Details

Time bar (total: 16.5s)

sample27.0ms

Algorithm
intervals
Results
14.0ms256×body80valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01114
11514
22214
32414
done2414

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

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))

rewrite189.0ms

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:
16.0ms
(+ (* x x) (* y y))
110.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
60.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series343.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(+ (* x x) (* y y))
85.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
224.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.9s

Counts
74 → 74
Iterations

Useful iterations: 3 (677.0ms)

IterNodesCost
01281436
12911370
28551241
327631233
done50011233

prune308.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.2b

localize21.0ms

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))
35.1b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite140.0ms

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:
8.0ms
(+ (* x x) (* y y))
83.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
45.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series520.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(+ (* x x) (* y y))
340.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
136.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.6s

Counts
98 → 98
Iterations

Useful iterations: 3 (488.0ms)

IterNodesCost
01412253
12922035
27271965
317921945
done50001945

prune386.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.8b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.4b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
35.1b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×sqrt-prod
16×*-un-lft-identity associate-*r*
14×add-cube-cbrt
13×times-frac
9×sqrt-div
8×pow1 unswap-sqr
6×associate-*l*
5×add-exp-log add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 pow1/2 pow-prod-down
2×frac-times associate-*l/
1×+-commutative rem-sqrt-square sqrt-unprod associate-*r/ prod-exp sum-log *-commutative cbrt-unprod div-inv
Counts
3 → 75
Calls
3 calls:
8.0ms
(+ (* x x) (* y y))
140.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
61.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series452.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(+ (* x x) (* y y))
275.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
126.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.1s

Counts
84 → 84
Iterations

Useful iterations: 3 (781.0ms)

IterNodesCost
01401688
13151536
27941451
322391429
done50001429

prune317.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.8b

localize6.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ x (sqrt 3.0))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×sqrt-prod
6×associate-/r*
3×add-exp-log add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv frac-2neg div-exp clear-num div-inv add-log-exp
Counts
1 → 39
Calls
1 calls:
8.0ms
(/ x (sqrt 3.0))

series72.0ms

Counts
1 → 3
Calls
1 calls:
72.0ms
(/ x (sqrt 3.0))

simplify5.4s

Counts
42 → 42
Iterations

Useful iterations: 3 (113.0ms)

IterNodesCost
066371
1103334
2192324
3303322
4503322
5764322
61430322
74878322
done5001322

prune105.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 12.8b

regimes812.0ms

Accuracy

47.9% (13.3b remaining)

Error of 25.5b against oracle of 12.2b and baseline of 37.7b

bsearch245.0ms

Steps
ItersRangePoint
10
4.022397810881141e+88
1.565796980266273e+101
1.6811337377551001e+93
4
2.847040915761575e-141
4.8334812650979246e-141
3.157422220345379e-141
9
1.5258936540952977e-176
3.1017552524573808e-170
4.8080105705282596e-173
8
8.068763620842616e-290
5.260554892635578e-285
2.963930732093339e-286
6
-7.526302520782567e-184
-8.46579077171639e-185
-1.3008260738260694e-184
1
-4.90105109200061e+89
-4.6551667645331244e+89
-4.839580010133739e+89

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04394
15194
done5194

end0.0ms

sample1.3s

Algorithm
intervals
Results
917.0ms8000×body80valid