Details

Time bar (total: 11.4s)

sample19.0ms

Algorithm
intervals
Results
8.0ms348×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
1147
2207
3227
done227

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite23.0ms

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:
22.0ms
(* x (+ 1.0 (* y y)))

series58.0ms

Counts
1 → 3
Calls
1 calls:
58.0ms
(* x (+ 1.0 (* y y)))

simplify2.1s

Counts
25 → 25
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
050247
1143240
2451206
31576206
done5000206

prune58.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.2b

localize13.0ms

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)))

rewrite106.0ms

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:
20.0ms
(* x (sqrt (+ 1.0 (* y y))))
68.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
8.0ms
(sqrt (+ 1.0 (* y y)))
8.0ms
(sqrt (+ 1.0 (* y y)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* x (sqrt (+ 1.0 (* y y))))
75.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
60.0ms
(sqrt (+ 1.0 (* y y)))
59.0ms
(sqrt (+ 1.0 (* y y)))

simplify2.1s

Counts
95 → 95
Iterations

Useful iterations: 3 (986.0ms)

IterNodesCost
01221468
13031152
28351012
327461002
done50021002

prune305.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 4.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(* 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)))

rewrite66.0ms

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:
47.0ms
(* x (* (cbrt (+ 1.0 (* y y))) (cbrt (+ 1.0 (* y y)))))
5.0ms
(cbrt (+ 1.0 (* y y)))
6.0ms
(cbrt (+ 1.0 (* y y)))
6.0ms
(cbrt (+ 1.0 (* y y)))

series825.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(* x (* (cbrt (+ 1.0 (* y y))) (cbrt (+ 1.0 (* y y)))))
206.0ms
(cbrt (+ 1.0 (* y y)))
250.0ms
(cbrt (+ 1.0 (* y y)))
210.0ms
(cbrt (+ 1.0 (* y y)))

simplify1.5s

Counts
78 → 78
Iterations

Useful iterations: 3 (489.0ms)

IterNodesCost
01251323
12981228
27831109
320591065
done50011065

prune330.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 4.2b

localize33.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (+ 1.0 (* y y)))
4.0b
(sqrt (+ 1.0 (* y y)))
4.2b
(cbrt (+ 1.0 (* y y)))
4.2b
(cbrt (+ 1.0 (* y y)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
11.0ms
(sqrt (+ 1.0 (* y y)))
19.0ms
(sqrt (+ 1.0 (* y y)))
6.0ms
(cbrt (+ 1.0 (* y y)))
6.0ms
(cbrt (+ 1.0 (* y y)))

series606.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(sqrt (+ 1.0 (* y y)))
65.0ms
(sqrt (+ 1.0 (* y y)))
245.0ms
(cbrt (+ 1.0 (* y y)))
234.0ms
(cbrt (+ 1.0 (* y y)))

simplify1.6s

Counts
68 → 68
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0105920
1237834
2650776
32159754
done5000748

prune355.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 4.2b

regimes128.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
187
done87

end0.0ms

sample728.0ms

Algorithm
intervals
Results
377.0ms10714×body80valid