Average Error: 0.0 → 0.0
Time: 6.8s
Precision: 64
Internal Precision: 128
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(b \cdot a + c \cdot a\right) + d \cdot a\]

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

Original0.0
Target0.0
Herbie0.0
\[a \cdot b + a \cdot \left(c + d\right)\]

Derivation

  1. Initial program 0.0

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

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{a \cdot \left(b + c\right) + a \cdot d}\]
  4. Using strategy rm

  5. Applied distribute-rgt-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019005 
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789 a 98765) (<= 0 b 1) (<= 0 c 0.0016773) (<= 0 d 0.0016773))

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

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

Details

Time bar (total: 6.4s)Debug log

sample49.0ms

Algorithm
intervals

simplify49.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

48.0ms
(* a (+ (+ b c) d))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 2 expressions with local error:

0.0b
(* a (+ (+ b c) d))
0.0b
(+ (+ b c) d)

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
2 → 26
Calls

2 calls. Slowest were:

8.0ms
(* a (+ (+ b c) d))
5.0ms
(+ (+ b c) d)

series49.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

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

simplify281.0ms

Counts
13 → 32
Calls

13 calls. Slowest were:

159.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
37.0ms
(+ (* a d) (+ (* a b) (* a c)))
24.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune233.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(* a (+ b c))
0.0b
(+ (* a (+ b c)) (* a d))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

5.0ms
(+ (* a (+ b c)) (* a d))
2.0ms
(* a (+ b c))

series52.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

29.0ms
(* a (+ b c))
23.0ms
(+ (* a (+ b c)) (* a d))

simplify208.0ms

Counts
17 → 35
Calls

17 calls. Slowest were:

88.0ms
(* (exp (* a (+ b c))) (exp (* a d)))
33.0ms
(+ (* b b) (- (* c c) (* b c)))
23.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune211.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* b a) (* c a))
0.0b
(+ (+ (* b a) (* c a)) (* a d))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
2 → 26
Calls

2 calls. Slowest were:

8.0ms
(+ (+ (* b a) (* c a)) (* a d))
2.0ms
(+ (* b a) (* c a))

series40.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

22.0ms
(+ (+ (* b a) (* c a)) (* a d))
18.0ms
(+ (* b a) (* c a))

simplify182.0ms

Counts
12 → 32
Calls

12 calls. Slowest were:

46.0ms
(* (exp (+ (* b a) (* c a))) (exp (* a d)))
41.0ms
(* (* (exp (* b a)) (exp (* c a))) (exp (* a d)))
36.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune271.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (* a (+ b c))) (sqrt (* a (+ b c))))
0.1b
(sqrt (* a (+ b c)))
0.1b
(sqrt (* a (+ b c)))
0.0b
(* a (+ b c))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

12.0ms
(* (sqrt (* a (+ b c))) (sqrt (* a (+ b c))))
2.0ms
(* a (+ b c))
1.0ms
(sqrt (* a (+ b c)))

series152.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

51.0ms
(sqrt (* a (+ b c)))
48.0ms
(sqrt (* a (+ b c)))
26.0ms
(* a (+ b c))
26.0ms
(* (sqrt (* a (+ b c))) (sqrt (* a (+ b c))))

simplify2.2s

Counts
55 → 83
Calls

55 calls. Slowest were:

331.0ms
(* (sqrt (* a (- (* b b) (* c c)))) (sqrt (* a (+ (pow b 3) (pow c 3)))))
279.0ms
(* (* a (+ b c)) (* a (+ b c)))
254.0ms
(* (sqrt (* a (+ (pow b 3) (pow c 3)))) (sqrt (* a (- (* b b) (* c c)))))

prune838.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes375.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.0s

Algorithm
intervals