Expression, p14

Average Error: 0.0 → 0.0

Time: 2.2s

Precision: 64

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

Math

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

↓

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

C

double code(double a, double b, double c, double d) {
	return (a * ((b + c) + d));
}

↓

double code(double a, double b, double c, double d) {
	return (a * ((b + c) + d));
}

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. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020091 
(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)))