Details

Time bar (total: 16.3s)

sample60.0ms

Algorithm
intervals
Results
11.0ms245×body80nan
8.0ms38×body1280valid
8.0ms151×body80valid
7.0ms39×body640valid
2.0ms17×body320valid
1.0ms11×body160valid

simplify8.0ms

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

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite101.0ms

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:
12.0ms
(sqrt (+ x 1.0))
87.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series127.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(sqrt (+ x 1.0))
97.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.7s

Counts
41 → 41
Iterations

Useful iterations: done (2.7s)

IterNodesCost
084488
1183440
2432410
31028402
42702390
done5000382

prune97.0ms

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)))

rewrite132.0ms

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))
50.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
63.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series315.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(sqrt (+ x 1.0))
87.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
195.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.0s

Counts
80 → 80
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01521125
13431018
2891935
32607919
done5000915

prune285.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

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)))))

rewrite559.0ms

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:
74.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
81.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
67.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
313.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
500.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
232.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
187.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
187.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.7s

Counts
262 → 262
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03116170
16414386
220044124
done50014023

prune827.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

localize16.0ms

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)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite667.0ms

Algorithm
rewrite-expression-head
Rules
298×sqrt-prod
262×*-un-lft-identity
181×times-frac
154×add-sqr-sqrt
101×add-cube-cbrt
92×distribute-lft-out
60×associate-*r*
27×associate-*l*
15×associate-/r* unswap-sqr
13×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/l*
7×pow1 sqrt-div
5×flip3-+ flip-+ div-inv
4×add-log-exp
3×cbrt-undiv sqrt-undiv div-exp
2×rem-sqrt-square frac-2neg prod-exp clear-num cbrt-unprod
1×frac-times sqrt-pow1 pow1/2 sqrt-unprod associate-*r/ swap-sqr pow-prod-down associate-*l/ rem-square-sqrt *-commutative
Counts
4 → 282
Calls
4 calls:
64.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
74.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
90.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
400.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
457.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
476.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
248.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
199.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.6s

Counts
294 → 294
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03716832
18356014
224465810
done50005746

prune736.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

end0.0ms

sample1.8s

Algorithm
intervals
Results
540.0ms4098×body80valid
318.0ms7863×body80nan
295.0ms1245×body640valid
241.0ms1691×body1280valid
52.0ms611×body320valid
20.0ms355×body160valid