Details

sample22.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify14.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize19.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (fma y y (fma x x (* z z))) 3.0)
36.0b	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

5.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
4.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

series324.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
231.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify2.0s

Counts

64 → 64

Iterations

Iter	Nodes
done	5026
4	2561
3	760
2	323
1	169
0	103

prune380.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.9b

localize17.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (fma y y (fma z z (* x x))) 0.3333333333333333)
35.9b	(sqrt (* (fma y y (fma z z (* x x))) 0.3333333333333333))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 35

Calls

2 calls:

11.0ms	(* (fma y y (fma z z (* x x))) 0.3333333333333333)
5.0ms	(sqrt (* (fma y y (fma z z (* x x))) 0.3333333333333333))

series347.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(* (fma y y (fma z z (* x x))) 0.3333333333333333)
259.0ms	(sqrt (* (fma y y (fma z z (* x x))) 0.3333333333333333))

simplify1.3s

Counts

41 → 41

Iterations

Iter	Nodes
done	5002
3	1239
2	307
1	124
0	62

prune232.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.6b

localize19.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
35.9b	(sqrt (fma y y (fma x x (* z z))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
32×	`add-sqr-sqrt`
31×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log`
3×	`pow1`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

2 → 80

Calls

2 calls:

13.0ms	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
2.0ms	(sqrt (fma y y (fma x x (* z z))))

series460.0ms

Counts

2 → 6

Calls

2 calls:

299.0ms	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
161.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify3.2s

Counts

86 → 86

Iterations

Iter	Nodes
done	5005
6	3954
5	1975
4	1091
3	492
2	271
1	163
0	106

prune418.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.5b

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(* z (sqrt 0.3333333333333333))

rewrite11.0ms

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:

10.0ms

(* z (sqrt 0.3333333333333333))

series64.0ms

Counts

1 → 3

Calls

1 calls:

64.0ms

(* z (sqrt 0.3333333333333333))

simplify4.5s

Counts

28 → 28

Iterations

Iter	Nodes
done	5000
5	4122
4	1647
3	532
2	205
1	76
0	40

prune100.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 11.5b

regimes437.0ms

Accuracy

48.2% (12.2b remaining)

Error of 24.1b against oracle of 11.9b and baseline of 35.4b

bsearch64.0ms

Steps

Iters	Range		Point
6	1.7188298815878508e+127	8.190230609024e+127	6.86482775038648e+127
8	-1.3198903247987554e+155	-1.1250773400730914e+152	-3.397008026592871e+153

simplify4.0ms

Iterations

Iter	Nodes
done	22
1	22
0	20

end0.0ms

sample799.0ms

Algorithm

intervals

Results

611.0ms

8000×

body

valid