Details

Time bar (total: 8.1s)

sample29.0ms

Algorithm
intervals
Results
11.0ms338×body80valid

simplify16.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
1147
2207
3227
done227

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ 1.0 (* y y))
4.0b
(* x (+ 1.0 (* y y)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
4×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
2×flip3-+ associate-*r/ flip-+
1×+-commutative distribute-rgt-in distribute-lft-in pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
2 → 33
Calls
2 calls:
7.0ms
(+ 1.0 (* y y))
20.0ms
(* x (+ 1.0 (* y y)))

series114.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(+ 1.0 (* y y))
72.0ms
(* x (+ 1.0 (* y y)))

simplify648.0ms

Counts
39 → 39
Iterations

Useful iterations: done (646.0ms)

IterNodesCost
059371
1189363
2879315
done5000307

prune156.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.2b

localize17.0ms

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))))
4.0b
(sqrt (+ 1.0 (* y y)))
4.0b
(sqrt (+ 1.0 (* y y)))

rewrite125.0ms

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:
29.0ms
(* x (sqrt (+ 1.0 (* y y))))
77.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
7.0ms
(sqrt (+ 1.0 (* y y)))
9.0ms
(sqrt (+ 1.0 (* y y)))

series244.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* x (sqrt (+ 1.0 (* y y))))
79.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
48.0ms
(sqrt (+ 1.0 (* y y)))
43.0ms
(sqrt (+ 1.0 (* y y)))

simplify944.0ms

Counts
95 → 95
Iterations

Useful iterations: done (941.0ms)

IterNodesCost
01221468
13201152
216541040
done50011016

prune412.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
4.0b
(sqrt (+ 1.0 (* y y)))
4.0b
(sqrt (+ 1.0 (* y y)))
4.0b
(sqrt (+ 1.0 (* y y)))

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
96×sqrt-div
30×flip3-+ flip-+
28×frac-times
26×associate-*r/
18×sqrt-prod
16×pow1
14×associate-*l/
13×add-exp-log add-sqr-sqrt add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
9×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×associate-*l* *-commutative
Counts
4 → 98
Calls
4 calls:
210.0ms
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
9.0ms
(sqrt (+ 1.0 (* y y)))
9.0ms
(sqrt (+ 1.0 (* y y)))
14.0ms
(sqrt (+ 1.0 (* y y)))

series216.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
45.0ms
(sqrt (+ 1.0 (* y y)))
51.0ms
(sqrt (+ 1.0 (* y y)))
61.0ms
(sqrt (+ 1.0 (* y y)))

simplify1.4s

Counts
110 → 110
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01652960
14622353
223982003
done50001703

prune609.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 4.2b

localize23.0ms

Local error

Found 4 expressions with local error:

1.3b
(* x (* (cbrt (+ 1.0 (* y y))) (cbrt (+ 1.0 (* y y)))))
4.2b
(cbrt (+ 1.0 (* y y)))
4.2b
(cbrt (+ 1.0 (* y y)))
4.2b
(cbrt (+ 1.0 (* y y)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
10×associate-*r/
9×pow1 add-exp-log cbrt-prod add-sqr-sqrt flip3-+ flip-+
8×add-cube-cbrt *-un-lft-identity
7×add-cbrt-cube
4×frac-times add-log-exp
3×pow1/3 associate-*l* pow-prod-down prod-exp cbrt-unprod
2×associate-*l/
1×associate-*r* *-commutative unswap-sqr
Counts
4 → 66
Calls
4 calls:
44.0ms
(* x (* (cbrt (+ 1.0 (* y y))) (cbrt (+ 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)))

series722.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(* x (* (cbrt (+ 1.0 (* y y))) (cbrt (+ 1.0 (* y y)))))
186.0ms
(cbrt (+ 1.0 (* y y)))
189.0ms
(cbrt (+ 1.0 (* y y)))
198.0ms
(cbrt (+ 1.0 (* y y)))

simplify676.0ms

Counts
78 → 78
Iterations

Useful iterations: done (672.0ms)

IterNodesCost
01251323
13061228
210471109
done50001071

prune380.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 4.2b

regimes197.0ms

Accuracy

0% (0.2b remaining)

Error of 5.3b against oracle of 5.1b and baseline of 5.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
187
done87

end0.0ms

sample807.0ms

Algorithm
intervals
Results
362.0ms10680×body80valid