Average Error: 0.0 → 0.0
Time: 16.3s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot d + \left(c + b\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot d + \left(c + b\right) \cdot a
double f(double a, double b, double c, double d) {
        double r3409091 = a;
        double r3409092 = b;
        double r3409093 = c;
        double r3409094 = r3409092 + r3409093;
        double r3409095 = d;
        double r3409096 = r3409094 + r3409095;
        double r3409097 = r3409091 * r3409096;
        return r3409097;
}
↓
double f(double a, double b, double c, double d) {
        double r3409098 = a;
        double r3409099 = d;
        double r3409100 = r3409098 * r3409099;
        double r3409101 = c;
        double r3409102 = b;
        double r3409103 = r3409101 + r3409102;
        double r3409104 = r3409103 * r3409098;
        double r3409105 = r3409100 + r3409104;
        return r3409105;
}

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-rgt-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 +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)))