Average Error: 0.4 → 0.2
Time: 8.5s
Precision: 64
Internal Precision: 128
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
\[e + \left(d + \left(a + \left(b + c\right)\right)\right)\]

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

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

    \[\leadsto \color{blue}{\left(\left(e + d\right) + \left(c + b\right)\right)} + a\]
  4. Using strategy rm
  5. Applied associate-+l+0.3

    \[\leadsto \color{blue}{\left(e + d\right) + \left(\left(c + b\right) + a\right)}\]
  6. Using strategy rm
  7. Applied associate-+l+0.2

    \[\leadsto \color{blue}{e + \left(d + \left(\left(c + b\right) + a\right)\right)}\]
  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019002 
(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: 7.7s)Debug log

sample27.0ms

Algorithm
intervals

simplify165.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

164.0ms
(+ (+ (+ (+ e d) c) b) a)

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite71.0ms

Algorithm
rewrite-expression-head
Counts
3 → 33
Calls

3 calls. Slowest were:

58.0ms
(+ (+ (+ (+ e d) c) b) a)
10.0ms
(+ (+ (+ e d) c) b)
2.0ms
(+ (+ e d) c)

series75.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

36.0ms
(+ (+ (+ (+ e d) c) b) a)
20.0ms
(+ (+ (+ e d) c) b)
18.0ms
(+ (+ e d) c)

simplify82.0ms

Counts
11 → 42
Calls

11 calls. Slowest were:

12.0ms
(+ e (+ c d))
11.0ms
(+ e (+ c d))
10.0ms
(+ (+ e d) c)

prune361.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

14.0ms
(+ (+ (+ e d) (+ c b)) a)
3.0ms
(+ (+ e d) (+ c b))

series59.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

36.0ms
(+ (+ (+ e d) (+ c b)) a)
23.0ms
(+ (+ e d) (+ c b))

simplify2.3s

Counts
17 → 35
Calls

17 calls. Slowest were:

472.0ms
(+ (* (- (* e e) (* d d)) (- c b)) (* (- e d) (- (* c c) (* b b))))
438.0ms
(+ (* (+ (pow e 3) (pow d 3)) (- c b)) (* (+ (* e e) (- (* d d) (* e d))) (- (* c c) (* b b))))
424.0ms
(* (+ (* e e) (- (* d d) (* e d))) (- c b))

prune397.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

8.0ms
(+ (+ e d) (+ (+ c b) a))
3.0ms
(+ (+ c b) a)

series64.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

52.0ms
(+ (+ e d) (+ (+ c b) a))
12.0ms
(+ (+ c b) a)

simplify1.9s

Counts
16 → 35
Calls

16 calls. Slowest were:

378.0ms
(* (- e d) (- (+ c b) a))
328.0ms
(* (exp (+ e d)) (exp (+ (+ c b) a)))
255.0ms
(* (+ (* e e) (- (* d d) (* e d))) (- (+ c b) a))

prune312.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
3 → 33
Calls

3 calls. Slowest were:

3.0ms
(+ e (+ d (+ (+ c b) a)))
2.0ms
(+ d (+ (+ c b) a))
2.0ms
(+ (+ c b) a)

series90.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

52.0ms
(+ e (+ d (+ (+ c b) a)))
27.0ms
(+ d (+ (+ c b) a))
11.0ms
(+ (+ c b) a)

simplify93.0ms

Counts
10 → 42
Calls

10 calls. Slowest were:

11.0ms
(+ (+ c b) a)
11.0ms
(+ e (+ c d))
10.0ms
(+ a (+ b c))

prune261.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes388.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch1.0ms

end0.0ms

sample946.0ms

Algorithm
intervals