Average Error: 0.0 → 0.0
Time: 1.1m
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 2018360 
(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: 1.0m)Debug log

start46.0ms

Algorithm
intervals

setup72.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

11.0ms
(* (+ (+ b c) d) a)

series18.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify836.0ms

Counts
7 → 16
Calls

7 calls. Slowest were:

523.0ms
(* (+ (pow (+ b c) 3) (pow d 3)) a)
195.0ms
(* (- (* (+ b c) (+ b c)) (* d d)) a)
50.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune150.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

14.0ms
(* (sqrt (+ (+ b c) d)) (* (sqrt (+ (+ b c) d)) a))
9.0ms
(* (sqrt (+ (+ b c) d)) a)
5.0ms
(sqrt (+ (+ b c) d))

series210.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

72.0ms
(* (sqrt (+ (+ b c) d)) (* (sqrt (+ (+ b c) d)) a))
62.0ms
(* (sqrt (+ (+ b c) d)) a)
45.0ms
(sqrt (+ (+ b c) d))
31.0ms
(sqrt (+ (+ b c) d))

simplify5.7s

Counts
51 → 82
Calls

51 calls. Slowest were:

809.0ms
(sqrt (- (* (+ b c) (+ b c)) (* d d)))
772.0ms
(sqrt (- (* (+ b c) (+ b c)) (* d d)))
693.0ms
(* (* (* (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)))

prune880.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (+ b c) d))
0.6b
(cbrt (+ d (+ c b)))
0.4b
(* (sqrt (cbrt (+ (+ b c) d))) (* (sqrt (+ (+ b c) d)) a))
0.4b
(* (fabs (cbrt (+ d (+ c b)))) (* (sqrt (cbrt (+ (+ b c) d))) (* (sqrt (+ (+ b c) d)) a)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Counts
4 → 81
Calls

4 calls. Slowest were:

66.0ms
(* (fabs (cbrt (+ d (+ c b)))) (* (sqrt (cbrt (+ (+ b c) d))) (* (sqrt (+ (+ b c) d)) a)))
29.0ms
(* (sqrt (cbrt (+ (+ b c) d))) (* (sqrt (+ (+ b c) d)) a))
3.0ms
(cbrt (+ (+ b c) d))

series1.7s

Counts
4 → 12
Calls

4 calls. Slowest were:

748.0ms
(* (fabs (cbrt (+ d (+ c b)))) (* (sqrt (cbrt (+ (+ b c) d))) (* (sqrt (+ (+ b c) d)) a)))
594.0ms
(* (sqrt (cbrt (+ (+ b c) d))) (* (sqrt (+ (+ b c) d)) a))
185.0ms
(cbrt (+ (+ b c) d))
181.0ms
(cbrt (+ d (+ c b)))

simplify6.0s

Counts
62 → 93
Calls

62 calls. Slowest were:

917.0ms
(cbrt (- (* d d) (* (+ c b) (+ c b))))
896.0ms
(cbrt (- (* (+ b c) (+ b c)) (* d d)))
322.0ms
(* (sqrt (cbrt (+ (pow (+ b c) 3) (pow d 3)))) (* (sqrt (+ (+ b c) d)) a))

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

2.4b
(cbrt (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d))))
0.5b
(* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d)))
0.4b
(* (cbrt (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))) (* (sqrt (+ (+ b c) d)) a))
0.2b
(* (sqrt (+ (+ b c) d)) a)

rewrite90.0ms

Algorithm
rewrite-expression-head
Counts
4 → 186
Calls

4 calls. Slowest were:

38.0ms
(* (cbrt (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))) (* (sqrt (+ (+ b c) d)) a))
20.0ms
(cbrt (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d))))
10.0ms
(* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d)))

series199.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

72.0ms
(* (sqrt (+ (+ b c) d)) a)
58.0ms
(* (cbrt (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))) (* (sqrt (+ (+ b c) d)) a))
35.0ms
(cbrt (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d))))
33.0ms
(* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d)))

simplify40.2s

Counts
219 → 198
Calls

219 calls. Slowest were:

659.0ms
(* (* (* (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)))
575.0ms
(* (cbrt (* (* (sqrt (+ (pow (+ b c) 3) (pow d 3))) (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (+ (+ b c) d)))) (* (sqrt (+ (pow (+ b c) 3) (pow d 3))) a))
511.0ms
(* (cbrt (* (* (sqrt (+ (pow (+ b c) 3) (pow d 3))) (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (+ (+ b c) d)))) (* (sqrt (+ (+ b c) d)) a))

prune3.8s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes343.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms