Details

Time bar (total: 2.8s)

sample14.0ms

Algorithm
intervals
Results
5.0ms340×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0143
1203
2223
3223

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.8b

localize4.0ms

Local error

Found 1 expressions with local error:

6.4b
(* x (+ 1.0 (* y y)))

rewrite16.0ms

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:
15.0ms
(* x (+ 1.0 (* y y)))

series49.0ms

Counts
1 → 3
Calls
1 calls:
49.0ms
(* x (+ 1.0 (* y y)))

simplify79.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0144115
1712101
23303100
35003100

prune43.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.6b

localize7.0ms

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))))
6.4b
(sqrt (+ 1.0 (* y y)))
6.4b
(sqrt (+ 1.0 (* y y)))

rewrite75.0ms

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:
18.0ms
(* x (sqrt (+ 1.0 (* y y))))
44.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
5.0ms
(sqrt (+ 1.0 (* y y)))
5.0ms
(sqrt (+ 1.0 (* y y)))

series180.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* x (sqrt (+ 1.0 (* y y))))
49.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
37.0ms
(sqrt (+ 1.0 (* y y)))
41.0ms
(sqrt (+ 1.0 (* y y)))

simplify44.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0306681
11316604
25002594

prune194.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
6.4b
(sqrt (+ 1.0 (* y y)))
6.4b
(sqrt (+ 1.0 (* y y)))
6.4b
(sqrt (+ 1.0 (* y y)))

rewrite176.0ms

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:
152.0ms
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
5.0ms
(sqrt (+ 1.0 (* y y)))
8.0ms
(sqrt (+ 1.0 (* y y)))
5.0ms
(sqrt (+ 1.0 (* y y)))

series172.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
41.0ms
(sqrt (+ 1.0 (* y y)))
39.0ms
(sqrt (+ 1.0 (* y y)))
42.0ms
(sqrt (+ 1.0 (* y y)))

simplify57.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04481458
117471223
250011105

prune313.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 6.6b

localize16.0ms

Local error

Found 4 expressions with local error:

6.4b
(sqrt (+ 1.0 (* y y)))
6.4b
(sqrt (+ 1.0 (* y y)))
6.6b
(cbrt (+ 1.0 (* y y)))
6.6b
(cbrt (+ 1.0 (* y y)))

rewrite18.0ms

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:
5.0ms
(sqrt (+ 1.0 (* y y)))
5.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(cbrt (+ 1.0 (* y y)))
3.0ms
(cbrt (+ 1.0 (* y y)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ 1.0 (* y y)))
48.0ms
(sqrt (+ 1.0 (* y y)))
163.0ms
(cbrt (+ 1.0 (* y y)))
164.0ms
(cbrt (+ 1.0 (* y y)))

simplify126.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (119.0ms)

IterNodesCost
0237466
1804446
23603434
35002432

prune318.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 6.6b

regimes107.0ms

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

sample390.0ms

Algorithm
intervals
Results
182.0ms10679×body80valid