Average Error: 0.0 → 0.0
Time: 26.2s
Precision: 64
Internal Precision: 128
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[b \cdot a + \left(d + c\right) \cdot a\]

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. Taylor expanded around inf 0.0

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

  3. Simplified0.0

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

  5. Applied distribute-rgt-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019002 
(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: 25.7s)Debug log

sample48.0ms

Algorithm
intervals

simplify39.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

39.0ms
(* a (+ (+ b c) d))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

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

series24.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify229.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

129.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
27.0ms
(+ (* a d) (+ (* a b) (* a c)))
23.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune123.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
2 → 26
Calls

2 calls. Slowest were:

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

series30.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

19.0ms
(* a (+ b (+ d c)))
10.0ms
(+ b (+ d c))

simplify340.0ms

Counts
13 → 32
Calls

13 calls. Slowest were:

187.0ms
(+ (* b b) (- (* (+ d c) (+ d c)) (* b (+ d c))))
47.0ms
(+ (* a d) (+ (* a b) (* a c)))
24.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune292.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
2 → 25
Calls

2 calls. Slowest were:

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

series45.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

28.0ms
(+ (* b a) (* (+ d c) a))
17.0ms
(* (+ d c) a)

simplify472.0ms

Counts
12 → 31
Calls

12 calls. Slowest were:

280.0ms
(* (- (* d d) (* c c)) a)
74.0ms
(* (exp (* b a)) (exp (* (+ d c) a)))
36.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune222.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

24.4b
(cbrt (* (* (* (+ d c) a) (* (+ d c) a)) (* (+ d c) a)))
0.4b
(* (* (+ d c) a) (* (+ d c) a))
0.2b
(* (* (* (+ d c) a) (* (+ d c) a)) (* (+ d c) a))
0.0b
(* (+ d c) a)

rewrite72.0ms

Algorithm
rewrite-expression-head
Counts
4 → 122
Calls

4 calls. Slowest were:

32.0ms
(* (* (* (+ d c) a) (* (+ d c) a)) (* (+ d c) a))
23.0ms
(cbrt (* (* (* (+ d c) a) (* (+ d c) a)) (* (+ d c) a)))
11.0ms
(* (* (+ d c) a) (* (+ d c) a))

series84.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

32.0ms
(* (* (* (+ d c) a) (* (+ d c) a)) (* (+ d c) a))
22.0ms
(* (* (+ d c) a) (* (+ d c) a))
15.0ms
(cbrt (* (* (* (+ d c) a) (* (+ d c) a)) (* (+ d c) a)))
14.0ms
(* (+ d c) a)

simplify20.7s

Counts
122 → 134
Calls

122 calls. Slowest were:

1.4s
(* (* (* (* (+ d c) a) (* (+ d c) a)) (* (+ d c) a)) (* (* (* (+ d c) a) (* (+ d c) a)) (* (+ d c) a)))
1.1s
(cbrt (* (* (* (- (* d d) (* c c)) a) (* (- (* d d) (* c c)) a)) (* (- (* d d) (* c c)) a)))
967.0ms
(* (* (* (+ d c) a) (* (+ (pow d 3) (pow c 3)) a)) (* (+ d c) a))

prune1.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes161.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.1s

Algorithm
intervals