Details

Time bar (total: 12.0s)

sample39.0ms

Algorithm
intervals
Results
8.0ms62×body640valid
6.0ms238×body80nan
6.0ms39×body1280valid
4.0ms123×body80valid
2.0ms25×body320valid
0.0ms7×body160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done14
214
111
08

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.7b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
2.7b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
70×add-sqr-sqrt
69×times-frac
46×sqrt-prod
40×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
7×add-cbrt-cube add-exp-log distribute-lft-out
6×associate-/l*
5×add-log-exp
4×div-inv
3×pow1
2×cbrt-undiv clear-num frac-2neg sqrt-div div-exp associate-/r/
1×sub-neg flip3-+ flip3-- diff-log frac-sub flip-+ flip--
Counts
3 → 117
Calls
3 calls:
17.0ms
(/ 1.0 (sqrt (+ x 1.0)))
9.0ms
(/ 1.0 (sqrt x))
76.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series324.0ms

Counts
3 → 9
Calls
3 calls:
94.0ms
(/ 1.0 (sqrt (+ x 1.0)))
52.0ms
(/ 1.0 (sqrt x))
178.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.7s

Counts
126 → 126
Iterations
IterNodes
done5003
33146
21066
1427
0202

prune520.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.1b

localize28.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
2.7b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
11×*-un-lft-identity sqrt-prod
10×add-cbrt-cube add-exp-log
9×add-cube-cbrt
7×pow1 associate-*r*
6×associate-*l*
5×add-log-exp
4×sqrt-div associate-*r/ unswap-sqr
3×times-frac pow-prod-down associate-/l*
2×cbrt-undiv sqrt-pow1 flip3-+ flip3-- pow1/2 div-exp prod-exp associate-/r/ cbrt-unprod flip-+ flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv distribute-lft-out
Counts
3 → 71
Calls
3 calls:
36.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
20.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
24.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series505.0ms

Counts
3 → 9
Calls
3 calls:
324.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
68.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
113.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.7s

Counts
80 → 80
Iterations
IterNodes
done5001
21891
1512
0178

prune346.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
0.5b
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
2.2b
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
86×pow1
37×pow-prod-down
30×add-cbrt-cube add-exp-log
17×prod-exp cbrt-unprod
16×add-sqr-sqrt associate-*r/
14×sqrt-div
11×sqrt-prod
10×*-un-lft-identity
9×associate-*r*
8×associate-*l* pow-sqr pow-prod-up add-cube-cbrt
7×flip3-+ flip-+
6×add-log-exp
4×frac-times pow-plus unswap-sqr
3×*-commutative
2×pow2 sqrt-pow1 pow1/2 swap-sqr associate-*l/
1×sub-neg flip3-- sqrt-unprod diff-log flip-- distribute-lft-out difference-of-squares
Counts
4 → 122
Calls
4 calls:
53.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
20.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
30.0ms
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
67.0ms
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

series149.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
59.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
29.0ms
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
19.0ms
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

simplify1.1s

Counts
134 → 134
Iterations
IterNodes
done5001
21411
1458
0172

prune465.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
0.1b
(/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
0.2b
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
38×add-sqr-sqrt
32×*-un-lft-identity
30×add-cube-cbrt
20×add-cbrt-cube add-exp-log
18×associate-/l*
11×sqrt-prod
8×pow1 associate-/r/
7×cbrt-undiv div-exp associate-*r*
6×flip3-+ associate-*l* flip-+ add-log-exp
4×associate-/r* sqrt-div associate-*r/ div-inv unswap-sqr
3×pow-prod-down prod-exp cbrt-unprod
2×clear-num frac-2neg sqrt-pow1 pow1/2
1×+-commutative sum-log sqrt-unprod *-commutative distribute-lft-out associate-/l/
Counts
4 → 125
Calls
4 calls:
12.0ms
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
17.0ms
(/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
46.0ms
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
23.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series954.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
196.0ms
(/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
589.0ms
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.4s

Counts
137 → 137
Iterations
IterNodes
done5004
22692
1770
0280

prune550.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes82.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done20
120
013

end0.0ms

sample1.6s

Algorithm
intervals
Results
571.0ms1200×body1280valid
288.0ms1863×body640valid
269.0ms8087×body80nan
160.0ms4023×body80valid
91.0ms614×body320valid
20.0ms300×body160valid