Details

sample37.0ms

Algorithm

intervals

Results

20.0ms

256×

body

valid

simplify21.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	29
3	29
2	24
1	14
0	9

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize25.0ms

Local error

Found 1 expressions with local error:

35.7b

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
1×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 16

Calls

1 calls:

2.0ms

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

series200.0ms

Counts

1 → 3

Calls

1 calls:

200.0ms

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

simplify3.5s

Counts

19 → 19

Iterations

Iter	Nodes
done	5000
9	1093
8	457
7	293
6	230
5	197
4	139
3	82
2	52
1	39
0	27

prune124.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (fma z z (fma y y (* x x)))))
0.2b	(* (fabs (cbrt (fma z z (fma y y (* x x))))) (sqrt (cbrt (fma z z (fma y y (* x x))))))
36.9b	(cbrt (fma z z (fma y y (* x x))))
36.9b	(cbrt (fma z z (fma y y (* x x))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`cbrt-prod` `sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 78

Calls

4 calls:

2.0ms	(sqrt (cbrt (fma z z (fma y y (* x x)))))
21.0ms	(* (fabs (cbrt (fma z z (fma y y (* x x))))) (sqrt (cbrt (fma z z (fma y y (* x x))))))
2.0ms	(cbrt (fma z z (fma y y (* x x))))
2.0ms	(cbrt (fma z z (fma y y (* x x))))

series811.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(sqrt (cbrt (fma z z (fma y y (* x x)))))
212.0ms	(* (fabs (cbrt (fma z z (fma y y (* x x))))) (sqrt (cbrt (fma z z (fma y y (* x x))))))
222.0ms	(cbrt (fma z z (fma y y (* x x))))
198.0ms	(cbrt (fma z z (fma y y (* x x))))

simplify2.8s

Counts

90 → 90

Iterations

Iter	Nodes
done	5018
3	3456
2	819
1	270
0	127

prune630.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 17.6b

localize23.0ms

Local error

Found 2 expressions with local error:

6.1b	(exp (log (sqrt (fma z z (fma y y (* x x))))))
35.7b	(sqrt (fma z z (fma y y (* x x))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`log-prod` `exp-prod` `*-un-lft-identity` `exp-sum` `add-cube-cbrt` `sqrt-prod`
5×	`pow1`
3×	`log-pow`
2×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `rem-exp-log`

Counts

2 → 39

Calls

2 calls:

10.0ms	(exp (log (sqrt (fma z z (fma y y (* x x))))))
3.0ms	(sqrt (fma z z (fma y y (* x x))))

series314.0ms

Counts

2 → 6

Calls

2 calls:

146.0ms	(exp (log (sqrt (fma z z (fma y y (* x x))))))
168.0ms	(sqrt (fma z z (fma y y (* x x))))

simplify3.7s

Counts

45 → 45

Iterations

Iter	Nodes
done	5002
8	3525
7	1406
6	665
5	416
4	267
3	173
2	113
1	83
0	61

prune217.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 17.6b

localize55.0ms

Local error

Found 4 expressions with local error:

6.0b	(pow (exp (* (cbrt (log (sqrt (fma z z (fma y y (* x x)))))) (cbrt (log (sqrt (fma z z (fma y y (* x x)))))))) (cbrt (log (sqrt (fma z z (fma y y (* x x)))))))
35.7b	(sqrt (fma z z (fma y y (* x x))))
35.7b	(sqrt (fma z z (fma y y (* x x))))
35.7b	(sqrt (fma z z (fma y y (* x x))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow-unpow` `sqrt-prod`
6×	`cbrt-prod`
5×	`add-log-exp`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `unpow-prod-down` `pow-pow` `log-pow`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow-exp` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

18.0ms	(pow (exp (* (cbrt (log (sqrt (fma z z (fma y y (* x x)))))) (cbrt (log (sqrt (fma z z (fma y y (* x x)))))))) (cbrt (log (sqrt (fma z z (fma y y (* x x)))))))
3.0ms	(sqrt (fma z z (fma y y (* x x))))
3.0ms	(sqrt (fma z z (fma y y (* x x))))
3.0ms	(sqrt (fma z z (fma y y (* x x))))

series1.6s

Counts

4 → 12

Calls

4 calls:

983.0ms	(pow (exp (* (cbrt (log (sqrt (fma z z (fma y y (* x x)))))) (cbrt (log (sqrt (fma z z (fma y y (* x x)))))))) (cbrt (log (sqrt (fma z z (fma y y (* x x)))))))
203.0ms	(sqrt (fma z z (fma y y (* x x))))
200.0ms	(sqrt (fma z z (fma y y (* x x))))
197.0ms	(sqrt (fma z z (fma y y (* x x))))

simplify2.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
4	3069
3	915
2	359
1	179
0	82

prune583.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 17.6b

regimes381.0ms

Accuracy

64.6% (6.3b remaining)

Error of 23.3b against oracle of 17.1b and baseline of 34.7b

bsearch105.0ms

Steps

Iters	Range		Point
8	2.8170052152113808e+153	5.25084911742593e+156	6.809472127167789e+153
9	-8.708528334203602e+158	-3.1388980512684937e+149	-4.907860111955181e+151

simplify3.0ms

Iterations

Iter	Nodes
done	14
0	14

end0.0ms

sample661.0ms

Algorithm

intervals

Results

500.0ms

8000×

body

valid