Average Error: 0.1 → 0
Time: 1.2s
Precision: 64
Internal Precision: 128
\[\left(x \cdot x\right) \cdot x\]
↓
\[{x}^{3}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0
Herbie0
\[{x}^{3}\]

Derivation

  1. Initial program 0.1

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

  2. Simplified0

    \[\leadsto \color{blue}{{x}^{3}}\]

  3. Final simplification0

    \[\leadsto {x}^{3}\]

Reproduce

herbie shell --seed 2019016 
(FPCore (x)
  :name "math.cube on real"

  :herbie-target
  (pow x 3)

  (* (* x x) x))

Details

Time bar (total: 963.0ms)Debug log

sample37.0ms

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

simplify2.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
2.0ms
(* (* x x) x)

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune5.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample905.0ms

Algorithm
intervals
Results
12053×(pre true 80)
12053×(body real 80)