(c + d\right)
double f(double a, double b, double c, double d) {
        double r72407 = a;
        double r72408 = b;
        double r72409 = c;
        double r72410 = r72408 + r72409;
        double r72411 = d;
        double r72412 = r72410 + r72411;
        double r72413 = r72407 * r72412;
        return r72413;
}
↓
double f(double a, double b, double c, double d) {
        double r72414 = a;
        double r72415 = b;
        double r72416 = r72414 * r72415;
        double r72417 = c;
        double r72418 = d;
        double r72419 = r72417 + r72418;
        double r72420 = r72414 * r72419;
        double r72421 = r72416 + r72420;
        return r72421;
}

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

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

Reproduce

herbie shell --seed 2020047 
(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)))