Details

Time bar (total: 6.8s)

sample15.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
2.0ms90×body80nan

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
056
175
done75

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize4.0ms

Local error

Found 1 expressions with local error:

19.3b
(sqrt (fma x x y))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt sqrt-prod
2×pow1 add-cube-cbrt *-un-lft-identity
1×add-exp-log expm1-log1p-u rem-sqrt-square sqrt-pow1 pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
1 → 15
Calls
1 calls:
1.0ms
(sqrt (fma x x y))

series52.0ms

Counts
1 → 3
Calls
1 calls:
52.0ms
(sqrt (fma x x y))

simplify1.2s

Counts
18 → 18
Iterations

Useful iterations: 4 (276.0ms)

IterNodesCost
037145
175127
2175120
3494118
41453117
done5001117

prune45.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (fma x x y)))
0.5b
(* (sqrt (sqrt (fma x x y))) (sqrt (sqrt (fma x x y))))
19.3b
(sqrt (fma x x y))
19.3b
(sqrt (fma x x y))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
31×pow1
20×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×expm1-log1p-u rem-sqrt-square log1p-expm1-u add-log-exp
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 128
Calls
4 calls:
1.0ms
(sqrt (sqrt (fma x x y)))
13.0ms
(* (sqrt (sqrt (fma x x y))) (sqrt (sqrt (fma x x y))))
1.0ms
(sqrt (fma x x y))
1.0ms
(sqrt (fma x x y))

series226.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(sqrt (sqrt (fma x x y)))
51.0ms
(* (sqrt (sqrt (fma x x y))) (sqrt (sqrt (fma x x y))))
51.0ms
(sqrt (fma x x y))
48.0ms
(sqrt (fma x x y))

simplify3.0s

Counts
140 → 140
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01141885
12141111
26681039
340421011
done50001008

prune242.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (sqrt (fma x x y))) (sqrt (fabs (cbrt (fma x x y)))))
19.3b
(sqrt (fma x x y))
20.0b
(cbrt (fma x x y))
20.0b
(cbrt (fma x x y))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
24×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
9×pow1 associate-*l*
6×add-exp-log cbrt-prod associate-*r* add-cbrt-cube unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2 pow-prod-down
2×pow1/3
1×rem-sqrt-square sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 78
Calls
4 calls:
10.0ms
(* (sqrt (sqrt (fma x x y))) (sqrt (fabs (cbrt (fma x x y)))))
1.0ms
(sqrt (fma x x y))
0.0ms
(cbrt (fma x x y))
1.0ms
(cbrt (fma x x y))

series319.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (sqrt (sqrt (fma x x y))) (sqrt (fabs (cbrt (fma x x y)))))
49.0ms
(sqrt (fma x x y))
85.0ms
(cbrt (fma x x y))
88.0ms
(cbrt (fma x x y))

simplify886.0ms

Counts
90 → 90
Iterations

Useful iterations: done (884.0ms)

IterNodesCost
01181182
12381102
26401043
319581035
done50001034

prune322.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize5.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes77.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.3b

bsearch55.0ms

Steps
ItersRangePoint
9
4.342265995353652e+77
8.721286125398812e+82
1.2922566123944575e+80
9
-1.1045029026290381e+161
-1.4102566258715918e+152
-1.3778733035656446e+154

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01426
done1426

end0.0ms

sample384.0ms

Algorithm
intervals
Results
167.0ms8000×body80valid
52.0ms2570×body80nan