Details

Time bar (total: 14.2s)

sample24.0ms

Algorithm
intervals
Results
12.0ms256×body80valid

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01114
11613
22612
33312
done3312

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize17.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (fma z z (fma x x (* y y))) 3.0)
33.6b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite22.0ms

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))

series433.0ms

Counts
2 → 6
Calls
2 calls:
92.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
341.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify1.6s

Counts
62 → 62
Iterations

Useful iterations: 3 (421.0ms)

IterNodesCost
01011118
11681062
2454977
32048974
done5002974

prune305.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.6b

localize26.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
33.7b
(sqrt (fma z z (fma x x (* y y))))

rewrite61.0ms

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:
53.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
3.0ms
(sqrt (fma z z (fma x x (* y y))))

series447.0ms

Counts
2 → 6
Calls
2 calls:
282.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
165.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify3.6s

Counts
68 → 68
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
0991192
11761089
25191032
334711030
done50011030

prune239.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.6b

localize21.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
33.7b
(sqrt (fma z z (fma x x (* y y))))

rewrite17.0ms

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

series447.0ms

Counts
2 → 6
Calls
2 calls:
290.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
157.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify1.3s

Counts
84 → 84
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01041761
11611588
24641546
320791546
done50011544

prune274.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 11.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (fma z z (fma x x (* y y))) (sqrt 3.0))
0.3b
(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (fma z z (fma x x (* y y))) (sqrt 3.0))))
1.0b
(/ 1 (sqrt 3.0))
33.8b
(sqrt (/ (fma z z (fma x x (* y y))) (sqrt 3.0)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
170×sqrt-prod
148×add-sqr-sqrt
120×times-frac
83×*-un-lft-identity
75×add-cube-cbrt
25×associate-*r* associate-*l*
24×unswap-sqr
12×add-exp-log associate-/r*
11×pow1
10×add-cbrt-cube
6×associate-/l*
5×sqrt-div div-inv
4×expm1-log1p-u sqrt-pow1 pow1/2 log1p-expm1-u add-log-exp
3×rem-sqrt-square pow-flip div-exp pow-prod-down
2×cbrt-undiv frac-2neg clear-num
1×frac-times rec-exp sqrt-unprod 1-exp associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod inv-pow
Counts
4 → 218
Calls
4 calls:
12.0ms
(/ (fma z z (fma x x (* y y))) (sqrt 3.0))
89.0ms
(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (fma z z (fma x x (* y y))) (sqrt 3.0))))
13.0ms
(/ 1 (sqrt 3.0))
8.0ms
(sqrt (/ (fma z z (fma x x (* y y))) (sqrt 3.0)))

series1.1s

Counts
4 → 10
Calls
4 calls:
180.0ms
(/ (fma z z (fma x x (* y y))) (sqrt 3.0))
398.0ms
(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (fma z z (fma x x (* y y))) (sqrt 3.0))))
0.0ms
(/ 1 (sqrt 3.0))
526.0ms
(sqrt (/ (fma z z (fma x x (* y y))) (sqrt 3.0)))

simplify1.5s

Counts
228 → 228
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02444745
14214424
217184232
done50004230

prune910.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.8b

regimes494.0ms

Accuracy

48% (13.5b remaining)

Error of 25.3b against oracle of 11.8b and baseline of 37.8b

bsearch1.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03071
13571
done3571

end0.0ms

sample1.1s

Algorithm
intervals
Results
746.0ms8000×body80valid