Details

Time bar (total: 2.7s)

sample14.0ms

Algorithm
intervals
Results
6.0ms343×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0143
1203
2223
3223

prune1.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize4.0ms

Local error

Found 1 expressions with local error:

3.5b
(* x (+ 1.0 (* y y)))

rewrite7.0ms

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:
7.0ms
(* x (+ 1.0 (* y y)))

series57.0ms

Counts
1 → 3
Calls
1 calls:
56.0ms
(* x (+ 1.0 (* y y)))

simplify76.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0144115
1712101
23303100
35003100

prune43.0ms

Filtered
25 candidates to 17 candidates (68.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.7b

localize6.0ms

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))))
3.5b
(sqrt (+ 1.0 (* y y)))
3.5b
(sqrt (+ 1.0 (* y y)))

rewrite35.0ms

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:
8.0ms
(* x (sqrt (+ 1.0 (* y y))))
19.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
2.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* x (sqrt (+ 1.0 (* y y))))
67.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
45.0ms
(sqrt (+ 1.0 (* y y)))
48.0ms
(sqrt (+ 1.0 (* y y)))

simplify40.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0306681
11316604
25002594

prune205.0ms

Filtered
95 candidates to 67 candidates (70.5%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (+ 1.0 (* y y))))
3.5b
(sqrt (+ 1.0 (* y y)))
3.5b
(sqrt (+ 1.0 (* y y)))
3.5b
(sqrt (+ 1.0 (* y y)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
96×sqrt-div
30×flip3-+ flip-+
28×frac-times
26×associate-*r/
16×pow1
14×associate-*l/
13×add-exp-log add-cbrt-cube
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
6×associate-*r* 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 → 95
Calls
4 calls:
88.0ms
(* (* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (+ 1.0 (* y y))))
2.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (+ 1.0 (* y y))))
48.0ms
(sqrt (+ 1.0 (* y y)))
44.0ms
(sqrt (+ 1.0 (* y y)))
50.0ms
(sqrt (+ 1.0 (* y y)))

simplify59.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04321396
118441143
250021028

prune296.0ms

Filtered
107 candidates to 75 candidates (70.1%)
Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.7b

localize11.0ms

Local error

Found 4 expressions with local error:

2.5b
(* x (* (sqrt (+ 1.0 (* y y))) (fabs (cbrt (+ 1.0 (* y y))))))
3.5b
(sqrt (+ 1.0 (* y y)))
3.7b
(cbrt (+ 1.0 (* y y)))
3.7b
(cbrt (+ 1.0 (* y y)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1
9×add-exp-log add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
4×cbrt-div flip3-+ sqrt-div flip-+ add-log-exp
3×associate-*l* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×pow1/3 associate-*r/ associate-*l/
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative
Counts
4 → 61
Calls
4 calls:
15.0ms
(* x (* (sqrt (+ 1.0 (* y y))) (fabs (cbrt (+ 1.0 (* y y))))))
2.0ms
(sqrt (+ 1.0 (* y y)))
1.0ms
(cbrt (+ 1.0 (* y y)))
2.0ms
(cbrt (+ 1.0 (* y y)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* x (* (sqrt (+ 1.0 (* y y))) (fabs (cbrt (+ 1.0 (* y y))))))
44.0ms
(sqrt (+ 1.0 (* y y)))
170.0ms
(cbrt (+ 1.0 (* y y)))
172.0ms
(cbrt (+ 1.0 (* y y)))

simplify38.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0363635
11292575
25001567

prune253.0ms

Filtered
73 candidates to 62 candidates (84.9%)
Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 3.7b

regimes108.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083
183

end0.0ms

sample396.0ms

Algorithm
intervals
Results
218.0ms10729×body80valid