Average Error: 0.0 → 0.0
Time: 4.0s
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 2019016 
(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: 3.8s)Debug log

sample31.0ms

Algorithm
intervals
Results
256×(pre true 80)
256×(body real 80)

simplify58.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
58.0ms
(+ (* x (* x x)) (* x x))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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
Rules
4×add-log-exp
2×add-cube-cbrt
2×add-exp-log
2×add-cbrt-cube
2×*-un-lft-identity
2×pow1
2×add-sqr-sqrt
1×distribute-lft-out
1×flip-+
1×*-commutative
1×associate-*r*
1×cube-unmult
1×flip3-+
1×distribute-lft1-in
1×sum-log
1×+-commutative
Counts
2 → 23
Calls
2 calls:
Slowest
5.0ms
(+ (* x (* x x)) (* x x))
2.0ms
(* x (* x x))

series68.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
46.0ms
(+ (* x (* x x)) (* x x))
23.0ms
(* x (* x x))

simplify101.0ms

Counts
9 → 29
Calls
9 calls:
Slowest
60.0ms
(* (exp (* x (* x x))) (exp (* x x)))
10.0ms
(+ (* x x) x)
10.0ms
(+ (pow x 3) (pow x 2))
7.0ms
(+ (pow x 3) (pow x 2))
6.0ms
(+ (pow x 3) (pow x 2))

prune160.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 4 expressions with local error:

32.5b
(sqrt (+ (* x (* x x)) (* x x)))
32.5b
(sqrt (+ (* x (* x x)) (* x x)))
0.1b
(* x (* x x))
0.1b
(* x (* x x))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
10×sqrt-prod
8×add-sqr-sqrt
6×add-cube-cbrt
6×*-un-lft-identity
4×add-log-exp
4×add-exp-log
4×sqrt-div
4×add-cbrt-cube
4×pow1
2×distribute-lft-out
2×flip-+
2×*-commutative
2×associate-*r*
2×cube-unmult
2×pow1/2
2×flip3-+
2×distribute-lft1-in
2×rem-sqrt-square
Counts
4 → 52
Calls
4 calls:
Slowest
3.0ms
(sqrt (+ (* x (* x x)) (* x x)))
3.0ms
(sqrt (+ (* x (* x x)) (* x x)))
1.0ms
(* x (* x x))
1.0ms
(* x (* x x))

series67.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
21.0ms
(sqrt (+ (* x (* x x)) (* x x)))
17.0ms
(sqrt (+ (* x (* x x)) (* x x)))
15.0ms
(* x (* x x))
14.0ms
(* x (* x x))

simplify2.0s

Counts
28 → 64
Calls
28 calls:
Slowest
696.0ms
(sqrt (+ (pow (* x (* x x)) 3) (pow (* x x) 3)))
287.0ms
(sqrt (- (* (* x (* x x)) (* x (* x x))) (* (* x x) (* x x))))
223.0ms
(sqrt (- (* (* x (* x x)) (* x (* x x))) (* (* x x) (* x x))))
205.0ms
(sqrt (+ (pow (* x (* x x)) 3) (pow (* x x) 3)))
149.0ms
(- (+ x (* 1/2 (pow x 2))) (* 1/8 (pow x 3)))

prune493.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample702.0ms

Algorithm
intervals
Results
8000×(pre true 80)
8000×(body real 80)