Average Error: 38.8 → 0.0
Time: 10.9s
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 2019005 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))

Details

Time bar (total: 10.7s)Debug log

sample98.0ms

Algorithm
intervals

simplify421.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

420.0ms
(- (* (+ x 1) (+ x 1)) 1)

prune11.0ms

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)

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

4.0ms
(* (+ 2 x) x)

series26.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

26.0ms
(* (+ 2 x) x)

simplify249.0ms

Counts
7 → 18
Calls

7 calls. Slowest were:

213.0ms
(* (- (* 2 2) (* x x)) x)
15.0ms
(* (+ (pow 2 3) (pow x 3)) x)
6.0ms
(+ (* 2 x) (pow x 2))

prune79.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

7.4b
(/ (* (- (* 2 2) (* x x)) x) (- 2 x))
0.1b
(* (- (* 2 2) (* x x)) x)

rewrite11.0ms

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)

series75.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

47.0ms
(/ (* (- (* 2 2) (* x x)) x) (- 2 x))
29.0ms
(* (- (* 2 2) (* x x)) x)

simplify1.3s

Counts
27 → 47
Calls

27 calls. Slowest were:

188.0ms
(/ (- (* 2 2) (* x x)) (* (cbrt (- 2 x)) (cbrt (- 2 x))))
173.0ms
(* (- (* (* 2 2) (* 2 2)) (* (* x x) (* x x))) x)
170.0ms
(* (- (* (* 2 2) (* 2 2)) (* (* x x) (* x x))) x)

prune214.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

7.4b
(/ (* x (- (* 2 2) (* x x))) (- 2 x))
0.1b
(* x (- (* 2 2) (* x x)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
2 → 47
Calls

2 calls. Slowest were:

6.0ms
(/ (* x (- (* 2 2) (* x x))) (- 2 x))
3.0ms
(* x (- (* 2 2) (* x x)))

series72.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

43.0ms
(/ (* x (- (* 2 2) (* x x))) (- 2 x))
29.0ms
(* x (- (* 2 2) (* x x)))

simplify1.7s

Counts
33 → 53
Calls

33 calls. Slowest were:

683.0ms
(/ (- (* 2 2) (* x x)) (- 2 x))
158.0ms
(- (log (* x (- (* 2 2) (* x x)))) (log (- 2 x)))
134.0ms
(* x (- (* (* 2 2) (* 2 2)) (* (* x x) (* x x))))

prune236.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

7.8b
(/ (* (- (* 2 2) (* x x)) x) (- (pow 2 3) (pow x 3)))
0.1b
(* (- (* 2 2) (* x x)) x)
0.0b
(* (/ (* (- (* 2 2) (* x x)) x) (- (pow 2 3) (pow x 3))) (fma (+ 2 x) x 4))

rewrite28.0ms

Algorithm
rewrite-expression-head
Counts
3 → 80
Calls

3 calls. Slowest were:

13.0ms
(* (/ (* (- (* 2 2) (* x x)) x) (- (pow 2 3) (pow x 3))) (fma (+ 2 x) x 4))
10.0ms
(/ (* (- (* 2 2) (* x x)) x) (- (pow 2 3) (pow x 3)))
4.0ms
(* (- (* 2 2) (* x x)) x)

series140.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

83.0ms
(* (/ (* (- (* 2 2) (* x x)) x) (- (pow 2 3) (pow x 3))) (fma (+ 2 x) x 4))
29.0ms
(/ (* (- (* 2 2) (* x x)) x) (- (pow 2 3) (pow x 3)))
28.0ms
(* (- (* 2 2) (* x x)) x)

simplify4.1s

Counts
61 → 89
Calls

61 calls. Slowest were:

199.0ms
(* (- (* 2 2) (* x x)) x)
180.0ms
(+ (- (log (* (- (* 2 2) (* x x)) x)) (log (- (pow 2 3) (pow x 3)))) (log (fma (+ 2 x) x 4)))
168.0ms
(* (- (* (* 2 2) (* 2 2)) (* (* x x) (* x x))) x)

prune640.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes20.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm
intervals