Details

Time bar (total: 3.1s)

sample21.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1227
2247
3247

prune3.0ms

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: 37.6b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.0b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×sqrt-prod
11×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1
4×sum-log
3×flip3-+ associate-/r* flip-+ associate-/l*
2×+-commutative rem-sqrt-square div-inv associate-/l/
1×cbrt-undiv associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 78
Calls
4 calls:
5.0ms
(+ (* x x) (* y y))
7.0ms
(+ (+ (* x x) (* y y)) (* z z))
9.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series284.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* x x) (* y y))
38.0ms
(+ (+ (* x x) (* y y)) (* z z))
49.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
170.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0325828
11345761
25001755

prune271.0ms

Filtered
90 candidates to 71 candidates (78.9%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New85590
Fresh000
Picked101
Done000
Total86591

Merged error: 18.4b

Counts
91 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
34.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
11×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube associate-/l*
5×pow1
4×flip3-+ sqrt-div sum-log flip-+
2×+-commutative associate-/l/
1×cbrt-undiv rem-sqrt-square associate-+l+ sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 102
Calls
4 calls:
4.0ms
(+ (* x x) (* y y))
7.0ms
(+ (+ (* x x) (* y y)) (* z z))
10.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
6.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ (* x x) (* y y))
35.0ms
(+ (+ (* x x) (* y y)) (* z z))
215.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
97.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify43.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03301316
113381241
250021218

prune208.0ms

Filtered
114 candidates to 73 candidates (64.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1113114
Fresh044
Picked011
Done000
Total1118119

Merged error: 18.3b

Counts
119 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.4b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
34.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×sqrt-prod
17×*-un-lft-identity
16×associate-*r*
15×add-cube-cbrt
13×times-frac
11×add-log-exp
9×pow1 sqrt-div
8×unswap-sqr
6×add-exp-log associate-*l* add-cbrt-cube
5×flip3-+ flip-+
4×sum-log
3×sqrt-pow1 pow1/2 pow-prod-down
2×+-commutative frac-times associate-*l/
1×rem-sqrt-square associate-+l+ sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 88
Calls
4 calls:
4.0ms
(+ (* x x) (* y y))
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
17.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
6.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series326.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ (* x x) (* y y))
36.0ms
(+ (+ (* x x) (* y y)) (* z z))
162.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
99.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify44.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0354986
11482945
25001924

prune203.0ms

Filtered
100 candidates to 69 candidates (69.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1000100
Fresh066
Picked011
Done011
Total1008108

Merged error: 18.3b

Counts
108 → 8

localize3.0ms

Local error

Found 1 expressions with local error:

0.2b
(* z (sqrt 0.3333333333333333))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×associate-*r*
4×add-cube-cbrt *-un-lft-identity sqrt-prod
3×pow1 add-exp-log associate-*l* add-cbrt-cube
2×unswap-sqr
1×pow-prod-down prod-exp *-commutative cbrt-unprod add-log-exp
Counts
1 → 22
Calls
1 calls:
5.0ms
(* z (sqrt 0.3333333333333333))

series41.0ms

Counts
1 → 3
Calls
1 calls:
41.0ms
(* z (sqrt 0.3333333333333333))

simplify57.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
06984
124580
256978
389378
4200178
5500178

prune25.0ms

Filtered
25 candidates to 14 candidates (56.0%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New23225
Fresh055
Picked011
Done022
Total231033

Merged error: 18.3b

Counts
33 → 10

regimes384.0ms

Accuracy

63.1% (7.2b remaining)

Error of 25.5b against oracle of 18.3b and baseline of 37.7b

bsearch72.0ms

Steps
ItersRangePoint
10
1.0552035162483894e+111
5.722192015150889e+120
4.1598843652442944e+111
5
-3.222127529430611e+149
-1.364030571909353e+149
-1.7013657575679381e+149

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02913
13113
23113

end0.0ms

sample514.0ms

Algorithm
intervals
Results
350.0ms8000×body80valid

Profiling

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