Details

Time bar (total: 17.5s)

sample84.0ms

Algorithm
intervals
Results
22.0ms126×body80valid
14.0ms59×body1280valid
13.0ms260×body80nan
8.0ms44×body640valid
3.0ms19×body320valid
1.0ms8×body160valid

simplify7.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ 1.0 x))
1.6b
(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity sqrt-prod
4×add-log-exp difference-of-squares
3×pow1 add-cube-cbrt distribute-lft-out--
2×add-cbrt-cube sqrt-div add-exp-log distribute-lft-out
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Counts
2 → 35
Calls
2 calls:
10.0ms
(sqrt (+ 1.0 x))
63.0ms
(- (sqrt (+ 1.0 x)) (sqrt x))

series151.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(sqrt (+ 1.0 x))
107.0ms
(- (sqrt (+ 1.0 x)) (sqrt x))

simplify1.6s

Counts
41 → 41
Iterations
IterNodes
done5000
32897
2676
1193
086

prune148.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (sqrt (+ 1.0 x)) (sqrt x))
0.0b
(sqrt (+ 1.0 x))
0.1b
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
24×sqrt-prod
21×distribute-lft-out
18×times-frac
16×add-sqr-sqrt
15×add-cube-cbrt
6×associate-/r*
5×add-cbrt-cube add-exp-log add-log-exp
4×pow1
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
3 → 71
Calls
3 calls:
51.0ms
(+ (sqrt (+ 1.0 x)) (sqrt x))
12.0ms
(sqrt (+ 1.0 x))
48.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

series428.0ms

Counts
3 → 9
Calls
3 calls:
118.0ms
(+ (sqrt (+ 1.0 x)) (sqrt x))
53.0ms
(sqrt (+ 1.0 x))
255.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify826.0ms

Counts
80 → 80
Iterations
IterNodes
done5000
21550
1371
0156

prune351.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite316.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
700×sqrt-prod
594×times-frac
280×distribute-lft-out
254×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
14×flip3-+ flip-+
12×div-inv
11×add-cbrt-cube add-exp-log
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Counts
4 → 445
Calls
4 calls:
43.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
29.0ms
(sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))
43.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
166.0ms
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

series1.4s

Counts
4 → 12
Calls
4 calls:
236.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
233.0ms
(sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))
456.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
520.0ms
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

simplify683.0ms

Counts
457 → 457
Iterations
IterNodes
done5000
11157
0474

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite604.0ms

Algorithm
rewrite-expression-head
Rules
2118×times-frac
2108×sqrt-prod
1299×*-un-lft-identity
782×add-sqr-sqrt
767×add-cube-cbrt
304×distribute-lft-out
92×div-inv
84×associate-/l*
68×sqrt-div
29×add-cbrt-cube add-exp-log
25×associate-/r/
22×associate-/r*
19×flip3-+ flip-+
16×pow1
14×cbrt-undiv div-exp
12×sqrt-pow1 associate-*r*
9×associate-*l*
8×pow1/2
6×pow-prod-up unswap-sqr
4×frac-times sqrt-undiv add-log-exp
3×pow-prod-down prod-exp cbrt-unprod
2×clear-num frac-2neg sqrt-unprod pow3 associate-*l/ associate-*r/
1×rem-sqrt-square *-commutative associate-/l/
Counts
4 → 1073
Calls
4 calls:
27.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
179.0ms
(* (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) (sqrt (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))
198.0ms
(/ (/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))) (/ (* (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) (sqrt (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt 1.0)))
72.0ms
(/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
201.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
551.0ms
(* (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) (sqrt (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))
243.0ms
(/ (/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))) (/ (* (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) (sqrt (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt 1.0)))
608.0ms
(/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))))

simplify1.9s

Counts
1085 → 1085
Iterations
IterNodes
done5000
13444
01059

prune3.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes59.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done9
19
07

end0.0ms

sample2.0s

Algorithm
intervals
Results
738.0ms8020×body80nan
395.0ms1724×body1280valid
263.0ms1214×body640valid
181.0ms4115×body80valid
68.0ms622×body320valid
24.0ms325×body160valid