Average Error: 0.0 → 0.0
Time: 34.6s
Precision: 64
Internal Precision: 128
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(d + \left(c + b\right)\right) \cdot a\]

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. Initial simplification0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2018362 
(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: 32.0s)Debug log

start53.0ms

Algorithm
intervals

setup55.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (+ (+ b c) d) a)
0.0b
(+ (+ b c) d)

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
2 → 24
Calls

2 calls. Slowest were:

10.0ms
(* (+ (+ b c) d) a)
4.0ms
(+ (+ b c) d)

series46.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

30.0ms
(* (+ (+ b c) d) a)
17.0ms
(+ (+ b c) d)

simplify423.0ms

Counts
10 → 30
Calls

10 calls. Slowest were:

218.0ms
(* (- (* (+ b c) (+ b c)) (* d d)) a)
116.0ms
(* (+ (pow (+ b c) 3) (pow d 3)) a)
24.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune195.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Counts
4 → 69
Calls

4 calls. Slowest were:

15.0ms
(* (sqrt (* (+ (+ b c) d) a)) (sqrt (* (+ (+ b c) d) a)))
5.0ms
(* (+ (+ b c) d) a)
1.0ms
(sqrt (* (+ (+ b c) d) a))

series141.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

55.0ms
(sqrt (* (+ (+ b c) d) a))
49.0ms
(sqrt (* (+ (+ b c) d) a))
19.0ms
(* (sqrt (* (+ (+ b c) d) a)) (sqrt (* (+ (+ b c) d) a)))
18.0ms
(* (+ (+ b c) d) a)

simplify5.2s

Counts
52 → 81
Calls

52 calls. Slowest were:

616.0ms
(* (* (* (sqrt (* (+ (+ b c) d) a)) (sqrt (* (+ (+ b c) d) a))) (sqrt (* (+ (+ b c) d) a))) (* (* (sqrt (* (+ (+ b c) d) a)) (sqrt (* (+ (+ b c) d) a))) (sqrt (* (+ (+ b c) d) a))))
517.0ms
(* (* (+ (+ b c) d) a) (* (+ (+ b c) d) a))
492.0ms
(* (* (+ (+ b c) d) a) (* (+ (+ b c) d) a))

prune847.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (+ (+ b c) d)) (* (sqrt (+ (+ b c) d)) a))
0.3b
(* (sqrt (+ (+ b c) d)) a)
0.0b
(sqrt (+ (+ b c) d))
0.0b
(sqrt (+ (+ b c) d))

rewrite40.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

28.0ms
(* (sqrt (+ (+ b c) d)) (* (sqrt (+ (+ b c) d)) a))
5.0ms
(* (sqrt (+ (+ b c) d)) a)
3.0ms
(sqrt (+ (+ b c) d))

series185.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

65.0ms
(* (sqrt (+ (+ b c) d)) a)
55.0ms
(* (sqrt (+ (+ b c) d)) (* (sqrt (+ (+ b c) d)) a))
36.0ms
(sqrt (+ (+ b c) d))
29.0ms
(sqrt (+ (+ b c) d))

simplify5.2s

Counts
51 → 82
Calls

51 calls. Slowest were:

984.0ms
(* (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d))) (* (* (* (sqrt (+ (+ b c) d)) a) (* (sqrt (+ (+ b c) d)) a)) (* (sqrt (+ (+ b c) d)) a)))
687.0ms
(sqrt (+ (pow (+ b c) 3) (pow d 3)))
472.0ms
(* (sqrt (+ (pow (+ b c) 3) (pow d 3))) (* (sqrt (+ (+ b c) d)) a))

prune922.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt (* (+ (+ b c) d) a))) (* (sqrt (sqrt (* (+ (+ b c) d) a))) (sqrt (* (+ (+ b c) d) a))))
0.3b
(* (sqrt (sqrt (* (+ (+ b c) d) a))) (sqrt (* (+ (+ b c) d) a)))
0.1b
(sqrt (* (+ (+ b c) d) a))
0.1b
(sqrt (* (+ (+ b c) d) a))

rewrite61.0ms

Algorithm
rewrite-expression-head
Counts
4 → 110
Calls

4 calls. Slowest were:

36.0ms
(* (sqrt (sqrt (* (+ (+ b c) d) a))) (* (sqrt (sqrt (* (+ (+ b c) d) a))) (sqrt (* (+ (+ b c) d) a))))
15.0ms
(* (sqrt (sqrt (* (+ (+ b c) d) a))) (sqrt (* (+ (+ b c) d) a)))
2.0ms
(sqrt (* (+ (+ b c) d) a))

series337.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

214.0ms
(* (sqrt (sqrt (* (+ (+ b c) d) a))) (sqrt (* (+ (+ b c) d) a)))
51.0ms
(sqrt (* (+ (+ b c) d) a))
51.0ms
(sqrt (* (+ (+ b c) d) a))
21.0ms
(* (sqrt (sqrt (* (+ (+ b c) d) a))) (* (sqrt (sqrt (* (+ (+ b c) d) a))) (sqrt (* (+ (+ b c) d) a))))

simplify16.1s

Counts
111 → 122
Calls

111 calls. Slowest were:

1.3s
(* (* (* (sqrt (sqrt (* (+ (+ b c) d) a))) (sqrt (sqrt (* (+ (+ b c) d) a)))) (sqrt (sqrt (* (+ (+ b c) d) a)))) (* (* (* (sqrt (sqrt (* (+ (+ b c) d) a))) (sqrt (* (+ (+ b c) d) a))) (* (sqrt (sqrt (* (+ (+ b c) d) a))) (sqrt (* (+ (+ b c) d) a)))) (* (sqrt (sqrt (* (+ (+ b c) d) a))) (sqrt (* (+ (+ b c) d) a)))))
701.0ms
(* (* (* (sqrt (sqrt (* (+ (+ b c) d) a))) (sqrt (sqrt (* (+ (+ b c) d) a)))) (sqrt (sqrt (* (+ (+ b c) d) a)))) (* (* (sqrt (* (+ (+ b c) d) a)) (sqrt (* (+ (+ b c) d) a))) (sqrt (* (+ (+ b c) d) a))))
497.0ms
(* (sqrt (sqrt (* (- (* (+ b c) (+ b c)) (* d d)) a))) (sqrt (* (+ (pow (+ b c) 3) (pow d 3)) a)))

prune1.8s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes379.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms