Details

Time bar (total: 7.7s)

sample18.0ms

Algorithm
intervals
Results
7.0ms330×body80valid

simplify23.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.1b

localize5.0ms

Local error

Found 1 expressions with local error:

6.7b
(* x (+ 1.0 (* y y)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
3×pow1 add-exp-log add-cube-cbrt *-un-lft-identity associate-*r* associate-*l* add-cbrt-cube
2×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ add-log-exp unswap-sqr
Counts
1 → 22
Calls
1 calls:
19.0ms
(* x (+ 1.0 (* y y)))

series79.0ms

Counts
1 → 3
Calls
1 calls:
79.0ms
(* x (+ 1.0 (* y y)))

simplify1.1s

Counts
25 → 25

prune51.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (sqrt (+ 1.0 (* y y))))
0.1b
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
6.6b
(sqrt (+ 1.0 (* y y)))
6.6b
(sqrt (+ 1.0 (* y y)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-div
17×add-sqr-sqrt
13×pow1 sqrt-prod
12×associate-*r*
11×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
10×associate-*r/
9×flip3-+ flip-+
4×frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative unswap-sqr
Counts
4 → 83
Calls
4 calls:
28.0ms
(* x (sqrt (+ 1.0 (* y y))))
51.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
7.0ms
(sqrt (+ 1.0 (* y y)))
5.0ms
(sqrt (+ 1.0 (* y y)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(* x (sqrt (+ 1.0 (* y y))))
65.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
52.0ms
(sqrt (+ 1.0 (* y y)))
63.0ms
(sqrt (+ 1.0 (* y y)))

simplify600.0ms

Counts
95 → 95

prune315.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
6.6b
(sqrt (+ 1.0 (* y y)))
6.6b
(sqrt (+ 1.0 (* y y)))
6.6b
(sqrt (+ 1.0 (* y y)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-div
18×sqrt-prod
13×add-sqr-sqrt
12×pow1
10×add-cube-cbrt *-un-lft-identity
9×add-exp-log flip3-+ associate-*r* add-cbrt-cube flip-+
8×associate-*r/
4×frac-times add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp cbrt-unprod
2×associate-*l/
1×associate-*l* *-commutative
Counts
4 → 77
Calls
4 calls:
58.0ms
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
5.0ms
(sqrt (+ 1.0 (* y y)))
7.0ms
(sqrt (+ 1.0 (* y y)))
8.0ms
(sqrt (+ 1.0 (* y y)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
62.0ms
(sqrt (+ 1.0 (* y y)))
67.0ms
(sqrt (+ 1.0 (* y y)))
67.0ms
(sqrt (+ 1.0 (* y y)))

simplify1.2s

Counts
89 → 89

prune401.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.8b

localize32.0ms

Local error

Found 4 expressions with local error:

6.6b
(sqrt (+ 1.0 (* y y)))
6.9b
(cbrt (+ 1.0 (* y y)))
6.9b
(cbrt (+ 1.0 (* y y)))
6.9b
(cbrt (+ 1.0 (* y y)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
8.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(cbrt (+ 1.0 (* y y)))
3.0ms
(cbrt (+ 1.0 (* y y)))
3.0ms
(cbrt (+ 1.0 (* y y)))

series816.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(sqrt (+ 1.0 (* y y)))
256.0ms
(cbrt (+ 1.0 (* y y)))
246.0ms
(cbrt (+ 1.0 (* y y)))
258.0ms
(cbrt (+ 1.0 (* y y)))

simplify1.0s

Counts
66 → 66

prune463.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 6.8b

regimes146.0ms

Accuracy

9.3% (0.2b remaining)

Error of 5.7b against oracle of 5.5b and baseline of 5.7b

bsearch0.0ms

simplify29.0ms

end0.0ms

sample628.0ms

Algorithm
intervals
Results
303.0ms10638×body80valid