Average Error: 0.0 → 0.0
Time: 4.5s
Precision: 64
Internal Precision: 128
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(\left(b \cdot a\right) \cdot 2 + {b}^{2}\right) + {a}^{2}\]

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(b \cdot a + b \cdot b\right) + b \cdot a\right) + a \cdot a\]

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{a}^{2} + \left({b}^{2} + 2 \cdot \left(a \cdot b\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \left(\left(b \cdot a\right) \cdot 2 + {b}^{2}\right) + {a}^{2}\]

Reproduce

herbie shell --seed 2019002 
(FPCore (a b)
  :name "Expression 4, p15"
  :pre (and (<= 5 a 10) (<= 0 b 0.001))

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

  (* (+ a b) (+ a b)))

Details

Time bar (total: 4.2s)Debug log

sample21.0ms

Algorithm
intervals

simplify17.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

17.0ms
(* (+ a b) (+ a b))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ a b) (+ a b))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 30
Calls

1 calls. Slowest were:

7.0ms
(* (+ a b) (+ a b))

series14.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

14.0ms
(* (+ a b) (+ a b))

simplify2.2s

Counts
28 → 33
Calls

28 calls. Slowest were:

418.0ms
(* (+ (* a a) (- (* b b) (* a b))) (- a b))
312.0ms
(* (- (* a a) (* b b)) (+ a b))
309.0ms
(* (- (* a a) (* b b)) (+ (pow a 3) (pow b 3)))

prune228.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (pow b 2) (* 2 (* a b)))
0.0b
(+ (pow a 2) (+ (pow b 2) (* 2 (* a b))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
2 → 25
Calls

2 calls. Slowest were:

8.0ms
(+ (pow a 2) (+ (pow b 2) (* 2 (* a b))))
3.0ms
(+ (pow b 2) (* 2 (* a b)))

series61.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

37.0ms
(+ (pow b 2) (* 2 (* a b)))
24.0ms
(+ (pow a 2) (+ (pow b 2) (* 2 (* a b))))

simplify538.0ms

Counts
11 → 31
Calls

11 calls. Slowest were:

147.0ms
(* (exp (pow a 2)) (* (exp (pow b 2)) (exp (* 2 (* a b)))))
144.0ms
(* (exp (pow a 2)) (exp (+ (pow b 2) (* 2 (* a b)))))
65.0ms
(* (exp (pow b 2)) (exp (* 2 (* a b))))

prune281.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes99.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch2.0ms

end0.0ms

sample676.0ms

Algorithm
intervals