Average Error: 0.0 → 0.0
Time: 4.8s
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 -inf 0.0

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

  3. Final simplification0.0

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

Runtime

Time bar (total: 4.8s)Debug log

start49.0ms

Algorithm
intervals

setup48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 30
Calls

1 calls. Slowest were:

4.0ms
(* (+ a b) (+ a b))

series10.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

10.0ms
(* (+ a b) (+ a b))

simplify2.4s

Counts
28 → 33
Calls

28 calls. Slowest were:

432.0ms
(* (- (* a a) (* b b)) (+ a b))
350.0ms
(* (+ (* a a) (- (* b b) (* a b))) (- a b))
325.0ms
(* (+ (* a a) (- (* b b) (* a b))) (+ (* a a) (- (* b b) (* a b))))

prune248.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 11
Calls

1 calls. Slowest were:

5.0ms
(+ (pow b 2) (* 2 (* a b)))

series21.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

21.0ms
(+ (pow b 2) (* 2 (* a b)))

simplify83.0ms

Counts
4 → 14
Calls

4 calls. Slowest were:

43.0ms
(* (exp (pow b 2)) (exp (* 2 (* a b))))
18.0ms
(+ (pow b 2) (* 2 (* a b)))
11.0ms
(+ (pow b 2) (* 2 (* a b)))

prune157.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

herbie shell --seed 2018359 
(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)))