Average Error: 3.7 → 2.8
Time: 10.7s
Precision: 64
Internal Precision: 128
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(a + \left(b + c\right)\right) + d\right) \cdot 2\]

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
Target3.8
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. 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. Using strategy rm

  6. Applied associate-+l+2.8

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

  7. Final simplification2.8

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

Reproduce

herbie shell --seed 2018365 +o rules:numerics
(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: 6.1s)Debug log

start49.0ms

Algorithm
intervals

setup304.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize20.0ms

Local error

Found 1 expressions with local error:

3.2b
(+ (+ a c) (+ b d))

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
1 → 23
Calls

1 calls. Slowest were:

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

series27.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify2.7s

Counts
15 → 26
Calls

15 calls. Slowest were:

655.0ms
(+ (* (+ (pow a 3) (pow c 3)) (- b d)) (* (+ (* a a) (- (* c c) (* a c))) (- (* b b) (* d d))))
640.0ms
(* (+ (* a a) (- (* c c) (* a c))) (+ (* b b) (- (* d d) (* b d))))
520.0ms
(+ (* (- (* a a) (* c c)) (- b d)) (* (- a c) (- (* b b) (* d d))))

prune314.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.9b

localize7.0ms

Local error

Found 2 expressions with local error:

2.8b
(+ (+ (+ a c) b) d)
0.2b
(+ (+ a c) b)

rewrite15.0ms

Algorithm
rewrite-expression-head
Counts
2 → 32
Calls

2 calls. Slowest were:

12.0ms
(+ (+ (+ a c) b) d)
2.0ms
(+ (+ a c) b)

series34.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

23.0ms
(+ (+ (+ a c) b) d)
11.0ms
(+ (+ a c) b)

simplify81.0ms

Counts
11 → 38
Calls

11 calls. Slowest were:

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

prune441.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.6b

localize23.0ms

Local error

Found 1 expressions with local error:

2.8b
(+ (+ a (+ c b)) d)

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 16
Calls

1 calls. Slowest were:

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

series33.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

33.0ms
(+ (+ a (+ c b)) d)

simplify69.0ms

Counts
5 → 19
Calls

5 calls. Slowest were:

15.0ms
(* (cbrt (+ a (+ c b))) (cbrt (+ a (+ c b))))
13.0ms
(+ b (+ c d))
13.0ms
(sqrt (+ a (+ c b)))

prune235.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 1.6b

localize18.0ms

Local error

Found 2 expressions with local error:

2.8b
(+ (+ a (+ c b)) d)
1.0b
(log (exp (+ (+ a (+ c b)) d)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Counts
2 → 34
Calls

2 calls. Slowest were:

21.0ms
(log (exp (+ (+ a (+ c b)) d)))
10.0ms
(+ (+ a (+ c b)) d)

series73.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

37.0ms
(log (exp (+ (+ a (+ c b)) d)))
36.0ms
(+ (+ a (+ c b)) d)

simplify498.0ms

Counts
16 → 40
Calls

16 calls. Slowest were:

138.0ms
(log (* (cbrt (exp (+ (+ a (+ c b)) d))) (cbrt (exp (+ (+ a (+ c b)) d)))))
110.0ms
(log (exp (+ a (+ c b))))
88.0ms
(log (sqrt (exp (+ (+ a (+ c b)) d))))

prune454.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 1.5b

regimes627.0ms

Accuracy

0% (1.3b remaining)

Error of 2.8b against oracle of 1.4b and baseline of 2.8b

bsearch1.0ms