Details

sample26.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify14.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (fma y y (fma x x (* z z))) 3.0)
33.7b	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

rewrite8.0ms

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` `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 → 56

Calls

2 calls:

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

series387.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
298.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify2.3s

Counts

62 → 62

Iterations

Iter	Nodes
done	5007
4	2661
3	787
2	323
1	167
0	101

prune427.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.6b

localize23.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
33.7b	(sqrt (fma y y (fma x x (* z z))))

rewrite34.0ms

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` `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 → 62

Calls

2 calls:

29.0ms	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
2.0ms	(sqrt (fma y y (fma x x (* z z))))

series401.0ms

Counts

2 → 6

Calls

2 calls:

238.0ms	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
163.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify3.2s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
4	1945
3	667
2	353
1	176
0	99

prune373.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.6b

localize16.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ (sqrt (fma y y (fma z z (* x x)))) (sqrt 3.0))
33.7b	(sqrt (fma y y (fma z z (* x x))))

rewrite9.0ms

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` `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 → 78

Calls

2 calls:

6.0ms	(/ (sqrt (fma y y (fma z z (* x x)))) (sqrt 3.0))
1.0ms	(sqrt (fma y y (fma z z (* x x))))

series504.0ms

Counts

2 → 6

Calls

2 calls:

324.0ms	(/ (sqrt (fma y y (fma z z (* x x)))) (sqrt 3.0))
180.0ms	(sqrt (fma y y (fma z z (* x x))))

simplify3.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
5	2356
4	1192
3	501
2	270
1	161
0	104

prune576.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 13.4b

localize9.0ms

Local error

Found 1 expressions with local error:

0.2b	(* z (sqrt 0.3333333333333333))

rewrite15.0ms

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` `log1p-expm1-u` `add-log-exp`

Counts

1 → 24

Calls

1 calls:

14.0ms

(* z (sqrt 0.3333333333333333))

series67.0ms

Counts

1 → 3

Calls

1 calls:

67.0ms

(* z (sqrt 0.3333333333333333))

simplify5.0s

Counts

27 → 27

Iterations

Iter	Nodes
done	5001
5	3988
4	1522
3	478
2	197
1	75
0	39

prune96.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 13.4b

regimes746.0ms

Accuracy

46.3% (13.5b remaining)

Error of 26.7b against oracle of 13.2b and baseline of 38.3b

bsearch91.0ms

Steps

Iters	Range		Point
10	3.8846249050047975e+135	1.224134824105336e+149	1.8626358800272506e+138
8	-1.549186037423091e+87	-4.081557637458966e+84	-1.5326597111246728e+87

simplify16.0ms

Iterations

Iter	Nodes
done	27
2	27
1	24
0	21

end0.0ms

sample1.2s

Algorithm

intervals

Results

953.0ms

8000×

body

valid