Average Error: 0.0 → 0.0
Time: 10.0s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot b + \left(d + c\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot b + \left(d + c\right) \cdot a
double f(double a, double b, double c, double d) {
        double r5746345 = a;
        double r5746346 = b;
        double r5746347 = c;
        double r5746348 = r5746346 + r5746347;
        double r5746349 = d;
        double r5746350 = r5746348 + r5746349;
        double r5746351 = r5746345 * r5746350;
        return r5746351;
}
↓
double f(double a, double b, double c, double d) {
        double r5746352 = a;
        double r5746353 = b;
        double r5746354 = r5746352 * r5746353;
        double r5746355 = d;
        double r5746356 = c;
        double r5746357 = r5746355 + r5746356;
        double r5746358 = r5746357 * r5746352;
        double r5746359 = r5746354 + r5746358;
        return r5746359;
}

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

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789.0 a 98765.0) (<= 0.0 b 1.0) (<= 0.0 c 0.0016773) (<= 0.0 d 0.0016773))

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

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