Details

Time bar (total: 2.5s)

sample24.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1227
2247
3247

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 39.6b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.9b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×associate-/r* associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num sum-log
Counts
3 → 65
Calls
3 calls:
6.0ms
(+ (* x x) (* y y))
7.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series44.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* x x) (* y y))
12.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
26.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify118.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (110.0ms)

IterNodesCost
0294707
11224644
24391642
35001640

prune130.0ms

Filtered
60 candidates to 74 candidates (-23.3%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New69574
Fresh000
Picked101
Done000
Total70575

Merged error: 19.9b

Counts
75 → 5

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
36.9b
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
7×pow1
6×add-sqr-sqrt associate-*r*
5×distribute-lft-out
4×add-exp-log add-cube-cbrt associate-*r/ add-cbrt-cube
3×unpow-prod-down associate-*l*
2×sqrt-pow1 flip3-+ sqrt-div pow-prod-down flip-+ add-log-exp
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
2 → 38
Calls
2 calls:
13.0ms
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
11.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

series39.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
26.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

simplify39.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0211340
11120308
25002307

prune97.0ms

Filtered
27 candidates to 44 candidates (-63.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New44044
Fresh044
Picked011
Done000
Total44549

Merged error: 19.9b

Counts
49 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.3b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
36.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
33×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 sqrt-div
3×flip3-+ flip-+
2×associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 89
Calls
3 calls:
3.0ms
(+ (* x x) (* y y))
9.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series57.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* x x) (* y y))
31.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
20.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify100.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
02941188
110831124
240691101
350021101

prune120.0ms

Filtered
62 candidates to 98 candidates (-58.1%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New95398
Fresh033
Picked011
Done011
Total958103

Merged error: 19.8b

Counts
103 → 8

localize3.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ z (sqrt 3.0))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×sqrt-prod
6×associate-/r*
3×add-exp-log add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv frac-2neg div-exp clear-num div-inv add-log-exp
Counts
1 → 39
Calls
1 calls:
4.0ms
(/ z (sqrt 3.0))

series5.0ms

Counts
1 → 3
Calls
1 calls:
5.0ms
(/ z (sqrt 3.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 4 (50.0ms)

IterNodesCost
0103217
1273207
2715197
32013197
45002196

prune47.0ms

Filtered
26 candidates to 42 candidates (-61.5%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New39342
Fresh055
Picked011
Done022
Total391150

Merged error: 19.8b

Counts
50 → 11

regimes856.0ms

Accuracy

61.8% (7.5b remaining)

Error of 25.9b against oracle of 18.4b and baseline of 38.0b

bsearch26.0ms

Steps
ItersRangePoint
4
1.4862045023064263e+141
2.752263984466097e+141
1.8149088570815288e+141
8
-1.1446708155820095e+92
-2.5782862618072367e+89
-1.1335390936445571e+92

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02912
13012
23012

end0.0ms

sample648.0ms

Algorithm
intervals
Results
356.0ms8000×body80valid

Profiling

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