Average Error: 0.0 → 0.0
Time: 8.3s
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 2019002 
(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: 8.0s)Debug log

sample16.0ms

Algorithm
intervals

simplify32.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))

series59.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

40.0ms
(+ (* x (* x x)) (* x x))
18.0ms
(* x (* x x))

simplify70.0ms

Counts
9 → 29
Calls

9 calls. Slowest were:

41.0ms
(* (exp (* x (* x x))) (exp (* x x)))
7.0ms
(+ (pow x 3) (pow x 2))
6.0ms
(+ (pow x 3) (pow x 2))

prune177.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 16
Calls

1 calls. Slowest were:

5.0ms
(* x (+ (* x x) x))

series49.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

49.0ms
(* x (+ (* x x) x))

simplify631.0ms

Counts
10 → 19
Calls

10 calls. Slowest were:

557.0ms
(+ (* (* x x) (* x x)) (- (* x x) (* (* x x) x)))
13.0ms
(sqrt (+ (* x x) x))
11.0ms
(+ (pow x 3) (pow x 2))

prune111.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (pow x 3) (pow x 2))

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
1 → 14
Calls

1 calls. Slowest were:

7.0ms
(+ (pow x 3) (pow x 2))

series45.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

45.0ms
(+ (pow x 3) (pow x 2))

simplify80.0ms

Counts
7 → 17
Calls

7 calls. Slowest were:

15.0ms
(* (exp (pow x 3)) (exp (pow x 2)))
11.0ms
(+ (* x x) x)
11.0ms
(+ (pow x 3) (pow x 2))

prune180.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

46.4b
(/ (* x (+ (pow (* x x) 3) (pow x 3))) (* (* x x) (+ (- 1 x) (* x x))))
0.1b
(pow (* x x) 3)
0.1b
(* x (+ (pow (* x x) 3) (pow x 3)))
0.0b
(* (* x x) (+ (- 1 x) (* x x)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

21.0ms
(/ (* x (+ (pow (* x x) 3) (pow x 3))) (* (* x x) (+ (- 1 x) (* x x))))
14.0ms
(* (* x x) (+ (- 1 x) (* x x)))
11.0ms
(* x (+ (pow (* x x) 3) (pow x 3)))

series237.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

113.0ms
(/ (* x (+ (pow (* x x) 3) (pow x 3))) (* (* x x) (+ (- 1 x) (* x x))))
79.0ms
(* x (+ (pow (* x x) 3) (pow x 3)))
30.0ms
(pow (* x x) 3)
14.0ms
(* (* x x) (+ (- 1 x) (* x x)))

simplify4.7s

Counts
53 → 91
Calls

53 calls. Slowest were:

961.0ms
(/ (* (* (* 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)))))
736.0ms
(/ (* (* (* 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)))))
386.0ms
(* x (+ (pow (pow (* x x) 3) 3) (pow (pow x 3) 3)))

prune719.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample655.0ms

Algorithm
intervals