Average Error: 38.8 → 0.0
Time: 5.4s
Precision: 64
Internal Precision: 128
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[\left(x + 2\right) \cdot x\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.8

    \[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(2 + x\right) \cdot x}\]

  3. Final simplification0.0

    \[\leadsto \left(x + 2\right) \cdot x\]

Reproduce

herbie shell --seed 2019004 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))

Details

Time bar (total: 5.3s)Debug log

sample101.0ms

Algorithm
intervals

simplify442.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

441.0ms
(- (* (+ x 1) (+ x 1)) 1)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ 2 x) x)

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

4.0ms
(* (+ 2 x) x)

series25.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

25.0ms
(* (+ 2 x) x)

simplify254.0ms

Counts
7 → 18
Calls

7 calls. Slowest were:

210.0ms
(* (- (* 2 2) (* x x)) x)
15.0ms
(* (+ (pow 2 3) (pow x 3)) x)
6.0ms
(+ (* 2 x) (pow x 2))

prune333.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

7.0b
(/ (* (- (* 2 2) (* x x)) x) (- 2 x))
0.1b
(* (- (* 2 2) (* x x)) x)

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
2 → 41
Calls

2 calls. Slowest were:

7.0ms
(/ (* (- (* 2 2) (* x x)) x) (- 2 x))
4.0ms
(* (- (* 2 2) (* x x)) x)

series72.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

42.0ms
(/ (* (- (* 2 2) (* x x)) x) (- 2 x))
29.0ms
(* (- (* 2 2) (* x x)) x)

simplify1.4s

Counts
27 → 47
Calls

27 calls. Slowest were:

192.0ms
(/ (- (* 2 2) (* x x)) (* (cbrt (- 2 x)) (cbrt (- 2 x))))
176.0ms
(* (- (* (* 2 2) (* 2 2)) (* (* x x) (* x x))) x)
175.0ms
(* (- (* (* 2 2) (* 2 2)) (* (* x x) (* x x))) x)

prune215.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (- 4 (* x x)) (/ (- 2 x) x))
0.0b
(/ (- 2 x) x)

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
2 → 55
Calls

2 calls. Slowest were:

3.0ms
(/ (- 4 (* x x)) (/ (- 2 x) x))
2.0ms
(/ (- 2 x) x)

series60.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

41.0ms
(/ (- 4 (* x x)) (/ (- 2 x) x))
19.0ms
(/ (- 2 x) x)

simplify984.0ms

Counts
46 → 61
Calls

46 calls. Slowest were:

295.0ms
(/ (* (* (- 4 (* x x)) (- 4 (* x x))) (- 4 (* x x))) (* (* (/ (- 2 x) x) (/ (- 2 x) x)) (/ (- 2 x) x)))
127.0ms
(- (* 4 4) (* (* x x) (* x x)))
58.0ms
(/ (- 4 (* x x)) (/ 1 x))

prune270.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes17.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.1s

Algorithm
intervals