Details

Time bar (total: 15.5s)

sample44.0ms

Algorithm
intervals
Results
9.0ms54×body1280valid
8.0ms251×body80nan
5.0ms135×body80valid
4.0ms37×body640valid
2.0ms21×body320valid
1.0ms9×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.3b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite93.0ms

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))
85.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series146.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(sqrt (+ x 1.0))
93.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.8s

Counts
41 → 41
Iterations

Useful iterations: done (2.8s)

IterNodesCost
084488
1183440
2432410
31028402
42702390
done5000382

prune124.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

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)))

rewrite149.0ms

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:
14.0ms
(sqrt (+ x 1.0))
56.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
75.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series353.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(sqrt (+ x 1.0))
97.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
201.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.2s

Counts
80 → 80
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01521125
13431018
2891935
32607919
done5000915

prune236.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

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))))

rewrite441.0ms

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:
54.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
54.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
47.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
227.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.2s

Counts
4 → 12
Calls
4 calls:
267.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
212.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
483.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
237.0ms
(/ (/ 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 (1.6s)

IterNodesCost
044015237
1103112250
2220811576
done500010949

prune834.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (sqrt (+ x 1.0)))
0.3b
(cbrt (sqrt (+ x 1.0)))
0.3b
(cbrt (sqrt (+ x 1.0)))
0.3b
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
69×cbrt-prod
44×add-sqr-sqrt
42×*-un-lft-identity
40×sqrt-prod
22×add-cube-cbrt
18×cbrt-div sqrt-div
14×swap-sqr
11×pow1
10×associate-*r* associate-*l*
9×flip3-+ pow1/3 flip-+ distribute-lft-out unswap-sqr
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 120
Calls
4 calls:
10.0ms
(cbrt (sqrt (+ x 1.0)))
11.0ms
(cbrt (sqrt (+ x 1.0)))
5.0ms
(cbrt (sqrt (+ x 1.0)))
91.0ms
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))

series472.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(cbrt (sqrt (+ x 1.0)))
97.0ms
(cbrt (sqrt (+ x 1.0)))
137.0ms
(cbrt (sqrt (+ x 1.0)))
126.0ms
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))

simplify2.1s

Counts
132 → 132
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01722150
13561967
29101880
322981693
done50001557

prune435.0ms

Pruning

8 alts after pruning (5 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
732.0ms8028×body80nan
325.0ms1737×body1280valid
231.0ms4108×body80valid
210.0ms1307×body640valid
47.0ms574×body320valid
16.0ms274×body160valid