Average Error: 3.7 → 2.8
Time: 6.9s
Precision: 64
Internal Precision: 128
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(\left(b + c\right) + d\right) + a\right)\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.7
Target3.8
Herbie2.8
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.7

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

  3. Applied associate-+r+2.8

    \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]

  4. Final simplification2.8

    \[\leadsto 2 \cdot \left(\left(\left(b + c\right) + d\right) + a\right)\]

Reproduce

herbie shell --seed 2019005 
(FPCore (a b c d)
  :name "Expression, p6"
  :pre (and (<= -14 a -13) (<= -3 b -2) (<= 3 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2) (* (+ c d) 2))

  (* (+ a (+ b (+ c d))) 2))

Details

Time bar (total: 5.2s)Debug log

sample52.0ms

Algorithm
intervals

simplify230.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

230.0ms
(* (+ a (+ b (+ c d))) 2)

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.7b

localize22.0ms

Local error

Found 2 expressions with local error:

2.4b
(+ a (+ b (+ c d)))
0.5b
(+ b (+ c d))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
2 → 22
Calls

2 calls. Slowest were:

2.0ms
(+ a (+ b (+ c d)))
1.0ms
(+ b (+ c d))

series48.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

32.0ms
(+ a (+ b (+ c d)))
16.0ms
(+ b (+ c d))

simplify74.0ms

Counts
7 → 28
Calls

7 calls. Slowest were:

15.0ms
(+ b (+ c d))
11.0ms
(+ b (+ c d))
11.0ms
(+ a (+ b c))

prune266.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.1b

localize20.0ms

Local error

Found 1 expressions with local error:

2.4b
(+ a (+ (+ b c) d))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 11
Calls

1 calls. Slowest were:

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

series32.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

32.0ms
(+ a (+ (+ b c) d))

simplify41.0ms

Counts
3 → 14
Calls

3 calls. Slowest were:

15.0ms
(+ b (+ c d))
12.0ms
(+ a (+ b c))
12.0ms
(+ b (+ c d))

prune153.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.8b

localize9.0ms

Local error

Found 2 expressions with local error:

2.4b
(+ a (+ (+ b c) d))
0.9b
(log (exp (+ a (+ (+ b c) d))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Counts
2 → 27
Calls

2 calls. Slowest were:

20.0ms
(log (exp (+ a (+ (+ b c) d))))
3.0ms
(+ a (+ (+ b c) d))

series63.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

34.0ms
(log (exp (+ a (+ (+ b c) d))))
28.0ms
(+ a (+ (+ b c) d))

simplify370.0ms

Counts
13 → 33
Calls

13 calls. Slowest were:

108.0ms
(log (sqrt (exp (+ a (+ (+ b c) d)))))
105.0ms
(log (* (cbrt (exp (+ a (+ (+ b c) d)))) (cbrt (exp (+ a (+ (+ b c) d))))))
45.0ms
(+ a (+ (+ b c) d))

prune478.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 1.6b

localize15.0ms

Local error

Found 2 expressions with local error:

2.4b
(+ (+ a (+ b c)) d)
0.9b
(log (exp (+ (+ a (+ b c)) d)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
2 → 27
Calls

2 calls. Slowest were:

12.0ms
(log (exp (+ (+ a (+ b c)) d)))
4.0ms
(+ (+ a (+ b c)) d)

series64.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

33.0ms
(+ (+ a (+ b c)) d)
31.0ms
(log (exp (+ (+ a (+ b c)) d)))

simplify445.0ms

Counts
14 → 33
Calls

14 calls. Slowest were:

105.0ms
(log (* (cbrt (exp (+ (+ a (+ b c)) d))) (cbrt (exp (+ (+ a (+ b c)) d)))))
97.0ms
(log (sqrt (exp (+ (+ a (+ b c)) d))))
69.0ms
(log (exp (+ a (+ b c))))

prune297.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 1.4b

regimes956.0ms

Accuracy

0% (1.1b remaining)

Error of 2.8b against oracle of 1.6b and baseline of 2.8b

bsearch3.0ms

end0.0ms

sample1.5s

Algorithm
intervals