Details

Time bar (total: 20.4s)

sample25.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01114
11613
22612
33212
done3212

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.0b
(fma x x (* y y))
0.1b
(/ (fma z z (fma x x (* y y))) 3.0)
34.1b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×sqrt-prod
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×rem-sqrt-square fma-udef div-inv
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 76
Calls
4 calls:
0.0ms
(fma z z (fma x x (* y y)))
0.0ms
(fma x x (* y y))
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))

series461.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(fma z z (fma x x (* y y)))
62.0ms
(fma x x (* y y))
84.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
253.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify3.6s

Counts
88 → 88
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
01181382
11831320
24201191
312401191
448221191
done50001191

prune379.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.0b
(fma x x (* y y))
0.3b
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
34.0b
(sqrt (fma z z (fma x x (* y y))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×sqrt-prod
17×*-un-lft-identity
16×associate-*r*
15×add-cube-cbrt
13×times-frac
9×pow1
8×unswap-sqr
6×add-exp-log associate-*l* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2 pow-prod-down
2×fma-udef
1×rem-sqrt-square sqrt-unprod sqrt-div associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 82
Calls
4 calls:
1.0ms
(fma z z (fma x x (* y y)))
1.0ms
(fma x x (* y y))
32.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
2.0ms
(sqrt (fma z z (fma x x (* y y))))

series548.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(fma z z (fma x x (* y y)))
44.0ms
(fma x x (* y y))
258.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
172.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify2.0s

Counts
94 → 94
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
01221456
12041335
24371247
312571247
done50001247

prune434.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
34.0b
(sqrt (fma z z (fma x x (* y y))))
34.0b
(sqrt (fma z z (fma x x (* y y))))
34.1b
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0)) (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
49×sqrt-prod
36×add-sqr-sqrt times-frac
34×add-cube-cbrt *-un-lft-identity
14×pow1
8×sqrt-pow1
6×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square pow1/2 sqrt-div
1×cbrt-undiv pow2 frac-times sqrt-undiv frac-2neg pow-plus associate-*r/ div-exp pow-prod-down associate-*l/ clear-num pow-sqr pow-prod-up div-inv
Counts
4 → 114
Calls
4 calls:
15.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
3.0ms
(sqrt (fma z z (fma x x (* y y))))
3.0ms
(sqrt (fma z z (fma x x (* y y))))
24.0ms
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0)) (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
332.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
179.0ms
(sqrt (fma z z (fma x x (* y y))))
175.0ms
(sqrt (fma z z (fma x x (* y y))))
343.0ms
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0)) (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))))

simplify3.9s

Counts
126 → 126
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
01252466
11822013
23141939
35561939
411231939
518231939
635491939
done50001939

prune414.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 16.2b

localize4.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ z (sqrt 3.0))

rewrite7.0ms

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
(/ z (sqrt 3.0))

series83.0ms

Counts
1 → 3
Calls
1 calls:
83.0ms
(/ z (sqrt 3.0))

simplify6.0s

Counts
44 → 44
Iterations

Useful iterations: 3 (80.0ms)

IterNodesCost
068381
1105344
2190334
3301332
4504332
5763332
61424332
74858332
done5002332

prune94.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 16.2b

regimes320.0ms

Accuracy

63.8% (7.2b remaining)

Error of 25.6b against oracle of 18.4b and baseline of 38.2b

bsearch90.0ms

Steps
ItersRangePoint
9
3.3911511265698697e+126
1.3870714403563658e+135
4.171828716999667e+130
10
-3.7885935661345695e+111
-7.715368434473106e+100
-3.746938595761261e+111

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02637
13137
23337
done3337

end0.0ms

sample877.0ms

Algorithm
intervals
Results
560.0ms8000×body80valid