Average Error: 0.0 → 0.0
Time: 30.1s
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 2019007 
(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: 29.5s)Debug log

sample54.0ms

Algorithm
intervals

simplify57.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

57.0ms
(* a (+ (+ b c) d))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

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

series20.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

20.0ms
(* a (+ (+ b c) d))

simplify258.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

147.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
38.0ms
(+ (* a d) (+ (* a b) (* a c)))
27.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune139.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

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))

rewrite39.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

17.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))
9.0ms
(* a (sqrt (+ (+ b c) d)))
6.0ms
(sqrt (+ (+ b c) d))

series181.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

60.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))
51.0ms
(* a (sqrt (+ (+ b c) d)))
38.0ms
(sqrt (+ (+ b c) d))
32.0ms
(sqrt (+ (+ b c) d))

simplify3.5s

Counts
53 → 82
Calls

53 calls. Slowest were:

417.0ms
(* (* a (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (+ (+ b c) d)))
400.0ms
(sqrt (+ (pow (+ b c) 3) (pow d 3)))
369.0ms
(* (* a (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (+ (pow (+ b c) 3) (pow d 3))))

prune869.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* a (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))
0.3b
(* (* (* a (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))) (sqrt (sqrt (+ (+ b c) d))))
0.2b
(* a (sqrt (+ (+ b c) d)))
0.1b
(sqrt (sqrt (+ (+ b c) d)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Counts
4 → 113
Calls

4 calls. Slowest were:

40.0ms
(* (* (* a (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))) (sqrt (sqrt (+ (+ b c) d))))
23.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))
6.0ms
(* a (sqrt (+ (+ b c) d)))

series816.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

450.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))
242.0ms
(sqrt (sqrt (+ (+ b c) d)))
73.0ms
(* (* (* a (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))) (sqrt (sqrt (+ (+ b c) d))))
51.0ms
(* a (sqrt (+ (+ b c) d)))

simplify12.8s

Counts
112 → 125
Calls

112 calls. Slowest were:

612.0ms
(* (* (* (* (* a (sqrt (+ (+ b c) d))) (* a (sqrt (+ (+ b c) d)))) (* a (sqrt (+ (+ b c) d)))) (* (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))) (sqrt (sqrt (+ (+ b c) d))))) (* (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))) (sqrt (sqrt (+ (+ b c) d)))))
501.0ms
(* (* (* a (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (sqrt (+ (pow (+ b c) 3) (pow d 3))))) (sqrt (sqrt (+ (pow (+ b c) 3) (pow d 3)))))
455.0ms
(* (* (* a (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (sqrt (+ (+ b c) d)))) (sqrt (sqrt (+ (pow (+ b c) 3) (pow d 3)))))

prune1.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (* a (+ (+ b c) d)))
0.7b
(cbrt (* a (+ (+ b c) d)))
0.7b
(cbrt (* a (+ (+ b c) d)))
0.5b
(* (cbrt (* a (+ (+ b c) d))) (cbrt (* a (+ (+ b c) d))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

8.0ms
(* (cbrt (* a (+ (+ b c) d))) (cbrt (* a (+ (+ b c) d))))
2.0ms
(cbrt (* a (+ (+ b c) d)))
2.0ms
(cbrt (* a (+ (+ b c) d)))

series519.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

160.0ms
(* (cbrt (* a (+ (+ b c) d))) (cbrt (* a (+ (+ b c) d))))
128.0ms
(cbrt (* a (+ (+ b c) d)))
128.0ms
(cbrt (* a (+ (+ b c) d)))
103.0ms
(cbrt (* a (+ (+ b c) d)))

simplify6.3s

Counts
49 → 77
Calls

49 calls. Slowest were:

496.0ms
(* (cbrt (* a (- (* (+ b c) (+ b c)) (* d d)))) (cbrt (* a (+ (pow (+ b c) 3) (pow d 3)))))
446.0ms
(* (* a (+ (+ b c) d)) (* a (+ (+ b c) d)))
439.0ms
(* (* a (+ (+ b c) d)) (* a (+ (+ b c) d)))

prune970.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes367.0ms

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