Details

Time bar (total: 23.5s)

sample34.0ms

Algorithm
intervals
Results
17.0ms256×body80valid

simplify15.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01114
11613
22612
33212
done3212

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize38.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (fma z z (fma x x (* y y))) 3.0)
32.6b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite23.0ms

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:
10.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
9.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series386.0ms

Counts
2 → 6
Calls
2 calls:
102.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
284.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify3.7s

Counts
62 → 62
Iterations

Useful iterations: 3 (252.0ms)

IterNodesCost
01011118
11641062
2362977
3933974
43336974
done5000974

prune280.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.6b

localize28.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
32.7b
(sqrt (fma z z (fma x x (* y y))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
29×sqrt-prod
16×associate-*r*
15×*-un-lft-identity
13×add-cube-cbrt times-frac
8×unswap-sqr
7×pow1
6×associate-*l*
4×add-exp-log add-cbrt-cube
3×sqrt-pow1 pow1/2 pow-prod-down
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-unprod sqrt-div associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
2 → 62
Calls
2 calls:
52.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
3.0ms
(sqrt (fma z z (fma x x (* y y))))

series481.0ms

Counts
2 → 6
Calls
2 calls:
290.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
191.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify6.4s

Counts
68 → 68
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
0991192
11701077
23301030
37021030
420301030
548341030
done50001030

prune246.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.6b

localize24.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
32.7b
(sqrt (fma z z (fma x x (* y y))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
32×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
3×pow1
2×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 div-inv
Counts
2 → 78
Calls
2 calls:
14.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
3.0ms
(sqrt (fma z z (fma x x (* y y))))

series488.0ms

Counts
2 → 6
Calls
2 calls:
311.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
177.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify3.0s

Counts
84 → 84
Iterations

Useful iterations: 3 (124.0ms)

IterNodesCost
01041761
11551588
22791546
34871544
49101544
514001544
628941544
done50001544

prune335.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.3b

localize5.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ y (sqrt 3.0))

rewrite8.0ms

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:
6.0ms
(/ y (sqrt 3.0))

series57.0ms

Counts
1 → 3
Calls
1 calls:
57.0ms
(/ y (sqrt 3.0))

simplify6.3s

Counts
44 → 44
Iterations

Useful iterations: 3 (108.0ms)

IterNodesCost
068381
1105344
2190334
3301332
4504332
5763332
61424332
74858332
done5002332

prune113.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 9.3b

regimes523.0ms

Accuracy

47.8% (13.5b remaining)

Error of 25.2b against oracle of 11.7b and baseline of 37.5b

bsearch74.0ms

Steps
ItersRangePoint
2
1.9335275214306354e+121
2.2438624246711994e+121
2.188536514136267e+121
10
-1.153867539103521e+97
-6.21347482068611e+82
-3.017165361738838e+89

simplify15.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02436
13136
23536
33636
done3636

end0.0ms

sample913.0ms

Algorithm
intervals
Results
585.0ms8000×body80valid