Details

Time bar (total: 2.6s)

analyze16.0ms

Algorithm
search

sample22.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1227
2247
3247

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 36.4b

Counts
2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.7b
(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:
4.0ms
(+ (* x x) (* y y))
9.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series45.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* x x) (* y y))
13.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
26.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify120.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (112.0ms)

IterNodesCost
0294707
11224644
24391642
35001640

prune129.0ms

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: 18.4b

Counts
75 → 5

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
0.1b
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
33.7b
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
10×distribute-lft-out
8×pow1 add-log-exp
7×add-sqr-sqrt
6×unpow-prod-down associate-*r*
5×add-exp-log add-cube-cbrt add-cbrt-cube
4×associate-*r/
3×flip3-+ associate-*l* sum-log flip-+
2×sqrt-pow1 sqrt-div pow-prod-down
1×+-commutative distribute-rgt-in associate-+r+ distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
3 → 54
Calls
3 calls:
11.0ms
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
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)))))

series50.0ms

Counts
3 → 9
Calls
3 calls:
10.0ms
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
12.0ms
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
28.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

simplify35.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0225478
11152435
25002433

prune120.0ms

Filtered
39 candidates to 63 candidates (-61.5%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New63063
Fresh044
Picked011
Done000
Total63568

Merged error: 18.4b

Counts
68 → 5

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
33.6b
(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))
8.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series55.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* x x) (* y y))
29.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
20.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify94.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
02941188
110831124
240691101
350021101

prune116.0ms

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: 18.3b

Counts
103 → 8

localize3.0ms

Local error

Found 1 expressions with local error:

0.2b
(* z (sqrt 0.3333333333333333))

rewrite5.0ms

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:
4.0ms
(* z (sqrt 0.3333333333333333))

series4.0ms

Counts
1 → 3
Calls
1 calls:
4.0ms
(* z (sqrt 0.3333333333333333))

simplify56.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
06984
124580
256978
389378
4200178
5500178

prune27.0ms

Filtered
14 candidates to 25 candidates (-78.6%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New22325
Fresh055
Picked011
Done022
Total221133

Merged error: 18.3b

Counts
33 → 11

regimes905.0ms

Accuracy

63.2% (7.3b remaining)

Error of 25.6b against oracle of 18.3b and baseline of 38.1b

bsearch71.0ms

Steps
ItersRangePoint
6
2.395086637548115e+98
3.237922195700299e+99
3.1742129263662725e+99
9
-6.921603234181645e+138
-5.350404021357512e+133
-5.486791059586406e+136

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03112
13312
23312

end0.0ms

analyze15.0ms

Algorithm
search

sample593.0ms

Algorithm
intervals
Results
429.0ms8000×body80valid

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