Expression, p14

Average Error: 0.0 → 0.0

Time: 7.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.0016773000000000001 \land 0.0 \le d \le 0.0016773000000000001\]

Math

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

↓

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

C

double f(double a, double b, double c, double d) {
        double r87070 = a;
        double r87071 = b;
        double r87072 = c;
        double r87073 = r87071 + r87072;
        double r87074 = d;
        double r87075 = r87073 + r87074;
        double r87076 = r87070 * r87075;
        return r87076;
}

↓

double f(double a, double b, double c, double d) {
        double r87077 = a;
        double r87078 = b;
        double r87079 = c;
        double r87080 = r87078 + r87079;
        double r87081 = r87077 * r87080;
        double r87082 = d;
        double r87083 = r87077 * r87082;
        double r87084 = r87081 + r87083;
        return r87084;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

   \[a \cdot \left(\left(b + c\right) + d\right)\]
2. Using strategy rm

3. Applied distribute-lft-in 0.0

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

4. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020046 
(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)))