Details

Time bar (total: 7.8s)

sample16.0ms

Algorithm
intervals
Results
4.0ms57×body640valid
3.0ms58×body320valid
2.0ms128×body80valid
1.0ms13×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
069
199
2129
done129

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize5.0ms

Local error

Found 1 expressions with local error:

3.4b
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
17×add-sqr-sqrt
16×times-frac
8×distribute-lft-out--
5×add-cube-cbrt
4×difference-of-squares
3×distribute-lft-out add-log-exp
2×div-inv
1×pow1 add-exp-log sub-neg flip3-- diff-log frac-sub add-cbrt-cube flip--
Counts
1 → 25
Calls
1 calls:
43.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

series57.0ms

Counts
1 → 3
Calls
1 calls:
57.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

simplify2.4s

Counts
28 → 28
Iterations

Useful iterations: 4 (1.4s)

IterNodesCost
074436
1172425
2391397
31076395
44187391
done5000391

prune56.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ x 1.0) x)
0.1b
(/ (- 0 (* 1.0 1.0)) (* (+ x 1.0) x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×*-un-lft-identity
6×add-cube-cbrt
4×pow1 times-frac associate-*l* associate-*l/ associate-/l*
3×associate-*r*
2×cbrt-undiv flip3-+ div-exp prod-exp associate-/r/ cbrt-unprod flip-+ associate-/l/ add-log-exp difference-of-squares
1×flip3-- frac-2neg sub0-neg div-sub distribute-frac-neg pow-prod-down clear-num associate-/r* *-commutative flip-- div-inv distribute-lft-out unswap-sqr
Counts
2 → 50
Calls
2 calls:
13.0ms
(* (+ x 1.0) x)
10.0ms
(/ (- 0 (* 1.0 1.0)) (* (+ x 1.0) x))

series85.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(* (+ x 1.0) x)
38.0ms
(/ (- 0 (* 1.0 1.0)) (* (+ x 1.0) x))

simplify1.5s

Counts
56 → 56
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0108700
1291633
2989535
done5002531

prune100.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.1b
(/ (/ (- (* 1.0 1.0)) (+ 1.0 x)) x)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
124×*-un-lft-identity
76×add-sqr-sqrt add-cube-cbrt
30×associate-/l*
24×distribute-lft-out
16×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in
8×associate-/r/
6×add-exp-log add-cbrt-cube
5×div-inv
4×flip3-+ flip-+
3×cbrt-undiv div-exp associate-/r*
2×div-sub distribute-frac-neg
1×pow1 neg-sub0 frac-2neg clear-num associate-/l/ add-log-exp
Counts
1 → 140
Calls
1 calls:
17.0ms
(/ (/ (- (* 1.0 1.0)) (+ 1.0 x)) x)

series37.0ms

Counts
1 → 3
Calls
1 calls:
37.0ms
(/ (/ (- (* 1.0 1.0)) (+ 1.0 x)) x)

simplify1.4s

Counts
143 → 143
Iterations

Useful iterations: 2 (528.0ms)

IterNodesCost
02732672
16542511
221612443
done50012443

prune257.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(* (sqrt (+ x 1.0)) x)
0.0b
(/ (- 0 (* 1.0 1.0)) (* (sqrt (+ x 1.0)) (* (sqrt (+ x 1.0)) x)))
0.0b
(* (sqrt (+ x 1.0)) (* (sqrt (+ x 1.0)) x))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
28×sqrt-div
20×add-exp-log add-cbrt-cube
19×add-sqr-sqrt
18×*-un-lft-identity associate-*l/
14×flip3-+ associate-*l* flip-+
13×sqrt-prod
12×pow1 add-cube-cbrt
8×frac-times associate-/r/
7×prod-exp cbrt-unprod
4×times-frac associate-*r/ associate-*r* pow-prod-down associate-/l* add-log-exp
3×cbrt-undiv div-exp distribute-lft-out
2×*-commutative associate-/l/ difference-of-squares unswap-sqr
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 sub0-neg pow1/2 div-sub distribute-frac-neg clear-num associate-/r* flip-- div-inv
Counts
4 → 108
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
12.0ms
(* (sqrt (+ x 1.0)) x)
24.0ms
(/ (- 0 (* 1.0 1.0)) (* (sqrt (+ x 1.0)) (* (sqrt (+ x 1.0)) x)))
27.0ms
(* (sqrt (+ x 1.0)) (* (sqrt (+ x 1.0)) x))

series184.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1.0))
69.0ms
(* (sqrt (+ x 1.0)) x)
38.0ms
(/ (- 0 (* 1.0 1.0)) (* (sqrt (+ x 1.0)) (* (sqrt (+ x 1.0)) x)))
42.0ms
(* (sqrt (+ x 1.0)) (* (sqrt (+ x 1.0)) x))

simplify914.0ms

Counts
120 → 120
Iterations

Useful iterations: done (911.0ms)

IterNodesCost
01921958
15221486
218001270
done50011266

prune233.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes16.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
11310
21510
done1510

end0.0ms

sample396.0ms

Algorithm
intervals
Results
137.0ms1900×body640valid
85.0ms4191×body80valid
66.0ms1283×body320valid
22.0ms626×body160valid