Details

Time bar (total: 6.3s)

sample35.0ms

Algorithm
intervals
Results
15.0ms357×body80valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
1147
2207
3227
done227

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.9b

localize6.0ms

Local error

Found 1 expressions with local error:

4.4b
(* x (+ 1.0 (* y y)))

rewrite30.0ms

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:
30.0ms
(* x (+ 1.0 (* y y)))

series65.0ms

Counts
1 → 3
Calls
1 calls:
65.0ms
(* x (+ 1.0 (* y y)))

simplify605.0ms

Counts
25 → 25
Iterations

Useful iterations: done (604.0ms)

IterNodesCost
050247
1161244
2756208
done5000206

prune56.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.7b

localize8.0ms

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))))
4.5b
(sqrt (+ 1.0 (* y y)))
4.5b
(sqrt (+ 1.0 (* y y)))

rewrite132.0ms

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:
36.0ms
(* x (sqrt (+ 1.0 (* y y))))
76.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
6.0ms
(sqrt (+ 1.0 (* y y)))
10.0ms
(sqrt (+ 1.0 (* y y)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(* x (sqrt (+ 1.0 (* y y))))
80.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
55.0ms
(sqrt (+ 1.0 (* y y)))
60.0ms
(sqrt (+ 1.0 (* y y)))

simplify1.1s

Counts
95 → 95
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01221468
13201152
216541040
done50011016

prune309.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y)))))
4.5b
(sqrt (+ 1.0 (* y y)))
4.5b
(sqrt (+ 1.0 (* y y)))
4.5b
(sqrt (+ 1.0 (* y y)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
24×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:
54.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y)))))
6.0ms
(sqrt (+ 1.0 (* y y)))
6.0ms
(sqrt (+ 1.0 (* y y)))
10.0ms
(sqrt (+ 1.0 (* y y)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y)))))
66.0ms
(sqrt (+ 1.0 (* y y)))
56.0ms
(sqrt (+ 1.0 (* y y)))
46.0ms
(sqrt (+ 1.0 (* y y)))

simplify829.0ms

Counts
89 → 89
Iterations

Useful iterations: done (826.0ms)

IterNodesCost
01321489
13401307
216371133
done50001101

prune382.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 4.7b

localize24.0ms

Local error

Found 4 expressions with local error:

4.5b
(sqrt (+ 1.0 (* y y)))
4.5b
(sqrt (+ 1.0 (* y y)))
4.5b
(sqrt (+ 1.0 (* y y)))
4.5b
(sqrt (+ 1.0 (* y y)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
9.0ms
(sqrt (+ 1.0 (* y y)))
6.0ms
(sqrt (+ 1.0 (* y y)))
6.0ms
(sqrt (+ 1.0 (* y y)))
7.0ms
(sqrt (+ 1.0 (* y y)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(sqrt (+ 1.0 (* y y)))
51.0ms
(sqrt (+ 1.0 (* y y)))
56.0ms
(sqrt (+ 1.0 (* y y)))
62.0ms
(sqrt (+ 1.0 (* y y)))

simplify409.0ms

Counts
72 → 72
Iterations

Useful iterations: done (405.0ms)

IterNodesCost
058856
1141752
2628696
done5000688

prune375.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 4.7b

regimes132.0ms

Accuracy

0% (0.2b remaining)

Error of 5.5b against oracle of 5.3b and baseline of 5.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0815
11115
done1115

end0.0ms

sample796.0ms

Algorithm
intervals
Results
417.0ms10660×body80valid