Average Error: 0.0 → 0.0
Time: 5.3s
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 2018360 
(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: 4.2s)Debug log

start33.0ms

Algorithm
intervals

setup60.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

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))
21.0ms
(* x (* x x))

simplify72.0ms

Counts
9 → 29
Calls

9 calls. Slowest were:

29.0ms
(* (exp (* x (* x x))) (exp (* x x)))
12.0ms
(+ (pow x 3) (pow x 2))
12.0ms
(+ (pow x 3) (pow x 2))

prune211.0ms

Pruning

3 alts after pruning (2 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))

series28.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

28.0ms
(* (+ x 1) (* x x))

simplify679.0ms

Counts
10 → 20
Calls

10 calls. Slowest were:

429.0ms
(* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (* x x) (* x x)) (* x x)))
144.0ms
(* (- (* x x) (* 1 1)) (* x x))
40.0ms
(* (+ (pow x 3) (pow 1 3)) (* x x))

prune222.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

28.5b
(sqrt (+ (* x (* x x)) (* x x)))
28.5b
(sqrt (+ (* x (* x x)) (* x x)))
0.1b
(* x (* x x))
0.1b
(* x (* x x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
4 → 52
Calls

4 calls. Slowest were:

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

series96.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

35.0ms
(* x (* x x))
26.0ms
(sqrt (+ (* x (* x x)) (* x x)))
19.0ms
(* x (* x x))
16.0ms
(sqrt (+ (* x (* x x)) (* x x)))

simplify2.0s

Counts
28 → 64
Calls

28 calls. Slowest were:

565.0ms
(sqrt (- (* (* x (* x x)) (* x (* x x))) (* (* x x) (* x x))))
538.0ms
(sqrt (- (* (* x (* x x)) (* x (* x x))) (* (* x x) (* x x))))
212.0ms
(sqrt (+ (pow (* x (* x x)) 3) (pow (* x x) 3)))

prune569.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes74.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms