Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[56789 \leq a \land a \leq 98765 \land 0 \leq b \land b \leq 1 \land 0 \leq c \land c \leq 0.0016773 \land 0 \leq d \land d \leq 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot b + a \cdot \left(c + d\right)\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot b + a \cdot \left(c + d\right)
(FPCore (a b c d) :precision binary64 (* a (+ (+ b c) d)))
↓
(FPCore (a b c d) :precision binary64 (+ (* a b) (* a (+ c d))))
double code(double a, double b, double c, double d) {
	return ((double) (a * ((double) (((double) (b + c)) + d))));
}
↓
double code(double a, double b, double c, double d) {
	return ((double) (((double) (a * b)) + ((double) (a * ((double) (c + d))))));
}

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 Error: 0.0 bits

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

  3. Applied distribute-lft-inError: 0.0 bits

    \[\leadsto \color{blue}{a \cdot \left(b + c\right) + a \cdot d}\]
  4. Using strategy rm

  5. Applied distribute-lft-inError: 0.0 bits

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

  6. Applied associate-+l+Error: 0.0 bits

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

  7. SimplifiedError: 0.0 bits

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

  8. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (a b c d)
  :name "Expression, p14"
  :precision binary64
  :pre (and (<= 56789.0 a 98765.0) (<= 0.0 b 1.0) (<= 0.0 c 0.0016773) (<= 0.0 d 0.0016773))

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

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