Details

Time bar (total: 31.3s)

sample48.0ms

Algorithm
intervals
Results
9.0ms275×body80nan
9.0ms56×body1280valid
5.0ms40×body640valid
5.0ms136×body80valid
2.0ms17×body320valid
0.0ms7×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.3b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite96.0ms

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:
8.0ms
(sqrt (+ x 1.0))
87.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series132.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(sqrt (+ x 1.0))
100.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.4s

Counts
41 → 41
Iterations

Useful iterations: done (1.4s)

IterNodesCost
084488
1188440
2638410
32563402
done5000400

prune128.0ms

Pruning

3 alts after pruning (3 fresh and 0 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)))

rewrite97.0ms

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))
32.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
55.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series318.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(sqrt (+ x 1.0))
91.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
188.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify745.0ms

Counts
80 → 80
Iterations

Useful iterations: done (742.0ms)

IterNodesCost
01521125
13611018
21505937
done5001929

prune232.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

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)))
0.1b
(/ 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))))

rewrite387.0ms

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:
63.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
50.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
52.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
176.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.0s

Counts
4 → 12
Calls
4 calls:
221.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
214.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
401.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
174.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.7s

Counts
457 → 457
Iterations

Useful iterations: done (1.7s)

IterNodesCost
044015237
1106612250
2406311774
done500211088

prune797.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
21584×sqrt-prod
15024×*-un-lft-identity
14958×times-frac
5512×distribute-lft-out
5380×add-sqr-sqrt
5378×add-cube-cbrt
586×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
6×pow1
4×sqrt-pow1 add-log-exp
3×frac-2neg clear-num
2×rem-sqrt-square pow1/2 associate-/l/
Counts
4 → 5792
Calls
4 calls:
53.0ms
(sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
55.0ms
(/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
450.0ms
(/ (/ (/ 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))))
208.0ms
(/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series2.3s

Counts
4 → 12
Calls
4 calls:
423.0ms
(sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
659.0ms
(/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
163.0ms
(/ (/ (/ 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))))
1.0s
(/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify2.8s

Counts
5804 → 5804
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02648333199
done5000305965

prune14.8s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes45.0ms

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 (0.0ms)

IterNodesCost
079
199
done99

end0.0ms

sample1.9s

Algorithm
intervals
Results
604.0ms1234×body640valid
342.0ms1741×body1280valid
286.0ms8189×body80nan
251.0ms4120×body80valid
60.0ms602×body320valid
19.0ms303×body160valid