Details

sample39.0ms

Algorithm

intervals

Results

25.0ms

256×

body

valid

simplify13.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize32.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (fma y y (fma x x (* z z))) 3.0)
35.8b	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

rewrite19.0ms

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:

9.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
7.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

series339.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
254.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify2.2s

Counts

64 → 64

Iterations

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

prune335.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

localize19.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
35.7b	(sqrt (fma y y (fma x x (* z z))))

rewrite23.0ms

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:

20.0ms	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
2.0ms	(sqrt (fma y y (fma x x (* z z))))

series351.0ms

Counts

2 → 6

Calls

2 calls:

207.0ms	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
144.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify2.8s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
4	2025
3	672
2	301
1	178
0	101

prune386.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.4b

localize23.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ (sqrt (fma y y (fma z z (* x x)))) (sqrt 3.0))
35.7b	(sqrt (fma y y (fma z z (* x x))))

rewrite12.0ms

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:

8.0ms	(/ (sqrt (fma y y (fma z z (* x x)))) (sqrt 3.0))
2.0ms	(sqrt (fma y y (fma z z (* x x))))

series415.0ms

Counts

2 → 6

Calls

2 calls:

265.0ms	(/ (sqrt (fma y y (fma z z (* x x)))) (sqrt 3.0))
151.0ms	(sqrt (fma y y (fma z z (* x x))))

simplify2.5s

Counts

86 → 86

Iterations

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

prune329.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 13.5b

localize8.0ms

Local error

Found 1 expressions with local error:

0.2b	(* y (sqrt 0.3333333333333333))

rewrite16.0ms

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:

15.0ms

(* y (sqrt 0.3333333333333333))

series50.0ms

Counts

1 → 3

Calls

1 calls:

50.0ms

(* y (sqrt 0.3333333333333333))

simplify4.0s

Counts

28 → 28

Iterations

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

prune72.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 13.5b

regimes464.0ms

Accuracy

46.4% (12.1b remaining)

Error of 24.4b against oracle of 12.3b and baseline of 34.9b

bsearch82.0ms

Steps

Iters	Range		Point
8	3.2407605759015045e+140	1.292919298649766e+143	1.2764865492717349e+143
6	-5.475978031765872e+141	-5.9028139372446406e+140	-2.9088365088923405e+141

simplify9.0ms

Iterations

Iter	Nodes
done	32
2	32
1	29
0	23

end0.0ms

sample873.0ms

Algorithm

intervals

Results

678.0ms

8000×

body

valid