Average Error: 0.4 → 0.3
Time: 13.2s
Precision: 64
Internal Precision: 128
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(b + a\right) + \left(c + \left(d + e\right)\right)\]

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

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019005 
(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: 11.8s)Debug log

sample32.0ms

Algorithm
intervals

simplify226.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

226.0ms
(+ (+ (+ (+ e d) c) b) a)

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite98.0ms

Algorithm
rewrite-expression-head
Counts
3 → 33
Calls

3 calls. Slowest were:

75.0ms
(+ (+ (+ (+ e d) c) b) a)
18.0ms
(+ (+ (+ e d) c) b)
4.0ms
(+ (+ e d) c)

series83.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

53.0ms
(+ (+ (+ (+ e d) c) b) a)
19.0ms
(+ (+ (+ e d) c) b)
10.0ms
(+ (+ e d) c)

simplify61.0ms

Counts
11 → 42
Calls

11 calls. Slowest were:

7.0ms
(+ e (+ c d))
6.0ms
(+ e (+ c d))
6.0ms
(+ e (+ c d))

prune373.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

11.0ms
(+ (+ (+ e d) c) (+ b a))
2.0ms
(+ (+ e d) c)

series49.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

38.0ms
(+ (+ (+ e d) c) (+ b a))
11.0ms
(+ (+ e d) c)

simplify2.2s

Counts
17 → 35
Calls

17 calls. Slowest were:

401.0ms
(* (- (+ e d) c) (- b a))
332.0ms
(* (- (+ e d) c) (+ (* b b) (- (* a a) (* b a))))
235.0ms
(+ (+ (+ e d) c) (+ b a))

prune385.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

3.3b
(exp (+ (+ a (+ d e)) (+ c b)))
0.3b
(+ a (+ d e))
0.2b
(+ (+ a (+ d e)) (+ c b))
0.0b
(log (exp (+ (+ a (+ d e)) (+ c b))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Counts
4 → 60
Calls

4 calls. Slowest were:

24.0ms
(log (exp (+ (+ a (+ d e)) (+ c b))))
15.0ms
(exp (+ (+ a (+ d e)) (+ c b)))
9.0ms
(+ (+ a (+ d e)) (+ c b))

series214.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

69.0ms
(exp (+ (+ a (+ d e)) (+ c b)))
64.0ms
(+ (+ a (+ d e)) (+ c b))
63.0ms
(log (exp (+ (+ a (+ d e)) (+ c b))))
19.0ms
(+ a (+ d e))

simplify4.5s

Counts
38 → 72
Calls

38 calls. Slowest were:

303.0ms
(* (+ (* a a) (- (* (+ d e) (+ d e)) (* a (+ d e)))) (- c b))
278.0ms
(exp (* (cbrt (+ (+ a (+ d e)) (+ c b))) (cbrt (+ (+ a (+ d e)) (+ c b)))))
274.0ms
(log (sqrt (exp (+ (+ a (+ d e)) (+ c b)))))

prune963.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite39.0ms

Algorithm
rewrite-expression-head
Counts
3 → 33
Calls

3 calls. Slowest were:

30.0ms
(+ (+ (+ e (+ d c)) b) a)
7.0ms
(+ (+ e (+ d c)) b)
1.0ms
(+ e (+ d c))

series113.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

59.0ms
(+ (+ (+ e (+ d c)) b) a)
37.0ms
(+ (+ e (+ d c)) b)
16.0ms
(+ e (+ d c))

simplify108.0ms

Counts
10 → 42
Calls

10 calls. Slowest were:

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

prune400.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes577.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm
intervals