Details

Time bar (total: 1.5m)

sample29.0ms

Algorithm
intervals
Results
6.0ms54×body1280valid
5.0ms253×body80nan
3.0ms143×body80valid
3.0ms34×body640valid
1.0ms14×body320valid
0.0ms11×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06162
19162
210162
done10162

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.5b
(- (sqrt (+ x 1.0)) (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:
6.0ms
(sqrt (+ x 1.0))
68.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series155.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(sqrt (+ x 1.0))
102.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.0s

Counts
41 → 41
Iterations

Useful iterations: done (2.0s)

IterNodesCost
08612737
11939896
26719452
328629252
done50009211

prune127.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite120.0ms

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:
6.0ms
(sqrt (+ x 1.0))
51.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
61.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series287.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(sqrt (+ x 1.0))
87.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
160.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.3s

Counts
80 → 80
Iterations

Useful iterations: done (1.3s)

IterNodesCost
015627666
137122028
2154821050
done500020890

prune329.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

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))))

rewrite326.0ms

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:
44.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
40.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
49.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
151.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.1s

Counts
4 → 12
Calls
4 calls:
207.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
246.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
414.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
247.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify3.7s

Counts
457 → 457
Iterations

Useful iterations: done (3.6s)

IterNodesCost
0442299517
11072249725
24125245184
done5002243664

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.4s

Algorithm
rewrite-expression-head
Rules
56169×sqrt-prod
42381×times-frac
38028×*-un-lft-identity
14256×add-sqr-sqrt add-cube-cbrt
13584×distribute-lft-out
1391×sqrt-div
1389×associate-/r/
714×div-inv
676×flip3-+ flip-+
383×associate-/r*
51×associate-/l*
15×add-cbrt-cube add-exp-log
6×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg add-log-exp
3×sqrt-undiv associate-/l/
Counts
4 → 12717
Calls
4 calls:
60.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
74.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
659.0ms
(/ (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))
145.0ms
(/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

series2.0s

Counts
4 → 12
Calls
4 calls:
543.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
499.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
218.0ms
(/ (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))
717.0ms
(/ (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

simplify18.7s

Counts
12729 → 12729
Iterations

Useful iterations: 0 (10.5s)

IterNodesCost
0626615152374
done626615152374

prune49.9s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes58.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07202
19202
done9202

end0.0ms

sample1.5s

Algorithm
intervals
Results
463.0ms7946×body80nan
307.0ms1750×body1280valid
177.0ms4066×body80valid
156.0ms1314×body640valid
86.0ms560×body320valid
18.0ms310×body160valid