Details

Time bar (total: 3.1s)

sample18.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify8.0ms

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 (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.8b

Counts
2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.0b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
313×*-un-lft-identity
160×distribute-lft-out
104×associate-*l*
85×times-frac
46×sqrt-prod
44×add-sqr-sqrt
41×add-cube-cbrt
28×associate-/l*
24×swap-sqr
22×sqrt-div
6×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l/
3×pow1
2×rem-sqrt-square frac-2neg flip3-+ clear-num flip-+ div-inv add-log-exp
1×cbrt-undiv sqrt-pow1 pow1/2 div-exp
Counts
2 → 152
Calls
2 calls:
28.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
31.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series235.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
181.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify160.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
02621517
19761449
240791449
350021449

prune160.0ms

Filtered
158 candidates to 58 candidates (63.3%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1535158
Fresh000
Picked101
Done000
Total1545159

Merged error: 17.9b

Counts
159 → 5

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
36.1b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
51×sqrt-prod
49×sqrt-div
43×associate-*l*
40×distribute-lft-out
38×add-sqr-sqrt
19×add-cube-cbrt
18×frac-times
16×associate-*r*
13×times-frac
11×flip3-+ flip-+
9×associate-*r/ associate-/r* associate-/l*
8×unswap-sqr
7×pow1
6×swap-sqr
4×add-exp-log add-cbrt-cube
3×frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num
2×associate-*l/ add-log-exp
1×rem-sqrt-square sqrt-unprod prod-exp *-commutative cbrt-unprod div-inv
Counts
2 → 110
Calls
2 calls:
38.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
24.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series290.0ms

Counts
2 → 6
Calls
2 calls:
180.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
110.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify94.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
03031437
18181391
226331361
350011361

prune176.0ms

Filtered
116 candidates to 61 candidates (47.4%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1133116
Fresh314
Picked011
Done000
Total1165121

Merged error: 17.9b

Counts
121 → 5

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
36.1b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
325×*-un-lft-identity
166×sqrt-prod
160×distribute-lft-out
104×associate-*l*
102×times-frac
54×add-sqr-sqrt
53×add-cube-cbrt
24×swap-sqr
17×associate-/l*
6×associate-/r*
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 → 166
Calls
2 calls:
32.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
24.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series359.0ms

Counts
2 → 6
Calls
2 calls:
248.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
112.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify76.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
02172007
15731942
217231939
350021926

prune145.0ms

Filtered
172 candidates to 52 candidates (69.8%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1693172
Fresh033
Picked011
Done011
Total1698177

Merged error: 17.8b

Counts
177 → 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:
5.0ms
(* z (sqrt 0.3333333333333333))

series49.0ms

Counts
1 → 3
Calls
1 calls:
49.0ms
(* z (sqrt 0.3333333333333333))

simplify74.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
06984
124580
256678
388978
4199278
5500278

prune21.0ms

Filtered
25 candidates to 14 candidates (44.0%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New20525
Fresh055
Picked101
Done022
Total211233

Merged error: 17.8b

Counts
33 → 12

regimes502.0ms

Accuracy

62.8% (7.2b remaining)

Error of 25.6b against oracle of 18.4b and baseline of 37.8b

bsearch80.0ms

Steps
ItersRangePoint
8
6.6320067326423015e+100
1.8928424626778097e+105
1.859793817919116e+105
9
-5.622918692562569e+111
-1.8179009786912424e+102
-3.95689621740472e+111

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03315
13515
23515

end0.0ms

sample446.0ms

Algorithm
intervals
Results
277.0ms8000×body80valid