Average Error: 0.0 → 0.0
Time: 12.8s
Precision: 64
Internal Precision: 128
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[d \cdot a + \left(b + c\right) \cdot a\]

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019008 
(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: 11.8s)Debug log

sample49.0ms

Algorithm
intervals

simplify31.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 1 expressions with local error:

0.1b
(* a (+ (+ b c) d))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

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

series41.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

41.0ms
(* a (+ (+ b c) d))

simplify249.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

132.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
35.0ms
(+ (* a d) (+ (* a b) (* a c)))
27.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune201.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

6.0ms
(+ (* a (+ b c)) (* a d))
2.0ms
(* a (+ b c))

series73.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

41.0ms
(+ (* a (+ b c)) (* a d))
32.0ms
(* a (+ b c))

simplify287.0ms

Counts
17 → 35
Calls

17 calls. Slowest were:

102.0ms
(* (exp (* a (+ b c))) (exp (* a d)))
66.0ms
(+ (* b b) (- (* c c) (* b c)))
33.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune374.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize17.0ms

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))

rewrite22.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

16.0ms
(* (sqrt (* a (+ b c))) (sqrt (* a (+ b c))))
2.0ms
(* a (+ b c))
1.0ms
(sqrt (* a (+ b c)))

series164.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

53.0ms
(sqrt (* a (+ b c)))
52.0ms
(sqrt (* a (+ b c)))
30.0ms
(* a (+ b c))
29.0ms
(* (sqrt (* a (+ b c))) (sqrt (* a (+ b c))))

simplify3.0s

Counts
55 → 83
Calls

55 calls. Slowest were:

352.0ms
(* (sqrt (* a (+ (pow b 3) (pow c 3)))) (sqrt (* a (- (* b b) (* c c)))))
320.0ms
(* (sqrt (* a (- (* b b) (* c c)))) (sqrt (* a (+ (pow b 3) (pow c 3)))))
315.0ms
(* (sqrt (* a (- (* b b) (* c c)))) (sqrt (* a (+ b c))))

prune986.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))
0.2b
(* a (sqrt (+ (+ b c) d)))
0.0b
(sqrt (+ (+ b c) d))
0.0b
(sqrt (+ (+ b c) d))

rewrite50.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

28.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))
9.0ms
(* a (sqrt (+ (+ b c) d)))
6.0ms
(sqrt (+ (+ b c) d))

series191.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

79.0ms
(* a (sqrt (+ (+ b c) d)))
50.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))
33.0ms
(sqrt (+ (+ b c) d))
28.0ms
(sqrt (+ (+ b c) d))

simplify3.6s

Counts
53 → 82
Calls

53 calls. Slowest were:

440.0ms
(sqrt (+ (pow (+ b c) 3) (pow d 3)))
363.0ms
(* (* a (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (+ (+ b c) d)))
362.0ms
(sqrt (+ (pow (+ b c) 3) (pow d 3)))

prune829.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes349.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals