Details

Time bar (total: 17.5s)

sample126.0ms

Algorithm
intervals
Results
76.0ms82×body1280valid
17.0ms136×body80valid
11.0ms20×body640valid
5.0ms12×body320valid
1.0ms6×body160valid

simplify16.0ms

Counts
1 → 1
Iterations
IterNodes
323
223
119
09

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1/2 (hypot 1 x))
0.0b
(hypot 1 x)
2.1b
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×*-un-lft-identity
11×add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log add-log-exp
4×sqrt-prod difference-of-squares
3×pow1 associate-/r* associate-/l* distribute-lft-out--
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-- diff-log div-exp div-inv flip-- distribute-lft-out
Counts
3 → 53
Calls
3 calls:
3.0ms
(/ 1/2 (hypot 1 x))
0.0ms
(hypot 1 x)
32.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series74.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(/ 1/2 (hypot 1 x))
1.0ms
(hypot 1 x)
66.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify2.4s

Counts
62 → 62
Iterations
IterNodes
42688
3874
2333
1160
087

prune548.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1 x)
0.0b
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.0b
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
1.6b
(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt *-un-lft-identity
44×times-frac
32×distribute-lft-out
18×add-cube-cbrt
16×sqrt-prod difference-of-squares
8×distribute-lft-out-- add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×pow1
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
4 → 101
Calls
4 calls:
0.0ms
(hypot 1 x)
12.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
43.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
12.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(hypot 1 x)
66.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
118.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
56.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify1.4s

Counts
113 → 113
Iterations
IterNodes
32739
2926
1330
0138

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1 x)
0.0b
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.0b
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
1.6b
(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt *-un-lft-identity
44×times-frac
32×distribute-lft-out
18×add-cube-cbrt
16×sqrt-prod difference-of-squares
8×distribute-lft-out-- add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×pow1
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
4 → 101
Calls
4 calls:
0.0ms
(hypot 1 x)
15.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
49.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
11.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(hypot 1 x)
69.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
133.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
36.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify1.3s

Counts
113 → 113
Iterations
IterNodes
32739
2926
1330
0138

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 15.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
0.5b
(cbrt (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
0.5b
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (* (cbrt (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))) (cbrt (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))))
1.6b
(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×*-un-lft-identity
16×cbrt-div
12×cbrt-prod
9×times-frac add-exp-log
8×flip3-+ associate-/r/ add-cube-cbrt flip-+ distribute-lft-out
7×add-cbrt-cube
6×associate-/l* add-log-exp difference-of-squares
4×frac-times pow1 sqrt-prod
3×distribute-lft-out--
2×cbrt-undiv flip3-- pow1/3 div-exp associate-*l/ associate-*r/ flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub prod-exp cbrt-unprod div-inv
Counts
4 → 85
Calls
4 calls:
11.0ms
(cbrt (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
11.0ms
(cbrt (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
56.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (* (cbrt (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))) (cbrt (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))))
5.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series807.0ms

Counts
4 → 12
Calls
4 calls:
237.0ms
(cbrt (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
214.0ms
(cbrt (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
310.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (* (cbrt (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))) (cbrt (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))))
46.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify3.4s

Counts
97 → 97
Iterations
IterNodes
34409
21103
1331
0135

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 15.0b

regimes77.0ms

Accuracy

0% (0.0b remaining)

Error of 14.8b against oracle of 14.8b and baseline of 14.8b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
212
112
010

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.8s2773×body1280valid
676.0ms637×body640valid
505.0ms4152×body80valid
87.0ms288×body320valid
29.0ms150×body160valid