Details

Time bar (total: 14.2s)

sample56.0ms

Algorithm
intervals
Results
31.0ms474×body80valid

simplify77.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (23.0ms)

IterNodesCost
0913
11812
24510
3789
4869
5949
done949

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma x (fma y 2.0 x) (* y y))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(fma x (fma y 2.0 x) (* y y))

series40.0ms

Counts
1 → 3
Calls
1 calls:
40.0ms
(fma x (fma y 2.0 x) (* y y))

simplify515.0ms

Counts
13 → 13
Iterations

Useful iterations: 3 (116.0ms)

IterNodesCost
023165
143165
2133138
3584135
done5000135

prune84.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x (fma y 2.0 x) (* y y))
0.0b
(* (sqrt (fma x (fma y 2.0 x) (* y y))) (sqrt (fma x (fma y 2.0 x) (* y y))))
5.1b
(sqrt (fma x (fma y 2.0 x) (* y y)))
5.1b
(sqrt (fma x (fma y 2.0 x) (* y y)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod fma-udef
Counts
4 → 91
Calls
4 calls:
1.0ms
(fma x (fma y 2.0 x) (* y y))
23.0ms
(* (sqrt (fma x (fma y 2.0 x) (* y y))) (sqrt (fma x (fma y 2.0 x) (* y y))))
3.0ms
(sqrt (fma x (fma y 2.0 x) (* y y)))
3.0ms
(sqrt (fma x (fma y 2.0 x) (* y y)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(fma x (fma y 2.0 x) (* y y))
48.0ms
(* (sqrt (fma x (fma y 2.0 x) (* y y))) (sqrt (fma x (fma y 2.0 x) (* y y))))
99.0ms
(sqrt (fma x (fma y 2.0 x) (* y y)))
105.0ms
(sqrt (fma x (fma y 2.0 x) (* y y)))

simplify3.1s

Counts
103 → 103
Iterations

Useful iterations: done (3.1s)

IterNodesCost
0771929
11511327
24751177
325761120
done50001086

prune609.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs (cbrt (fma x (fma y 2.0 x) (* y y)))) (sqrt (cbrt (fma x (fma y 2.0 x) (* y y)))))
5.1b
(sqrt (fma x (fma y 2.0 x) (* y y)))
5.6b
(cbrt (fma x (fma y 2.0 x) (* y y)))
5.6b
(cbrt (fma x (fma y 2.0 x) (* y y)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity sqrt-prod
10×cbrt-prod
9×associate-*r*
7×pow1
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* unswap-sqr
2×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 69
Calls
4 calls:
31.0ms
(* (fabs (cbrt (fma x (fma y 2.0 x) (* y y)))) (sqrt (cbrt (fma x (fma y 2.0 x) (* y y)))))
3.0ms
(sqrt (fma x (fma y 2.0 x) (* y y)))
2.0ms
(cbrt (fma x (fma y 2.0 x) (* y y)))
2.0ms
(cbrt (fma x (fma y 2.0 x) (* y y)))

series816.0ms

Counts
4 → 12
Calls
4 calls:
264.0ms
(* (fabs (cbrt (fma x (fma y 2.0 x) (* y y)))) (sqrt (cbrt (fma x (fma y 2.0 x) (* y y)))))
96.0ms
(sqrt (fma x (fma y 2.0 x) (* y y)))
231.0ms
(cbrt (fma x (fma y 2.0 x) (* y y)))
224.0ms
(cbrt (fma x (fma y 2.0 x) (* y y)))

simplify2.8s

Counts
81 → 81
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01291642
12761547
29601403
343091395
done50001395

prune725.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

5.1b
(sqrt (fma y y (* x (fma y 2.0 x))))
5.6b
(cbrt (fma x (fma y 2.0 x) (* y y)))
5.6b
(cbrt (fma x (fma y 2.0 x) (* y y)))
5.6b
(cbrt (fma x (fma y 2.0 x) (* y y)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
3.0ms
(sqrt (fma y y (* x (fma y 2.0 x))))
1.0ms
(cbrt (fma x (fma y 2.0 x) (* y y)))
1.0ms
(cbrt (fma x (fma y 2.0 x) (* y y)))
2.0ms
(cbrt (fma x (fma y 2.0 x) (* y y)))

series871.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(sqrt (fma y y (* x (fma y 2.0 x))))
261.0ms
(cbrt (fma x (fma y 2.0 x) (* y y)))
249.0ms
(cbrt (fma x (fma y 2.0 x) (* y y)))
236.0ms
(cbrt (fma x (fma y 2.0 x) (* y y)))

simplify1.0s

Counts
66 → 66
Iterations

Useful iterations: done (1.0s)

IterNodesCost
070926
1128886
2302817
31109808
done5000805

prune739.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes119.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
done69

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.5s14278×body80valid