Details

Time bar (total: 17.0s)

sample26.0ms

Algorithm
intervals
Results
5.0ms267×body80nan
4.0ms55×body1280valid
3.0ms55×body640valid
2.0ms118×body80valid
1.0ms18×body320valid
0.0ms10×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104
done104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.4b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite49.0ms

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-exp-log sqrt-div add-cbrt-cube distribute-lft-out
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+
Counts
2 → 35
Calls
2 calls:
7.0ms
(sqrt (+ x 1.0))
41.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series99.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(sqrt (+ x 1.0))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify55.0ms

Counts
41 → 41
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0182265
1544243
22020233
35002230
done5002230

prune81.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite85.0ms

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-exp-log add-cbrt-cube add-log-exp
4×pow1
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 71
Calls
3 calls:
7.0ms
(sqrt (+ x 1.0))
31.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
45.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series230.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(sqrt (+ x 1.0))
67.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
134.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify43.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0341624
11239566
25001533
done5001533

prune160.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite275.0ms

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-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 445
Calls
4 calls:
38.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
39.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
43.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
119.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series783.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
152.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
325.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
146.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify127.0ms

Counts
457 → 457
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
010338862
141207704
250017681
done50017681

prune569.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
21574×sqrt-prod
15023×*-un-lft-identity
14958×times-frac
5512×distribute-lft-out
5378×add-sqr-sqrt
5377×add-cube-cbrt
584×sqrt-div
555×associate-/l*
292×associate-/r/
147×flip3-+ flip-+
146×div-inv
33×associate-/r*
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
5×pow1
4×add-log-exp
3×frac-2neg clear-num
2×associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 5786
Calls
4 calls:
38.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
46.0ms
(/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
129.0ms
(/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
367.0ms
(/ (/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.0s

Counts
4 → 12
Calls
4 calls:
148.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
415.0ms
(/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
304.0ms
(/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
137.0ms
(/ (/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.5s

Counts
5798 → 5798
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
05001219969
done5001219969

prune9.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
095
195
done95

end0.0ms

sample690.0ms

Algorithm
intervals
Results
141.0ms1783×body1280valid
135.0ms8113×body80nan
75.0ms1231×body640valid
72.0ms4030×body80valid
29.0ms629×body320valid
10.0ms327×body160valid