Average Error: 39.3 → 0.0
Time: 8.4s
Precision: 64
Internal Precision: 128
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot \left(2 + x\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.3

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

  2. Initial simplification0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2018360 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))

Details

Time bar (total: 6.8s)Debug log

start99.0ms

Algorithm
intervals

setup631.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ x 2) x)

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

4.0ms
(* (+ x 2) x)

series25.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

25.0ms
(* (+ x 2) x)

simplify128.0ms

Counts
7 → 16
Calls

7 calls. Slowest were:

96.0ms
(* (- (* x x) (* 2 2)) x)
12.0ms
(* (+ (pow x 3) (pow 2 3)) x)
5.0ms
(+ (* 2 x) (pow x 2))

prune94.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* (+ x 2) x))
0.6b
(cbrt (* (+ x 2) x))
0.6b
(cbrt (* (+ x 2) x))
0.5b
(* (cbrt (* (+ x 2) x)) (cbrt (* (+ x 2) x)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

8.0ms
(* (cbrt (* (+ x 2) x)) (cbrt (* (+ x 2) x)))
1.0ms
(cbrt (* (+ x 2) x))
1.0ms
(cbrt (* (+ x 2) x))

series175.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

48.0ms
(* (cbrt (* (+ x 2) x)) (cbrt (* (+ x 2) x)))
46.0ms
(cbrt (* (+ x 2) x))
41.0ms
(cbrt (* (+ x 2) x))
41.0ms
(cbrt (* (+ x 2) x))

simplify2.8s

Counts
49 → 77
Calls

49 calls. Slowest were:

241.0ms
(- (+ (* 1/6 (* x (exp (* 1/3 (+ (log 2) (log x)))))) (exp (* 1/3 (+ (log 2) (log x))))) (* 1/36 (* (pow x 2) (exp (* 1/3 (+ (log 2) (log x)))))))
238.0ms
(- (+ (* 1/6 (* x (exp (* 1/3 (+ (log 2) (log x)))))) (exp (* 1/3 (+ (log 2) (log x))))) (* 1/36 (* (pow x 2) (exp (* 1/3 (+ (log 2) (log x)))))))
235.0ms
(- (+ (* 1/6 (* x (exp (* 1/3 (+ (log 2) (log x)))))) (exp (* 1/3 (+ (log 2) (log x))))) (* 1/36 (* (pow x 2) (exp (* 1/3 (+ (log 2) (log x)))))))

prune497.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

5.8b
(/ (+ (pow x 3) (* -4 x)) (- x 2))
0.0b
(+ (pow x 3) (* -4 x))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
2 → 47
Calls

2 calls. Slowest were:

10.0ms
(/ (+ (pow x 3) (* -4 x)) (- x 2))
3.0ms
(+ (pow x 3) (* -4 x))

series78.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

47.0ms
(/ (+ (pow x 3) (* -4 x)) (- x 2))
31.0ms
(+ (pow x 3) (* -4 x))

simplify617.0ms

Counts
43 → 53
Calls

43 calls. Slowest were:

131.0ms
(- (* (pow x 3) (pow x 3)) (* (* -4 x) (* -4 x)))
77.0ms
(/ (* (* (+ (pow x 3) (* -4 x)) (+ (pow x 3) (* -4 x))) (+ (pow x 3) (* -4 x))) (* (* (- x 2) (- x 2)) (- x 2)))
69.0ms
(+ (pow (pow x 3) 3) (pow (* -4 x) 3))

prune365.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
2 → 58
Calls

2 calls. Slowest were:

4.0ms
(/ (- x 2) (+ (* x x) -4))
1.0ms
(/ x (/ (- x 2) (+ (* x x) -4)))

series51.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

39.0ms
(/ x (/ (- x 2) (+ (* x x) -4)))
12.0ms
(/ (- x 2) (+ (* x x) -4))

simplify686.0ms

Counts
52 → 64
Calls

52 calls. Slowest were:

173.0ms
(/ (* (* (- x 2) (- x 2)) (- x 2)) (* (* (+ (* x x) -4) (+ (* x x) -4)) (+ (* x x) -4)))
60.0ms
(+ (* (* x x) (* x x)) (- (* -4 -4) (* (* x x) -4)))
60.0ms
(- (+ (* 4 (/ 1 (pow x 3))) (/ 1 x)) (* 2 (/ 1 (pow x 2))))

prune389.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes23.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms