Details

Time bar (total: 2.3s)

sample16.0ms

Algorithm
intervals
Results
8.0ms363×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: 6.1b

localize4.0ms

Local error

Found 1 expressions with local error:

5.7b
(* x (+ 1.0 (* y y)))

rewrite8.0ms

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)))

series50.0ms

Counts
1 → 3
Calls
1 calls:
50.0ms
(* x (+ 1.0 (* y y)))

simplify81.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0144115
1712101
23303100
35003100

prune45.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.9b

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))))
5.7b
(sqrt (+ 1.0 (* y y)))
5.7b
(sqrt (+ 1.0 (* y y)))

rewrite39.0ms

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:
9.0ms
(* x (sqrt (+ 1.0 (* y y))))
22.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))

series196.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* x (sqrt (+ 1.0 (* y y))))
53.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
44.0ms
(sqrt (+ 1.0 (* y y)))
42.0ms
(sqrt (+ 1.0 (* y y)))

simplify41.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0306681
11316604
25002594

prune192.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.9b

localize9.0ms

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)))))
5.7b
(sqrt (+ 1.0 (* y y)))
5.7b
(sqrt (+ 1.0 (* y y)))
5.7b
(sqrt (+ 1.0 (* y y)))

rewrite92.0ms

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:
77.0ms
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))

series187.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
42.0ms
(sqrt (+ 1.0 (* y y)))
45.0ms
(sqrt (+ 1.0 (* y y)))
42.0ms
(sqrt (+ 1.0 (* y y)))

simplify59.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04481458
117471223
250011105

prune303.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.9b

localize12.0ms

Local error

Found 4 expressions with local error:

5.7b
(sqrt (+ 1.0 (* y y)))
5.7b
(sqrt (+ 1.0 (* y y)))
5.7b
(sqrt (+ 1.0 (* y y)))
11.0b
(cbrt (pow (sqrt (+ 1.0 (* y y))) 3))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
15×add-sqr-sqrt sqrt-prod
12×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×unpow-prod-down cube-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cube-div cbrt-div
1×cube-mult pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 74
Calls
4 calls:
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))
5.0ms
(cbrt (pow (sqrt (+ 1.0 (* y y))) 3))

series178.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(sqrt (+ 1.0 (* y y)))
42.0ms
(sqrt (+ 1.0 (* y y)))
46.0ms
(sqrt (+ 1.0 (* y y)))
43.0ms
(cbrt (pow (sqrt (+ 1.0 (* y y))) 3))

simplify101.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0233486
1810481
23411473
35003473

prune256.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 5.9b

regimes102.0ms

Accuracy

0% (0.2b remaining)

Error of 5.1b against oracle of 5.0b and baseline of 5.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083
183

end0.0ms

sample343.0ms

Algorithm
intervals
Results
187.0ms10695×body80valid