Details

Time bar (total: 17.2s)

sample53.0ms

Algorithm
intervals
Results
10.0ms245×body80nan
7.0ms38×body1280valid
7.0ms151×body80valid
6.0ms39×body640valid
2.0ms17×body320valid
1.0ms11×body160valid

simplify7.0ms

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: 25.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite63.0ms

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:
13.0ms
(sqrt (+ x 1.0))
48.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series125.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(sqrt (+ x 1.0))
86.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify3.3s

Counts
41 → 41
Iterations

Useful iterations: done (3.3s)

IterNodesCost
084488
1183440
2432410
31028402
42702390
done5000382

prune134.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

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)))

rewrite143.0ms

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:
18.0ms
(sqrt (+ x 1.0))
37.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
83.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series303.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(sqrt (+ x 1.0))
73.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
188.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.3s

Counts
80 → 80
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01521125
13431018
2891935
32607919
done5000915

prune268.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite572.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
274×sqrt-prod
157×times-frac
119×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
41×swap-sqr
27×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 250
Calls
4 calls:
75.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
70.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
58.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
335.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
604.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
229.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
200.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
273.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.6s

Counts
262 → 262
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03116170
16414386
220044124
done50014023

prune810.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

rewrite331.0ms

Algorithm
rewrite-expression-head
Rules
190×*-un-lft-identity sqrt-prod
110×times-frac
81×add-sqr-sqrt
71×add-cube-cbrt
68×distribute-lft-out
27×associate-*l*
15×associate-/r*
10×add-exp-log add-cbrt-cube
9×associate-/l*
8×associate-/r/
7×pow1
4×flip3-+ sqrt-div flip-+ div-inv add-log-exp
3×associate-*r* unswap-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×sqrt-undiv sqrt-pow1 pow1/2 pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 206
Calls
4 calls:
59.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
66.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
60.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
129.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
559.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
427.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
206.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
458.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

simplify1.5s

Counts
218 → 218
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03525050
17684599
221424399
done50003977

prune791.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes102.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

end0.0ms

sample1.8s

Algorithm
intervals
Results
716.0ms7863×body80nan
370.0ms1691×body1280valid
160.0ms4098×body80valid
141.0ms1245×body640valid
48.0ms611×body320valid
19.0ms355×body160valid