Average Error: 3.7 → 2.8
Time: 9.1s
Precision: 64
Internal Precision: 128
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(a + \left(c + b\right)\right) + d\right) \cdot 2\]

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
Target3.9
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. Initial simplification3.1

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

  4. Applied associate-+r+3.1

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

  5. Taylor expanded around 0 2.8

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

  6. Final simplification2.8

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

Reproduce

herbie shell --seed 2018362 
(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: 5.3s)Debug log

start50.0ms

Algorithm
intervals

setup167.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.8b

localize16.0ms

Local error

Found 1 expressions with local error:

2.9b
(+ (+ a c) (+ b d))

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
1 → 18
Calls

1 calls. Slowest were:

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

series27.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

27.0ms
(+ (+ a c) (+ b d))

simplify2.4s

Counts
13 → 21
Calls

13 calls. Slowest were:

520.0ms
(+ (* (+ (pow a 3) (pow c 3)) (- b d)) (* (+ (* a a) (- (* c c) (* a c))) (- (* b b) (* d d))))
439.0ms
(* (+ (* a a) (- (* c c) (* a c))) (+ (* b b) (- (* d d) (* b d))))
415.0ms
(+ (* (- (* a a) (* c c)) (- b d)) (* (- a c) (- (* b b) (* d d))))

prune265.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 1.7b

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b
(+ (+ (+ a c) b) d)
0.3b
(+ (+ a c) b)

rewrite28.0ms

Algorithm
rewrite-expression-head
Counts
2 → 22
Calls

2 calls. Slowest were:

23.0ms
(+ (+ (+ a c) b) d)
4.0ms
(+ (+ a c) b)

series31.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

20.0ms
(+ (+ (+ a c) b) d)
10.0ms
(+ (+ a c) b)

simplify39.0ms

Counts
7 → 28
Calls

7 calls. Slowest were:

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

prune405.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.6b

localize14.0ms

Local error

Found 1 expressions with local error:

2.6b
(+ (+ a (+ b c)) d)

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 11
Calls

1 calls. Slowest were:

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

series24.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

24.0ms
(+ (+ a (+ b c)) d)

simplify20.0ms

Counts
3 → 14
Calls

3 calls. Slowest were:

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

prune224.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 1.5b

localize9.0ms

Local error

Found 2 expressions with local error:

2.6b
(+ (+ 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)))
3.0ms
(+ (+ a (+ b c)) d)

series58.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

29.0ms
(log (exp (+ (+ a (+ b c)) d)))
28.0ms
(+ (+ a (+ b c)) d)

simplify536.0ms

Counts
14 → 33
Calls

14 calls. Slowest were:

129.0ms
(log (sqrt (exp (+ (+ a (+ b c)) d))))
116.0ms
(log (* (cbrt (exp (+ (+ a (+ b c)) d))) (cbrt (exp (+ (+ a (+ b c)) d)))))
94.0ms
(log (exp (+ a (+ b c))))

prune304.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 1.4b

regimes637.0ms

Accuracy

0% (1.3b remaining)

Error of 2.8b against oracle of 1.5b and baseline of 2.8b

bsearch2.0ms