Details

Time bar (total: 3.4s)

sample14.0ms

Algorithm
intervals
Results
6.0ms343×body80valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0143
1233
2303
3313
4313

prune1.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize5.0ms

Local error

Found 1 expressions with local error:

3.5b
(* 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 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:
7.0ms
(* x (+ 1.0 (* y y)))

series67.0ms

Counts
1 → 3
Calls
1 calls:
67.0ms
(* x (+ 1.0 (* y y)))

simplify116.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0148123
1742103
23453100
35001100

prune56.0ms

Filtered
27 candidates to 22 candidates (81.5%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.7b

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

rewrite37.0ms

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:
9.0ms
(* x (sqrt (+ 1.0 (* y y))))
20.0ms
(* (* 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)))

series197.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* x (sqrt (+ 1.0 (* y y))))
53.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
41.0ms
(sqrt (+ 1.0 (* y y)))
44.0ms
(sqrt (+ 1.0 (* y y)))

simplify42.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0318722
11367620
25002595

prune252.0ms

Filtered
105 candidates to 84 candidates (80.0%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.7b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-div
20×pow1
18×add-exp-log add-cbrt-cube
15×sqrt-prod
14×add-sqr-sqrt
12×associate-*r*
10×add-cube-cbrt *-un-lft-identity associate-*r/ associate-*l/
9×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative hypot-def
Counts
4 → 95
Calls
4 calls:
33.0ms
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (hypot (sqrt 1.0) y))
110.0ms
(* (* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (hypot (sqrt 1.0) y)) (sqrt (sqrt (+ 1.0 (* y y)))))
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))

series637.0ms

Counts
4 → 12
Calls
4 calls:
269.0ms
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (hypot (sqrt 1.0) y))
275.0ms
(* (* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (hypot (sqrt 1.0) y)) (sqrt (sqrt (+ 1.0 (* y y)))))
46.0ms
(sqrt (+ 1.0 (* y y)))
46.0ms
(sqrt (+ 1.0 (* y y)))

simplify63.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05031174
122851049
25001930

prune378.0ms

Filtered
107 candidates to 82 candidates (76.6%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (hypot (sqrt 1.0) y))
0.0b
(hypot (sqrt 1.0) y)
0.0b
(hypot (sqrt 1.0) y)
0.1b
(* (hypot (sqrt 1.0) y) (* x (hypot (sqrt 1.0) y)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×hypot-udef *-commutative
1×unswap-sqr
Counts
4 → 60
Calls
4 calls:
3.0ms
(* x (hypot (sqrt 1.0) y))
0.0ms
(hypot (sqrt 1.0) y)
0.0ms
(hypot (sqrt 1.0) y)
6.0ms
(* (hypot (sqrt 1.0) y) (* x (hypot (sqrt 1.0) y)))

series548.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(* x (hypot (sqrt 1.0) y))
97.0ms
(hypot (sqrt 1.0) y)
98.0ms
(hypot (sqrt 1.0) y)
196.0ms
(* (hypot (sqrt 1.0) y) (* x (hypot (sqrt 1.0) y)))

simplify98.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (92.0ms)

IterNodesCost
0213439
1803361
23698352
35002344

prune185.0ms

Filtered
72 candidates to 57 candidates (79.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes124.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0136
1136

end0.0ms

sample365.0ms

Algorithm
intervals
Results
198.0ms10729×body80valid