Details

sample15.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
2.0ms	90×	body	80	nan

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	5	6
1	7	5
done	7	5

prune5.0ms

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))

series51.0ms

Counts

1 → 3

Calls

1 calls:

51.0ms

(sqrt (fma x x y))

simplify1.7s

Counts

18 → 18

Iterations

Useful iterations: 5 (698.0ms)

Iter	Nodes	Cost
0	37	145
1	75	127
2	166	120
3	421	118
4	923	117
5	2198	116
done	5000	116

prune55.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize7.0ms

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))

series233.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (sqrt (fma x x y)))
49.0ms	(* (sqrt (sqrt (fma x x y))) (sqrt (sqrt (fma x x y))))
51.0ms	(sqrt (fma x x y))
53.0ms	(sqrt (fma x x y))

simplify2.3s

Counts

140 → 140

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	114	1885
1	214	1111
2	513	1039
3	1475	1011
4	4197	984
done	5000	984

prune254.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

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))

series309.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (sqrt (sqrt (fma x x y))) (sqrt (fabs (cbrt (fma x x y)))))
50.0ms	(sqrt (fma x x y))
81.0ms	(cbrt (fma x x y))
82.0ms	(cbrt (fma x x y))

simplify2.2s

Counts

90 → 90

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	118	1182
1	238	1102
2	621	1043
3	1568	1028
4	4424	1026
done	5000	1026

prune320.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize4.0ms

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)

Iter	Nodes	Cost
0	0	0
done	0	0

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes76.0ms

Accuracy

98.3% (0.4b remaining)

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

bsearch53.0ms

Steps

Iters	Range		Point
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)

Iter	Nodes	Cost
0	14	26
done	14	26

end0.0ms

sample376.0ms

Algorithm

intervals

Results

161.0ms	8000×	body	80	valid
45.0ms	2570×	body	80	nan