Average Error: 0.0 → 0.0
Time: 8.8s
Precision: 64
Internal Precision: 128
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(\left(b + c\right) + d\right) \cdot a\]

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2018365 +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: 7.0s)Debug log

start59.0ms

Algorithm
intervals

setup71.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

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

series32.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify99.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

55.0ms
(+ (* a d) (+ (* a b) (* a c)))
43.0ms
(+ (* a d) (+ (* a b) (* a c)))
0.0ms
0

prune135.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

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

series36.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

36.0ms
(* a (+ (+ b c) d))

simplify419.0ms

Counts
10 → 20
Calls

10 calls. Slowest were:

207.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
75.0ms
(+ (* a d) (+ (* a b) (* a c)))
70.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune229.0ms

Pruning

5 alts after pruning (3 fresh and 2 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))

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
2 → 34
Calls

2 calls. Slowest were:

9.0ms
(+ (* a (+ b c)) (* a d))
2.0ms
(* a (+ b c))

series76.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

45.0ms
(+ (* a (+ b c)) (* a d))
30.0ms
(* a (+ b c))

simplify393.0ms

Counts
17 → 40
Calls

17 calls. Slowest were:

134.0ms
(* (exp (* a (+ b c))) (exp (* a d)))
96.0ms
(+ (* b b) (- (* c c) (* b c)))
57.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune399.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

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))

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

9.0ms
(* (sqrt (* a (+ b c))) (sqrt (* a (+ b c))))
1.0ms
(* a (+ b c))
1.0ms
(sqrt (* a (+ b c)))

series134.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

51.0ms
(sqrt (* a (+ b c)))
33.0ms
(sqrt (* a (+ b c)))
31.0ms
(* a (+ b c))
18.0ms
(* (sqrt (* a (+ b c))) (sqrt (* a (+ b c))))

simplify3.0s

Counts
55 → 91
Calls

55 calls. Slowest were:

568.0ms
(* (* (* (sqrt (* a (+ b c))) (sqrt (* a (+ b c)))) (sqrt (* a (+ b c)))) (* (* (sqrt (* a (+ b c))) (sqrt (* a (+ b c)))) (sqrt (* a (+ b c)))))
235.0ms
(* (sqrt (* a (- (* b b) (* c c)))) (sqrt (* a (- (* b b) (* c c)))))
228.0ms
(* (sqrt (* a (- (* b b) (* c c)))) (sqrt (* a (+ (pow b 3) (pow c 3)))))

prune1.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes377.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms