Details

Time bar (total: 27.8s)

sample511.0ms

Algorithm
intervals
Results
15.0ms339×body80valid

simplify522.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
067
197
2167
3267
4337
done337

prune232.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize129.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (* x x) y)

rewrite329.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
2×add-sqr-sqrt
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- *-un-lft-identity diff-log add-cbrt-cube flip-- difference-of-squares
Counts
1 → 13
Calls
1 calls:
268.0ms
(- (* x x) y)

series55.0ms

Counts
1 → 3
Calls
1 calls:
54.0ms
(- (* x x) y)

simplify4.0s

Counts
16 → 16
Iterations

Useful iterations: 2 (187.0ms)

IterNodesCost
032136
187133
2312113
31761113
done5000113

prune283.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* x x) y))
0.0b
(- (* x x) y)
0.0b
(- (* x x) y)
0.2b
(* (sqrt (- (* x x) y)) (sqrt (- (* x x) y)))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
26×sqrt-prod
20×pow1
14×sqrt-div
13×add-cube-cbrt *-un-lft-identity
9×flip3-- sqrt-pow1 pow1/2 swap-sqr flip--
8×add-log-exp
7×associate-*r* associate-*l* difference-of-squares
6×add-exp-log add-cbrt-cube
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×sub-neg diff-log associate-*r/ associate-*l/
1×pow2 rem-sqrt-square pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 102
Calls
4 calls:
25.0ms
(sqrt (- (* x x) y))
19.0ms
(- (* x x) y)
16.0ms
(- (* x x) y)
163.0ms
(* (sqrt (- (* x x) y)) (sqrt (- (* x x) y)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
238.0ms
(sqrt (- (* x x) y))
65.0ms
(- (* x x) y)
49.0ms
(- (* x x) y)
42.0ms
(* (sqrt (- (* x x) y)) (sqrt (- (* x x) y)))

simplify3.4s

Counts
114 → 114
Iterations

Useful iterations: done (3.4s)

IterNodesCost
01121614
12581152
21019992
done5000975

prune915.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (- (* x x) y)))
0.1b
(sqrt (sqrt (- (* x x) y)))
0.2b
(* (sqrt (- (* x x) y)) (* (sqrt (sqrt (- (* x x) y))) (sqrt (sqrt (- (* x x) y)))))
0.4b
(* (sqrt (sqrt (- (* x x) y))) (sqrt (sqrt (- (* x x) y))))

rewrite915.0ms

Algorithm
rewrite-expression-head
Rules
122×sqrt-div
104×sqrt-prod
91×sqrt-pow1
69×pow1
67×add-sqr-sqrt
47×pow1/2
39×pow-prod-up
35×flip3-- flip--
32×frac-times
22×add-cube-cbrt *-un-lft-identity
18×swap-sqr
17×associate-*l*
16×associate-*r/
12×pow-prod-down
11×add-exp-log associate-*r* pow-sqr add-cbrt-cube unswap-sqr
10×associate-*l/
7×difference-of-squares
4×rem-sqrt-square prod-exp cbrt-unprod add-log-exp
3×sqrt-unprod
2×*-commutative
1×pow2 pow-plus rem-square-sqrt
Counts
4 → 203
Calls
4 calls:
54.0ms
(sqrt (sqrt (- (* x x) y)))
53.0ms
(sqrt (sqrt (- (* x x) y)))
521.0ms
(* (sqrt (- (* x x) y)) (* (sqrt (sqrt (- (* x x) y))) (sqrt (sqrt (- (* x x) y)))))
160.0ms
(* (sqrt (sqrt (- (* x x) y))) (sqrt (sqrt (- (* x x) y))))

series1.6s

Counts
4 → 12
Calls
4 calls:
452.0ms
(sqrt (sqrt (- (* x x) y)))
476.0ms
(sqrt (sqrt (- (* x x) y)))
70.0ms
(* (sqrt (- (* x x) y)) (* (sqrt (sqrt (- (* x x) y))) (sqrt (sqrt (- (* x x) y)))))
607.0ms
(* (sqrt (sqrt (- (* x x) y))) (sqrt (sqrt (- (* x x) y))))

simplify8.2s

Counts
215 → 215
Iterations

Useful iterations: done (8.0s)

IterNodesCost
02294808
16003048
228722503
done50002425

prune2.8s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes433.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
067
177
done77

end0.0ms

sample2.8s

Algorithm
intervals
Results
994.0ms10670×body80valid