Details

Time bar (total: 14.7s)

sample44.0ms

Algorithm
intervals
Results
22.0ms256×body80valid

simplify27.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
01114
11613
22612
33212
done3212

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize20.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (fma z z (fma x x (* y y))) 3.0)
34.9b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
4×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×expm1-log1p-u rem-sqrt-square log1p-expm1-u div-inv add-log-exp
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
2 → 56
Calls
2 calls:
5.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
4.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series351.0ms

Counts
2 → 6
Calls
2 calls:
98.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
252.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify2.6s

Counts
62 → 62
Iterations

Useful iterations: 3 (272.0ms)

IterNodesCost
01011118
11641062
2362977
3933974
43336974
done5000974

prune304.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.3333333333333333 (fma x x (fma y y (pow z 2))))
34.9b
(sqrt (* 0.3333333333333333 (fma x x (fma y y (pow z 2)))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×add-sqr-sqrt
4×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×associate-*r* associate-*l*
2×expm1-log1p-u sqrt-pow1 pow-prod-down fma-udef log1p-expm1-u add-log-exp
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
2 → 35
Calls
2 calls:
11.0ms
(* 0.3333333333333333 (fma x x (fma y y (pow z 2))))
6.0ms
(sqrt (* 0.3333333333333333 (fma x x (fma y y (pow z 2)))))

series373.0ms

Counts
2 → 6
Calls
2 calls:
109.0ms
(* 0.3333333333333333 (fma x x (fma y y (pow z 2))))
264.0ms
(sqrt (* 0.3333333333333333 (fma x x (fma y y (pow z 2)))))

simplify1.1s

Counts
41 → 41
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
064567
1124533
2303473
31210473
done5000473

prune214.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.0b

localize36.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (fma z z (fma x x (* y y))) (sqrt 3.0)) (sqrt 3.0))
0.2b
(/ (fma z z (fma x x (* y y))) (sqrt 3.0))
34.9b
(sqrt (/ (/ (fma z z (fma x x (* y y))) (sqrt 3.0)) (sqrt 3.0)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
526×times-frac
405×sqrt-prod
295×add-sqr-sqrt
278×add-cube-cbrt *-un-lft-identity
25×associate-/l*
16×div-inv
12×associate-/r*
10×add-exp-log add-cbrt-cube
7×rem-sqrt-square
4×pow1 cbrt-undiv div-exp
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×sqrt-pow1 pow1/2 sqrt-div associate-/l/
Counts
3 → 373
Calls
3 calls:
22.0ms
(/ (/ (fma z z (fma x x (* y y))) (sqrt 3.0)) (sqrt 3.0))
6.0ms
(/ (fma z z (fma x x (* y y))) (sqrt 3.0))
40.0ms
(sqrt (/ (/ (fma z z (fma x x (* y y))) (sqrt 3.0)) (sqrt 3.0)))

series886.0ms

Counts
3 → 9
Calls
3 calls:
311.0ms
(/ (/ (fma z z (fma x x (* y y))) (sqrt 3.0)) (sqrt 3.0))
188.0ms
(/ (fma z z (fma x x (* y y))) (sqrt 3.0))
387.0ms
(sqrt (/ (/ (fma z z (fma x x (* y y))) (sqrt 3.0)) (sqrt 3.0)))

simplify2.9s

Counts
382 → 382
Iterations

Useful iterations: done (2.8s)

IterNodesCost
043311938
173910910
2131110312
3314910146
done500110081

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize11.0ms

Local error

Found 1 expressions with local error:

0.2b
(* z (sqrt 0.3333333333333333))

rewrite22.0ms

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×expm1-log1p-u pow-prod-down prod-exp *-commutative cbrt-unprod log1p-expm1-u add-log-exp
Counts
1 → 24
Calls
1 calls:
21.0ms
(* z (sqrt 0.3333333333333333))

series74.0ms

Counts
1 → 3
Calls
1 calls:
74.0ms
(* z (sqrt 0.3333333333333333))

simplify2.7s

Counts
27 → 27
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
039168
171151
2126143
3173143
4219143
5359143
6834143
72754143
done5001143

prune74.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 4.8b

regimes362.0ms

Accuracy

39.3% (19.4b remaining)

Error of 25.7b against oracle of 6.4b and baseline of 38.2b

bsearch116.0ms

Steps
ItersRangePoint
10
1.0123409507895924e+148
2.5004073983328303e+162
1.432510219356762e+148
8
-1.1693040193819057e+90
-8.809443151937589e+85
-9.992239971519508e+87

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01929
12529
22729
done2729

end0.0ms

sample1.3s

Algorithm
intervals
Results
978.0ms8000×body80valid