Average Error: 0.4 → 0.2
Time: 10.4s
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 2018360 
(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: 7.5s)Debug log

start30.0ms

Algorithm
intervals

setup229.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

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)

rewrite80.0ms

Algorithm
rewrite-expression-head
Counts
3 → 33
Calls

3 calls. Slowest were:

56.0ms
(+ (+ (+ (+ e d) c) b) a)
21.0ms
(+ (+ (+ e d) c) b)
2.0ms
(+ (+ e d) c)

series84.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

38.0ms
(+ (+ (+ (+ e d) c) b) a)
30.0ms
(+ (+ (+ e d) c) b)
16.0ms
(+ (+ e d) c)

simplify104.0ms

Counts
11 → 42
Calls

11 calls. Slowest were:

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

prune402.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

28.0ms
(+ (+ (+ e d) (+ c b)) a)
7.0ms
(+ (+ e d) (+ c b))

series70.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

44.0ms
(+ (+ (+ e d) (+ c b)) a)
26.0ms
(+ (+ e d) (+ c b))

simplify2.1s

Counts
17 → 35
Calls

17 calls. Slowest were:

436.0ms
(* (+ (* e e) (- (* d d) (* e d))) (+ (* c c) (- (* b b) (* c b))))
412.0ms
(* (+ (* e e) (- (* d d) (* e d))) (- c b))
412.0ms
(+ (* (+ (pow e 3) (pow d 3)) (- c b)) (* (+ (* e e) (- (* d d) (* e d))) (- (* c c) (* b b))))

prune435.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.4b
(+ (+ e d) (+ (+ c b) a))
0.2b
(+ (+ c b) a)

rewrite21.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

16.0ms
(+ (+ e d) (+ (+ c b) a))
5.0ms
(+ (+ c b) a)

series84.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

64.0ms
(+ (+ e d) (+ (+ c b) a))
19.0ms
(+ (+ c b) a)

simplify1.8s

Counts
16 → 35
Calls

16 calls. Slowest were:

299.0ms
(* (- e d) (- (+ c b) a))
262.0ms
(+ (* (- (* e e) (* d d)) (+ (* (+ c b) (+ c b)) (- (* a a) (* (+ c b) a)))) (* (- e d) (+ (pow (+ c b) 3) (pow a 3))))
213.0ms
(* (exp (+ e d)) (exp (+ (+ c b) a)))

prune458.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
3 → 33
Calls

3 calls. Slowest were:

6.0ms
(+ e (+ d (+ (+ c b) a)))
5.0ms
(+ d (+ (+ c b) a))
5.0ms
(+ (+ c b) a)

series97.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

62.0ms
(+ e (+ d (+ (+ c b) a)))
21.0ms
(+ d (+ (+ c b) a))
14.0ms
(+ (+ c b) a)

simplify108.0ms

Counts
10 → 42
Calls

10 calls. Slowest were:

14.0ms
(+ a (+ b c))
13.0ms
(+ b (+ c d))
12.0ms
(+ a (+ b c))

prune415.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes820.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms