Average Error: 0.0 → 0.0
Time: 4.9s
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. Initial simplification0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2018362 
(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: 3.6s)Debug log

start40.0ms

Algorithm
intervals

setup44.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 30
Calls

1 calls. Slowest were:

8.0ms
(* (+ b a) (+ b a))

series13.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

12.0ms
(* (+ b a) (+ b a))

simplify2.2s

Counts
28 → 33
Calls

28 calls. Slowest were:

443.0ms
(* (- (* b b) (* a a)) (+ b a))
416.0ms
(* (+ (* b b) (- (* a a) (* b a))) (- b a))
270.0ms
(* (- (* b b) (* a a)) (+ (pow b 3) (pow a 3)))

prune198.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
3 → 34
Calls

3 calls. Slowest were:

7.0ms
(+ (pow a 2) (+ (pow b 2) (* 2 (* a b))))
5.0ms
(+ (pow b 2) (* 2 (* a b)))
1.0ms
(* 2 (* a b))

series66.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

31.0ms
(+ (pow b 2) (* 2 (* a b)))
24.0ms
(+ (pow a 2) (+ (pow b 2) (* 2 (* a b))))
11.0ms
(* 2 (* a b))

simplify519.0ms

Counts
14 → 43
Calls

14 calls. Slowest were:

142.0ms
(* (exp (pow a 2)) (* (exp (pow b 2)) (exp (* 2 (* a b)))))
131.0ms
(* (exp (pow a 2)) (exp (+ (pow b 2) (* 2 (* a b)))))
42.0ms
(* (exp (pow b 2)) (exp (* 2 (* a b))))

prune370.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms