Details

Time bar (total: 2.5s)

sample27.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02114
12114

prune7.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 38.0b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.2b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite23.0ms

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:
5.0ms
(+ (* x x) (* y y))
10.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series54.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ (* x x) (* y y))
14.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify26.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
050111233

prune145.0ms

Filtered
62 candidates to 74 candidates (-19.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New68674
Fresh000
Picked101
Done000
Total69675

Merged error: 18.1b

Counts
75 → 6

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
35.2b
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×add-sqr-sqrt
4×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l/ add-cbrt-cube
3×associate-*r* associate-*l*
2×sqrt-pow1 flip3-+ sqrt-div pow-prod-down flip-+ add-log-exp
1×pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
2 → 33
Calls
2 calls:
9.0ms
(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
7.0ms
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

series46.0ms

Counts
2 → 6
Calls
2 calls:
14.0ms
(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
32.0ms
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

simplify36.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
05438569

prune62.0ms

Filtered
26 candidates to 39 candidates (-50.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New39039
Fresh055
Picked011
Done000
Total39645

Merged error: 18.1b

Counts
45 → 6

localize11.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
35.1b
(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
32×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
4×add-exp-log sqrt-div add-cbrt-cube
3×pow1
2×flip3-+ flip-+ associate-/l/ add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
2 → 78
Calls
2 calls:
11.0ms
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
6.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

series59.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
21.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify54.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049431814
149431814

prune111.0ms

Filtered
50 candidates to 84 candidates (-68.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New81384
Fresh044
Picked011
Done011
Total81990

Merged error: 18.0b

Counts
90 → 9

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (+ (* x x) (+ (* y y) (* z z))) 3.0)
6.0b
(exp (log (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) 3.0))))
35.2b
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) 3.0))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
28×times-frac
27×add-cube-cbrt *-un-lft-identity
26×sqrt-prod
16×log-prod exp-sum
6×pow1 exp-prod
5×add-exp-log add-cbrt-cube
3×associate-/r* log-pow div-inv associate-/l* add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 sqrt-div associate-/l/
1×cbrt-undiv log-div frac-2neg flip3-+ exp-diff div-exp clear-num flip-+ rem-exp-log
Counts
3 → 85
Calls
3 calls:
13.0ms
(/ (+ (* x x) (+ (* y y) (* z z))) 3.0)
10.0ms
(exp (log (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) 3.0))))
8.0ms
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) 3.0))

series75.0ms

Counts
3 → 9
Calls
3 calls:
15.0ms
(/ (+ (* x x) (+ (* y y) (* z z))) 3.0)
30.0ms
(exp (log (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) 3.0))))
30.0ms
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) 3.0))

simplify29.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
056471706

prune151.0ms

Filtered
71 candidates to 94 candidates (-32.4%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New90494
Fresh066
Picked101
Done022
Total9112103

Merged error: 18.0b

Counts
103 → 12

regimes705.0ms

Accuracy

61.2% (7.8b remaining)

Error of 26.3b against oracle of 18.5b and baseline of 38.6b

bsearch42.0ms

Steps
ItersRangePoint
9
1.8411122634403785e+125
1.1065228347393604e+132
3.888633308672755e+130
9
-5.390869519443976e+66
-4.144836468798277e+57
-4.494031953760747e+66

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02931
12931

end0.0ms

sample742.0ms

Algorithm
intervals
Results
405.0ms8000×body80valid

Profiling

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