Details

Time bar (total: 2.8s)

sample12.0ms

Algorithm
intervals
Results
5.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
074
174

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
27.5b
(sqrt (+ (* x x) (* y y)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
2 → 26
Calls
2 calls:
2.0ms
(+ (* x x) (* y y))
3.0ms
(sqrt (+ (* x x) (* y y)))

series65.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(+ (* x x) (* y y))
36.0ms
(sqrt (+ (* x x) (* y y)))

simplify48.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0125177
1530163
21540163
35001162

prune71.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (+ (* x x) (* y y))))
0.5b
(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
27.5b
(sqrt (+ (* x x) (* y y)))
27.5b
(sqrt (+ (* x x) (* y y)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
32×sqrt-div
31×pow1
20×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
2×associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 134
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ (* x x) (* y y))))
27.0ms
(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
3.0ms
(sqrt (+ (* x x) (* y y)))
3.0ms
(sqrt (+ (* x x) (* y y)))

series201.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (sqrt (+ (* x x) (* y y))))
36.0ms
(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
38.0ms
(sqrt (+ (* x x) (* y y)))
36.0ms
(sqrt (+ (* x x) (* y y)))

simplify47.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
02511056
1952985
25002964

prune299.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (sqrt (+ (* x x) (* y y))))) (sqrt (sqrt (sqrt (+ (* x x) (* y y))))))
27.5b
(sqrt (+ (* x x) (* y y)))
27.5b
(sqrt (+ (* x x) (* y y)))
27.5b
(sqrt (+ (* x x) (* y y)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
165×sqrt-prod
82×add-sqr-sqrt
75×sqrt-pow1
42×sqrt-div
38×pow1
27×pow1/2
24×swap-sqr
23×add-cube-cbrt *-un-lft-identity
16×unswap-sqr
13×pow-prod-up
12×associate-*r* associate-*l*
9×flip3-+ flip-+
7×pow-prod-down pow-sqr
6×add-exp-log add-cbrt-cube
4×frac-times add-log-exp
3×rem-sqrt-square
2×associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 158
Calls
4 calls:
32.0ms
(* (sqrt (sqrt (sqrt (+ (* x x) (* y y))))) (sqrt (sqrt (sqrt (+ (* x x) (* y y))))))
3.0ms
(sqrt (+ (* x x) (* y y)))
3.0ms
(sqrt (+ (* x x) (* y y)))
3.0ms
(sqrt (+ (* x x) (* y y)))

series201.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (sqrt (sqrt (sqrt (+ (* x x) (* y y))))) (sqrt (sqrt (sqrt (+ (* x x) (* y y))))))
40.0ms
(sqrt (+ (* x x) (* y y)))
35.0ms
(sqrt (+ (* x x) (* y y)))
40.0ms
(sqrt (+ (* x x) (* y y)))

simplify50.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
02911436
110821310
250011275

prune306.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.5b

localize19.0ms

Local error

Found 4 expressions with local error:

27.5b
(sqrt (+ (* x x) (* y y)))
27.5b
(sqrt (+ (* x x) (* y y)))
27.5b
(sqrt (+ (* x x) (* y y)))
27.5b
(sqrt (+ (* x x) (* y y)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
3.0ms
(sqrt (+ (* x x) (* y y)))
3.0ms
(sqrt (+ (* x x) (* y y)))
6.0ms
(sqrt (+ (* x x) (* y y)))
3.0ms
(sqrt (+ (* x x) (* y y)))

series147.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(sqrt (+ (* x x) (* y y)))
41.0ms
(sqrt (+ (* x x) (* y y)))
35.0ms
(sqrt (+ (* x x) (* y y)))
35.0ms
(sqrt (+ (* x x) (* y y)))

simplify139.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 5 (134.0ms)

IterNodesCost
089400
1215388
2503388
31265388
44227388
55002384

prune322.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.5b

regimes289.0ms

Accuracy

59.2% (9.7b remaining)

Error of 17.8b against oracle of 8.1b and baseline of 31.9b

bsearch93.0ms

Steps
ItersRangePoint
11
5.10808278574109e+145
3.366560557353129e+171
1.2142912145306137e+146
9
1.1741963849460375e-217
2.1903360009039515e-208
1.1600661433813666e-208
7
2.00818341296373e-296
3.449635196547704e-295
9.194803090293717e-296
7
-6.579287999353623e+83
-2.1130938932944453e+82
-6.485144449769119e+83

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0239
1239

end0.0ms

sample311.0ms

Algorithm
intervals
Results
176.0ms8000×body80valid