Details

Time bar (total: 9.2s)

sample25.0ms

Algorithm
intervals
Results
4.0ms57×body1280valid
4.0ms239×body80nan
2.0ms38×body640valid
2.0ms128×body80valid
1.0ms21×body320valid
0.0ms12×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104
done104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.5b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite51.0ms

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))
43.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series100.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(sqrt (+ x 1.0))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify55.0ms

Counts
41 → 41
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0182265
1544243
22020233
35002230
done5002230

prune90.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

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)))

rewrite84.0ms

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))
31.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
44.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series242.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(sqrt (+ x 1.0))
68.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
144.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify38.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0341624
11239566
25001533
done5001533

prune171.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

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))))

rewrite277.0ms

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:
37.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
37.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
44.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
120.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series782.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
158.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
324.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
136.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify119.0ms

Counts
457 → 457
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
010338862
141207704
250017681
done50017681

prune590.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
5224×sqrt-prod
3310×*-un-lft-identity
3260×times-frac
1755×add-sqr-sqrt
1273×add-cube-cbrt
1164×distribute-lft-out
708×associate-*r*
105×unswap-sqr
92×sqrt-div
90×associate-/l*
78×associate-*l*
48×associate-/r/
34×add-exp-log add-cbrt-cube
33×associate-/r*
24×flip3-+ flip-+ div-inv
14×cbrt-undiv div-exp
7×sqrt-undiv
6×pow1 prod-exp cbrt-unprod
4×add-log-exp
3×frac-2neg clear-num
1×frac-times sqrt-unprod associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 1933
Calls
4 calls:
992.0ms
(* (/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
134.0ms
(/ (/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
48.0ms
(/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
52.0ms
(/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
172.0ms
(* (/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
582.0ms
(/ (/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
467.0ms
(/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
478.0ms
(/ (sqrt 1.0) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify583.0ms

Counts
1945 → 1945
Iterations

Useful iterations: 1 (56.0ms)

IterNodesCost
0323149219
1500244417
done500244417

prune2.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
095
195
done95

end0.0ms

sample690.0ms

Algorithm
intervals
Results
135.0ms1694×body1280valid
129.0ms7837×body80nan
80.0ms1228×body640valid
75.0ms4137×body80valid
31.0ms618×body320valid
10.0ms323×body160valid