Details

Time bar (total: 19.9s)

sample43.0ms

Algorithm
intervals
Results
7.0ms62×body640valid
7.0ms238×body80nan
6.0ms39×body1280valid
4.0ms123×body80valid
2.0ms25×body320valid
0.0ms7×body160valid

simplify11.0ms

Counts
1 → 1
Iterations
IterNodes
done14
214
111
08

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.7b

localize51.0ms

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))))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
875×*-un-lft-identity
742×add-sqr-sqrt
712×add-cube-cbrt
594×prod-diff
562×sqrt-prod
73×distribute-lft-out
54×div-inv
46×sqrt-div associate-/r/
23×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
7×add-cbrt-cube add-exp-log
6×associate-/l*
5×add-log-exp
3×expm1-log1p-u pow1 log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg div-exp
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
3 → 739
Calls
3 calls:
10.0ms
(/ 1.0 (sqrt (+ x 1.0)))
5.0ms
(/ 1.0 (sqrt x))
99.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series362.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(/ 1.0 (sqrt (+ x 1.0)))
70.0ms
(/ 1.0 (sqrt x))
175.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.7s

Counts
748 → 748
Iterations
IterNodes
done5000
24868
11566
0692

prune4.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 21.1b

localize57.0ms

Local error

Found 4 expressions with local error:

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)))))
0.3b
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
0.6b
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
2.6b
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite331.0ms

Algorithm
rewrite-expression-head
Rules
362×times-frac
331×*-un-lft-identity
258×add-sqr-sqrt
180×sqrt-prod
174×add-cube-cbrt
88×distribute-lft-out
67×swap-sqr
49×associate-*r* associate-*l*
30×add-cbrt-cube add-exp-log
19×div-inv
18×pow1 frac-sub unswap-sqr
16×difference-of-squares
14×frac-times associate-/r* associate-*l/ associate-*r/
11×associate-/r/ associate-/l/
9×cbrt-undiv div-exp
8×sqrt-div prod-exp cbrt-unprod
6×add-log-exp
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u associate-/l*
2×pow2 pow-plus flip3-- pow-prod-down pow-sqr *-commutative pow-prod-up flip--
1×clear-num sub-neg frac-2neg fma-neg diff-log div-sub prod-diff frac-add
Counts
4 → 364
Calls
4 calls:
167.0ms
(/ (- (* (/ 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)))))
82.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
30.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
21.0ms
(- (* (/ 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:
492.0ms
(/ (- (* (/ 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)))))
52.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
39.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
79.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify1.9s

Counts
376 → 376
Iterations
IterNodes
done5001
11815
0530

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 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)))))
2.2b
(- (+ x 1.0) x)

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
319×*-un-lft-identity
296×times-frac
124×sqrt-prod
121×distribute-lft-out
116×add-sqr-sqrt
114×add-cube-cbrt
37×add-cbrt-cube add-exp-log
35×associate-/r/
34×div-inv
30×associate-*l/
27×associate-/r*
17×flip3-+ flip-+
15×cbrt-undiv div-exp
13×associate-/l*
12×prod-diff
9×prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u pow1 fma-neg log1p-expm1-u
3×clear-num frac-2neg
2×sqrt-div diff-log distribute-lft-out--
1×sum-log sub-neg flip3-- frac-add associate--l+ flip-- difference-of-squares associate-/l/
Counts
4 → 272
Calls
4 calls:
14.0ms
(/ 1.0 (sqrt (+ x 1.0)))
9.0ms
(/ 1.0 (sqrt x))
161.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
57.0ms
(- (+ x 1.0) x)

series701.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ 1.0 (sqrt (+ x 1.0)))
46.0ms
(/ 1.0 (sqrt x))
573.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.0ms
(- (+ x 1.0) x)

simplify1.3s

Counts
284 → 284
Iterations
IterNodes
done5001
11425
0495

prune944.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
0.8b
(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
7.2b
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
298×*-un-lft-identity
297×times-frac
124×sqrt-prod
116×distribute-lft-out
106×add-sqr-sqrt add-cube-cbrt
58×add-cbrt-cube add-exp-log
37×associate-/r/
35×div-inv
32×associate-*l/
28×associate-/r*
21×cbrt-undiv div-exp
18×flip3-+ prod-exp cbrt-unprod flip-+
14×associate-/l*
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
2×sqrt-div
1×frac-add associate-/l/
Counts
4 → 266
Calls
4 calls:
10.0ms
(/ 1.0 (sqrt (+ x 1.0)))
5.0ms
(/ 1.0 (sqrt x))
23.0ms
(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
121.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

series663.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ 1.0 (sqrt (+ x 1.0)))
45.0ms
(/ 1.0 (sqrt x))
38.0ms
(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
506.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

simplify1.1s

Counts
278 → 278
Iterations
IterNodes
done5002
11337
0461

prune834.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done16
116
013

end0.0ms

sample1.7s

Algorithm
intervals
Results
600.0ms1863×body640valid
303.0ms8087×body80nan
266.0ms1200×body1280valid
197.0ms4023×body80valid
60.0ms614×body320valid
40.0ms300×body160valid