Average Error: 0.4 → 0.3
Time: 9.5s
Precision: 64
Internal Precision: 128
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(c + \left(a + b\right)\right) + \left(d + e\right)\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.3
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

Derivation

  1. Initial program 0.4

    \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
  2. Using strategy rm

  3. Applied associate-+l+0.3

    \[\leadsto \color{blue}{\left(\left(e + d\right) + c\right) + \left(b + a\right)}\]
  4. Using strategy rm

  5. Applied associate-+l+0.3

    \[\leadsto \color{blue}{\left(e + d\right) + \left(c + \left(b + a\right)\right)}\]

  6. Final simplification0.3

    \[\leadsto \left(c + \left(a + b\right)\right) + \left(d + e\right)\]

Reproduce

herbie shell --seed 2019008 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))

Details

Time bar (total: 8.5s)Debug log

sample45.0ms

Algorithm
intervals

simplify193.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

193.0ms
(+ (+ (+ (+ e d) c) b) a)

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b
(+ (+ (+ (+ e d) c) b) a)
0.3b
(+ (+ (+ e d) c) b)
0.3b
(+ (+ e d) c)

rewrite110.0ms

Algorithm
rewrite-expression-head
Counts
3 → 33
Calls

3 calls. Slowest were:

85.0ms
(+ (+ (+ (+ e d) c) b) a)
21.0ms
(+ (+ (+ e d) c) b)
4.0ms
(+ (+ e d) c)

series97.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

45.0ms
(+ (+ (+ (+ e d) c) b) a)
34.0ms
(+ (+ (+ e d) c) b)
18.0ms
(+ (+ e d) c)

simplify106.0ms

Counts
11 → 42
Calls

11 calls. Slowest were:

13.0ms
(+ b (+ c d))
13.0ms
(+ e (+ c d))
13.0ms
(+ e (+ c d))

prune364.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.3b
(+ (+ (+ e d) c) (+ b a))
0.3b
(+ (+ e d) c)

rewrite18.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

13.0ms
(+ (+ (+ e d) c) (+ b a))
5.0ms
(+ (+ e d) c)

series59.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

48.0ms
(+ (+ (+ e d) c) (+ b a))
10.0ms
(+ (+ e d) c)

simplify2.7s

Counts
17 → 35
Calls

17 calls. Slowest were:

765.0ms
(* (- (+ e d) c) (- b a))
456.0ms
(* (- (+ e d) c) (+ (* b b) (- (* a a) (* b a))))
284.0ms
(* (+ (* (+ e d) (+ e d)) (- (* c c) (* (+ e d) c))) (- b a))

prune425.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b
(+ (+ e d) (+ c (+ b a)))
0.2b
(+ c (+ b a))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

8.0ms
(+ (+ e d) (+ c (+ b a)))
1.0ms
(+ c (+ b a))

series58.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

41.0ms
(+ (+ e d) (+ c (+ b a)))
17.0ms
(+ c (+ b a))

simplify1.5s

Counts
17 → 35
Calls

17 calls. Slowest were:

266.0ms
(* (- e d) (- c (+ b a)))
232.0ms
(+ (* (- (* e e) (* d d)) (+ (* c c) (- (* (+ b a) (+ b a)) (* c (+ b a))))) (* (- e d) (+ (pow c 3) (pow (+ b a) 3))))
226.0ms
(* (exp (+ e d)) (exp (+ c (+ b a))))

prune405.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b
(+ (+ (+ e (+ c d)) b) a)
0.3b
(+ (+ e (+ c d)) b)
0.2b
(+ e (+ c d))

rewrite20.0ms

Algorithm
rewrite-expression-head
Counts
3 → 33
Calls

3 calls. Slowest were:

15.0ms
(+ (+ (+ e (+ c d)) b) a)
4.0ms
(+ (+ e (+ c d)) b)
1.0ms
(+ e (+ c d))

series76.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

38.0ms
(+ (+ (+ e (+ c d)) b) a)
21.0ms
(+ (+ e (+ c d)) b)
17.0ms
(+ e (+ c d))

simplify101.0ms

Counts
10 → 42
Calls

10 calls. Slowest were:

13.0ms
(+ e (+ c d))
13.0ms
(+ e (+ c d))
12.0ms
(+ e (+ c d))

prune349.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes460.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm
intervals