Details

Time bar (total: 20.9s)

sample42.0ms

Algorithm
intervals
Results
20.0ms256×body80valid

simplify31.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
01114
11613
22612
33212
done3212

prune13.0ms

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))

rewrite13.0ms

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)
5.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series479.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(fma z z (fma x x (* y y)))
64.0ms
(fma x x (* y y))
94.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
238.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify3.7s

Counts
88 → 88
Iterations

Useful iterations: 2 (124.0ms)

IterNodesCost
01181382
11831320
24201191
312401191
448221191
done50001191

prune476.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.3b

localize19.0ms

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))))

rewrite39.0ms

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))
30.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
2.0ms
(sqrt (fma z z (fma x x (* y y))))

series550.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(fma z z (fma x x (* y y)))
50.0ms
(fma x x (* y y))
240.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
179.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify2.6s

Counts
94 → 94
Iterations

Useful iterations: 2 (127.0ms)

IterNodesCost
01221456
12041335
24371247
312571247
done50001247

prune406.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.3b

localize27.0ms

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 3.0))
34.0b
(sqrt (fma z z (fma x x (* y y))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
6×add-exp-log associate-/r* add-cbrt-cube associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×fma-udef
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 98
Calls
4 calls:
1.0ms
(fma z z (fma x x (* y y)))
1.0ms
(fma x x (* y y))
16.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
3.0ms
(sqrt (fma z z (fma x x (* y y))))

series698.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(fma z z (fma x x (* y y)))
60.0ms
(fma x x (* y y))
374.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
176.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify2.6s

Counts
110 → 110
Iterations

Useful iterations: 3 (253.0ms)

IterNodesCost
01272025
11891846
23851763
39511761
434141761
done50001761

prune381.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 16.2b

localize5.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ (- z) (sqrt 3.0))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
44×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
33×sqrt-prod
21×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/l*
7×neg-mul-1
6×associate-/r*
3×add-exp-log add-cbrt-cube
1×pow1 cbrt-undiv neg-sub0 expm1-log1p-u frac-2neg div-sub distribute-frac-neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 92
Calls
1 calls:
10.0ms
(/ (- z) (sqrt 3.0))

series103.0ms

Counts
1 → 3
Calls
1 calls:
103.0ms
(/ (- z) (sqrt 3.0))

simplify6.8s

Counts
95 → 95
Iterations

Useful iterations: 3 (462.0ms)

IterNodesCost
01331051
1233942
2494930
31208928
43263928
done5000928

prune215.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 16.2b

regimes465.0ms

Accuracy

63.8% (7.2b remaining)

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

bsearch118.0ms

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

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02637
13137
23337
done3337

end0.0ms

sample1.0s

Algorithm
intervals
Results
647.0ms8000×body80valid