Average Error: 0.0 → 0.0
Time: 6.9s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.0016773000000000001 \land 0.0 \le d \le 0.0016773000000000001\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[b \cdot a + a \cdot \left(c + d\right)\]
a \cdot \left(\left(b + c\right) + d\right)
↓
b \cdot a + a \cdot \left(c + d\right)
double f(double a, double b, double c, double d) {
        double r66257 = a;
        double r66258 = b;
        double r66259 = c;
        double r66260 = r66258 + r66259;
        double r66261 = d;
        double r66262 = r66260 + r66261;
        double r66263 = r66257 * r66262;
        return r66263;
}
↓
double f(double a, double b, double c, double d) {
        double r66264 = b;
        double r66265 = a;
        double r66266 = r66264 * r66265;
        double r66267 = c;
        double r66268 = d;
        double r66269 = r66267 + r66268;
        double r66270 = r66265 * r66269;
        double r66271 = r66266 + r66270;
        return r66271;
}

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-rgt-in0.0

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

  6. Applied associate-+l+0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

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)))