Average Error: 0.0 → 0.0
Time: 11.9s
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. 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 2019005 
(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: 11.6s)Debug log

sample34.0ms

Algorithm
intervals

simplify26.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

26.0ms
(* (+ a b) (+ a b))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))

series12.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify2.4s

Counts
28 → 33
Calls

28 calls. Slowest were:

380.0ms
(* (- (* a a) (* b b)) (+ a b))
364.0ms
(* (* (* (+ a b) (+ a b)) (+ a b)) (* (* (+ a b) (+ a b)) (+ a b)))
305.0ms
(* (+ (* a a) (- (* b b) (* a b))) (- a b))

prune232.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
2 → 25
Calls

2 calls. Slowest were:

11.0ms
(+ (pow a 2) (+ (pow b 2) (* 2 (* a b))))
6.0ms
(+ (pow b 2) (* 2 (* a b)))

series42.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

23.0ms
(+ (pow a 2) (+ (pow b 2) (* 2 (* a b))))
19.0ms
(+ (pow b 2) (* 2 (* a b)))

simplify466.0ms

Counts
11 → 31
Calls

11 calls. Slowest were:

130.0ms
(* (exp (pow a 2)) (* (exp (pow b 2)) (exp (* 2 (* a b)))))
117.0ms
(* (exp (pow a 2)) (exp (+ (pow b 2) (* 2 (* a b)))))
72.0ms
(* (exp (pow b 2)) (exp (* 2 (* a b))))

prune225.0ms

Pruning

2 alts after pruning (1 fresh and 1 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))

rewrite35.0ms

Algorithm
rewrite-expression-head
Counts
4 → 115
Calls

4 calls. Slowest were:

27.0ms
(* (sqrt (+ a b)) (* (sqrt (+ a b)) (+ a b)))
5.0ms
(* (sqrt (+ a b)) (+ a b))
1.0ms
(sqrt (+ a b))

series111.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

32.0ms
(* (sqrt (+ a b)) (+ a b))
31.0ms
(sqrt (+ a b))
28.0ms
(sqrt (+ a b))
20.0ms
(* (sqrt (+ a b)) (* (sqrt (+ a b)) (+ a b)))

simplify6.1s

Counts
116 → 127
Calls

116 calls. Slowest were:

274.0ms
(* (* (* (sqrt (+ a b)) (sqrt (+ a b))) (sqrt (+ a b))) (* (* (* (sqrt (+ a b)) (sqrt (+ a b))) (sqrt (+ a b))) (* (* (+ a b) (+ a b)) (+ a b))))
270.0ms
(* (sqrt (+ (* a a) (- (* b b) (* a b)))) (* (sqrt (- a b)) (+ (* a a) (- (* b b) (* a b)))))
261.0ms
(* (sqrt (- a b)) (* (sqrt (+ (* a a) (- (* b b) (* a b)))) (+ (* a a) (- (* b b) (* a b)))))

prune860.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes119.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample831.0ms

Algorithm
intervals