Details

Time bar (total: 9.1s)

sample56.0ms

Algorithm
intervals
Results
12.0ms67×body640valid
10.0ms271×body80nan
8.0ms38×body1280valid
5.0ms125×body80valid
3.0ms19×body320valid
1.0ms7×body160valid

simplify2.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.4b

localize10.0ms

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))
2.1b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite115.0ms

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:
8.0ms
(sqrt (+ x 1.0))
16.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
80.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series401.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(sqrt (+ x 1.0))
119.0ms
(/ 1.0 (sqrt (+ x 1.0)))
58.0ms
(/ 1.0 (sqrt x))
176.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify96.0ms

Counts
145 → 145

prune509.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (sqrt x))
0.3b
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.5b
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
2.1b
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
260×times-frac
240×*-un-lft-identity
167×add-sqr-sqrt
125×add-cube-cbrt
120×sqrt-prod
70×distribute-lft-out
28×swap-sqr
22×associate-*r* associate-*l*
20×add-exp-log associate-/r* add-cbrt-cube
18×frac-sub
16×div-inv difference-of-squares
13×frac-times associate-*r/ associate-*l/
11×pow1 associate-/l/
9×unswap-sqr
7×associate-/l*
6×cbrt-undiv div-exp add-log-exp
4×prod-exp cbrt-unprod
3×associate-/r/
2×flip3-- frac-2neg clear-num flip--
1×pow2 sub-neg flip3-+ pow-plus diff-log div-sub pow-prod-down frac-add pow-sqr *-commutative pow-prod-up flip-+
Counts
4 → 267
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt x))
192.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
39.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
19.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series661.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ 1.0 (sqrt x))
501.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
41.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
71.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify85.0ms

Counts
279 → 279

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
0.3b
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.5b
(- (+ x 1.0) x)

rewrite321.0ms

Algorithm
rewrite-expression-head
Rules
303×*-un-lft-identity
296×times-frac
124×sqrt-prod
117×distribute-lft-out
108×add-sqr-sqrt
106×add-cube-cbrt
37×add-exp-log add-cbrt-cube
35×associate-/r/
34×div-inv
30×associate-*l/
27×associate-/r*
17×flip3-+ flip-+
15×cbrt-undiv div-exp
13×associate-/l*
9×prod-exp cbrt-unprod add-log-exp
4×pow1
3×frac-2neg clear-num
2×sqrt-div diff-log distribute-lft-out--
1×sub-neg flip3-- frac-add associate--l+ sum-log flip-- associate-/l/ difference-of-squares
Counts
4 → 248
Calls
4 calls:
15.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
218.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
43.0ms
(- (+ x 1.0) x)

series957.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ 1.0 (sqrt (+ x 1.0)))
64.0ms
(/ 1.0 (sqrt x))
788.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
2.0ms
(- (+ x 1.0) x)

simplify69.0ms

Counts
260 → 260

prune902.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
1.5b
(- (+ x 1.0) x)
1.5b
(- (+ x 1.0) x)

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
39×add-sqr-sqrt times-frac
35×add-cube-cbrt
28×sqrt-prod
14×add-log-exp
13×associate-/r*
8×add-exp-log add-cbrt-cube
6×distribute-lft-out associate-/l*
4×pow1 diff-log distribute-lft-out--
2×cbrt-undiv sub-neg flip3-- frac-2neg sqrt-div div-exp associate--l+ clear-num sum-log associate-/r/ flip-- div-inv difference-of-squares
1×flip3-+ flip-+
Counts
4 → 118
Calls
4 calls:
12.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
64.0ms
(- (+ x 1.0) x)
55.0ms
(- (+ x 1.0) x)

series191.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ 1.0 (sqrt (+ x 1.0)))
46.0ms
(/ 1.0 (sqrt x))
2.0ms
(- (+ x 1.0) x)
2.0ms
(- (+ x 1.0) x)

simplify75.0ms

Counts
130 → 130

prune671.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.3b

regimes50.0ms

Accuracy

98.6% (0.2b remaining)

Error of 5.5b against oracle of 5.2b and baseline of 19.6b

bsearch89.0ms

Steps
ItersRangePoint
8
32504.544960343763
384900706.45945185
138832.08552856877

simplify31.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
566.0ms1834×body640valid
543.0ms4037×body80valid
290.0ms8052×body80nan
275.0ms1121×body1280valid
161.0ms681×body320valid
27.0ms327×body160valid