Average Error: 0.0 → 0.0
Time: 13.3s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot \left(\left(b + c\right) + d\right)\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot \left(\left(b + c\right) + d\right)
double f(double a, double b, double c, double d) {
        double r63677 = a;
        double r63678 = b;
        double r63679 = c;
        double r63680 = r63678 + r63679;
        double r63681 = d;
        double r63682 = r63680 + r63681;
        double r63683 = r63677 * r63682;
        return r63683;
}
↓
double f(double a, double b, double c, double d) {
        double r63684 = a;
        double r63685 = b;
        double r63686 = c;
        double r63687 = r63685 + r63686;
        double r63688 = d;
        double r63689 = r63687 + r63688;
        double r63690 = r63684 * r63689;
        return r63690;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (a b c d)
  :name "Expression, p14"
  :precision binary64
  :pre (and (<= 56789 a 98765) (<= 0.0 b 1) (<= 0.0 c 0.0016773000000000001) (<= 0.0 d 0.0016773000000000001))

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

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