Details

Time bar (total: 2.8s)

sample14.0ms

Algorithm
intervals
Results
5.0ms330×body80valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0143
1233
2303
3313
4313

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.3b

localize4.0ms

Local error

Found 1 expressions with local error:

5.0b
(* 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 expm1-log1p-u distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ log1p-expm1-u add-log-exp unswap-sqr
Counts
1 → 24
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
27 → 27
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0148123
1742103
23453100
35001100

prune54.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.1b

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))))
5.0b
(sqrt (+ 1.0 (* y y)))
5.0b
(sqrt (+ 1.0 (* y y)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×sqrt-div
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×expm1-log1p-u frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative hypot-def unswap-sqr
Counts
4 → 93
Calls
4 calls:
18.0ms
(* x (sqrt (+ 1.0 (* y y))))
45.0ms
(* (* 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)))

series193.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* x (sqrt (+ 1.0 (* y y))))
52.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
41.0ms
(sqrt (+ 1.0 (* y y)))
40.0ms
(sqrt (+ 1.0 (* y y)))

simplify42.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0318722
11367620
25002595

prune267.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

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)))))
5.0b
(sqrt (+ 1.0 (* y y)))
5.0b
(sqrt (+ 1.0 (* y y)))
5.0b
(sqrt (+ 1.0 (* y y)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-div
18×sqrt-prod
16×add-sqr-sqrt
12×pow1
10×add-cube-cbrt *-un-lft-identity
9×add-exp-log flip3-+ associate-*r* add-cbrt-cube flip-+
8×associate-*r/
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp cbrt-unprod hypot-def
2×associate-*l/
1×associate-*l* *-commutative
Counts
4 → 88
Calls
4 calls:
54.0ms
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
5.0ms
(sqrt (+ 1.0 (* y y)))
5.0ms
(sqrt (+ 1.0 (* y y)))
5.0ms
(sqrt (+ 1.0 (* y y)))

series177.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
37.0ms
(sqrt (+ 1.0 (* y y)))
42.0ms
(sqrt (+ 1.0 (* y y)))
38.0ms
(sqrt (+ 1.0 (* y y)))

simplify125.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0307781
11108687
24896660
35001660

prune296.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (sqrt (+ 1.0 (* y y))))
5.0b
(sqrt (+ 1.0 (* y y)))
5.0b
(sqrt (+ 1.0 (* y y)))
5.0b
(sqrt (+ 1.0 (* y y)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×sqrt-prod
9×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×cbrt-prod
4×add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
2×cbrt-div
1×pow1/3
Counts
4 → 72
Calls
4 calls:
4.0ms
(cbrt (sqrt (+ 1.0 (* y y))))
5.0ms
(sqrt (+ 1.0 (* y y)))
5.0ms
(sqrt (+ 1.0 (* y y)))
5.0ms
(sqrt (+ 1.0 (* y y)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(cbrt (sqrt (+ 1.0 (* y y))))
45.0ms
(sqrt (+ 1.0 (* y y)))
39.0ms
(sqrt (+ 1.0 (* y y)))
44.0ms
(sqrt (+ 1.0 (* y y)))

simplify127.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (120.0ms)

IterNodesCost
0271524
1927498
24108481
35001476

prune345.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 5.1b

regimes89.0ms

Accuracy

0% (0.2b remaining)

Error of 5.5b against oracle of 5.4b and baseline of 5.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083
183

end0.0ms

sample409.0ms

Algorithm
intervals
Results
183.0ms10661×body80valid