Details

Time bar (total: 3.8s)

sample20.0ms

Algorithm
intervals
Results
12.0ms256×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0136
1206
2226
3226

prune2.0ms

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: 38.8b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
36.0b
(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:
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series132.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(+ (+ (* x x) (* y y)) (* z z))
96.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify68.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0143270
1608254
22522250
35001249

prune71.0ms

Filtered
34 candidates to 26 candidates (76.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New29534
Fresh000
Picked011
Done000
Total29635

Merged error: 19.2b

Counts
35 → 6

localize11.0ms

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)))))
37.2b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
37.2b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite27.0ms

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:
6.0ms
(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
10.0ms
(* (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)))

series440.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
136.0ms
(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
103.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
104.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify44.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03201178
113041101
250011084

prune257.0ms

Filtered
86 candidates to 75 candidates (87.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New85186
Fresh134
Picked011
Done011
Total86692

Merged error: 19.2b

Counts
92 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (exp (log (cbrt (+ (+ (* x x) (* y y)) (* z z)))))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
5.5b
(exp (log (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
37.2b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
37.2b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
13×cbrt-prod add-cube-cbrt *-un-lft-identity
9×associate-*r*
8×cbrt-div sqrt-prod
7×pow1
6×add-exp-log log-prod exp-sum add-cbrt-cube
5×exp-prod
4×flip3-+ flip-+ add-log-exp
3×pow1/3 associate-*l* unswap-sqr
2×log-div exp-diff sqrt-div associate-*r/ log-pow
1×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log
Counts
4 → 75
Calls
4 calls:
10.0ms
(* (fabs (exp (log (cbrt (+ (+ (* x x) (* y y)) (* z z)))))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
7.0ms
(exp (log (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
5.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
8.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(* (fabs (exp (log (cbrt (+ (+ (* x x) (* y y)) (* z z)))))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
105.0ms
(exp (log (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
104.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
105.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify45.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03341265
112801146
250021099

prune341.0ms

Filtered
87 candidates to 77 candidates (88.5%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New86187
Fresh033
Picked101
Done022
Total87693

Merged error: 19.2b

Counts
93 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

37.2b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
37.2b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
37.2b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
37.2b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 52
Calls
4 calls:
6.0ms
(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)))
5.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
105.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
105.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
111.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify64.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0136700
1502648
22017620
35001620

prune318.0ms

Filtered
64 candidates to 60 candidates (93.8%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New63164
Fresh033
Picked101
Done022
Total64670

Merged error: 19.2b

Counts
70 → 6

regimes373.0ms

Accuracy

65.5% (6.7b remaining)

Error of 25.1b against oracle of 18.3b and baseline of 37.9b

bsearch78.0ms

Steps
ItersRangePoint
10
8.565423343579683e+117
8.152131796852354e+127
6.706873256878666e+122
11
-1.4185660712987705e+171
-7.633398144368219e+146
-9.469007215145339e+149

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0217
1217

end0.0ms

sample466.0ms

Algorithm
intervals
Results
305.0ms8000×body80valid