Average Error: 0.0 → 0.0
Time: 3.1s
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 2019005 
(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: 2.8s)Debug log

sample33.0ms

Algorithm
intervals

simplify59.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

59.0ms
(+ (* x (* x x)) (* x x))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 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))

series46.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

32.0ms
(+ (* x (* x x)) (* x x))
14.0ms
(* x (* x x))

simplify93.0ms

Counts
9 → 29
Calls

9 calls. Slowest were:

42.0ms
(* (exp (* x (* x x))) (exp (* x x)))
12.0ms
(+ (pow x 3) (pow x 2))
11.0ms
(+ (pow x 3) (pow x 2))

prune188.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 27
Calls

2 calls. Slowest were:

5.0ms
(* x (+ (* x x) x))
2.0ms
(+ (* x x) x)

series46.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

27.0ms
(* x (+ (* x x) x))
19.0ms
(+ (* x x) x)

simplify491.0ms

Counts
14 → 33
Calls

14 calls. Slowest were:

423.0ms
(+ (* (* x x) (* x x)) (- (* x x) (* (* x x) x)))
12.0ms
(sqrt (+ (* x x) x))
12.0ms
(cbrt (+ (* x x) x))

prune237.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ x 1) (* x x))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

7.0ms
(* (+ x 1) (* x x))

series37.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

37.0ms
(* (+ x 1) (* x x))

simplify765.0ms

Counts
10 → 20
Calls

10 calls. Slowest were:

490.0ms
(* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (* x x) (* x x)) (* x x)))
126.0ms
(* (- (* x x) (* 1 1)) (* x x))
93.0ms
(* (+ (pow x 3) (pow 1 3)) (* x x))

prune119.0ms

Pruning

2 alts after pruning (0 fresh and 2 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

sample617.0ms

Algorithm
intervals