Details

Time bar (total: 12.7s)

sample26.0ms

Algorithm
intervals
Results
12.0ms256×body80valid

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01114
11613
22612
33312
done3312

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (fma z z (fma x x (* y y))) 3.0)
33.9b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite12.0ms

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:
6.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
5.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series337.0ms

Counts
2 → 6
Calls
2 calls:
76.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
261.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify1.7s

Counts
62 → 62
Iterations

Useful iterations: 3 (470.0ms)

IterNodesCost
01011118
11681062
2454977
32048974
done5002974

prune303.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.6b

localize28.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
33.9b
(sqrt (fma z z (fma x x (* y y))))

rewrite24.0ms

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:
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))))

series568.0ms

Counts
2 → 6
Calls
2 calls:
395.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
173.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify1.6s

Counts
84 → 84
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01041761
11611588
24641546
320791546
done50011544

prune336.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.3b

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)))
33.9b
(sqrt (fma z z (fma x x (* y y))))

rewrite59.0ms

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:
42.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
12.0ms
(sqrt (fma z z (fma x x (* y y))))

series415.0ms

Counts
2 → 6
Calls
2 calls:
239.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
176.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify3.1s

Counts
68 → 68
Iterations

Useful iterations: 3 (760.0ms)

IterNodesCost
0991192
11761089
25191032
334711030
done50011030

prune247.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.3b

localize6.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ y (sqrt 3.0))

rewrite9.0ms

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:
7.0ms
(/ y (sqrt 3.0))

series78.0ms

Counts
1 → 3
Calls
1 calls:
78.0ms
(/ y (sqrt 3.0))

simplify1.0s

Counts
44 → 44
Iterations

Useful iterations: done (1.0s)

IterNodesCost
068381
1110344
2280334
31135334
done5000332

prune98.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 11.2b

regimes458.0ms

Accuracy

46.4% (13.4b remaining)

Error of 25.7b against oracle of 12.3b and baseline of 37.3b

bsearch368.0ms

Steps
ItersRangePoint
5
5.27504975729178e+78
1.3973016344357461e+79
1.3803741179654927e+79
9
3.7161142089086124e-124
2.5175280247742622e-116
6.697712028762041e-123
9
2.3371402087332088e-213
3.418136761922523e-208
7.254479271513616e-209
8
-3.147983072638376e-273
-1.4202703439685317e-276
-1.7921086023675116e-274
9
-3.9961896893098386e-175
-1.7951566216382208e-183
-1.2324940922667923e-182
10
-6.403623541351439e+114
-2.5566587326602513e+98
-5.008523466085166e+110

simplify14.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
047101
153101
done53101

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.5s8000×body80valid