Average Error: 0.0 → 0.0
Time: 13.5s
Precision: 64
Internal Precision: 128
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(a + b\right) \cdot \left(a + b\right)\]

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2018360 
(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: 12.4s)Debug log

start42.0ms

Algorithm
intervals

setup42.0ms

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:

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

series15.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify2.7s

Counts
28 → 33
Calls

28 calls. Slowest were:

619.0ms
(* (* (* (+ b a) (+ b a)) (+ b a)) (* (* (+ b a) (+ b a)) (+ b a)))
353.0ms
(* (- (* b b) (* a a)) (+ b a))
300.0ms
(* (+ (* b b) (- (* a a) (* b a))) (- b a))

prune331.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (* (- (* b b) (* a a)) (+ b a)) (- b a))
0.3b
(* (- (* b b) (* a a)) (+ b a))

rewrite15.0ms

Algorithm
rewrite-expression-head
Counts
2 → 59
Calls

2 calls. Slowest were:

8.0ms
(/ (* (- (* b b) (* a a)) (+ b a)) (- b a))
6.0ms
(* (- (* b b) (* a a)) (+ b a))

series83.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

42.0ms
(/ (* (- (* b b) (* a a)) (+ b a)) (- b a))
41.0ms
(* (- (* b b) (* a a)) (+ b a))

simplify8.5s

Counts
53 → 65
Calls

53 calls. Slowest were:

980.0ms
(* (- (* (* b b) (* b b)) (* (* a a) (* a a))) (- (* b b) (* a a)))
532.0ms
(* (- (* (* b b) (* b b)) (* (* a a) (* a a))) (- (* b b) (* a a)))
414.0ms
(* (- (* (* b b) (* b b)) (* (* a a) (* a a))) (+ (pow b 3) (pow a 3)))

prune524.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes43.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms