Details

Time bar (total: 20.0s)

sample47.0ms

Algorithm
intervals
Results
28.0ms256×body80valid

simplify28.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
01114
11613
22612
33212
done3212

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize13.0ms

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))

rewrite222.0ms

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×expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative fma-def frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num sum-log
Counts
3 → 72
Calls
3 calls:
17.0ms
(+ (* x x) (* y y))
137.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
63.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series407.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (* x x) (* y y))
96.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
275.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.6s

Counts
81 → 81
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01341510
13071332
29331139
331261133
done50011132

prune430.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.2b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (pow y 2))
0.4b
(/ (sqrt (fma z z (fma x x (pow y 2)))) (sqrt 3.0))
35.1b
(sqrt (fma z z (fma x x (pow y 2))))

rewrite15.0ms

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
4×pow1
3×expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num fma-udef div-inv
Counts
3 → 88
Calls
3 calls:
0.0ms
(fma x x (pow y 2))
8.0ms
(/ (sqrt (fma z z (fma x x (pow y 2)))) (sqrt 3.0))
2.0ms
(sqrt (fma z z (fma x x (pow y 2))))

series638.0ms

Counts
3 → 9
Calls
3 calls:
66.0ms
(fma x x (pow y 2))
368.0ms
(/ (sqrt (fma z z (fma x x (pow y 2)))) (sqrt 3.0))
204.0ms
(sqrt (fma z z (fma x x (pow y 2))))

simplify3.3s

Counts
97 → 97
Iterations

Useful iterations: 3 (196.0ms)

IterNodesCost
01161869
11741693
23351631
36481629
413571629
530931629
done50011629

prune329.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (pow y 2))
0.4b
(* (sqrt (fma z z (fma x x (pow y 2)))) (sqrt (/ 1 3.0)))
35.1b
(sqrt (fma z z (fma x x (pow y 2))))

rewrite36.0ms

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
8×pow1 unswap-sqr
6×associate-*l*
5×add-exp-log add-cbrt-cube
3×expm1-log1p-u sqrt-pow1 pow1/2 pow-prod-down log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-unprod sqrt-div associate-*r/ prod-exp *-commutative cbrt-unprod fma-udef div-inv
Counts
3 → 72
Calls
3 calls:
0.0ms
(fma x x (pow y 2))
30.0ms
(* (sqrt (fma z z (fma x x (pow y 2)))) (sqrt (/ 1 3.0)))
3.0ms
(sqrt (fma z z (fma x x (pow y 2))))

series482.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(fma x x (pow y 2))
277.0ms
(* (sqrt (fma z z (fma x x (pow y 2)))) (sqrt (/ 1 3.0)))
162.0ms
(sqrt (fma z z (fma x x (pow y 2))))

simplify3.6s

Counts
81 → 81
Iterations

Useful iterations: 2 (135.0ms)

IterNodesCost
01111300
11891182
23881115
38881115
427161115
done50001115

prune344.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.2b

localize6.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ y (sqrt 3.0))

rewrite15.0ms

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 expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 41
Calls
1 calls:
12.0ms
(/ y (sqrt 3.0))

series75.0ms

Counts
1 → 3
Calls
1 calls:
75.0ms
(/ y (sqrt 3.0))

simplify5.8s

Counts
44 → 44
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
068381
1105344
2190334
3301332
4504332
5763332
61424332
74858332
done5002332

prune92.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.2b

regimes227.0ms

Accuracy

38.6% (19.2b remaining)

Error of 25.6b against oracle of 6.4b and baseline of 37.7b

bsearch45.0ms

Steps
ItersRangePoint
10
4.022397810881141e+88
1.565796980266273e+101
1.537188568549187e+101
1
-4.90105109200061e+89
-4.6551667645331244e+89
-4.839580010133739e+89

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02130
12630
22830
done2830

end0.0ms

sample1.2s

Algorithm
intervals
Results
973.0ms8000×body80valid