Details

sample45.0ms

Algorithm

intervals

Results

29.0ms

256×

body

valid

simplify25.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	32
3	32
2	26
1	16
0	11

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* z z))
0.3b	(/ (fma y y (fma x x (* z z))) 3.0)
36.9b	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`times-frac`
18×	`*-un-lft-identity` `add-cube-cbrt`
13×	`sqrt-prod`
5×	`add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`rem-sqrt-square` `div-inv`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `fma-udef`

Counts

3 → 69

Calls

3 calls:

0.0ms	(fma x x (* z z))
8.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
5.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

series455.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(fma x x (* z z))
88.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
323.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify2.1s

Counts

78 → 78

Iterations

Iter	Nodes
done	5010
4	2393
3	829
2	360
1	182
0	115

prune468.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
0.4b	(* (sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 1)) (sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0)))
37.1b	(sqrt (fma y y (fma x x (* z z))))
37.1b	(sqrt (fma y y (fma x x (* z z))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

152×	`sqrt-prod`
122×	`add-sqr-sqrt`
84×	`times-frac`
55×	`*-un-lft-identity`
47×	`add-cube-cbrt`
25×	`associate-r` `associate-l`
24×	`unswap-sqr`
11×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
5×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-div`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `div-inv`
1×	`frac-times` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 164

Calls

4 calls:

5.0ms	(sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
30.0ms	(* (sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 1)) (sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0)))
1.0ms	(sqrt (fma y y (fma x x (* z z))))
1.0ms	(sqrt (fma y y (fma x x (* z z))))

series737.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
243.0ms	(* (sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 1)) (sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0)))
150.0ms	(sqrt (fma y y (fma x x (* z z))))
158.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify2.6s

Counts

176 → 176

Iterations

Iter	Nodes
done	5000
3	2641
2	831
1	348
0	210

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.2b

localize43.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt (fma y y (fma z z (* x x)))) (sqrt (/ 1 3.0)))
37.1b	(sqrt (fma y y (fma z z (* x x))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`associate-r`
15×	`*-un-lft-identity`
13×	`times-frac` `add-cube-cbrt`
8×	`unswap-sqr`
7×	`pow1`
6×	`associate-l`
4×	`add-cbrt-cube` `add-exp-log`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `sqrt-div` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `div-inv`

Counts

2 → 64

Calls

2 calls:

17.0ms	(* (sqrt (fma y y (fma z z (* x x)))) (sqrt (/ 1 3.0)))
3.0ms	(sqrt (fma y y (fma z z (* x x))))

series452.0ms

Counts

2 → 6

Calls

2 calls:

279.0ms	(* (sqrt (fma y y (fma z z (* x x)))) (sqrt (/ 1 3.0)))
172.0ms	(sqrt (fma y y (fma z z (* x x))))

simplify3.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
4	2179
3	676
2	316
1	178
0	101

prune335.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 12.1b

localize10.0ms

Local error

Found 1 expressions with local error:

0.2b	(* x (sqrt 0.3333333333333333))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-r`
4×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
3×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log`
2×	`unswap-sqr`
1×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 25

Calls

1 calls:

14.0ms

(* x (sqrt 0.3333333333333333))

series55.0ms

Counts

1 → 3

Calls

1 calls:

54.0ms

(* x (sqrt 0.3333333333333333))

simplify3.8s

Counts

28 → 28

Iterations

Iter	Nodes
done	5000
4	2217
3	638
2	233
1	76
0	40

prune71.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 12.0b

regimes626.0ms

Accuracy

48.2% (12.2b remaining)

Error of 24.3b against oracle of 12.1b and baseline of 35.7b

bsearch151.0ms

Steps

Iters	Range		Point
7	8.096098649992053e+154	1.0620767226758966e+157	8.243533173233274e+154
9	-5.599802959155633e+154	-4.186518194588193e+147	-1.3282248930815427e+154

simplify9.0ms

Iterations

Iter	Nodes
done	26
2	26
1	23
0	20

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.5s

8000×

body

valid