Details

Time bar (total: 2.4s)

sample22.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0136
1206
2226
3226

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.6b

Counts
2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
35.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
5×add-sqr-sqrt
4×pow1 add-cube-cbrt *-un-lft-identity sum-log
3×add-exp-log flip3-+ sqrt-prod add-cbrt-cube flip-+
2×+-commutative sqrt-div
1×rem-sqrt-square associate-+l+ sqrt-pow1 pow1/2
Counts
3 → 39
Calls
3 calls:
5.0ms
(+ (+ (* x x) (* y y)) (* z z))
3.0ms
(+ (* x x) (* y y))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series35.0ms

Counts
3 → 9
Calls
3 calls:
12.0ms
(+ (+ (* x x) (* y y)) (* z z))
5.0ms
(+ (* x x) (* y y))
18.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify83.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
0209340
1959320
23316316
35001315

prune66.0ms

Filtered
48 candidates to 37 candidates (22.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New44448
Fresh000
Picked011
Done000
Total44549

Merged error: 22.3b

Counts
49 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
0.3b
(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
37.1b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
37.1b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×cbrt-prod sqrt-prod
12×add-cube-cbrt *-un-lft-identity
9×associate-*r*
8×cbrt-div
7×pow1
6×add-exp-log add-cbrt-cube
4×flip3-+ sqrt-div flip-+ add-log-exp
3×pow1/3 associate-*l* unswap-sqr
2×rem-sqrt-square sqrt-pow1 associate-*r/
1×pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 74
Calls
4 calls:
5.0ms
(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
9.0ms
(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
5.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series150.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
58.0ms
(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
31.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
30.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify42.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03511262
112531185
250011135

prune125.0ms

Filtered
86 candidates to 75 candidates (12.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New84286
Fresh033
Picked101
Done011
Total85691

Merged error: 22.3b

Counts
91 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
35.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.1b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
43×cbrt-prod add-sqr-sqrt
26×sqrt-prod
19×add-cube-cbrt *-un-lft-identity
16×sqrt-div
14×cbrt-div
13×pow1
11×swap-sqr
9×flip3-+ associate-*r* associate-*l* flip-+ unswap-sqr
7×pow1/3
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 107
Calls
4 calls:
15.0ms
(* (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series96.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
18.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
18.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
29.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify119.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 3 (104.0ms)

IterNodesCost
02681893
19121803
239521660
350021555

prune131.0ms

Filtered
119 candidates to 80 candidates (32.8%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1181119
Fresh134
Picked011
Done011
Total1196125

Merged error: 22.3b

Counts
125 → 6

localize2.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New000
Fresh033
Picked011
Done022
Total066

Merged error: 22.3b

Counts
6 → 6

regimes723.0ms

Accuracy

63.6% (7.1b remaining)

Error of 25.5b against oracle of 18.5b and baseline of 37.9b

bsearch39.0ms

Steps
ItersRangePoint
10
9.505106128559536e+57
4.5942725875421524e+67
4.5518977389456156e+67
9
-8.861200960569297e+116
-1.4734112449091008e+108
-3.8835198140411694e+114

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0217
1217

end0.0ms

sample593.0ms

Algorithm
intervals
Results
317.0ms8000×body80valid

Profiling

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