Details

Time bar (total: 12.6s)

sample50.0ms

Algorithm
intervals
Results
9.0ms58×body640valid
9.0ms262×body80nan
7.0ms32×body1280valid
6.0ms140×body80valid
2.0ms20×body320valid
0.0ms6×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11111
21411
done1411

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
1.7b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
7.0ms
(sqrt (+ x 1.0))
23.0ms
(/ 1.0 (sqrt (+ x 1.0)))
17.0ms
(/ 1.0 (sqrt x))
118.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series392.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(sqrt (+ x 1.0))
90.0ms
(/ 1.0 (sqrt (+ x 1.0)))
67.0ms
(/ 1.0 (sqrt x))
193.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify876.0ms

Counts
145 → 145
Iterations

Useful iterations: done (870.0ms)

IterNodesCost
02151942
14631778
216801704
done50011700

prune763.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 19.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
1.7b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×sqrt-prod
20×*-un-lft-identity
18×add-exp-log add-cbrt-cube
9×pow1 add-cube-cbrt
7×associate-*r*
6×sqrt-div associate-*r/ associate-*l* add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp difference-of-squares unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+ distribute-lft-out distribute-lft-out--
2×flip3-- associate-/r/ flip-- associate-/l/
1×sub-neg rem-sqrt-square frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative div-inv associate-/l*
Counts
4 → 93
Calls
4 calls:
7.0ms
(sqrt (+ x 1.0))
64.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
36.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
56.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series567.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(sqrt (+ x 1.0))
344.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
93.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
95.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.5s

Counts
105 → 105
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01891624
15341471
230701232
done50011218

prune419.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 19.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite307.0ms

Algorithm
rewrite-expression-head
Rules
113×*-un-lft-identity
46×add-sqr-sqrt
39×sqrt-prod
37×times-frac distribute-lft-out
29×add-exp-log add-cbrt-cube
22×add-cube-cbrt
16×distribute-lft-out--
9×cbrt-undiv div-exp add-log-exp
8×pow1 prod-exp cbrt-unprod difference-of-squares
7×associate-*r* associate-/r* associate-/l*
6×associate-*l*
5×associate-*r/
4×sqrt-div associate-/r/ unswap-sqr
3×flip3-+ pow-prod-down flip-+ associate-/l/
2×flip3-- frac-2neg sqrt-pow1 pow1/2 diff-log clear-num flip-- div-inv
1×sub-neg sqrt-unprod div-sub associate--l+ sum-log *-commutative
Counts
4 → 143
Calls
4 calls:
121.0ms
(/ (- (+ x 1.0) x) (+ (sqrt x) (sqrt (+ x 1.0))))
88.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
43.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
48.0ms
(- (+ x 1.0) x)

series834.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ (- (+ x 1.0) x) (+ (sqrt x) (sqrt (+ x 1.0))))
609.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
73.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(- (+ x 1.0) x)

simplify495.0ms

Counts
155 → 155
Iterations

Useful iterations: done (488.0ms)

IterNodesCost
02703162
17962943
done50002554

prune481.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
31×sqrt-prod
29×add-exp-log add-cbrt-cube
27×add-sqr-sqrt
21×distribute-lft-out
19×add-cube-cbrt times-frac
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
7×associate-*r* associate-/r*
6×associate-*l* add-log-exp
5×associate-*r/
4×flip3-+ sqrt-div associate-/r/ flip-+ associate-/l* unswap-sqr
3×pow-prod-down
2×frac-2neg sqrt-pow1 pow1/2 clear-num div-inv
1×+-commutative sqrt-unprod sum-log *-commutative associate-/l/
Counts
4 → 116
Calls
4 calls:
24.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
62.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
54.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
56.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))

series882.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
159.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
63.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
589.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify2.2s

Counts
128 → 128
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02492311
17082098
245881767
done50001755

prune345.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes63.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01426
11926
done1926

end0.0ms

sample1.8s

Algorithm
intervals
Results
549.0ms4101×body80valid
375.0ms1834×body640valid
294.0ms1165×body1280valid
243.0ms8084×body80nan
60.0ms597×body320valid
21.0ms303×body160valid