Average Error: 0.0 → 0.0
Time: 16.1s
Precision: 64
Internal Precision: 128
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot \left(b + a\right) + \left(b + a\right) \cdot b\]

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. Using strategy rm

  3. Applied distribute-rgt-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019004 
(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: 15.7s)Debug log

sample37.0ms

Algorithm
intervals

simplify31.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

31.0ms
(* (+ a b) (+ a b))

prune8.0ms

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 30
Calls

1 calls. Slowest were:

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

series15.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

15.0ms
(* (+ a b) (+ a b))

simplify2.3s

Counts
28 → 33
Calls

28 calls. Slowest were:

392.0ms
(* (- (* a a) (* b b)) (+ a b))
343.0ms
(* (+ (* a a) (- (* b b) (* a b))) (- a b))
286.0ms
(* (- (* a a) (* b b)) (+ (pow a 3) (pow b 3)))

prune270.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
3 → 50
Calls

3 calls. Slowest were:

7.0ms
(+ (* a (+ a b)) (* b (+ a b)))
1.0ms
(* a (+ a b))
1.0ms
(* b (+ a b))

series44.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

15.0ms
(* b (+ a b))
15.0ms
(* a (+ a b))
15.0ms
(+ (* a (+ a b)) (* b (+ a b)))

simplify2.2s

Counts
38 → 59
Calls

38 calls. Slowest were:

560.0ms
(+ (* (* a (- (* a a) (* b b))) (- a b)) (* (- a b) (* b (- (* a a) (* b b)))))
322.0ms
(* (+ (* a a) (- (* b b) (* a b))) (- a b))
257.0ms
(* (+ (* a a) (- (* b b) (* a b))) (+ (* a a) (- (* b b) (* a b))))

prune517.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (+ a b)) (* (sqrt (+ a b)) (+ a b)))
0.3b
(* (sqrt (+ a b)) (+ a b))
0.0b
(sqrt (+ a b))
0.0b
(sqrt (+ a b))

rewrite40.0ms

Algorithm
rewrite-expression-head
Counts
4 → 115
Calls

4 calls. Slowest were:

25.0ms
(* (sqrt (+ a b)) (* (sqrt (+ a b)) (+ a b)))
9.0ms
(* (sqrt (+ a b)) (+ a b))
1.0ms
(sqrt (+ a b))

series99.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

35.0ms
(* (sqrt (+ a b)) (+ a b))
27.0ms
(* (sqrt (+ a b)) (* (sqrt (+ a b)) (+ a b)))
19.0ms
(sqrt (+ a b))
18.0ms
(sqrt (+ a b))

simplify8.0s

Counts
116 → 127
Calls

116 calls. Slowest were:

378.0ms
(* (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)))
369.0ms
(* (sqrt (- a b)) (* (sqrt (+ (* a a) (- (* b b) (* a b)))) (+ (* a a) (- (* b b) (* a b)))))
339.0ms
(* (sqrt (+ (* a a) (- (* b b) (* a b)))) (* (sqrt (+ (* a a) (- (* b b) (* a b)))) (- a b)))

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes164.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample749.0ms

Algorithm
intervals