Average Error: 0.0 → 0.0
Time: 6.1s
Precision: 64
Internal Precision: 128
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot \left(x \cdot x + x\right)\]

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. Using strategy rm

  3. Applied distribute-lft-out0.0

    \[\leadsto \color{blue}{x \cdot \left(x \cdot x + x\right)}\]

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019007 
(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: 5.8s)Debug log

sample27.0ms

Algorithm
intervals

simplify29.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

29.0ms
(+ (* x (* x x)) (* x x))

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
2 → 23
Calls

2 calls. Slowest were:

3.0ms
(+ (* x (* x x)) (* x x))
1.0ms
(* x (* x x))

series49.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

32.0ms
(+ (* x (* x x)) (* x x))
16.0ms
(* x (* x x))

simplify75.0ms

Counts
9 → 29
Calls

9 calls. Slowest were:

30.0ms
(* (exp (* x (* x x))) (exp (* x x)))
13.0ms
(+ (pow x 3) (pow x 2))
11.0ms
(+ (pow x 3) (pow x 2))

prune147.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 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))

series30.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

30.0ms
(* x (+ (* x x) x))

simplify431.0ms

Counts
10 → 19
Calls

10 calls. Slowest were:

377.0ms
(+ (* (* x x) (* x x)) (- (* x x) (* (* x x) x)))
11.0ms
(+ (pow x 3) (pow x 2))
10.0ms
(+ (pow x 3) (pow x 2))

prune150.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

8.9b
(/ (* x (- (* (* x x) (* x x)) (* x x))) (- (* x x) x))
0.2b
(* (* x x) (* x x))
0.1b
(* x (- (* (* x x) (* x x)) (* x x)))
0.0b
(- (* (* x x) (* x x)) (* x x))

rewrite40.0ms

Algorithm
rewrite-expression-head
Counts
4 → 72
Calls

4 calls. Slowest were:

13.0ms
(* x (- (* (* x x) (* x x)) (* x x)))
13.0ms
(/ (* x (- (* (* x x) (* x x)) (* x x))) (- (* x x) x))
10.0ms
(- (* (* x x) (* x x)) (* x x))

series235.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

83.0ms
(* x (- (* (* x x) (* x x)) (* x x)))
79.0ms
(/ (* x (- (* (* x x) (* x x)) (* x x))) (- (* x x) x))
55.0ms
(- (* (* x x) (* x x)) (* x x))
18.0ms
(* (* x x) (* x x))

simplify3.2s

Counts
48 → 84
Calls

48 calls. Slowest were:

538.0ms
(* x (- (pow (* (* x x) (* x x)) 3) (pow (* x x) 3)))
322.0ms
(- (log (* x (- (* (* x x) (* x x)) (* x x)))) (log (- (* x x) x)))
299.0ms
(/ (- (* (* x x) (* x x)) (* x x)) (- (* x x) x))

prune439.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes17.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample914.0ms

Algorithm
intervals