Details

Time bar (total: 4.7s)

sample23.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0136
1206
2226
3226

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.3b

Counts
2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
35.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
7×add-log-exp
4×add-sqr-sqrt
3×pow1 add-cube-cbrt *-un-lft-identity sum-log sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square associate-+l+ sqrt-pow1 pow1/2
Counts
2 → 28
Calls
2 calls:
5.0ms
(+ (+ (* x x) (* y y)) (* z z))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series128.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(+ (+ (* x x) (* y y)) (* z z))
94.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify65.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0143270
1608254
22522250
35001249

prune131.0ms

Filtered
34 candidates to 26 candidates (76.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New28634
Fresh000
Picked011
Done000
Total28735

Merged error: 19.6b

Counts
35 → 7

localize13.0ms

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)))))
35.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
40×cbrt-prod
29×sqrt-prod
19×add-cube-cbrt *-un-lft-identity
18×sqrt-div
14×pow1
12×cbrt-div
11×swap-sqr
9×flip3-+ associate-*r* associate-*l* flip-+ unswap-sqr
6×add-exp-log pow1/3
4×frac-times add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 109
Calls
4 calls:
18.0ms
(* (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
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
94.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
93.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
94.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify149.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 3 (133.0ms)

IterNodesCost
02301818
19031735
243151614
350021573

prune431.0ms

Filtered
121 candidates to 82 candidates (67.8%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1210121
Fresh055
Picked011
Done011
Total1217128

Merged error: 19.6b

Counts
128 → 7

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
6.0b
(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
35.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt *-un-lft-identity
6×pow1 log-prod exp-prod exp-sum sqrt-prod
4×sqrt-div
3×add-exp-log flip3-+ sum-log log-pow add-cbrt-cube flip-+
2×log-div sqrt-pow1 pow1/2 exp-diff
1×+-commutative rem-sqrt-square associate-+l+ rem-exp-log
Counts
3 → 50
Calls
3 calls:
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
9.0ms
(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series223.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (+ (* x x) (* y y)) (* z z))
94.0ms
(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
95.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify69.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
0190483
1679462
22658443
35001435

prune205.0ms

Filtered
59 candidates to 39 candidates (66.1%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New55459
Fresh044
Picked101
Done022
Total561066

Merged error: 19.6b

Counts
66 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

5.9b
(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
35.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×pow-unpow sqrt-prod
6×cbrt-prod sqrt-div
5×add-log-exp
4×add-exp-log sqrt-pow1 pow1/2 add-cbrt-cube
3×unpow-prod-down rem-sqrt-square pow-pow flip3-+ log-pow flip-+
1×pow-to-exp exp-prod exp-to-pow pow-exp sqr-pow
Counts
4 → 70
Calls
4 calls:
4.0ms
(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
8.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series649.0ms

Counts
4 → 12
Calls
4 calls:
359.0ms
(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
99.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
95.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
96.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify63.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 3 (51.0ms)

IterNodesCost
01901221
15591124
219881118
350011114

prune384.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New81182
Fresh077
Picked101
Done022
Total821092

Merged error: 19.6b

Counts
92 → 10

regimes1.0s

Accuracy

62.9% (7.4b remaining)

Error of 25.0b against oracle of 17.6b and baseline of 37.5b

bsearch79.0ms

Steps
ItersRangePoint
8
8.124947580121196e+141
2.3710053120370955e+144
1.2546636830809128e+144
11
-3.234739137796827e+160
-1.1042016886584325e+130
-3.0315072087379574e+131

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0217
1217

end0.0ms

sample561.0ms

Algorithm
intervals
Results
295.0ms8000×body80valid

Profiling

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