Average Error: 0.0 → 0.0
Time: 4.2s
Precision: 64
Internal Precision: 128
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot d + \left(c + b\right) \cdot a\]

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-rgt-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(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: 3.4s)Debug log

sample46.0ms

Algorithm
intervals

simplify52.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

52.0ms
(* a (+ (+ b c) d))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
2 → 33
Calls

2 calls. Slowest were:

4.0ms
(* a (+ (+ b c) d))
3.0ms
(+ (+ b c) d)

series48.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

30.0ms
(* a (+ (+ b c) d))
18.0ms
(+ (+ b c) d)

simplify422.0ms

Counts
15 → 39
Calls

15 calls. Slowest were:

179.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
77.0ms
(+ (* a d) (+ (* a b) (* a c)))
76.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune303.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
2 → 30
Calls

2 calls. Slowest were:

7.0ms
(+ (* (+ b c) a) (* d a))
4.0ms
(* (+ b c) a)

series48.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

31.0ms
(+ (* (+ b c) a) (* d a))
17.0ms
(* (+ b c) a)

simplify430.0ms

Counts
13 → 36
Calls

13 calls. Slowest were:

182.0ms
(* (- (* b b) (* c c)) a)
125.0ms
(* (exp (* (+ b c) a)) (exp (* d a)))
39.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune363.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

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

series25.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

25.0ms
(fma a (+ d b) (* c a))

simplify91.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

52.0ms
(+ (* a d) (+ (* a b) (* a c)))
38.0ms
(+ (* a d) (+ (* a b) (* a c)))
0.0ms
0

prune93.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes242.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.1s

Algorithm
intervals