Details

Time bar (total: 9.1s)

sample24.0ms

Algorithm
intervals
Results
6.0ms58×body640valid
4.0ms127×body80valid
3.0ms39×body320valid
2.0ms18×body1280valid
1.0ms14×body160valid

simplify84.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
11815
23115
34115
45215
55915
66815
78615
810715
911715
done11715

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.0b
(/ 1.0 (- x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
3.2b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity
47×times-frac
43×add-sqr-sqrt
23×add-cube-cbrt
14×distribute-lft-out--
13×distribute-lft-out
11×add-log-exp
9×associate-/r*
8×add-exp-log add-cbrt-cube difference-of-squares
6×associate-/l*
4×pow1 associate-/r/
3×flip3-- frac-add flip--
2×cbrt-undiv sub-neg associate-+l+ frac-2neg flip3-+ diff-log div-exp clear-num sum-log frac-sub flip-+ div-inv
1×+-commutative associate-+l-
Counts
4 → 114
Calls
4 calls:
5.0ms
(/ 1.0 (+ x 1.0))
5.0ms
(/ 1.0 (- x 1.0))
38.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
187.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ 1.0 (+ x 1.0))
29.0ms
(/ 1.0 (- x 1.0))
48.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
221.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.1s

Counts
126 → 126
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02131832
14991716
212881630
337771608
done50001607

prune261.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.0b
(/ (- 1.0) (- 1.0 x))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
3.2b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (- 1.0) (- 1.0 x)))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
144×*-un-lft-identity
94×times-frac
76×add-sqr-sqrt
42×add-cube-cbrt
27×distribute-lft-out--
22×distribute-rgt-neg-in
19×distribute-lft-out
18×distribute-lft-neg-in
15×difference-of-squares
13×associate-/l*
11×add-log-exp
9×associate-/r*
8×add-exp-log add-cbrt-cube
6×neg-mul-1
4×pow1 associate-/r/
3×flip3-- distribute-frac-neg frac-add flip--
2×cbrt-undiv neg-sub0 sub-neg associate-+l+ frac-2neg flip3-+ diff-log div-sub div-exp clear-num sum-log frac-sub flip-+ div-inv
1×+-commutative associate-+l- associate-+r- unsub-neg
Counts
4 → 165
Calls
4 calls:
5.0ms
(/ 1.0 (+ x 1.0))
8.0ms
(/ (- 1.0) (- 1.0 x))
39.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
206.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (- 1.0) (- 1.0 x)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ 1.0 (+ x 1.0))
28.0ms
(/ (- 1.0) (- 1.0 x))
41.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
213.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (- 1.0) (- 1.0 x)))

simplify772.0ms

Counts
177 → 177
Iterations

Useful iterations: done (767.0ms)

IterNodesCost
02782568
16532404
216602287
done50002262

prune360.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ x 1.0) x)
0.0b
(* (+ x 1.0) x)
0.0b
(* (* (+ x 1.0) x) (- 1.0 x))
16.8b
(- (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- 1.0 x)) (* (* (+ x 1.0) x) 1.0))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
48×associate-*l/
16×flip3-- frac-sub flip--
15×add-sqr-sqrt *-un-lft-identity
13×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
12×frac-times
11×associate-*r*
9×add-cube-cbrt associate-*l*
6×associate-*r/ add-log-exp
5×sub-neg pow-prod-down prod-exp cbrt-unprod
4×distribute-rgt-in distribute-lft-in associate--l+
3×*-commutative
2×distribute-lft-out unswap-sqr
1×diff-log distribute-lft-out-- difference-of-squares
Counts
4 → 106
Calls
4 calls:
18.0ms
(* (+ x 1.0) x)
10.0ms
(* (+ x 1.0) x)
20.0ms
(* (* (+ x 1.0) x) (- 1.0 x))
14.0ms
(- (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- 1.0 x)) (* (* (+ x 1.0) x) 1.0))

series198.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (+ x 1.0) x)
42.0ms
(* (+ x 1.0) x)
101.0ms
(* (* (+ x 1.0) x) (- 1.0 x))
9.0ms
(- (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- 1.0 x)) (* (* (+ x 1.0) x) 1.0))

simplify1.6s

Counts
118 → 118
Iterations

Useful iterations: 2 (528.0ms)

IterNodesCost
02152826
17672650
238592520
done50012520

prune304.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ x 1.0) x)
0.0b
(* (* (+ x 1.0) x) (- 1.0 x))
0.2b
(/ (- 2.0) (* (* (+ x 1.0) x) (- 1.0 x)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log add-cbrt-cube
18×associate-*l/
16×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
10×pow1 times-frac associate-/l*
8×frac-times associate-*r* associate-/r/
7×flip3-+ prod-exp cbrt-unprod flip-+
6×distribute-lft-neg-in flip3-- distribute-rgt-neg-in flip--
5×associate-*l*
4×associate-*r/ pow-prod-down
3×cbrt-undiv div-exp add-log-exp
2×distribute-rgt-in neg-mul-1 sub-neg distribute-lft-in *-commutative
1×neg-sub0 frac-2neg div-sub distribute-frac-neg clear-num associate-/r* div-inv distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 100
Calls
3 calls:
9.0ms
(* (+ x 1.0) x)
20.0ms
(* (* (+ x 1.0) x) (- 1.0 x))
19.0ms
(/ (- 2.0) (* (* (+ x 1.0) x) (- 1.0 x)))

series228.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(* (+ x 1.0) x)
104.0ms
(* (* (+ x 1.0) x) (- 1.0 x))
84.0ms
(/ (- 2.0) (* (* (+ x 1.0) x) (- 1.0 x)))

simplify1.1s

Counts
109 → 109
Iterations

Useful iterations: 2 (367.0ms)

IterNodesCost
01851546
15241485
223201317
done50001317

prune206.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes21.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11313
done1313

end0.0ms

sample591.0ms

Algorithm
intervals
Results
196.0ms1870×body640valid
115.0ms4077×body80valid
79.0ms989×body320valid
75.0ms567×body1280valid
32.0ms499×body160valid