Average Error: 0.0 → 0.0
Time: 6.9s
Precision: 64
Internal Precision: 128
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot x + x \cdot \left(x \cdot x\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(1.0 + x\right) \cdot x\right) \cdot x\]

Derivation

  1. Initial program 0.0

    \[x \cdot \left(x \cdot x\right) + x \cdot x\]

  2. Final simplification0.0

    \[\leadsto x \cdot x + x \cdot \left(x \cdot x\right)\]

Reproduce

herbie shell --seed 2019004 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

  :herbie-target
  (* (* (+ 1.0 x) x) x)

  (+ (* x (* x x)) (* x x)))

Details

Time bar (total: 6.5s)Debug log

sample31.0ms

Algorithm
intervals

simplify66.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

66.0ms
(+ (* x (* x x)) (* x x))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.1b
(* x (* x x))
0.0b
(+ (* x (* x x)) (* x x))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 23
Calls

2 calls. Slowest were:

6.0ms
(+ (* x (* x x)) (* x x))
2.0ms
(* x (* x x))

series50.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

28.0ms
(+ (* x (* x x)) (* x x))
22.0ms
(* x (* x x))

simplify62.0ms

Counts
9 → 29
Calls

9 calls. Slowest were:

33.0ms
(* (exp (* x (* x x))) (exp (* x x)))
6.0ms
(+ (pow x 3) (pow x 2))
6.0ms
(+ (pow x 3) (pow x 2))

prune180.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b
(* x (+ (* x x) x))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 16
Calls

1 calls. Slowest were:

3.0ms
(* x (+ (* x x) x))

series26.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

26.0ms
(* x (+ (* x x) x))

simplify569.0ms

Counts
10 → 19
Calls

10 calls. Slowest were:

514.0ms
(+ (* (* x x) (* x x)) (- (* x x) (* (* x x) x)))
11.0ms
(+ (pow x 3) (pow x 2))
8.0ms
(+ (pow x 3) (pow x 2))

prune83.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

43.2b
(/ (* x (+ (pow (* x x) 3) (pow x 3))) (* (* x x) (+ (- 1 x) (* x x))))
0.2b
(pow (* x x) 3)
0.1b
(* x (+ (pow (* x x) 3) (pow x 3)))
0.0b
(+ (- 1 x) (* x x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Counts
4 → 74
Calls

4 calls. Slowest were:

10.0ms
(/ (* x (+ (pow (* x x) 3) (pow x 3))) (* (* x x) (+ (- 1 x) (* x x))))
8.0ms
(* x (+ (pow (* x x) 3) (pow x 3)))
5.0ms
(+ (- 1 x) (* x x))

series257.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

123.0ms
(/ (* x (+ (pow (* x x) 3) (pow x 3))) (* (* x x) (+ (- 1 x) (* x x))))
93.0ms
(* x (+ (pow (* x x) 3) (pow x 3)))
30.0ms
(pow (* x x) 3)
12.0ms
(+ (- 1 x) (* x x))

simplify3.5s

Counts
44 → 86
Calls

44 calls. Slowest were:

644.0ms
(/ (* (* (* x (+ (pow (* x x) 3) (pow x 3))) (* x (+ (pow (* x x) 3) (pow x 3)))) (* x (+ (pow (* x x) 3) (pow x 3)))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ (- 1 x) (* x x)) (+ (- 1 x) (* x x))) (+ (- 1 x) (* x x)))))
493.0ms
(/ (* (* (* x (+ (pow (* x x) 3) (pow x 3))) (* x (+ (pow (* x x) 3) (pow x 3)))) (* x (+ (pow (* x x) 3) (pow x 3)))) (* (* (* (* x x) (+ (- 1 x) (* x x))) (* (* x x) (+ (- 1 x) (* x x)))) (* (* x x) (+ (- 1 x) (* x x)))))
415.0ms
(/ (+ (pow (* x x) 3) (pow x 3)) (+ (- 1 x) (* x x)))

prune890.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes59.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample607.0ms

Algorithm
intervals